recent research papers in crystal growth

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Themed collection Crystal Growth

Spin crossover crystalline materials engineered via single-crystal-to-single-crystal transformations.

This highlight illustrates the latest crystalline materials engineered via SCSC transformations, with emphasis on the onset and progress of spin crossover in a crystal control.

Progress in controlling the synthesis of atomically precise silver nanoclusters

This short review was designed to summarize the advances in synthesis methods of silver nanoclusters.

Epitaxial nanotwinned metals and alloys: synthesis-twin structure–property relations

Recent works of epitaxial nanotwinned metals and alloys with different stacking fault energies are reviewed to elaborate the relationship among synthesis conditions, intrinsic factors, twin structure and various properties.

Sublimation – a green route to new solid-state forms

Sublimation is an effective and ‘green’ method to prepare and identify new polymorphs, cocrystals, ionic cocrystals and molecular salts.

Electrochemically induced nucleation of oxidic crystals in melts – a review

Electrochemically induced nucleation refers to a method where an applied potential triggers an electrochemical reaction which changes the conditions in the melt so that nucleation can occur where it was previously not significantly possible.

Review on quasi-2D square planar nickelates

Quasi-2D square planar nickelates exhibit key ingredients of high- T c superconducting cuprates. Whether bulk samples are superconducting remains an open question, single crystals are ideal platforms for addressing such fundamental questions.

Micro-pulling-down growth of long YAG- and LuAG-based garnet fibres: advances and bottlenecks

A technological advance in shaped μ-PD crystal growth provided us with high-quality single crystalline fibres of rare-earth garnets with the good longitudinal transparency and light attenuation length of up to 1 m.

Dynamic force spectroscopy for quantifying single-molecule organo–mineral interactions

Organo–mineral interactions have long been the focus in the fields of biomineralization and geomineralization, since such interactions not only modulate the dynamics of crystal nucleation and growth but may also change crystal phases, morphologies, and structures.

Spectral characteristics of a Nd 3+ /Yb 3+ :YPO 4 single crystal with strong multi-wavelength emission

We report the growth and spectral characteristics of the 0.32 at%Nd 3+ /1.2 at%Yb 3+ :YPO 4 crystal.

Graphene-induced growth of Co 3 O 4 nanoplates with modulable oxygen vacancies for improved OER properties

Graphene-induced growth of Co(OH) 2 nanoplates from Co 3 O 4 nanospheres was reported, showing an ultralow overpotential of 240 mV at 10 mA cm −2 and a Tafel slope of 107.8 mV dec −1 .

Supporting ultrathin “fish scale-like” BiOBr nanosheets on Bi 6 Mo 2 O 15 sub-microwires for boosting photocatalytic performance

A BiOBr/Bi 6 Mo 2 O 15 edge-on heterostructure with fast electron transport could improve interface conductivity and accelerate charge-separation efficiency.

Investigation of various fatty acid surfactants on the microstructure of flexible hydroxyapatite nanofibers

The synthesis of hydroxyapatite nanofibers using various fatty acids and their influences on HA crystal characteristics were systematically explored.

In situ reconstruction of ZIF-8 loaded on fibrous supports

The fibre-supported ZIF-8 can undergo a full degradation–recrystallization cycle in a vapor phase with partial recovery of its porosity.

The synthesis and formation mechanism of nonpolar InN nanoplates

High-crystal-quality nonpolar indium nitride (InN) nanoplates were synthesized via deploying controllable chemical vapor deposition (CVD) technology using the M -plane of GaN nanowires (NWs) as a template.

A plastically bendable and polar organic crystal

An organic crystal of the polar space group Pc that is capable of plastic bending is reported, and its high dielectric constant and strong second-order harmonic generation (SHG) effect have been demonstrated.

Vapor–liquid–solid growth of 4H-SiC single crystal films with extremely low carrier densities in chemical vapor deposition with a Pt–Si alloy flux and X-ray topography analysis of their dislocation propagation behaviors

The CVD–VLS process for 4H-SiC films with a Pt–Si alloy flux achieved their low carrier densities of ∼10 15 cm −3 , demonstrating a remarkable etch back effect and a possible conversion of TEDs and TSDs in the substrate to BPDs in the films.

Asymmetric metal–organic frameworks with double helices for enantioselective recognition

A pair of homochiral metal–organic frameworks are elaborated by employing flexible enantiopure ligands.

Synthesis of morphology-improved single-crystalline iron silicide nanowires with enhanced physical characteristics

Morphology-improved single-crystalline β-FeSi 2 nanowires with enhanced physical characteristics were synthesized through a pre-deposition method.

Promoted crystallization of silicoaluminophosphate zeolites: an efficient way to accelerate crystallization rate and increase solid yield

SAPO-34 with 100% yield has been synthesized by an acid-assisted method, which is also applicable to the synthesis of other silicoaluminophosphate zeolites.

Competing hydrogen-bonding interactions in a high- T c organic molecular-ionic crystal with evident nonlinear optical response

An organic molecular-ionic crystal of (TPPO–H) 2 SO 4 exhibits moderate NLO response which is twice that of KDP and competing hydrogen-bonding interactions triggered high- T c phase transition.

A temperature-reduced method for the rapid growth of hybrid perovskite single crystals with primary alcohols

In this work, we present the simple and temperature-reduced reactive inverse temperature crystallisation (RITC) method to rapidly grow high-quality organic lead trihalide perovskite single crystals.

Growth mechanism of helical γ-Dy 2 S 3 single crystals

The nonequilibrium evaporation of a high-temperature SnS + Dy 2 S 3 solution leads to the implementation of a VLS-like mechanism of growth of γ-Dy 2 S 3 helical single crystals.

Solvent-assisted synthesis of dendritic cerium hexacyanocobaltate and derived porous dendritic Co 3 O 4 /CeO 2 as supercapacitor electrode materials

Here, we report a solvent-mediated synthetic route for preparing cerium hexacyanocobaltate with a dendritic shape. The porous dendritic Co 3 O 4 /CeO 2 was prepared after annealing at 500 °C, served as a supercapacitor electrode.

Adjacent N→O and C–NH 2 groups — a highly efficient amphoteric structure for energetic materials resulting from tautomerization proved by crystal engineering

A high- T c organic-ionic phase transition crystal obtained from a trivalent cation

The organic-ionic crystal of [1,4,7-triazacyclononammonium] Cl 3 , containing a trivalent cation, shows a high-temperature phase transition coupled with dielectric switching.

AB 11 O 16 (OH) 2 (A = K and Cs): interpenetrating 2D layers with large birefringence

By a cation substitution strategy, two new hydroxyborates AB 11 O 16 (OH) 2 (A = K and Cs) were synthesized, and KB 11 O 16 (OH) 2 exhibits a short DUV cutoff edge (195 nm) and a large birefringence.

Supercritical hydrothermal synthesis of UO 2+ x : stoichiometry, crystal shape and size, and homogeneity observed using 23 Na-NMR spectroscopy of (U, Na)O 2+ x

The hydrothermal synthesis of pure uranium dioxide under supercritical water (SCW) conditions was investigated using a starting material composed of a uranyl( VI ) nitrate solution at 450 °C.

The crystallization morphology and process of stereocomplex crystallites of polylactide under CO 2 : the effect of H-bonding and chain diffusion

The crystallization of PLA SC under CO 2 was in situ investigated for the first time.

Pair of chiral molecular ladders and successive hydration in single-crystal-to-single-crystal mode

Self-assembly of Zn(NO 3 ) 2 with a pair of new tridentate chiral Ls produced a pair of chiral ladder-type 1D coordination polymers, where crystals were transformed into different hydrated products of zigzag 1Ds depending on chirality in the SCSC mode.

New insight into the inductive effect of various seeds on the template-free synthesis of ZSM-5 zeolite

This work enables us to obtain an improved understanding of the role of seeds in the template-free synthesis of zeolite.

Exploration of structural transition phenomenon in flexible metal–organic framework formed on polymer substrate

We investigate the structural transition of directly formed flexible MOF crystals on a polymer substrate.

High-temperature inverted annealing for efficient perovskite photovoltaics

High-quality perovskite films with large grains and reduced surface defects were obtained via an inverted annealing process. Corresponding photovoltaic devices achieved a highest efficiency of 20.4% with a stabilized power conversion efficiency (PCE) of 19.8%.

Effect of the growth pulling direction on 3D anisotropic stress during different stages of semitransparent Li 2 MoO 4 growth

The three dimensional thermal stress field was calculated for different growth stages of a Li 2 MoO 4 (LMO) crystal grown in an inductively heated Czochralski furnace using the anisotropy and temperature-dependent mechanical properties.

Opposite effects of cations in enhancing and suppressing nucleation in the pathological crystallization of gout

“Opposite effects” were shown by cations, enhancing nucleation followed by suppressing nucleation at physiological pH and ionic strength.

Nucleation behaviour of racemic and enantiopure histidine

Small non-centrosymmetric domains are observed in the racemic crystal, due to the low nucleation activation energy of the conglomerate.

Polycyclic motif engineering in cyanostilbene-based donors towards highly efficient modulable emission properties in two-component systems

Cynostilbene based two-component materials are fabricated which exhibit tunable structures and excellent photophysical properties depending on the IP of the polycyclic moiety and organization of the donor-acceptor in the condensed phase.

Crystallization of paracetamol from mixtures of ethanol and water in a planar oscillatory flow crystallizer: effect of the oscillation conditions on the crystal growth kinetics

Crystal growth kinetic data is reported for a planar oscillatory flow crystallizer.

Sequential variation of super periodic structures emerged in Bi-layered perovskite pillar-matrix epitaxial nanocomposite films with spinel ferrites

The phase stability of Aurivillius bismuth-layer structured Bi 5 Ti 3 FeO 15 (BTFO15) has been investigated in an epitaxial pillar-matrix nanocomposite system with spinel ferrites.

Formation of double-cone-shaped ZnO mesocrystals by addition of ethylene glycol to ZnO dissolved choline chloride–urea deep eutectic solvents and observation of their manners of growth

ZnO mesocrystals were grown in ZnO dissolved CU-DESs with addition of ethylene glycol. Their manner of growth was observed and discussed.

Investigation of the blue color center in β-Ga 2 O 3 crystals by the EFG method

This work investigated the blue color center in β-Ga 2 O 3 crystals grown by the EFG and obtained an effective method to eliminate it.

Reactive molten-flux assisted syntheses of single crystals of Cs 19 Ln 19 Mn 10 Te 48 (Ln = Pr and Gd) crystallizing in a new structure type

Two new complex layered quaternary tellurides, Cs 19 Ln 19 Mn 10 Te 48 (Ln = Pr and Gd), were synthesized by the reactive molten flux method. The title compounds represent an unprecedented structure type.

Protein crystallisation facilitated by silica particles to compensate for the adverse impact from protein impurities

Nanonucleants for protein crystallisation in the presence of impurities.

Protein crystallisation with air bubble templates: case of gas–liquid–solid interfaces

Crystal formation on air bubble–liquid interface, as soft template to efficiently prompt nucleation of proteins.

Synthesis, structural characterization, and luminescence properties of heteroleptic bismuth-organic compounds

The synthesis and photoluminescent properties of four bismuth-organic compounds, their lanthanide doped analogs, and an isostructural europium complex are reported.

Taming CL-20 through hydrogen bond interaction with nitromethane

A novel cocrystal explosive of CL-20/nitromethane in a 1 : 2 molar.

Two Zr-based heterometal–organic frameworks for efficient CO 2 reduction under visible light

Two novel zirconium-based heterometal–organic framework catalysts can effectively improve photocatalytic activities for CO 2 photoreduction under visible light.

Photoluminescence study of N-rich B-doped diamonds grown in NiMnCo solvent before and after annealing

Incorporation of boron substantially decreases the luminescence of centers (NV − , Ni–N, and Co–N) in nitrogen-rich boron-doped diamonds before and after HPHT annealing.

Growth, spectral and laser properties of a Yb-doped strontium yttrium phosphate crystal with a disordered structure

A novel disordered crystal Yb:YSr 3 (PO 4 ) 3 is grown by the Czochralski method. Results indicate that it can be a promising candidate for ultrashort pulse generation and tunable broadband solid-state lasers.

Multilevel strategies for the composition and formation of DAAF/HNIW composite crystals

Insensitive energetic materials are still a great challenge for potential applications.

Competition between diamond nucleation and growth under bias voltage by microwave plasma chemical vapor deposition

A competition between diamond nucleation and growth is proposed in which the surface and bulk nucleation coexist and compete.

Green solvent assisted preparation of one-dimensional CsPbBr 3 nanocrystals with a controllable morphology for cyan-emitting applications

Upon tuning the polarity of antisolvent medium, the length of CsPbBr 3 NCs realizing the conversion from nanorods to NWs. Furthermore, the width of the NWs can be adjusted feasibly via the overgrowth of CsPbBr 3 NWs.

Suppressing barite crystallization with organophosphorus compounds

A naturally derived phosphorous-containing molecule, phytate, functions as a dual inhibitor of barium sulfate (barite) nucleation and growth, making it a potentially viable environmentally-friendly alternative to current barite scale treatments.

Reversed crystal growth of metal organic framework MIL-68(In)

A reversed crystal growth mechanism of MIL-68(In) is revealed. Nanorods of MIL-68 aggregate in parallel into microrods, followed by surface recrystallisation into a single crystal hexagonal shell and extension of crystallisation from surface to core.

Strong intermolecular interaction induced methylene-bridged asymmetric heterocyclic explosives

Methylene-bridged asymmetric heterocyclic explosives were designed and synthesized to attempt the possibility of realizing energetic materials with high-energy and adequate sensitivity.

Growth mechanism on graphene-regulated high-quality epitaxy of flexible AlN film

We report a novel diffusion–adsorption regulation growth method in the epitaxy of AlN on graphene for the high-quality and transferable large-size AlN film.

Involvement of various anions in tuning the structure of silver( I ) coordination polymers based on a S-donor ligand: syntheses, crystal structure and uptake properties

Ag( I ) coordination polymers based on a S-donor ligand containing of various anions were synthesized and characterized. Also, the absorption potential of the polymers was examined by the NH 3 and H 2 S gases.

Temperature-dependent phase composition of fluorinated zinc phthalocyanine thin films and their sensing properties towards gaseous NO 2

This work presents a temperature-dependent phase composition study of thin films (200 nm) of fluorinated zinc phthalocyanines (4F, 16F) and their chemiresistive response towards NO 2 gas.

Crystal growth and properties characterization of Nd 3+ :Na 5 Lu(MoO 4 ) 4 for continuous multi-wavelength NIR laser emission

The Nd 3+ :Na 5 Lu(MoO 4 ) 4 crystal was grown in a 4Na 2 O–5MoO 3 flux through the top-seeded solution growth technique, and achieved a continuous multi-wavelength NIR laser emission in the Nd 3+ :Na 5 Lu(MoO 4 ) 4 crystal for the first time.

Sisal-like Sn 2+ doped ZnO hierarchical structures: synthesis, growth mechanism, and their application in photocatalysis

Sisal-like Sn doped ZnO hierarchical structures were prepared by the hydrothermal method without employing templates or matrices. The architectures show enhanced light absorption, high photocatalytic properties, good stability and reusability.

Fabrication of a 2 inch free standing porous GaN crystal film and application in the growth of relaxed crack-free thick GaN

This paper describes the fabrication of a 2 inch free standing porous GaN crystal film and the application in the growth of relaxed crack-free thick GaN.

Growth of a large-aperture mid-infrared nonlinear optical La 3 Nb 0.5 Ga 5.5 O 14 crystal for optical parametric chirped-pulse amplification

A high optical quality 60 mm-diameter LGN crystal with wide transparency was grown by the Czochralski method. The origin of the wide transparency as for a traditional oxide crystal was investigated from the viewpoint of crystal symmetry.

Five new rubidium borates with 0D clusters, 1D chains, 2D layers and 3D frameworks

By tuning the synthetic conditions, borates with 0D clusters were transformed into a 1D chain, 2D layer and 3D framework.

Crystallization of paracetamol from aqueous solutions in a planar oscillatory flow crystallizer: effect of the oscillation conditions on the nucleation kinetics

Nucleation kinetic data is reported for a planar oscillatory flow crystallizer.

Simple and facile one-step synthesis of bowl-like hollow ZSM-5 zeolites

One-step synthesis of bowl-like hollow ZSM-5 zeolites via controlling the the hydrolysis temperature of TEOS.

Two pairs of chiral lanthanide–oxo clusters Ln 14 induced by amino acid derivatives

Two pairs of chiral lanthanide–oxo clusters L -/ D -Ln 14 (Ln = Y/Dy) have been obtained under the action of anion template. The solid-state circular dichroism (CD) spectra of L -Y 14 / D -Y 14 and L -Dy 14 / D -Dy 14 displayed mirror symmetry effects.

Growth of MSe semiconductor nanowires on metal substrates through an Ag 2 Se-catalyzed solution–solid–solid mechanism (M = Zn, Cd and Mn)

Solution-phase growth of MSe nanowires on their respective metal foil or flakes (M = Zn, Cd and Mn) has been realized by a recently developed solution–solid–solid mechanism initiated by preexisting Ag 2 Se seeds.

Quality improvement mechanism of sputtered AlN films on sapphire substrates with high-miscut-angles along different directions

We studied the annealing mechanism of the films with high-miscut-angles at low cost and high efficiency and revealed the essence of annealing to improve the film quality lies in the annihilation of grain boundaries during the recrystallization.

New phase transition pattern of fivefold twins transformed into lamellar structure in Ti 3 Al alloy

A new phase transition pattern of fivefold twins into a lamellar structure leading to a second phase transition was found in Ti 3 Al alloy.

Metastable growth and infrared spectra of CuB 2 O 4 :Ni single crystals

The formation of CuB 2 O 4 :Ni crystals in fluxes based on Li 2 WO 4 –Bi 2 O 3 –WO 3 has been studied. A distinctive feature of the used flux growing mode is the metastable nature of nucleation. IR reflection and transmission spectra are presented.

Optimized growth and anisotropic properties of Li 2 ZrTeO 6 nonlinear optical crystals

Centimeter-sized and high-quality Li 2 ZrTeO 6 crystals were grown by a modified top-seed solution growth method. The excellent thermal properties indicate that Li 2 ZrTeO 6 is an excellent candidate suitable for high-power nonlinear optical applications.

About this collection

The latest research on Crystal Growth published in CrystEngComm .

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• Open access
• Published: 31 January 2020

Current status of solid-state single crystal growth

• Iva Milisavljevic 1 &
• Yiquan Wu 1  

BMC Materials volume  2 , Article number:  2 ( 2020 ) Cite this article

19k Accesses

24 Citations

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Fabrication of single crystals has long been limited to melt- and solution-growth techniques. However, in recent years solid-state single crystal growth (SSCG) has appeared as a promising alternative to the conventional techniques due to its cost-effectiveness and simplicity in terms of processing. Moreover, the SSCG technique has enabled the fabrication of single crystals with complex chemical compositions and even incongruent melting behavior. A recently proposed mechanism of grain boundary migration known as the “mixed control mechanism” and the associated principles of microstructural evolution represent the basis of the SSCG technique. The mixed control mechanism has been successfully used to control the key aspects of the SSCG technique, which are the grain growth and the development of the microstructure during the conversion process of the single crystal from the polycrystalline matrix. This paper explains in brief basis of the mixed control mechanism and the underlying principles of microstructural evolution in polycrystalline materials and provides a comprehensive overview of the most recent research on single crystal materials fabricated via the solid-state single crystal growth technique and their properties.

Introduction

A need for single crystal fabrication.

Single crystals are one of the most important groups of materials due to their continuous, uniform, and highly-ordered structure which enables them to possess unique properties. In many aspects, single crystal materials can be found to be advantageous over polycrystalline materials, and many properties which are found in single crystals cannot be replicated in polycrystals [ 1 ]. Currently, even with the technological developments of advanced polycrystalline materials which are designed for specific applications, the electrical, optical, thermal, mechanical, and other properties of single crystals still remain superior. For these reasons, it is not surprising that single crystals, and the methods for their fabrication, are a topic of interest among many researchers.

Single crystals have found extensive use in optical, electronic, optoelectronic, and other applications. Specifically, single crystal semiconductors are one of the most widely researched and used materials. These materials have been applied for various electronic and optoelectronic devices and components, such as light-emitting diodes (LEDs), photodetectors, wide-bandgap devices, high-power lasers, consumer electronics, and more [ 2 , 3 ]. For example, current computer chip production is not possible without high-quality single crystal silicon (Si) wafers [ 4 ]. Due to their outstanding optical and electronic properties, single crystals of III–V semiconductors, such as GaAs, GaN, InP, InAs, and others, are an integral part of devices for application in fiber-optic communication, wireless and satellite communication, solid-state lighting, and more [ 2 ]. The importance of single crystal alumina, also known as sapphire, as well as yttrium aluminum garnet (YAG), for laser materials has also been demonstrated through numerous applications. Sapphire has been used in the electronics industry both as a passive substrate material and active device (e.g. silicon-on-sapphire); likewise, it is used for rocket domes, optical data storage, radiation detection, LED devices, optical windows, and other applications [ 5 ]. On the other hand, YAG single crystals, and especially Nd 3+ -doped YAG, are known for their important application in solid-state laser devices, such as waveguide lasers [ 6 ] and single crystal fibers for high-power lasers [ 7 ], as well as scintillation crystals, and others. Piezoelectric single crystal materials, which were initially developed and utilized as transducers for sonar devices and medical ultrasonic diagnostic devices, have also been applied in sensors, actuators, medical transducers, energy harvesters, and more [ 8 , 9 ]. As it can be seen, single crystal materials are capable of covering a wide variety of applications, which range from scientific- and research-related to daily life.

Another important use of single crystal materials is as substrates for films of different materials; this enables a whole new collection of applications. Single crystals can be used not only as a mechanical support or a surface at which layer or layers of materials are being deposited but can also act as a single crystal seed during epitaxial growth [ 10 ], when the deposited film takes on orientation of the substrate, and sometimes even a lattice structure. Likewise, the fabrication of single crystal epitaxial films on various substrates, which are a vital part of a wide range of devices for electronic, optoelectronic, magneto-optic, and many other applications, although very challenging, is an important goal in the thin film industry due to the numerous advantages of single crystal films [ 11 ].

As technological development increases, the need for high-quality single crystal materials, both in bulk and in thin films, grows simultaneously. The availability of various single crystal materials has enabled the development of a new generation of electronic, optical, optoelectronic, and other devices. However, growth of high-quality single crystals, with stable and reproducible quality, low defect density, with various chemical compositions and sometimes even extreme thermodynamic properties is still one of the greatest challenges today [ 12 ]. Furthermore, techniques which are currently used for growing single crystals experience many processing-related difficulties despite the technological advancements made throughout the years [ 13 ]. Therefore, a high demand for various single crystal materials has imposed a need for improving the growth techniques that are currently used as well as developing new, alternative single crystal growth techniques.

Conventional techniques of single crystal growth

Currently, there are three general approaches for the growth of bulk inorganic single crystals: growth from melt, solution and vapor phase.

Growth from melt is the most commonly used method and is based upon the solidification and crystallization of a melted material. The Czochralski and Bridgman methods are the two most utilized melt-growth techniques. The Czochralski method (Cz) is, for example, very important for the production of single crystals for electronic and optical applications, such as silicon and germanium single crystals, as well as some fluoride and oxide single crystals [ 13 ]. Single crystal growth from melt allows for the fabrication of large single crystals of excellent quality in a relatively short time when compared to other growth techniques [ 14 ]. However, the melt-growth technique shows some disadvantages as well, such as difficulties in maintaining a stable temperature during the crystal growth and in achieving very high melting points for some materials, achieving chemical homogeneity, especially in the case when multiple elements are present in the system, reactivity of the melted material with the crucible, and high costs of production and equipment.

Unlike the melt-growth technique, in which the material is melted first, the solution-growth technique involves the dissolution of the material to be crystallized within a suitable solvent or flux (e.g. PbO, PbF 2 , Bi 2 O 3 , Li 2 O, Na 2 O, K 2 O, KF, P 2 O 5 , etc.) [ 13 , 15 ]. Out of all the solution-growth techniques, high-temperature solution-growth, also known as flux-growth, has been the most utilized technique for the fabrication of single crystals thus far. This technique is especially convenient for materials that incongruently melt or when melt-growth techniques cannot be applied. The main advantage of this technique is that the crystals are grown below their melting temperatures and the growth of the crystal occurs spontaneously through nucleation or crystallization on a seed. On the other hand, the crystal growth rates for the solution-growth method are much slower than that of the melt-growth method and the presence of flux ions is unavoidable in the crystal. Growth of single crystals via the flux method has found many important applications in the production of single crystal materials such as garnets, various laser crystals, including borates, LiNbO 3 , BaTiO 3 , BaB 2 O 4 , and more complex systems such as Sr 1− x Ba x Nb 2 O 6 , Pb 1− x Ba x Nb 2 O 6 , and others [ 13 ].

Vapor-phase growth is the third method of growing single crystals, although it is more commonly applied to the fabrication of thin single crystals films on substrates than bulk single crystals. The growth of single crystals through the vapor phase can be accomplished via a sublimation process, reaction in the gas phase and transport reaction, such in the case of chemical vapor transport (CVT) and, physical vapor transport (PVT) [ 16 ]. Compared to the melt-growth method, the vapor-growth method utilizes lower processing temperatures which result in a significantly higher quality crystal due to avoidance of incorporating impurities, structural and compositional uniformities, and phase transitions. On the other hand, the low growth and transport rates in the vapor to the interface, associated with the low temperature, make this technique less favorable when compared to the other two growth techniques. However, this technique is still used if neither one of the other two techniques is applicable for the growth of single crystals, which is the case in, for example, SiC single crystals [ 15 ].

New technique for single crystal fabrication

Another pathway for growing single crystals which has recently received attention within the research community, is through the solid-state conversion of polycrystalline materials to single crystals. This method is based on a phenomenon which can be observed in many systems, known as abnormal grain growth (AGG).

Solid-state single crystal growth was first observed and studied in metals as a possible alternative to very difficult and expensive procedures used to fabricate metal single crystals. Most of the research on single crystal conversion in metals date to the middle of the last century and include the reports on single crystals of Fe, Mo, W, and other metals [ 17 , 18 , 19 ]. Later on, in the early 1980s, applying the same principles observed in the metal systems, Matsuzawa and Mase [ 20 , 21 ] performed research on the growth of single crystals from various polycrystalline oxide materials, including ferrites, garnets, and spinels. They demonstrated that single crystal growth using the solid-state conversion approach, which was reserved only for metals at the time, could also be applied to more complex materials’ systems. Furthermore, many issues associated with conventional single crystal growth techniques, such as heating at high temperatures, maintaining compositional uniformity, contamination from the crucibles, etc., were avoided during the solid-state single crystal growth and performed with much lower production costs. In the years that followed, most of the research focus was on BaTiO 3 and Pb(Mg 1/3 Nb 2/3 )O 3 ‒PbTiO 3 systems, however, still in a limited number.

Although it was observed for the first time decades ago, solid-state single crystal growth can still be considered to be a relatively new technique since it did not receive significant attention from the research community until recently once more work had been done. Due to considerable advancements made in nanotechnologies and sintering technology that have enabled the fabrication of high-quality ceramics, interest in solid-state single crystal growth from polycrystals has been renewed. Solid-state single crystal growth has been shown to be an effective and simple technique for obtaining single crystals with lower capital costs associated with production equipment and components, which could potentially allow for the mass production of single crystals for various existing as well as new applications [ 22 ]. The technique utilizes conventional sintering equipment, such as simple furnaces, which cost notably less than the equipment for conventional single crystal growth [ 23 ]. For comparison, a furnace for Cz growth of sapphires can cost between $400,000 and $1,000,000 [ 14 ], while regular furnaces can cost at least an order of magnitude less. Furthermore, the more complex the composition is, the harder it becomes to fabricate a single crystal using the conventional single crystal growth route, due to chemical inhomogeneities, the presence of elements that melt incongruently, volatility of certain elements, and so on. Therefore, solid-state single crystal growth has been found to be promising and applicable to many different systems, especially systems with complex chemical compositions. Net-shape production, when compared to cutting and shaping from the single crystal boules grown conventionally [ 14 ], is another advantage in cost-effectiveness of single crystals produced by solid-state growth since it reduces the number of machining steps after the growth process and even allows for growth of more complexly-shaped single crystals.

This review article will provide an overview of the current status of techniques utilized for the solid-state conversion of single crystals (here, solid-state single crystal growth (SSCG) will be used with the same meaning) and the principles behind them, including AGG, boundary migration, and microstructural evolution. Also, recent reports on the solid-state conversion of single crystals in different systems will be summarized and the most important findings highlighted. The review will be concluded with a discussion on some of the biggest challenges of the SSCG technique, followed by a brief summary and a future outlook.

Solid-state conversion of single crystals from polycrystals

In recent years, solid-state single crystal growth (SSCG) has emerged as a promising alternative technique for growth of single crystals through a conversion process in polycrystalline materials. This technique, which offers numerous advantages over conventional single crystal growth techniques, is based on the occurrence of AGG in polycrystals. More precisely, SSCG technique is developed around what is known as a “mixed control mechanism” [ 24 ] of grain boundary migration as well as principles of microstructural evolution. The mixed control mechanism can be used as a general guiding principle for suppressing growth and controlling the growth of single crystals from polycrystalline materials, which are the key requirements for SSCG.

In this section, the phenomenon of abnormal grain growth will be briefly explained and discussed. Furthermore, the mixed control mechanism of grain boundary migration and the principles of microstructural evolution will be presented and explained. However, for more details on the mixed control mechanism and the related phenomena, the reader is strongly encouraged to refer to the research articles of Dr. Kang and his associates who developed the mixed control mechanism and have conducted extensive research work in this field.

Abnormal grain growth (AGG)

In general, there are two different types of grain growth which can be observed during sintering. One, known as normal grain growth (NGG), involves a uniform rate of grain growth via thermally activated grain boundary migration which results in a uniformly developed microstructure with respect to the sintering time (stationary grain growth). The other type of grain growth is non-normal grain growth (non-NGG) and instead follows a non-stationary grain growth [ 23 ]. AGG is a type of a non-NGG and is referred to as the grain growth where a certain number of grains experience a much faster growth rate than the neighboring grains in the matrix. Such growth may significantly change a grain size distribution, leading to broadening or even a bimodal grain size distribution. With extended annealing time, the abnormal grains gradually increase in size by consuming the surrounding matrix grains until they impinge upon each other. This lowers the driving force for further growth of abnormal grains and they usually stop growing at this stage [ 25 ].

In general, AGG is a phenomenon which is not favorable during materials processing since the presence of abnormally grown grains may have a negative effect on microstructure development, and therefore on the physical properties of materials. The appearance of AGG has been observed in many different systems both ceramic and metallic. Many authors have tried to explain the occurrence of AGG, suggesting different mechanisms and models, however, the underlying reasons for AGG are still under debate [ 26 ]. Generally, the following phenomena have been suggested as the possible causes of AGG: (a) the presence of second phases, pores or impurities (b) high anisotropy of the interfacial energy and grain boundary mobility, and (c) the presence of a thin liquid film at the grain boundary which facilitates grain boundary mobility [ 23 , 24 ]. As explained in [ 23 ], in all of the aforementioned phenomena, it was originally thought that AGG was a result of atomic diffusion across the grain boundary. However, neither of these models could explain, nor be entirely applied to all of the systems which were studied thus far. Therefore, another explanation or model was necessary to more clearly explain the phenomenon of AGG.

Recently, a “mixed control mechanism” was proposed to explain AGG and other types of grain growth behavior; this further enabled the definition of the principles of evolution of the microstructure in polycrystalline materials [ 23 , 27 ].

• Mixed control mechanism

The classical understanding of the mechanisms of AGG, which were mentioned in the previous section, provide explanation for grain boundary migration which is based on atomistic diffusion. These models, however, can only be applied to some specific cases; for this reason, the mixed control mechanism, which is a more universal model, was suggested to explain different grain growth behaviors. The mixed control mechanism has its roots in the theories of crystal growth and experimental observations and explains the phenomenon of grain boundary migration considering the atomic structure of grain boundaries; this has not been taken into account in classical grain growth theory [ 24 ].

There are two different types of grain boundaries which can be identified by differences in structure. One is a rough (round) grain boundary which exhibits an atomically disordered structure, and the other is faceted grain boundary, whose interface is smooth and atomically ordered. In some recent studies [ 27 , 28 , 29 , 30 , 31 ], it was observed that the type of grain boundary has the most significant influence on the occurrence of AGG. While rough grain boundaries were observed to result in NGG, faceted grain boundaries were more likely to undergo AGG (or some other non-normal type of grain growth) [ 24 , 32 ]. In other words, the presence of faceted grain boundaries in the system can be regarded as a prerequisite for AGG. Such a phenomenon was explained by differences in the grain boundary mobilities of rough and faceted boundaries with regard to the driving force for grain boundary migration [ 33 ].

In the case of rough interfaces, grain boundary migration has been shown to have a direct relationship with respect to the driving force for the grain growth. Because of their atomically disordered structures, rough interfaces allow for a large number of attachment sites for atoms, which then enables a high rate of interfacial reactions. Since the migration kinetics are governed by the slowest process, in the case of rough grains, the diffusion, as the slowest process, will be the rate-determining process for grain boundary migration [ 26 ]. On the other hand, for faceted grains, the experimental results have shown that the grain growth is controlled by either interface reaction (attachment of atoms from one grain to an adjacent grain) or atomic diffusion across the grain boundary, depending on which process is slower. Furthermore, it has been demonstrated that there is a relationship between the grain boundary migration of faceted interfaces and the driving force being non-linear [ 33 , 34 , 35 ].

Each individual grain in the polycrystalline matrix possesses its own driving force for grain boundary migration and the maximum driving force for grain growth (Δ g max ) is defined by the average grain size and grain size distribution [ 24 ]. In addition, the maximum driving force is assigned to largest grain in the grain population and increases with decreasing average grain size as well as broadening of the grain size distribution [ 27 ]. Another important parameter in grain growth is the critical driving force (Δ g c ) for grain growth which depends mainly on the type of grain boundary interface and can be changed by varying the temperature, atmosphere, oxygen partial pressure, and presence of dopants [ 24 , 28 , 29 , 30 ].

According to Kang et al. [ 24 ], the ratio between Δ g max and Δ g c determines the type of the grain growth and can even help to further predict and explain the microstructure development. Additionally, the authors explained that there are, in general, four different grain growth behaviors which can be observed depending on the magnitude of Δ g max and Δ g c and their relation [ 24 , 36 ]:

Normal grain growth (NGG), which is a stationary grain growth for which Δ g c  = 0 (presented with a dashed line in Fig.  1 ).

Schematic illustration of the mixed control mechanism of grain growth: (left) Mixed control mechanism of grain growth for grains with rough and faceted grain boundaries; (right) Schematic of two systems with different microstructures due to the difference in Δ g max [ 24 ]

Pseudo-normal grain growth, when 0 < Δ g c   ≪  Δ g max .

Abnormal grain growth (AGG) occurs when Δ g c ≤ Δ g max .

Stagnant grain growth (SGG) occurs when Δ g max   ≪  Δ g c .

In systems with faceted grain boundaries, the growth of faceted grains is governed by the diffusion process when the driving force for growth is larger than the critical driving force. On the other hand, when the driving force is smaller than the critical, the growth rate is significantly smaller than that by diffusion and is led by the interface reaction instead [ 32 ]. Such non-linear grain growth behavior with respect to the driving force is therefore said to be mixed controlled by either a diffusion or interface reaction, as illustrated in Fig.  1 .

AGG, which is the focus of the SSCG method, occurs in systems with faceted grain boundaries. For an efficient solid-state single crystal conversion, it is preferred that the growth of grains within a polycrystalline matrix be negligible (with Δ g max lower than Δ g c ), while the growth of one or a small number of grains (acting as single crystal seeds) is promoted. For the latter case, the driving force should be larger than the critical driving force (Δ g c ) in order for the grains to begin experiencing AGG. For such growth conditions, and in order for single crystal conversion to occur, it is necessary to have a well-balanced ratio between Δ g max and Δ g c [ 23 ]. The average grain size and grain size distribution significantly impact Δ g max and, as a consequence, the ratio between the maximum and the critical driving force, as shown in Fig.  1 . Similarly, a variation in Δ g c , affected by the change in the grain boundary structure, will also impact the microstructural development.

The predictions set by the mixed control mechanism on microstructural evolution can be demonstrated best by observing the effects of a change in Δ g max under constant Δ g c , or vice versa. For example, in the experiments of Jung et al. [ 37 ], when Δ g c was kept constant, Δ g max could be manipulated by changing the initial particle size of the powder sample. As a result, the fine-grained BaTiO 3 sample exhibited AGG, while the same sample, but with coarser particles, underwent SGG due to differences in Δ g max . Such an observation confirms the predictions presented in Fig.  1 . Conversely, when Δ g c was varied, different scenarios could be observed depending on which parameter was affecting the grain boundary structure. A relationship between the change in oxygen partial pressure and the degree of faceting of grain boundaries is one of the best examples of how this parameter can affect the grain boundary structure and therefore lead to AGG; several studies conducted in which BaTiO 3 was used as a model system support this [ 28 , 29 , 37 ]. Other parameters that can affect the grain boundary structure (e.g. doping, temperature and sintering atmosphere) have also been investigated [ 28 , 30 , 33 , 38 , 39 ], and can be seen as an additional endorsement to the concept of the mixed control mechanism.

Furthermore, some experimental studies have confirmed that even different crystallographic directions will experience differences in migration kinetics in systems with faceted grain boundaries [ 33 , 35 , 40 ]. Under some experimental conditions, the migration in certain crystallographic directions was even completely omitted [ 35 ]. According to the authors of the studies, the presence of the critical driving force for grain boundary migration, Δ g c , which varied with crystallographic planes, was the reason for this discrepancy in results. Such observations are consistent with the assumptions of the mixed control mechanism and are further evidence that the microstructural development in the systems with faceted grain boundaries is a result of the non-linear relationship between the grain boundary migration and the driving force for migration.

SSCG technique

Despite the fact that abnormal grain growth was found to be an unwanted event during sintering, the SSCG technique was actually based on this phenomenon [ 41 ]. Furthermore, the SSCG technique was developed as a direct application of the principles of microstructural evolution which further supported the understanding of the mixed control mechanism [ 24 ].

In most practical cases, the SSCG technique uses a single crystal seed of a similar crystalline structure with the matrix material which is either embedded in the polycrystalline green body or placed on top of it, as illustrated in Fig.  2 [ 23 ]; this technique is known in the literature as the seeding method. The seed and the green body are both sintered at a temperature which is below the melting point of the crystal. This enables the formation (or conversion) of the single crystal material from the polycrystals through a controlled AGG process as well as in the crystallographic direction of the seed crystal. Figure  3 depicts the process of conversion where the small matrix grains are being consumed by a large single crystal seed. The same principle is used for the fabrication of single crystals from melt, except in this case, heating well above the melting temperature is necessary and, also, other issues associated with this processing method are difficult to avoid. Furthermore, single crystals can be grown using the “seed-free method” via prior nucleation of the seed crystal in the polycrystalline matrix by applying a temperature gradient or by adding a dopant material [ 23 ]. This method does not require embedding of the single crystal seed in the polycrystalline matrix as in the case of the seeding method, but the principle of the single crystal conversion is the same.

Schematic of the solid-state conversion of single crystal: a Seeding from the top side of the polycrystalline material; b embedding of the seed crystal [ 23 ]

Cross-section of the Nd:YAG single crystal grown by SSCG method [ 42 ]

Although the SSCG method has given very good results thus far, there are still certain aspects which need to be considered and which could be limiting, such as the choice of the seed crystal, density of polycrystalline matrix, size distribution of the grains, structural matching between the seed crystal and matrix, and control of the interface [ 41 ]. So far, the SSCG has been successfully applied to only a limited number of systems which mainly include oxides and piezoelectric ceramic materials.

The following section of this paper will provide an overview of the results which have been reported on single crystal growth via the SSCG technique.

Current developments on solid-state single crystal growth

Pb-based piezoelectric materials.

Solid-state conversion of single crystals has recently been proved to be a very successful way to produce piezoelectric single crystals for commercial usage. For example, single crystals such as Pb(Mg 1/3 Nb 2/3 )O 3 –PbTiO 3 (PMN–PT) and Pb(Mg 1/3 Nb 2/3 )O 3 –Pb(Zr,Ti)O 3 (PMN–PZT) are now produced by the SSCG method, while the conventional methods include growth via Bridgman or flux methods. By using the flux-method, it is difficult to obtain single crystals of size and quality required for the commercial usage. Another issue associated with this method is that it causes vaporization of the toxic PbO substance. With the Bridgman method it is hard, on the other hand, to achieve compositional uniformity within the growing crystal. The SSCG technique, therefore, has appeared as a very promising and effective method for production of lead-based piezoelectrics.

Single crystals of some relaxor-based ferroelectrics, such as Pb(Mg 1/3 Nb 2/3 )O 3 –PbTiO 3 (PMN–PT) exhibit superior properties compared to polycrystalline forms of the same composition. Especially important are PMN–PT materials with 35 mol% of PbTiO 3 added because of their potential application as electromechanical devices. A possibility to grow a single crystalline PMN–PT material by the SSCG method was recognized many years ago. In 1998, Li et al. [ 43 ] used a method of embedding a PbTiO 3 (PT) single crystal into polycrystalline Pb(Mg 1/3 Nb 2/3 )O 3 (PMN), to grow PMN–PT single crystals. A powder with a single crystal was cold isostatically pressed and then sintered and annealed under pressureless conditions in a range of temperatures. The authors were able to observe distinct boundaries between the grown single crystal area and polycrystal grains of matrix material. Khan et al. [ 44 ] reported a solid-state growth of the PMN–35 mol% PT single crystal using the same method which the previously mentioned group of authors used in their study. During preparation of the matrix material, a specific amount of PbO was mixed in. Following the sintering of PMN with the PT single crystal embedded in the material, the compact was annealed at 1150 °C for 10 h. During annealing, PbO was in a liquid phase, which, according to the authors, had a significant impact on the single crystal growth inside the polycrystalline matrix. The authors also showed that as the single crystal boundary migrated through the polycrystalline matrix, PbO as the second phase accumulated at the triple points in the matrix and remained entrapped in a form of spherical inclusions in the grown crystal.

In 2003, another group of authors reported [ 45 ] a study on the same material which included seeding of the PT single crystal in the PMN matrix with a small amount of liquid PbO, added to the matrix to increase the grain boundary mobility. In this study, the authors used a vacuum hot-pressing furnace following cold isostatic pressing of the green pellets to obtain the compact. They observed a clear boundary between the single crystal and polycrystal area. But what is more important, they observed a notable difference between the samples in which the liquid PbO was not added and when it was included in the matrix. A small amount of the liquid PbO increased the single crystal growth constant by nearly 100 times.

A common issue which was observed in all the previously mentioned studies was that the grown single crystals contained a significant number of pores as well as a PbO second phase entrapped inside the structure. This negatively affected the properties of the single crystals. An interesting observation made by Kim [ 45 ] was that the single crystal seed orientation had a great influence on the elimination of the PbO liquid phase from the grown single crystal.

Despite the issues related with the growth of PMN–PT single crystals in laboratory conditions, this type of material was successfully fabricated by scaling-up the SSCG process for commercial purposes. It is interesting to mention that by the SSCG method, it is possible to grow both undoped and doped (e.g. Fe, Mn) PMN–PT single crystals with very high quality and excellent dielectric and piezoelectric properties [ 47 ]. Recently, growth of undoped and Mn-doped 71PMN–29PT high-quality single crystals using the SSCG method were reported [ 46 ], in which excellent piezoelectric and electromechanical properties of both single crystals were demonstrated. With such results, these materials, and especially Mn-doped single crystal, could be utilized as high-power piezoelectric transducers in sonars and medical devices. In this study, undoped and Mn-doped (Mn–PMN–PT) PMN–PT single crystals were fabricated by Ceracomp Co., Ltd. from South Korea (Fig.  4 ), which has become well-known for their production of high-quality piezoelectric single crystals via the SSCG method. In another study, Mn–PMN–PT single crystals were grown into very thin plates (< 0.2 mm) which enabled them to show high stability and piezoelectric performance which is suitable for high frequency composites, medical ultrasound probes, non-destructive testing devices, and flexible devices applications [ 9 ].

Polished surfaces of 71PMN–29PT single crystals grown by SSCG method: (left) undoped and (right) Mn-doped [ 46 ]

Company Ceracomp Co. also introduced a method for obtaining PMN–PT single crystal ceramics by seeding with a BaTiO 3 single crystal. Figure  5 presents a schematic for obtaining such materials via the SSCG method. First, they prepared a PMN–PT ceramic using a hot-pressing furnace, after which they placed a BaTiO 3 single crystal on top of the ceramic and heat-treated the sample [ 48 ]. Using this process, they were able to fabricate a homogeneous and fully dense PMN–PT single crystal. Hot-pressing of the ceramic compact was found to be very beneficial for obtaining a high-density product at the end.

Schematic of experimental procedure for fabrication of PMN–PT single crystals by SSCG method [ 48 ]

Lim et al. [ 49 ] published their investigation on a ternary system comprised of BiScO 3 –Pb(Mg 1/3 Nb 2/3 )O 3 –PbTiO 3 (BS–PMN–PT) in which they grew a single crystalline BS–PMN–PT via the SSCG method which included embedding of the single crystal Ba(Zr,Ti)O 3 (BZT) into the matrix compact. The authors used four different fluxes (Bi 2 O 3 , LiBiO 2 , PbO/LiBiO 2 and PbO/Bi 2 O 3 ) in which they tried to grow single crystal BS–PMN–PT. The fluxes were added with the intention of enhancing the material transfer by forming a liquid phase during sintering. What they observed was that the PbO/Bi 2 O 3 flux enabled growth of the BS–PMN–PT single crystal from BZT single crystal, while other fluxes were inefficient, which indicated that the BZT single crystal was chemically stable against the PbO/Bi 2 O 3 flux.

Along with the PMN–PT single crystal relaxor ferroelectric, Pb(Mg 1/3 Nb 2/3 )O 3 –PbZrO 3 –PbTiO 3 ternary system, or shorter Pb(Mg 1/3 Nb 2/3 )O 3 –Pb(Zr,Ti)O 3 (PMN–PZT), is a very important material which has numerous applications in areas such as ultrasonic transducers and actuators due to its large piezoelectric coefficient and high electromechanical coupling factors in areas such as medical. Traditionally, these types of single crystal materials were grown via the flux method or the Bridgman method which were found to be costly and usually resulting in chemical inhomogeneity of the grown crystals. Zhang et al. [ 50 ] demonstrated single crystal growth of PMN–PZT by means of the SSCG technique. The matrix compact containing Pb 3 O 4 , MgNb 2 O 6 , ZrO 2 , and TiO 2 was prepared by mixing and pressing of the raw materials into pellets, sintering in the range from 1100 to 1200 °C, followed by hot isostatic pressing of the ceramics. BZT single crystal plates were used as seed crystals for single crystal growth during the SSCG process. The density of such obtained PMN–PZT single crystals was found to be greater than 99% of the theoretical density. The authors further investigated the electromechanical and piezoelectric properties of the fabricated PMN–PZT single crystals and showed that single crystals grown by the SSCG method exhibited properties which were greater than the previously investigated PMN–PT single crystals.

Further investigation on PMN–PZT single crystals obtained by the SSCG method was extended to doping of the same with manganese (Mn), iron (Fe), or even indium (In). In 2017, researchers from the Sunmoon University in South Korea, in collaboration with the Ceracomp Co., presented their study in which they doped single crystal PMN–PZT with Mn [ 8 ]. In this study, the authors used three different generations of piezoelectric single crystal materials (PMN–PT - first, PMN–PZT - second, and Mn-doped PMN–PZT - third generation) obtained by the SSCG method in order to compare the properties of each to one another. The preparation of the single crystals included attachment of the BZT single crystal as a seed crystal, after primary sintering. By applying the SSCG method they were able to obtain high-quality single crystals (Fig.  6 ) which exhibited good piezoelectric properties, among which Mn-doped PMN–PZT was shown to be the most promising.

Three generations of piezoelectric single crystals grown by the SSCG method [ 8 ]

Until now, the SSCG technique was shown to be the only method to produce large relaxor-PZT single crystals, such as PMN–PZT, of different ratios of Pb(Mg 1/3 Nb 2/3 )O 3 (PMN), PbZrO 3 (PZ) and PbTiO 3 (PT). The change of PMN/PZ/PT ratios has a significant influence on materials’ piezoelectric and dielectric properties [ 47 ]. Also, because of the PZ component in the PMN–PZT system, which exhibits incongruent melting behavior, and PbO which is very volatile, PMN–PZT single crystal has been successfully produced only by the SSCG technique so far.

An interesting report which was done by Hwang et al. [ 22 ] in 2015 demonstrated the possibility of fabricating thin film PMN–PZT single crystals by the SSCG method used for the fabrication of a high-performance energy harvester material. The authors used a BZT single crystal seed plate to attach it to the surface of the polycrystalline ceramic during the SSCG process. Afterwards, they were able to take the thin single crystal PMN–PZT film from the glass substrate and transfer it to the plastic substrate without making any damage to the material. A schematic illustration of the whole process is presented in Fig.  7 .

Flexible PMN–PZT thin film single crystal energy harvester: (left) schematic illustration of the SSCG process of fabrication; (right) scanning electron microscope (SEM) micrograph of the cross-section of PMN–PZT single crystal film on plastic substrate [ 22 ]

Pb-free piezoelectric materials

Conventionally, piezoelectric single crystals have been produced via the flux or the Bridgman method. As previously mentioned, these methods require high-temperature treatment for the melting of the raw materials which can, at the end, create chemical inhomogeneity and, more importantly, evaporation of highly toxic substances, such as lead. In the last few decades, the question of environmental and health issues concerning the production of the lead-based piezoelectric single crystal materials has been raised. As the growing market demand for these materials is rising more and more each year, a development of lead-free piezoelectric ceramics and single crystals which will be able to replace lead-based piezoelectric materials became necessary.

This paper will review the two most studied lead-free piezoelectric ceramic materials which were proven to be able to be fabricated by the SSCG technique. The two lead-free piezoelectric materials which will be presented here belong to the KNaNbO 3 (KNN) lead-free family and the (Na 1/2 Bi 1/2 )TiO 3 –BaTiO 3 –(K 1/2 Na 1/2 )NbO 3 (NBT–BT–KNN) family of single crystals.

KNN-based lead-free single crystals

KNaNbO 3 (KNN), a lead-free piezoelectric material has attracted a lot of attention in the past decade because of its desirable properties as a piezoelectric and dielectric, and a potential to replace lead-based piezoelectric ceramics and single crystals. KNN has a perovskite structure and exhibits three phase transitions, at around 160 °C from rhombohedral to orthorhombic phase, at around 200 °C from orthorhombic to tetragonal phase, and at 420 °C from tetragonal to cubic phase [ 51 ]. Of importance regarding this material is that it undergoes AGG during sintering after the temperature reaches a certain critical point, which in turn decreases its piezoelectric properties. On the other hand, such behavior is important in terms of the growth of the single crystal material by the SSCG method.

Two different approaches have been recognized so far which can be used for the fabrication of single crystalline KNN by the SSCG method. One approach utilizes growth of the single crystal by the seeding method and the other can be referred to as the “seed-free” method for the growth of single crystals.

KNN-based single crystals grown by seeding method

In the study conducted on obtaining single crystal KNN via the SSCG method, Fisher et al. [ 52 ] used a <110> KTaO 3 single crystal as a seed crystal which was found similar to KNN in terms of the unit cell parameters. The single crystal was embedded into the powder matrix and, following this, the green body was prepared by uniaxial pressing and subsequent cold isostatic pressing. The authors’ goal was to investigate the influence of the applied pressure on the quality and porosity of the grown KNN single crystal. They determined that certain loading pressures had significant impacts on the porosity of the grown single crystals. The single crystal obtained by heat treatment under applied pressure in a hot pressing furnace in comparison to the sample heat-treated under pressureless conditions experienced a much smaller number and size of the pores, demonstrating the crucial role of pressure in obtaining a high-density single crystal KNN. The SEM images presented in Fig.  8 depict interfaces between single crystal seed and grown single crystal, and grown single crystal and the polycrystalline matrix in the samples prepared in pressureless and pressure-assisted conditions.

SEM images of KNN single crystal grown by SSCG method in: a , b conventional furnace, and c , d hot pressing furnace [ 52 ]

Benčan et al. [ 53 ] investigated the single crystal growth of KNN and Li, Ta-doped KNN by the SSCG method. Their preparation method for the green compacts was similar to the work of Fisher et al. They also used KTaO 3 as a seed crystal due to its compatibility with KNN. The authors demonstrated that the single crystal growth in the hot press furnace is advantageous over the conventional furnace. They explained that in the conventional furnace, the growth of single crystal, matrix grains, and densification are all happening simultaneously, which might be a reason for the high number of pores left trapped inside the single crystal. Another point they made was on the influence of the addition of the sintering aid (in their case, K 4 CuNb 8 O 23 ) on single crystal growth. The sintering aid was shown to be helpful when 2 mol% was added because it allowed the growth of the matrix grains to some extent, after which the driving force for the single crystal remained constant, allowing the crystal to grow under extended annealing time. On the other hand, a smaller amount of sintering aid (0.5 mol%) was found to cause a reduction of the single crystal and matrix grain growth rates.

Similarly, Yang et al. [ 54 ] studied the single crystal growth mechanism by the SSCG method on a KNN-based piezoelectric material doped with lithium. Sintering of the matrix material with a buried single crystal seed of KTaO 3 was performed in the presence of a sintering aid, MnO 2 . The results demonstrated that the addition of the sintering aid created a liquid phase which resulted in interfacial reactions that significantly affected the crystal growth rate, but only up to a certain threshold. Also, the authors observed a high number of pores, which is the result of the fast movement of the interface between the growing single crystal and matrix grains which tend to increase in size as the growth of the crystal continues [ 54 ].

Although the SSCG method was found promising for growth of the lead-free piezoelectric single crystals, one of the biggest problems associated with this method is in the high porosity of the end product. Uwiragiye et al. [ 51 ] reported in their study on 0.96(K 0.48 Na 0.52 )NbO 3 –0.03(Bi 0.5 (Na 0.7 K 0.2 Li 0.1 ) 0.5 )ZrO 3 –0.01(Bi 0.5 Na 0.5 )TiO 3 in which they used a KTaO 3 seed crystal with <110> orientation, that the piezoelectric properties of the grown single crystal could be enhanced if the porosity of the crystal could be reduced. They observed that the porosity increases with distance from the seed crystals and that the pores are irregular in both shape and size.

KNN-based single crystals grown by seed-free method

Using a single crystal seed to instigate conversion of the polycrystalline matrix grains to a single crystal with a desired crystallographic direction can be achieved by the SSCG method. However, despite the difficulties associated with controlling the growth process, the quality of the grown crystal is also affected by the seed crystal. Therefore, a seed-free method of growing single crystals by the SSCG method has been proposed. This method is known as the seed-free solid-state single crystal growth, or SFSSCG.

In 2007, Zhen and Li reported their study on growth of single crystals in KNN and (Li 0.04 K 0.44 Na 0.52 )(Nb 0.85 Ta 0.15 )O 3 (LKNNT) ceramic materials prepared and sintered in a conventional way, without seed crystals [ 55 ]. The authors were able to observe a small number of coarse grains which experienced AGG in both samples. While the distribution of these grains was somewhat random in KNN, the distribution of grains in LKNNT was more ordered. An interesting phenomenon which the authors observed was that the abnormal grains had a core–shell structure, as can be seen in Fig.  9 a. Different structural features of the core and shell grains could be observed, but both regions showed to belong to a single crystal grain. Another interesting observation was how the core grains maintained their original grain size; this could not be explained using classical grain growth theory. The authors proposed a schematic explanation for the core–shell structure formation (Fig.  9 b). But despite the AGG, the ceramic materials exhibited good piezoelectric and dielectric properties, showing that the SFSSCG method could be a promising technique for the single crystal growth.

A core–shell structure in KNN: a SEM micrograph; b schematic diagram showing procedure for formation of the core–shell structure [ 55 ]

Following Zhen and Li, many other authors reported successful fabrication of KNN-based single crystals through the SFSSCG method. In 2010, Wang et al. [ 56 ] reported single crystal growth of KNN by utilizing the AGG mechanism. The authors used a sol-gel route for the powder preparation, and they were able to grow single crystals of KNN as big as 3 mm by sintering for 2 h at 950 °C.

Later on, Jiang et al. [ 57 ] showed in their study on KNN that it is possible to obtain a high-quality single crystal KNN of perovskite structure (11 × 9 × 3) mm 3 via the SFSSCG method through a relatively simple and low cost route. They observed that single crystal grains tend to form a structure with a self-assembled arrangement, with preferred orientation and layer stacking along the growth direction. They also performed a systematic study on the effects of sintering aid content (LiBiO 3 ), as well as sintering time and temperature on crystal growth. Figure  10 presents the results of their systematical study on crystal growth kinetics, where the growth of large grains was triggered under certain conditions. In the same year, Ahn et al. [ 58 ] reported self-growth of a centimeter-sized single crystal of 0.985(K 1/2 Na 1/2 )NbO 3 –0.015Ba(Cu 1/3 Nb 2/3 )O 3 (KNN–BCuN) by the SFSSCG method. The authors prepared a KNN polycrystalline powder in a conventional way, with the addition of Ba 2+ ions aimed to compensate for the loss of Na + ions due to Na 2 O volatilization during the liquid phase sintering, and CuO as sintering aid which is known to form a liquid phase at high temperatures. The authors were able to observe the self-growth of giant grains which were single crystals, as shown in Fig.  11 . They also stressed the importance of the CuO addition because it had a vital role in the stimulation of AGG. Although the giant single crystal of KNN–BCuN contained a significant number of pores, it showed excellent piezoelectric properties and was found to be a promising candidate for piezoelectric sensors and energy harvesting devices. Another important benefit presented by the authors was that the SFSSCG method was approximately 100 times faster than the SSCG method.

KNN samples with LiBiO 3 sintering aid, sintered under different temperature and time regimes [ 57 ]

Variation of sizes of KNN–BCuN single crystals with sintering temperature grown by seed-free SSCG method [ 58 ]

In the years following, there have been many different reports on single crystal growth in KNN-based ceramics by using the SFSSCG method in which the authors achieved improvements in piezoelectric properties of the grown crystals. Yang et al. [ 59 ] reported improved piezoelectric properties in their self-grown single crystal of (K 0.45 Na 0.55 ) 0.96 Li 0.04 NbO 3 . Another group reported CaZrO 3 -doped KNN-based single crystals [ 60 ] grown by the SFSSCG method, which showed improved piezoelectric and dielectric properties as well. In 2017, Hao et al. [ 61 ] reported their study on the effects of different ratios of sodium and potassium in KNN on the growth of the single crystal by the SFSSCG method. They summarized their results in a composition-temperature phase diagram at which they showed that the growth of the single crystal KNN is possible only in a very narrow range of Na/K ratios and temperatures.

In the most recent study, the group of authors who had already reported their study on KNN–BCuN ceramics [ 58 ], has now proposed a compositional design rule for the growth of large single crystals in KNN-based ceramics by the SFSSCG method [ 62 ]. They determined that the amount of Ba 2+ (donor ion) in the system had a significant role in AGG, and therefore on the growth of the single crystal. The authors came up with equations with which they were able to calculate, and in that way predict, how much of each ion is present or substituted in the system. Their calculations showed a good fit with the experimental data, so they were able to establish a rule for the design of the KNN-based single crystals based on their equations.

Later on, Jiang et al. [ 41 ] proposed a crystal growth method in their latest work which could qualitatively explain the SFSSCG mechanism in KNN-based ceramics. As they pointed out, the AGG at which the SFSSCG model is based on should no longer be regarded as abnormal, but normal since the process of grain growth is now understood much better, and in that way better controlled, at least in case of KNN-based materials.

NBT-based lead-free single crystals

Another group of promising lead-free piezoelectric ceramics which were found to be able to be converted to single crystal materials are (Na 1/2 Bi 1/2 )TiO 3 or NBT-based materials. These materials may be presented with a general formula (Na 1/2 Bi 1/2 )TiO 3 –BaTiO 3 –(K 1/2 Na 1/2 )NbO 3 or shorter NBT–BT–KNN. NBT–BT–KNN single crystals are traditionally fabricated via the flux or the Bridgman method, but both methods introduce the difficulties of getting the crystals to have uniform chemical compositions due to the volatility of Na- and Bi-oxides. This further creates difficulties in obtaining single crystalline NBT–BT–KNN with desired piezoelectric properties. The SSCG method, therefore, appeared as a promising technique for obtaining such single crystal materials.

In one of the earliest reported studies on the application of the SSCG method for the conversion of polycrystalline NBT‒BT‒KNN to single crystal, Park et al. [ 63 ] successfully grew an NBT–BT–KNN single crystal from conventionally prepared ceramic powder. In their experimental work, this group used a SrTiO 3 single crystal seed of <110> orientation embedded in a ceramic powder to initiate single crystal growth during a 50-h annealing period at a temperature of 800 °C. The grown single crystal exhibited good piezoelectric properties which were comparable to those of other lead-free single crystals. The same group of authors continued their research on the same material [ 64 ] and 2 years later reported their finding that the KNN content in NBT–BT–KNN had a significant effect on the piezoelectric properties of NBT–BT–KNN single crystals. Along with that, they were able to demonstrate that the SSCG method was a prospective method for growth of NBT–BT–KNN single crystals with high performance, which could replace Pb(Zr,Ti)O 3 for actuator applications. In the same year, the aforementioned group of authors presented their results on NBT–BT–KNN single crystals by seeding with a SrTiO 3 single crystal [ 65 ]. They fabricated a highly dense NBT–BT–KNN single crystal with significant improvements in its piezoelectric properties, which were higher than that of any previously reported ceramics or single crystal. The high relative density (96.6%) of a grown crystal was achieved by creating a layered structure which was composed of pre-sintered ceramic pellets between which a seed crystal was positioned, followed by a 30-h annealing period at 900 °C in air. This method enabled the authors to fabricate a single crystal which had a notably smaller number of pores, which typically remain entrapped in the powder compact.

Another group of NBT-based piezoelectric single crystals which will be covered by this review pertains to the solid solution of (Na 1/2 Bi 1/2 )TiO 3 (NBT) with alkali earth perovskite-type materials (CaTiO 3 , SrTiO 3 and BaTiO 3 ).

The solid solution system (Na 1/2 Bi 1/2 )TiO 3 –BaTiO 3 (NBT–BT) was found to be a promising environmentally friendly, lead-free piezoelectric material. In the study on NBT–BT single crystals obtained by the SSCG method, Moon et al. [ 66 ] demonstrated that the common problem associated with the insufficient AGG, which is important for the growth of single crystals of practical sizes, can be overcome. They fabricated NBT–BT single crystals by using a SrTiO 3 seed crystal embedded in the ceramic powder compact, which had a certain degree of porosity and density inhomogeneity, but still exhibited good piezoelectric properties. In 2016, Gürbüz et al. [ 67 ] reported their comparative study between NBT–BT single crystals grown by SSCG, which included both the conventional and spark plasma sintering (SPS) methods. The authors demonstrated a significant difference in porosity between the single crystals obtained using these two sintering techniques. They achieved 99% of the theoretical density of the grown single crystal for the sample sintered by SPS for 5 min at 950 °C, while conventional sintering in air for 2 h at 1130 °C produced a single crystal with 96% of the relative density. The same result was in favor to SPS sintering when the dielectric properties were measured, which demonstrated that SPS might be an efficient technique for fabrication of NBT-based single crystals by the SSCG method, providing high relative densities and low alkaline evaporation.

In literature, reports can also be found on NBT-based single crystals grown by the SSCG technique which used other alkali earth perovskites, such as CaTiO 3 and SrTiO 3 . For example, in 2016, Lee et al. [ 68 ] reported for the first time a single crystal 0.8(Na 1/2 Bi 1/2 )TiO 3 –0.2SrTiO 3 grown by the SSCG method, which was grown from the SrTiO 3 single crystal as a seed crystal. The grown single crystal exhibited high porosity. Le et al. [ 69 ] afterward reported growth of 0.75(Na 1/2 Bi 1/2 )TiO 3 –0.25SrTiO 3 single crystal using the same approach. They investigated the dependence of growth of the single crystal and matrix grains on sintering time and temperature, and showed that the results could be explained with the mixed control mechanism of microstructural evolution [ 23 ].

Later on and for the first time ever, a different group of authors reported on a fabricated 0.96(Na 1/2 Bi 1/2 )TiO 3 –0.04CaTiO 3 single crystal [ 70 ] via conversion of the polycrystalline powder matrix to a single crystal, in presence of SrTiO 3 as a seed crystal. The grown single crystal showed improved ferroelectric and piezoelectric properties compared to its polycrystalline ceramic counterpart.

Ferroelectric materials

Ferroelectric oxides are a class of perovskite-type materials which exhibit spontaneous electrical polarization that can be oriented in the presence of an external electric field. Also, these materials possess other properties such as piezoelectricity and pyroelectricity and may have large dielectric constants which are important for actuator and sensor applications. BaTiO 3 and Ba(Zr x Ti 1− x )O 3 or Ba(Zr,Ti)O 3 (BZT) are some of the most important ferroelectric oxides and, thus, will be covered in this review.

BaTiO 3 single crystals

One of the biggest issues in the fabrication of the BaTiO 3 single crystals lies in its hexagonal-tetragonal transition which occurs at 1430 °C and prevents the growth of a single crystal BaTiO 3 from a stoichiometric melt. Although the BaTiO 3 single crystal can be obtained from, for example, a BaTiO 3 –SrTiO 3 congruent melt, or by the flux-method if the transition temperature is below 1430 °C, these methods are somewhat complicated. [ 71 ] In 1994, Yamamoto and Sakuma [ 71 ] reported that a single crystal of BaTiO 3 can be grown via the SSCG method by utilizing the previously observed phenomenon of AGG in this type of material which occurs in the presence of a small excess of TiO 2 . The authors observed a non-uniform grain size distribution as well as AGG following annealing of the seeded ceramic compact at a temperature of 1300 °C. Although the size and quality of the single crystals could not be successfully controlled and there was a resulting high porosity, this study did show that SSCG could be a promising method for the fabrication of single crystals. A few years later, Yoo et al. [ 72 , 73 ] reported growth of BaTiO 3 single crystals without the presence of a seed crystal. The authors used previous observations in which BaTiO 3 experienced AGG in the presence of a small amount of SiO 2 , which is similar to what Yamamoto and Sakuma [ 71 ] had used in their work. In their experimental work, Yoo and co-workers prepared an SiO 2 slurry which they dropped on top of the surface of a polycrystalline green body of BaTiO 3 . This enabled the formation of the <111> fast-growing twin lamellae inside the polycrystalline BaTiO 3 during sintering, which continued to grow without limitation. According to the authors, the structure of the twin lamellas of the BaTiO 3 enabled easier grain growth when compared to two-dimensional nucleation. Also, they concluded that the formation of the twins was facilitated by the presence of liquid SiO 2 . The same authors also observed in [ 73 ] that there was greater success in forming single crystalline BaTiO 3 in the presence of liquid SiO 2 than in TiO 2 . Furthermore, Lee et al. [ 74 ] continued to investigate the AGG and formation of <111> twins of BaTiO 3 in the presence of TiO 2 . The authors observed at temperatures higher than the eutectic (1360–1370 °C), a phenomenon which they called secondary abnormal grain growth (SAGG). According to them, the grains which experienced SAGG all contained twins, and, at the previously described temperature range, had grown without any limitation in size.

In their study on diffuse dielectric anomaly in BaTiO 3 , Kang and co-workers [ 75 , 76 ] fabricated a BaTiO 3 single crystal with <100> direction by the SSCG method. They obtained a single crystal that was entirely free of grain boundaries after sintering for 200 h at 1360 °C. Also, they showed that the single crystal had a significantly higher electrical conductivity compared to the ceramic BaTiO 3 due to the absence of grain boundaries, which act as electrical barriers, and less oxygen vacancies, which have a direct influence on the diffuse dielectric anomaly.

Later on, Jung et al. [ 37 ] investigated grain growth behavior in BaTiO 3 with a small excess of TiO 2 during sintering in air with and without pre-sintering in H 2 environment. The authors provided a theoretical explanation to the influence of the oxygen partial pressure on AGG. They explained that pre-sintering in H 2 atmosphere for a long time led to an increase in the average grain size which in turn suppressed AGG during air sintering. In this way, the authors demonstrated that by increasing the initial average grain size in the polycrystalline matrix, it is possible to suppress AGG by reducing driving force for the growth of the faceted grains below the critical value.

Although ferroelectric oxides such as BaTiO 3 represent a very important group of materials with mainly electronic applications, there have not been many reports on SSCG of BaTiO 3 single crystals recently. Most of the recent studies on SSCG of BaTiO 3 were carried out by Ceracomp Co. which is now utilizing this method for the commercial production of BaTiO 3 single crystals. In one of their publicly available technical reports [ 48 ], they mentioned that the number density of the abnormally grown grains in BaTiO 3 can be controlled during the SSCG, thus implying that this method can be used for conversion of single crystals from polycrystalline ceramics (Fig.  12 a). They also determined that this method can be utilized for the fabrication of transparent BaTiO 3 single crystals (Fig.  12 b) and even layered Mn-, Cr-, and Ce-doped BaTiO 3 single crystals (Fig.  12 c) with compositional gradients. In the same report [ 48 ], Lee presented the study on BaTiO 3 single crystals obtained by the SSCG method doped with various ions (Ca, Ce, Zr, La, Nb, Nd, Cr, Co, Fe, Mg, and Mn). All these ions were successfully doped into BaTiO 3 and then converted into a single crystal. Lee pointed out in his report that for obtaining high-quality transparent single crystals via the SSCG method, it is crucial to increase the density of the polycrystalline ceramics and reduce porosity before conversion of the single crystal, which can be done in a hot press (Fig.  12 d).

SSCG growth of BaTiO 3 single crystals: a control of the number density of abnormal grains; b transparent BaTiO 3 ; c Mn-, Cr-, and Ce-doped BaTiO 3 single crystal with compositional gradient; d highly dense transparent BaTiO 3 single crystal obtained using a hot press [ 48 ]

BZT single crystals

Ba(Zr,Ti)O 3 (BZT) polycrystalline ceramics have recently found a wide range of applications as piezoelectric materials, especially due to their lead-free nature and the environmental concerns which are imposed by the usage of lead-containing piezoelectric materials such as Pb(Zr,Ti)O 3 (PZT). As it has been mentioned previously, single crystal materials show better dielectric, piezoelectric and many other properties compared to polycrystalline ceramics of the same composition. Therefore, development of technology which will be able to replace lead-containing ferroelectrics and piezoelectrics has become necessary.

The addition of Zr in a BaTiO 3 matrix was demonstrated to reduce the transition temperature from the cubic to tetragonal phases as well as increase the transition temperatures between the tetragonal and orthorhombic, and orthorhombic and rhombohedral phases. If the orthorhombic or rhombohedral phase is stabilized at room temperature, then the single crystal BZT shows good piezoelectric properties [ 47 ]. Due to their incongruent melting, BZT single crystals are hard to obtain by any conventional single crystal growth technique (flux, Bridgman, etc.). Therefore, SSCG method has been introduced as a promising technique for growth of high-quality BZT single crystals. In their study on the dielectric and piezoelectric properties of BZT single crystals, Lee and associates [ 77 ] were able to grow a rhombohedral BZT single crystal by the SSCG method. They prepared a single crystal by seeding a pre-sintered polycrystalline ceramic compact with a BaTiO 3 seed crystal and sintering it for 100 h. Since the sintering and single crystal conversion were performed at temperatures lower than the melting temperature, a homogeneous chemical composition was obtained for the single crystal. Furthermore, the authors showed that the SSCG-grown <001> BZT single crystal had a piezoelectric charge constant which was more than six times higher and dielectric loss more than nine times smaller than the BZT polycrystalline ceramic, as well as an electromechanical coupling factor greater than of PZT ceramics.

In his earlier studies, Lee [ 47 ] also obtained BZT single crystals by seeding a BZT ceramic compact. He was able to observe an obvious boundary between a grown <100> single crystal with a size of (50 × 50 × 10) mm 3 and polycrystalline matrix, as shown in Fig.  13 a. Another thing Lee pointed out was that the SSCG method allowed for the fabrication of more complex shapes compared to the conventional single crystal growth techniques. One of the examples given by him is shown in Fig.  13 b, which represents a ring-shaped single crystal obtained from a polycrystalline ceramic, which was uniaxially pressed, sintered, and later attached to a single crystal seed which enabled a single crystal conversion.

Growth of a <100> and b a ring-shaped BZT single crystal by SSCG method [ 47 ]

Al-based oxide materials

Al 2 o 3 and mgal 2 o 4 single crystals.

Polycrystalline alumina is an important industrial material that is used in various application, one of which being sodium vapor lamps [ 78 ]. Therefore, sintering this material is an important process for obtaining many different products. Fortunately, the majority of the problems associated with the usage of polycrystalline alumina can be overcome by instead using single crystal alumina, also known as sapphire.

The solid-state conversion of single crystals from polycrystals has appeared to be a promising technique which can be used for large-scale production of single crystal alumina. This method utilizes a well-known phenomenon that is related to AGG, which occurs in polycrystalline Al 2 O 3 during heat treatment. Moreover, there are many reports which discuss other interesting phenomena in which AGG can be induced in the presence of CaO or SiO 2 in alumina, or suppressed in the presence of MgO [ 79 , 80 , 81 ]. The effects of CaO and SiO 2 in alumina can be explained by the formation of a liquid phase during sintering which acts as a driving force for grain growth through the formation of straight and faceted grain boundaries. On the other hand, the presence of MgO was observed to suppress AGG by coarsening of the grain boundaries. All of the aforementioned observations were later used in studies with the goal of developing a new approach for Al 2 O 3 single crystal fabrication - SSCG.

In one of the earliest studies, Scott et al. [ 80 ] investigated the possibility of the conversion of polycrystalline Al 2 O 3 to single crystal sapphire without going through the melting process of the material. They sintered Al 2 O 3 with an amount of MgO which was enough to suppress AGG during sintering. Once they allowed grains to grow up to 20–30 μm in average (NGG), through a careful control of the sintering temperature, they managed to instigate the AGG despite the presence of MgO in the matrix. The high temperature of 1880 °C which they applied was sufficient to promote AGG by inhibition of various dragging forces for boundary movement. They observed very high velocities of grain boundary migration which reached as high as 1 cm/h. As a result, the authors obtained a centimeter-sized single crystal sapphire converted from the polycrystalline Al 2 O 3 (Fig.  14 ).

Single crystal sapphire grown by SSCG method: (left) large sapphire crystals grown at 1880 °C; (right) SEM micrograph of the interface between the polycrystalline Al 2 O 3 matrix and the grown single crystal [ 80 ]

Similar to the previous study, Thompson et al. [ 81 ] investigated the influence of localized surface co-doping with SiO 2 on the single crystal conversion of Al 2 O 3 . The co-doping with SiO 2 was done prior to sintering, which enabled AGG and conversion of the polycrystalline matrix from the outside to the inside of the ceramic tube sample as soon as the heat treatment started (Fig.  15 a, b). Their study demonstrated that it is indeed possible to obtain nearly transparent single crystals of Al 2 O 3 by the SSCG method (Fig.  15 c), with low porosity, high density, and good physical and optical properties. An interesting conclusion the authors made was that the SiO 2 co-dopant did not directly affect the densification of the converted single crystal sapphire. In the early stages, SiO 2 initiated conversion by removing the grain boundaries, which consequently provided a pathway for fast densification.

Optical micrographs of the single crystal Al 2 O 3 (sapphire) grown via the SSCG method: a , b cross-section of single crystal sapphire grown from polycrystalline Al 2 O 3 ; c translucent single crystal sapphire doped with MgO and SiO 2 [ 81 ]

In the years that followed, through a series of studies on controlled AGG in alumina in presence of MgO, CaO and SiO 2 , Dillon and Harmer tried to explain the phenomenon of single crystal conversion. They proposed a mechanism of single crystal conversion via the SSCG method in alumina which involved rapid diffusion through an intergranular film of 10–20 nm thickness at the grain boundaries [ 82 ]. They also emphasized that the different grain boundary structures in alumina have a direct influence on the grain boundary kinetics, which they used to explain the conversion process [ 83 , 84 , 85 ].

While the previously mentioned authors investigated the SSCG of MgO-doped alumina by controlling AGG in the presence of SiO 2 or CaO, the following authors utilized the SSCG approach to grow single crystals by the conversion of epitaxial film on substrates. The conversion of epitaxial films is a potential method for the fabrication of patterned single crystal substrates for various applications [ 86 ].

Park and Chan [ 87 ] reported their study on the epitaxial growth of single crystal alumina on a surface of sapphire which could be utilized to obtain a pristine sapphire surface when a high-quality surface finish is necessary (e.g. for substrate material for high-power blue LEDs and laser diodes). A thin film of Al was deposited by magnetron sputtering onto sapphire disks, after which a two-stage sintering was applied, first to oxidize the Al film at moderate temperatures and then to induce the growth of a single crystal at high temperatures by consumption of the oxide layer grains by the single crystal substrate. Furthermore, Browne et al. [ 88 ] conducted a somewhat similar investigation, but instead of single crystalline substrate, they used a polycrystalline MgAl 2 O 4 spinel. This approach can be considered analogous to the SSCG method which has been discussed thus far. The authors used a wet-chemical method to prepare a sol-gel for spin-coating of the MgAl 2 O 4 ceramic polycrystalline surface. After this step, the coated samples were heat-treated at different temperatures. The authors demonstrated that at 1400 °C, the coating was converted into an epitaxial layer by the growth of substrate grains and their corresponding absorption of the grains in the coating. A few years later, Dutta et al. [ 86 ] reported on a spin-coated sapphire substrate, which experienced a single crystal conversion of the coating to {0001} α -alumina (sapphire) following heat treatment in the range of 1100–1400 °C. During this heat treatment, the authors observed coarsening of the microstructure while retaining a higher level of porosity. But, a uniform conversion of the sol-gel coating was observed at the coating-sapphire interface.

After performing an extensive amount of research on materials with high laser performance, in 2007, Ikesue et al. [ 42 ] reported on the fabrication of Nd-doped yttrium aluminum garnet (YAG) single crystal (Nd:YAG) obtained through conversion from a polycrystalline material. The importance of Nd:YAG single crystals as laser materials has been covered elsewhere. The work of Ikesue has confirmed that it is possible to obtain a single crystal of high quality that is nearly pore-free using a fabrication method which is significantly different from conventional growth methods. The authors used a solid-state reaction method for the fabrication of an Nd:YAG polycrystalline powder, which was then pressed into a compact and sintered under vacuum. A seed crystal of YAG which was grown by the Cz method was placed on the top surface of the ceramic Nd:YAG and then sintered together in the range of 1700–1800 °C. This enabled the continuous growth of grains, which starts in the single crystal region and heads towards the polycrystalline grains. The authors observed abrupt abnormal grain growth at the single crystal-polycrystal interface, where the surface energy of the seed crystal was low enough compared to the surface energy of the polycrystals to consume the smaller polycrystalline grains. Continuous absorption of the smaller grains by the single crystal instigated a rapid grain boundary movement towards the rest of the polycrystalline region which at the end created a Nd:YAG single crystal.

A few years later, the influence of the different stoichiometries of Y 2 O 3 and Al 2 O 3 on the solid-state conversion of polycrystalline YAG to a single crystal was investigated by Bagayev et al. [ 89 ]. In their study, the authors used a <111> polished YAG single crystal as a seed crystal which they placed on the surface of the polycrystalline ceramic YAG. A micrograph of the thermally etched surface of the grown crystal which is entirely free of grain boundaries is shown in Fig.  16 . The authors also observed that the single crystal growth rates were highly temperature dependent and were faster in samples with excess Al 2 O 3 . The highest achieved growth velocity was 0.15 mm/h. Additionally, the authors did not observe any differences in the growth rates between the Nd-doped and the undoped YAG.

Micrograph showing surface of the grown single crystal YAG by SSCG method [ 89 ]

Other oxide materials

Aside from Al-based oxides and YAG, there are also some reports on attempts to grow single crystalline materials of other oxide materials by the SSCG method. Such reports which investigated the feasibility of the growth of single crystals of the apatite-type of oxide ionic conductors were given by Nakayama et al. In 2013, they reported on the growth of single crystals of hexagonal apatite-type La 9.33 Si 6 O 26 [ 90 ] by seeding with a single crystal of the same composition grown by the Cz method. As in the previous studies involving the SSCG method, the authors observed an abrupt motion of the grain boundary from the seed crystal with a low surface energy to a polycrystalline area with higher surface energy due to the seed crystal consuming the smaller, fine grains. In the same year, the authors reported on another study on apatite-type oxide La 9.33 Ge 6 O 26 [ 91 ] grown as a single crystal by the SSCG method. Compared to the previous, La 9.33 Ge 6 O 26 exhibited much less conductive anisotropy.

In 2016, Fisher et al. [ 92 ] reported on the growth of a BaFe 12 O 19 single crystal via the SSCG method. The authors prepared the samples by cold isostatic pressing the polycrystalline powder with a seed crystal which was buried inside the powder compact, following heat treatment. The authors used a mixed control mechanism model of grain growth [ 23 ] to explain the single crystal conversion in the system being studied. They observed a significant temperature influence on the porosity of the grown BaFe 12 O 19 single crystal as well as on the number of abnormally grown grains. Once the number of abnormal grains had become high, the growth of the single crystal stopped.

In more recent reports, Kappenberger et al. [ 93 ] reported on the growth of a single crystal LaFeAsO via the SSCG method. LaFeAsO belongs to the family of high temperature iron-based superconductors, which have considerable c -axis growth of the {1111} family of planes. This type of material is very difficult to obtain via conventionally used single crystal growth techniques such as the flux-method; therefore, the report of Kappenberger et al. has introduced a promising route for the fabrication of single crystals within this family of materials. The authors grew LaFeAsO single crystal from polycrystalline powder in the presence of a Na-As powder which turned into a liquid phase at around 550 °C during annealing, diffused into the pores of the polycrystalline compact and promoted crystal growth. A schematic representation of the steps for growth of LaFeAsO single crystals via the SSCG method is presented in Fig.  17 . It was shown that this method is successful for obtaining large single crystals with considerable growth along the c -axis, with high quality as well as good physical properties.

Schematic showing SSCG process for obtaining LaFeAsO single crystals [ 93 ]

Mn–Zn ferrite

In literature, studies can also be found on the growth of single crystal ferrites via the SSCG. The earliest report, which dates back to 1985, was done by Tanji and associates [ 94 ]. Conventionally, Mn–Zn ferrites were produced via the Bridgman method. These were, therefore, costly and difficult to obtain. The authors applied the SSCG method, and by seeding the polycrystalline Mn–Zn ferrite matrix with the single crystal seed, they were able to successfully grow Mn–Zn ferrite single crystals. A few years later, a different group reported on a study regarding the same material, but, in comparison to the previous study, they tried to explain the influence of different sintering additives on single crystal conversion of Mn–Zn ferrite via the SSCG method [ 95 ]. The experiment was conducted by this group by adjoining two pieces of the polycrystalline ceramic to a single crystal seed from both sides with the assistance of ethyl silicate as an adhesive. After this step, they annealed the sandwiched samples in the N 2 –O 2 atmosphere where they could observe AGG of the polycrystalline material which lead to single crystal conversion. Although the authors proved that the SSCG method can be used for the fabrication of Mn–Zn ferrites, the Bridgman method is still widely used [ 23 ].

Electric field-assisted single crystal growth

So far, this review has discussed solid-state single crystal conversion from a polycrystalline matrix either by the seeding method or by the control of AGG inside the ceramic during heat treatment (seed-free method). But reports are also available which discuss single crystal growth in the presence of an externally applied electric field. Liu et al. [ 96 ] investigated the influence of an applied electric field on single crystal conversion of Yb:Sr 5 (PO 4 ) 3 F from a seed crystal buried in the polycrystalline matrix during spark plasma sintering (SPS). It was thought that the applied direct current (DC) field during SPS had an influence on the grain boundary potential, and therefore on the activation energy for grain boundary motion. The authors showed that pressureless SPS sintering might be used for single crystal growth from polycrystalline material at temperatures and times which are significantly lower than usual for the material being used. In another study [ 97 ], the same authors used a Sr 5 (PO 4 ) 3 F polycrystalline powder which was sintered via SPS with the addition of NaF as a sintering aid and a single crystal seed embedded in the powder, and annealed further at the same temperature. The authors investigated the influence of the DC electric field on grain growth and noted that the DC field retarded the grain growth during post-sintering treatment, but induced grain boundary migration; this was beneficial for solid-state single crystal conversion.

In a different study, a group of researchers which were led by Chen [ 98 ] performed an investigation on the influence of a DC electric field on the AGG in KNN. The authors observed that the samples which were sintered under an applied non-contact electric field exhibited obvious grain growth and even exhibited AGG when compared to those sintered without a DC field. Also, the application of the electric field had a positive effect on the densification of KNN due to the formation of a liquid phase that could enhance mass transport. The authors pointed out that the observed behavior of the material when put under an applied electric field could be an advantageous approach for the solid-state conversion of polycrystalline KNN to a single crystal.

Challenges of SSCG

The challenges associated with current (conventional) technologies for the growth of single crystals may be overcome by the solid-state conversion of single crystals. At the moment, however, there are a few important challenges that should be overcome first. Control of the microstructure development during the conversion process of the polycrystalline material is the most important and most challenging part of the SSCG method [ 23 ]. Although the proposed mixed control mechanism [ 24 ] has made a significant contribution towards explaining and better understanding of the single crystal conversion phenomenon, especially in certain piezoelectric, ferroelectric, and a few other materials systems, there is still an insufficient amount of data and overall knowledge about the SSCG method, which would allow for it to be more commercially utilized. Porosity in the single crystals grown via the conversion process is another important issue associated with the SSCG method. The quality of the grown single crystal, and, in that way, its properties and the intended application, are greatly affected by the porosity.

At the moment, the sizes of the single crystals grown in the laboratory conditions via the SSCG method are limited to the scale of at most few centimeters. Growth of larger single crystals, comparable in size to the ones obtained via the conventional single crystal growth techniques, is necessary in order for SSCG to become a commercially used technique.

Because of the inability to fully control the growth and the development of single crystals during conversion, as well as other aspects, the SSCG technique is still constrained to a small number of systems, and the large-scale production is somewhat limited.

Summary and future outlook

Solid-state single crystal conversion (SSCG) has been shown to be a promising technique for the growth of single crystal materials from all of the investigations presented thus far. The SSCG method offers many advantages over conventional single crystal growth techniques, such as Bridgman, flux, Cz, and others. Among the strongest advantages of the SSCG method are the low fabrication costs, processing simplicity, and applicability of the method to the growth of single crystals of complex compositions with a high degree of chemical uniformity. However, there are still many issues related to this technique which are not yet well understood to be fully controllable. So far, this method has been successfully applied to the commercial production of high-quality piezoelectric single crystals, such as BaTiO 3 , BZT, PMN–PT, and more, while other types of materials still present problems when produced via the SSCG method. Therefore, the most important next step is to provide an even stronger theoretical background for the SSCG technique, which would extend the current knowledge and understanding of the microstructure control and the mechanisms associated with solid-state single crystal conversion. This would, consequently, help to overcome some of the challenges mentioned in the previous section and push the SSCG technique towards commercialization as an alternative, or in some cases, a unique technique [ 23 ] for the fabrication of single crystals.

So far, only a few groups have conducted research on solid-state conversion of single crystals; although these investigations have been thorough, they have only been conducted on a limited number of materials. Most of the investigations have been focused onto ferroelectric and piezoelectric materials, and a few other oxide materials, however, it is expected in the future for studies to expand onto other types of materials. Table  1 summarizes some of the relevant results presented in this paper. It contains information such as single crystal growth conditions, size of the grown single crystals, some important parameters or properties measured by the authors, or the authors’ observations, and potential applications. Until now, most of the single crystals grown by the SSCG method involved growth from a single crystal seed, which was placed either on top of the polycrystalline matrix or embedded within the matrix. For example, Ikesue et al. [ 42 ] showed that YAG single crystal, which is a very important material for different optical applications, can be fabricated via the SSCG seeding method. However, the selection of suitable single crystal seeds is another common issue associated with the SSCG method. Fortunately, some authors were able to grow single crystals without the use of seed crystals, which can even potentially reduce the production cost for the price of the seed crystals that can sometimes be very expensive. This fabrication route has been very successful for various commercially grown lead-free piezoelectric single crystals of centimeter-scale range [ 56 , 57 , 58 ]. The SSCG technique is still in its developing stage, so it is projected that more research work will be available in the future.

Availability of data and materials

Not applicable.

Abbreviations

abnormal grain growth

BiScO 3 –Pb(Mg 1/3 Nb 2/3 )O 3 –PbTiO 3

Ba(Zr,Ti)O 3

chemical vapor transport

Czochralski method

direct current

0.985(K 1/2 Na 1/2 )NbO 3 –0.015Ba(Cu 1/3 Nb 2/3 )O 3

light-emitting diode

(Li 0.04 K 0.44 Na 0.52 )(Nb 0.85 Ta 0.15 )O 3

(Na 1/2 Bi 1/2 )TiO 3

(Na 1/2 Bi 1/2 )TiO 3 –BaTiO 3

(Na 1/2 Bi 1/2 )TiO 3 –BaTiO 3 –(K 1/2 Na 1/2 )NbO 3

normal grain growth

Pb(Mg 1/3 Nb 2/3 )O 3

Pb(Mg 1/3 Nb 2/3 )O 3 –PbTiO 3

Pb(Mg 1/3 Nb 2/3 )O 3 –Pb(Zr,Ti)O 3

physical vapor transport

Pb(Zr,Ti)O 3

secondary abnormal grain growth

scanning electron microscope

seed-free solid-state single crystal growth

stagnant grain growth

spark plasma sintering

solid-state single crystal growth

yttrium aluminum garnet

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The authors gratefully acknowledge the NSF CAREER Grant (1554094) for funding this research. The authors also thank Professor Suk-Joong L. Kang from Korea Advanced Institute of Science and Technology for his suggestions on this paper.

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Milisavljevic, I., Wu, Y. Current status of solid-state single crystal growth. BMC Mat 2 , 2 (2020). https://doi.org/10.1186/s42833-020-0008-0

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A new home for studies of crystal growth and characterisation

a School of Chemistry, The University of Nottingham, Nottingham NG7 2RD, UK, b Science de l'Ingénierie des Matériaux et Procédés (SIMaP), 38402 Saint Martin d'Hères CEDEX, France, c School of Chemistry, University of Hyderabad, Hyderabad 500 046, India, d Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090, Russian Federation, e Novosibirsk State University, Novosibirsk 630090, Russian Federation, f Department of Materials Chemistry, Adam Mickiewicz University, 61-614 Poznan, Poland, g Institute of Geology and Mineralogy, Siberian Branch of Russian Academy of Science, Novosibirsk, Russian Federation, and h Department of Chemistry, Georgetown University, Washington, DC 20057, USA * Correspondence e-mail: [email protected]

Keywords: editorial ; crystal growth ; journal scope ; crystal engineering ; materials ; structural science ; high pressure ; in situ studies .

Crystal growth is fundamental to much of crystallography, but in contrast to articles describing the crystallization of biological macromolecules, which are catered for by Acta Crystallographica Sections D and F , those dealing with the growth of crystals of non-biological `small' molecules or those of extended organic, inorganic or hybrid materials have lacked equally obvious routes to publication in IUCr journals. It is therefore timely to emphasize that Acta Crystallographica Section B offers such a route, by devoting a segment of the journal to relevant submissions. The ambition is to attract high-quality articles on crystal growth that are of broad interest and high impact, and there will be no arbitrary limit on the number of such articles.

Studies of crystal growth submitted to Acta Crystallographica Section B should align with the general scope of the journal, the subtitle of which is `Structural Science, Crystal Engineering and Materials'. Structural science studies typically begin with the preparation of a crystal or other sample suitable for a diffraction experiment, but the importance of crystal growth in this context is far greater than simply producing a well diffracting crystal. Significant efforts are devoted to studying the mechanisms of crystal growth, as well as the melting, sublimation and dissolution behaviour of crystal forms. Moreover, control of crystal growth in aspects of both morphology (shape and size) and crystal polymorphism, based on the interplay of thermodynamics and kinetics, is fundamental to understanding the factors that determine crystal structure at the atomic, molecular, and macroscopic levels, and their impact on physical and chemical properties. Crystal engineering deals with the design, synthesis and growth of solid-state molecular assemblies with the aim of producing materials with defined desirable properties, since the bulk properties of many molecular materials are determined by the solid-state arrangement of the molecules. The method is based on a comprehensive understanding of intermolecular interactions and how they can be utilized to assemble extended crystal structures. A very wide range of intermolecular interactions, including hydrogen bonding, halogen bonding, π – π interactions and van der Waals interactions have been exploited for crystal growth in crystal engineering. The range of materials and properties ( e.g. hydrogen storage, catalysis, gas separation, pharmaceuticals, optoelectronic materials) which have been designed is so extensive that even a much longer list would still not be representative. Materials are often composed of crystals, either as individual large single crystals with sizes in the range of centimetres and even metres, or with polygrain structures. Even at the other extreme of the size range, nanocrystals also need to be grown prior to being studied. Growing single or polygrain crystals, mastering their defect concentration (either to avoid defects or to engineer defects for given physical properties) is at the heart of material science. The understanding of the growth process, its modelling, the detailed characterization of the atomic structure of the obtained crystals with defects, stoichiometry etc ., are key prerequisites to achieving an understanding of structure–property relationships.

Crystallization applies to most of condensed matter, including the naturally-occurring minerals, metals in almost infinitely various forms, organic compounds and many others. Recently we have witnessed enormous progress in crystallization methods, such as the special environments capable of reproducing in the laboratory the thermodynamic conditions of interstellar space, through hydrothermal baths, to the centre of Earth, extremely slow annealing in vacuum and ultrafast nucleation under terapascal (TPa) shocks, the size effects remarkably evident in nanotechnology, refined co-crystallizations, as well as the advanced methods of investigating the most subtle structural effects by super-intense microbeams combined with highly sensitive detectors. All this on one hand provides new information for better understanding the science and art of crystallization, and on the other hand opens new routes for obtaining new unprecedented forms of matter that can foster progress in scientific and technological development.

Some studies of crystal growth from more theoretical viewpoints have appeared in Acta Crystallographica Section A or Journal of Applied Crystallography , and we expect this to continue. However, as there are likely to be borderline cases, potential authors are encouraged to consult the Notes for Authors or contact a Main or Section Editor to discuss the most relevant journal for their submission.

The products of the crystal growth procedures, which may be single crystals, microcrystals, powders, nanocrystals, defect structures, incommensurate structures, etc ., must be characterized by direct structural analysis based on diffraction or atomic scale imaging techniques. An article which describes a technique for growing crystals of a material but lacks a distinct crystallographic component or a complete and convincing structural characterization is unlikely to be suitable for Acta Crystallographica Section B. Other existing journal criteria also apply to crystal growth papers: these include relevance to the scope of the journal, clear and complete descriptions of experimental procedures, evidence that demonstrates that the method described is reproducible and whether the resulting sample is homogeneous or otherwise.

To emphasize that Acta Crystallographica Section B actively welcomes such submissions, the Notes for Authors contains a completely new section ( §3 ) on crystal growth papers which present some examples of possible research topics. Our interest in publishing such papers is further signalled by the recent appointment of two Co-editors, Tatyana Bekker (Institute of Geology and Mineralogy, Siberian Branch of Russian Academy of Science, Novosibirsk, Russian Federation) and Karah Knope (Department of Chemistry, Georgetown University, Washington, DC, USA), who are experts in crystal growth. We are commissioning feature articles which will explain further the types of papers the journal is seeking to attract. Examples of crystallization under unusual conditions (high-pressure, cryogenic, levitation, confined medium, template-assisted, electric and magnetic field, laser irradiation, etc.) are welcome. A special collection of recent articles on crystal growth will be collated, followed later by a special issue comprising new papers.

These initiatives and developments demonstrate that Acta Crystallographica Section B is now a natural home for publications related to studies of crystal growth, and we invite the relevant communities to submit their work to the journal.

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AbstractThe crystallization of metastable liquid phase change materials releases stored energy as latent heat upon nucleation and may therefore provide a triggerable means of activating downstream processes that respond to changes in temperature. In this work, we describe a strategy for controlling the fast, exothermic crystallization of sodium acetate from a metastable aqueous solution into trihydrate crystals within a polyacrylamide hydrogel whose polymerization state has been patterned using photomasks. A comprehensive experimental study of crystal shapes, crystal growth front velocities and evolving thermal profiles showed that rapid growth of long needle-like crystals through unpolymerized solutions produced peak temperatures of up to 45˚C, while slower-crystallizing polymerized solutions produced polycrystalline composites and peaked at 30˚C due to lower rates of heat release relative to dissipation in these regions. This temperature difference in the propagating heat waves, which we describe using a proposed analytical model, enables the use of this strategy to selectively activate thermoresponsive processes in predefined areas.

Crystal growth, characterization and third order nonlinear optical studies of N’-[(E)-(4-chlorophenyl)(phenyl)methylene]-4-methylbenzenesulfonohydrazide for optical applications

Synthesis of zeolitic imidazolate framework-8 and gold nanoparticles in a sustained out-of-equilibrium state.

AbstractThe design and synthesis of crystalline materials are challenging due to the proper control over the size and polydispersity of the samples, which determine their physical and chemical properties and thus applicability. Metal − organic frameworks (MOFs) are promising materials in many applications due to their unique structure. MOFs have been predominantly synthesized by bulk methods, where the concentration of the reagents gradually decreased, which affected the further nucleation and crystal growth. Here we show an out-of-equilibrium method for the generation of zeolitic imidazolate framework-8 (ZIF-8) crystals, where the non-equilibrium crystal growth is maintained by a continuous two-side feed of the reagents in a hydrogel matrix. The size and the polydispersity of the crystals are controlled by the fixed and antagonistic constant mass fluxes of the reagents and by the reaction time. We also present that our approach can be extended to synthesize gold nanoparticles in a redox process.

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Recent progress in homoepitaxial single-crystal diamond growth via MPCVD

• Published: 05 March 2024
• Volume 35 , article number  525 , ( 2024 )

Cite this article

• Ying Ren   ORCID: orcid.org/0000-0002-5427-5283 1 ,
• Xiaogang Li 1 ,
• Haoyong Dong 2 ,
• Qiaohuan Cheng 1 ,
• Feng Yue 1 ,
• Nicolas Wöhrl 3 ,
• Joana Catarina Mendes 4 ,
• Xun Yang 5 &
• Zhengxin Li 1  

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Microwave plasma chemical vapor deposition (MPCVD) is regarded as one of the most promising techniques for the preparation of large-scale and high-quality epitaxial single-crystal diamonds. This review paper provides an overview of recent advancements in MPCVD single-crystal diamond growth, including discussions on the growth mechanism, substrate holder design, and seed crystal screening and pretreatment for achieving homogeneous epitaxial single-crystal diamond. Key growth parameters such as temperature, methane concentration, power density, etc., are investigated to guide the attainment of optimal growth conditions. Furthermore, critical growth techniques like three-dimensional growth, repeated growth, and mosaic splicing are analyzed to enhance the area coverage of single-crystal diamonds. The work on achieving low defect and high purity growth is also elucidated. Additionally, this paper discusses the progress made in n -type and p -type doping of diamond materials. Finally, a summary is provided highlighting the challenges encountered during MPCVD single-crystal diamonds growth.

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Coupling effects of ch4/h2/ar gas ratios and hot filament-substrate distance on the growth of nanocrystalline diamond, data availability.

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Acknowledgements

This work was financially supported by Science and Technology Major Project of Henan Province (No. 231100230300), Science and Technology Major Project of Henan Province (No. 221100230300) and the Innovative Funds Plan of Henan University of Technology (No. 2021ZKCJ06).

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Engineering and Technology Research Center of Diamond Composite Materials of Henan, School of Materials Science and Engineering, Henan University of Technology, Zhengzhou, 450001, China

Ying Ren, Xiaogang Li, Wei Lv, Qiaohuan Cheng, Feng Yue & Zhengxin Li

Changan Automobile Global Research and Development Center, ChongQing Changan Automobile Co., Ltd, Chongqing, 400054, China

Haoyong Dong

Faculty of Physics and CENIDE, University Duisburg Essen, Carl-Benz-Straße 199, 47057, Duisburg, Germany

Nicolas Wöhrl

Instituto de Telecomunicações e Departamento de Electrónica, Telecomunicações e Informática, University of Aveiro, 3810-193, Aveiro, Portugal

Joana Catarina Mendes

Henan Key Laboratory of Diamond Optoelectronic Materials and Devices, Key Laboratory of Material Physics, Ministry of Education, School of Physics and Microelectronics, Zhengzhou University, Zhengzhou, 450052, China

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Project administration, Zhengxin Li and Xun Yang.; writing—original draft, Ying Ren; writing—review and editing, Xiaogang Li, Wei Lv and Haoyong Dong; synergistic effect, Feng Yue.; review and editing, Nicolas Wöhrl and Joana Catarina Mendes. All authors have read and agreed to the published version of the manuscript.

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Ren, Y., Li, X., Lv, W. et al. Recent progress in homoepitaxial single-crystal diamond growth via MPCVD. J Mater Sci: Mater Electron 35 , 525 (2024). https://doi.org/10.1007/s10854-024-12267-3

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DOI : https://doi.org/10.1007/s10854-024-12267-3

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New crystal growth orientation method manipulates properties of materials

by Raven Wuebker, Texas A&M University College of Engineering

A new method to grow single crystals and simultaneously control their growth orientation without melt processing has been discovered by Texas A&M University materials science and engineering doctoral graduate Dr. Hande Ozcan and Dr. Ibrahim Karaman, department head and Chevron Professor.

The discovery of this new crystal growth and orientation control method in solid-state was recently published in the journal Acta Materialia . The research paper focuses on growing large single crystals and their ability to change their crystallographic orientation. Crystallographic orientation describes the alignment of the crystals within a bulk specimen.

"We have been working on single crystals over the last three decades, but growing the crystals with melt processing and controlling their orientations has been quite challenging," Karaman said. "The method Hande discovered now saves us a lot of time and provides more flexibility. There is more to explore; that's what makes us excited about this new method."

According to the research paper, controlling the size, shape and crystallographic orientation of single crystals is vital to exploit the desired properties. Ozcan said this method is important for applications that require materials with anisotropic properties.

"This mechanism allows these materials to change their orientation in solid-state without cumbersome and costly melt processing techniques. This is important because these materials exhibit different properties when they have different crystallographic directions," Ozcan said.

For the first time, Ozcan has seen crystallographic orientations can be changed at this large scale.

"This could fundamentally change how we look at single crystals and manipulate materials properties, because with solid-state methods, we can not only grow large single crystals very easily, but at the same time, we can now play with their crystallographic orientation," Ozcan said.

Single crystals are essential to microelectronics, optical crystals, magnetic devices, solar cells, piezoelectric components and multifunctional alloys. One specific use case example for these materials is multifunctional shape memory alloys. These materials can change their shape and recover upon applying heat or stress.

"For example, you can deform the material when you apply a load, but when you release it, it returns to its original shape," Ozcan said.

These properties strongly depend on the orientation of the single crystal ; some orientations exhibit this recovery in a perfect fashion, and some do not. Thus, the orientation control is critical in obtaining superior functional properties.

Another advantage to this technique, according to the research paper, is that it does not require complex and expensive equipment.

Traditionally, melt-growth techniques, called the Bridgman and Czochralski processes, are used to obtain large crystals with a preferred orientation. However, controlling the crystal orientation is still challenging.

These methods rely on the availability of proper seed crystals, precise nucleation and thermal profile control during processing.

Because of this complexity, these methods are very expensive. The new method is called the solid-state crystal growth (SSCG) technique, a method where large bulk crystals with different crystallographic orientations could be made with simple heat treatments.

In this process, the crystals produced are more versatile and can achieve better chemical homogeneity than in the traditionally used melt-growth techniques.

The research team at Texas A&M demonstrated the SSCG method in two alloy systems, FeMnAlNi and CuMnAl, and achieved repeated, massive orientation changes in the solid state.

These findings offer a new strategy for manipulating the orientation of large single crystals on demand to take advantage of their superior and highly anisotropic properties, according to the research paper.

"This process works with materials that have semicoherent precipitates and that have two-phase regions in their phase diagram," Ozcan said. "When you cycle the material from high to low temperatures in a two-phase region multiple times, precipitates nucleate and dissolve and leave subgrain boundaries behind. Then the grains start to grow, decreasing the excess subgrain boundary energy. These grains continue to grow and merge, and finally, you can get a single crystal."

When you continue to cycle the material after it becomes a single crystal, there are no other ways to reduce the excess energy in the system, and it activates a mechanism that changes its crystallographic orientation.

"We actually discovered this technique while we were working on something else. We were not specifically targeting to change the crystallographic orientation ," Ozcan said. "We were just working on growing large single crystals."

During that process, Ozcan and the team found that in just a few cycles, the alloys would turn into single crystals, and with additional cycles, she realized that the orientation of the single crystals started to change completely.

"I showed the results to Dr. Karaman, and I was so excited," she said. "After that, we started understanding what was going on and why the crystal orientation was changing; we tried different methods and processing schedules in order to manipulate this change."

This discovery will open up extensive research areas, she said. This is just the beginning of this exciting new path of finding new materials.

Journal information: Acta Materialia

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Recent advances on the mechanisms of kidney stone formation (Review)

1 Department of Urology, People's Hospital of Longhua, Southern Medical University, Shenzhen, Guangdong 518109, P.R. China

2 Central Laboratory, People's Hospital of Longhua, Southern Medical University, Shenzhen, Guangdong 518109, P.R. China

Jianwen Zhang

Associated data.

Not applicable.

Kidney stone disease is one of the oldest diseases known to medicine; however, the mechanisms of stone formation and development remain largely unclear. Over the past decades, a variety of theories and strategies have been developed and utilized in the surgical management of kidney stones, as a result of recent technological advances. Observations from the authors and other research groups suggest that there are five entirely different main mechanisms for kidney stone formation. Urinary supersaturation and crystallization are the driving force for intrarenal crystal precipitation. Randall's plaques are recognized as the origin of calcium oxalate stone formation. Sex hormones may be key players in the development of nephrolithiasis and may thus be potential targets for new drugs to suppress kidney stone formation. The microbiome, including urease-producing bacteria, nanobacteria and intestinal microbiota, is likely to have a profound effect on urological health, both positive and negative, owing to its metabolic output and other contributions. Lastly, the immune response, and particularly macrophage differentiation, play crucial roles in renal calcium oxalate crystal formation. In the present study, the current knowledge for each of these five aspects of kidney stone formation is reviewed. This knowledge may be used to explore novel research opportunities and improve the understanding of the initiation and development of kidney stones for urologists, nephrologists and primary care.

1. Introduction

Kidney stone disease, also known as nephrolithiasis or urolithiasis, is one of the oldest diseases known to medicine. It is estimated that 1-15% individuals suffer from kidney stone formation at some point during their lifetime, and the prevalence and incidence of kidney stone is reported to be increasing worldwide ( 1 , 2 ). A recent study concluded that the prevalence of kidney stones was 5.8% among Chinese adults (6.5% in men and 5.1% in women), with about 1 in 17 adults currently affected ( 3 ). Without proper treatment, kidney stones can cause the blockage of the ureter, blood in the urine, frequent urinary tract infections, vomiting or painful urination, culminating in the permanent functional damage of the kidneys ( 4 ). The worldwide prevalence of urolithiasis has increased over the past decades. Urolithiasis is often a recurrent and lifelong disease with a recurrence rate of 50% within 5-10 years and 75% within 20 years ( 5 ). Some studies have indicated that an increase in kidney stone occurrence is expected, due to multiple environmental factors, including changes in lifestyle and dietary habits, as well as global warming ( 1 , 4 , 6 ). However, precise factors responsible for the upward prevalence and recurrence of urolithiasis have not been identified yet. Due to its high prevalence in adults of working age, kidney stone disease has a substantial impact on the individual and society, and has become a public health issue, particularly in populations residing in regions with a hot and dry climate ( 7 , 8 ).

There are mainly five types of kidney stones according to the mineralogical composition, including calcium oxalate (CaOx; 65.9%), carbapatite (15.6%), urate (12.4%), struvite [(magnesium ammonium phosphate), 2.7%], brushite (1.7%) ( 9 , 10 ). Kidney stones can be broadly categorized into calcareous (calcium containing) stones and non-calcareous stones. The most common types of human kidney stones are CaOx and calcium phosphate (CaP), either alone or combined, which are calcareous and radio-opaque stones ( 9 , 11 ). Kidney stones form at a foundation of CaP termed Randall's plaques (RPs), which begins at the basement membranes of thin limbs of the loop of Henle on the renal papillary surface ( 12 ). CaOx and urate stones exhibit a higher occurrence in males, whereas higher percentages of carbapatite and struvite stones are observed in females than in males ( 10 , 13 ). However, the role of sex differences in the pathophysiological mechanisms of urinary stone disease are not yet fully understood.

Regardless of the type, kidney stone formation is a complex and multistep process that includes urinary supersaturation, crystal nucleation, growth and aggregation ( 11 , 14 ). Kidney stone formation is associated with systemic disorders, including diabetes ( 15 ), obesity, cardiovascular diseases, hypertension and metabolic syndrome ( 16 , 17 ). Conversely, nephrolithiasis patients [also known as kidney stone formers (KSF)] are at a risk of developing hypertension ( 18 ), chronic kidney disease (CKD) ( 19 ) and progression to end-stage renal disease (ESRD) ( 20 , 21 ). Multiple promoting factors and inhibitors have been reported to play critical roles in kidney stone formation. For example, hyperoxaluria, hyperuricosuria and phosphaturia are common promoting factors linked to kidney stone formation ( 22 , 23 ); inter-α-inhibitor (IαI), a member of the protease inhibitor family, has been shown to inhibit CaOx crystallization in vitro ( 24 ).

Although details of human stone formation have accumulated, kidney stone formation and growth mechanisms are far from being clarified. The present review provides an update on the mechanisms of kidney stone formation, in order to improve the understanding of kidney stones for urologists, nephrologists and primary care givers.

2. Physicochemical mechanism of kidney stone formation

Urinary supersaturation and crystallization are the driving force for intrarenal crystal precipitation and is mainly caused by inherited or acquired diseases associated with renal function impairment. Additionally, urinary supersaturation and crystallization are influenced by urine pH and specific concentrations of substance excess, including CaOx, CaP, uric acids and urates, struvite, amino acids (cysteine), purines (2,8-dihydroxyadenine and xanthine) and drugs (e.g., atazanavir, sulfamethoxazole, amoxicillin, ceftriaxone) ( 25 , 26 ). Additionally, crystal formation and development are influenced by multiple modulator molecules, which are known as receptors, promoters and inhibitors.

Promoters of stone formation

A number of receptors or receptor-like features have been reported to play critical roles in crystal-cell interaction, which is recognized as the most important process for crystal retention in kidney ( 8 , 27 ). Recently, protein alterations in a CaOx monohydrate (COM) crystal-cell interaction model were screened by the authors, and 1,141 differentially expressed proteins (DEPs) were identified in COM treated HK-2 cells ( 28 ). Proteins and glycosaminoglycan like CD44, nucleolin, hyaluronan (HA), heat shock protein 90 (HSP90) ( 29 ), Annexin II ( 30 ) and osteopontin (OPN) ( 28 , 31 ), have been reported to act as stone formation modulators, which has been thoroughly reviewed previously ( 32 ). Several structures and molecular components also play the role of receptor in crystal attachments, including the phosphatidylserine component of the lipid bilayer and the acidic side chains of proteins ( 33 ). Calcium, oxalate, urate and phosphate ions are the main promoters of crystal formation, which can promote crystallization of stone constituents or their aggregation through the activation of several mechanisms. Ketha et al ( 34 ) demonstrated that the first time nephrolithiasis patients had increased serum calcium and 1,25(OH)2D levels than the corresponding healthy individual serum calcium levels, suggesting that stone formation is a manifestation of altered calcium and vitamin D regulation. Higher serum calcium concentration acts as a promoter in lithogenesis, which directly regulated by the calcium-sensing receptor (CaSR) through different pathways ( 35 ). Similarly, urate and phosphate ions have also been reported to promote heterogeneous nucleation and enhance the attachment of crystals to epitheliums ( 36 , 37 ). Another important promoter of stone formation is urine pH ( 38 ). Low pH urine may lead to CaOx crystallization and crystal precipitation ( 39 ). High-alkaline urine may also promote precipitation and nucleation of CaOx crystals ( 40 , 41 ). Lysozyme and lactoferrin are two most recently identified proteins that promote COM growth through the acceleration of layer advancement rate on crystal surfaces ( 42 ).

Inhibitors of stone formation

Normal urine contains numerous inhibitors that act both in competition and cooperation, consequently decrease crystallization and inhibit crystals aggregation and/or adhesion to the tubular epithelial cells ( 43 , 44 ). These inhibitors can be divided into three groups: Anions, metallic cations and macromolecules. Anions such as citrate, can inhibit crystal growth very efficiently, at concentrations above 0.1 mM ( 45 , 46 ). A majority of nephrolithiasis patients exhibited a decrease in citrate excretion. Alkali supplements are widely used for hypocitraturic recurrent nephrolithiasis patients to restore citrate excretion ( 47 , 48 ). Hydroxycitrate is a structural analog of citrate, which has been reported to show equivalent capacity in forming complexes with calcium, in order to inhibit crystallization ( 49 , 50 ). Metallic cations such as magnesium, have been reported to inhibit crystal growth and aggregation, which is synergistic with citrate in acidic environments ( 51 - 53 ). Macromolecules are the most effective inhibitors of crystal growth. More specifically, OPN, Tamm-Horsfall protein (THP), urinary prothrombin fragment 1 (UPTF-1), nephrocalcin (NC) and some subunits of the serum IαI are able to inhibit crystal growth, aggregation and/or adhesion to the tubular cells ( 11 , 38 , 45 ).

However, there is a competition between supersaturation and inhibitors of crystallization as mentioned above, which ultimately determines the pattern of crystalluria in nephrolithiasis patients and healthy individuals ( 54 ). As a consequence of the increased promoters and reduced inhibitors, crystal formation and kidney stone occurrence have been observed ( Fig. 1 ).

Physicochemical mechanisms of kidney stone formation. The reduced inhibitors (left panel) and increased promoters (right panel) are suggested to play critical roles in kidney stone formation.

3. Randall's plaque and calcium oxalate stone formation

RPs, first proposed by Alexander Randall in 1937 ( 55 ), are regions of subepithelial mineralized tissue at the papillary tip, surrounding the openings of the ducts of Bellini containing CaP ( 56 ). Scanning electron microscopy (SEM) examination has shown that RP are made of a mixing of tubules with calcified walls and of tubules obstructed by CaP plugs ( 57 ). RP consists of CaP crystals mixed with an organic matrix that is rich in various proteins and lipids, and includes membrane-bound vesicles or exosomes, collagen fibers, as well as other components of the extracellular matrix ( 58 ). An increasing number of studies have suggested that RPs are the origin of renal stones ( 57 - 60 ). Winfree et al ( 61 ) clarified that kidney stones develop as an overgrowth on RP, which contains unique organic composition (fibrillar collagen) that can be differentiated from the stone overgrowth by specific autofluorescence signatures. Of note, a previous study using a murine mode of RP revealed that vitamin D supplementation and calcium intake could notably accelerate RP formation ( 60 ). However, the precise mechanisms of RP formation remain unclear.

Recently, studies indicated that long non-coding RNAs (lcnRNAs) H19 and MALAT1 mediated osteogenic differentiation of human renal interstitial fibroblasts (hRIFs) and participated in RP formation ( 62 - 64 ). lcnRNA H19 has been shown to be significantly upregulated in RP, which can promote the osteogenic differentiation of hRIFs by activating Wnt/β-catenin signaling ( 63 ). lcnRNA H19 can also serve as a facilitator in the process of CaOx nephrocalcinosis-induced oxidative stress and renal tubular epithelial cell injury through the interaction with miR-216b and exerts its effect via the HMGB1/TLR4/NF-κB signaling pathway ( 64 ). lcnRNA MALAT1 can function as a competing endogenous RNA (ceRNA) that sponges miR-320a-5p, upregulates Runx2 expression and thus promotes the osteogenic phenotype of hRIFs ( 62 ).

These studies provide novel insight into the pathogenesis of RP-mediated kidney stone disease, while further studies are urgently anticipated to explore the mechanisms of RP formation, as well as additional roles of RP in the context of stone formation.

4. Role of sex hormones in calcium oxalate nephrolithiasis

Statistical analyses have revealed that males have a higher incidence of CaOx nephrolithiasis than females at a ratio of 2-3:1 ( 4 , 65 ); however, the exact mechanism remain unclear. Previous studies have indicated that androgens increase and estrogens decrease urinary oxalate excretion, plasma oxalate concentration and kidney CaOx crystal deposition. Additionally, enhanced androgen signaling may be responsible for the association between sex and kidney stone formation ( 65 - 68 ). Androgen receptor (AR) signaling can directly upregulate hepatic glycolate oxidase ( 69 ) and kidney epithelial nicotinamide adenine dinucleotide phosphate oxidase (NAPDH), subunit p22-PHOX at the transcriptional level, so as to increase oxalate biosynthesis, ultimately leading to kidney stone formation ( 70 ). Peng et al ( 71 ) reported that testosterone contributes to nephrolithiasis development through the induction of renal tubular epithelial cells apoptosis and necrosis through HIF-1α/BNIP3 pathway. Changtong et al ( 72 ) revealed that testosterone could promote kidney stone disease via the enhanced COM crystal-cell adhesion by the increased surface α-enolase. Zhu et al ( 73 ) demonstrated that AR can inhibit the recruitment of macrophages and suppress the COM crystals phagocytic ability of macrophages via the decrease of the colony-stimulating factor 1 (CSF-1) signals, through miR-185-5p upregulation. These findings suggest that androgen receptor signaling may be a key player in the development of nephrolithiasis ( Fig. 2 ).

Role of sex hormones in calcium oxalate nephrolithiasis. The AR signaling could induce TECs apoptosis and necrosis and kidney tubular injury, promote COM crystallization and oxalate biosynthesis; however, macrophage recruitment and crystal phagocytosis are inhibited. Conversely, ER signaling can reduce ROS-mediated kidney tubular injury and COM crystallization. COM, calcium oxalate monohydrate; AR, androgen receptor; ER, estrogen receptor; ROS, reactive oxygen species.

Theoretically, AR may be a new potential target and can be evaluated for novel therapeutics for the suppression of kidney stone formation. The 5α-reductase inhibitor, finasteride, has been reported to abolish the promoting effect of testosterone on COM crystallization ( 74 ). Another newly developed AR degradation enhancer, dimethylcurcumin (ASC-J9), has been reported to suppress oxalate crystal formation via the modulation of oxalate biosynthesis and reactive oxygen species (ROS)-induced kidney tubular epithelial cell injury in a rat model ( 73 ). Reversely, estrogen may serve as a protective factor against kidney stone formation. An in vitro study demonstrated that estrogen led to changes in the cellular proteome of [Madin darby canine kidney (MDCK)] renal tubular cells that led to the decreased CaOx crystal receptor surface expression (annexin A1 and α-enolase), reduced intracellular ATP, and enhanced cell proliferation and renal tubular cell tissue healing ( 75 ). There is evidence to suggest that estrogen receptor β (ERβ) can suppress oxalate-induced oxidative stress via transcriptional suppression of the NADPH oxidase subunit 2 (NOX2) through the direct binding to the estrogen response elements (EREs) on the NOX2 5′ promoter ( 76 ), which exerts protective effects on renal CaOx crystal deposition.

All these findings may partly explain why a higher incidence of nephrolithiasis is encounter in males than in females. Targeting AR may be developed as a potential therapy for CaOx crystal-related kidney stone disease. However, these studies were performed in vitro and in vivo , using only cell lines or animal models. Further validation and clinical studies are required. Finasteride and ASC-J9 have been demonstrated to suppress a number of AR-mediated diseases, including prostate cancer ( 77 , 78 ), liver cancer and spinal and bulbar muscular atrophy neuron disease ( 79 ). However, additional future studies are necessary before the clinical application of finasteride and ASC-J9 in kidney stone prevention, considering the side-effects, including sexual dysfunction ( 80 ).

5. Role of the microbiome in stone formation

Emerging evidence has indicated that microorganisms belonging to the human microbiome, including microorganisms of the kidney and urinary tract, are likely to have a profound effect on urological health, both positive and negative, due to their metabolic output and other contributions ( 81 ).

Urease-producing bacteria

Urease-producing bacteria, such as Proteus mirabilis, Klebsiella pneumonia, Staphylococcus aureus, Pseudomonas aeruginosa, Providentia stuartii, Serratia and Morganella morganii , are always associated with struvite stone formation and recurrence ( 82 , 83 ). The bacterial urease degrades urea and promotes ammonia and carbon dioxide formation, leading to urine alkalinization and phosphate salt formation ( Fig. 3 ).

Role of urease-producing bacteria in stone formation. The urease-producing bacteria split urea and promote the formation of ammonia and carbon dioxide, leading to kidney tubular injury and urine alkalinization and subsequent formation of phosphate salts.

Urinary acidification and urease inhibitors have been proposed and implemented for the prevention and/or dissolution of struvite stones and encrustations in patients with infection by urea-degrading bacteria; however, their long term use is limited due to their ineffectiveness and toxicity ( 84 ). Secondarily infected stones caused by non-urease-producing bacteria, including Escherichia coli and Enterococcus spp., have also been described ( 85 , 86 ). However, whether kidney stones form and become secondarily infected or result from a nidus of infection that propagates stone formation remains largely unclear.

Nanobacteria (NB)

NB have been isolated from kidney stones for >30 years ( 87 - 89 ); however, the nature and the mechanisms involved remain obscure. Ansari et al ( 90 ) demonstrated that the size of cultured NB varies between 60 and 160 nm, and that they could infect patients with apatite kidney stone. Kajander et al ( 91 ) indicated that NB can adapt to growing in plain DMEM or RPMI-1640, through self-proliferation. In the study by Ciftçioglu et al ( 92 ), it was demonstrated that 70 out of 72 (97.2%) kidney stones contained NB. The presence of NB was independent of the stone type, although apatite-based kidney stones presented the highest immunopositivity ( 91 ). NB are considered to play roles in calcium nucleation, as they can produce sufficient calcium apatite in their cell walls to initiate pathologic calcifications and stone formation ( 93 - 95 ). This evidence is strongly in favor of the suggestion that NB are living organisms.

However, an increasing number of studies have indicated that NB, also termed 'Calcifying nanoparticles (CNPs)', 'nanobacteria-like particles' or 'Nanobes', are merely mineral protein nanoparticles with biomimetic functions ( 88 , 89 ). Although the definition and nature of these nanoparticles remains controversial ( 96 ), their roles in kidney stone diseases has been widely reported. CNPs have been identified in RPs and have been proven to be cytotoxic to 3T6 fibroblasts and HK-2 cells in vitro ( 89 ), which contributes to the renal tubular epithelial cell injury linked to kidney stone formation. Hong et al ( 97 ) demonstrated that catalase (CAT) and malonaldehyde (MDA) levels were significantly higher in CNP-treated HK-2 cells than the HK-2 control group, suggesting that CNPs may induce lipid peroxidation and result in damaging HK-2 cells. Wu et al ( 89 ) demonstrated that the CNPs may: Induce ROS production through JNK activation; decrease mitochondrial membrane potential and promote cell apoptosis through the downregulation of Bcl-2 expression and the upregulation of Bax expression; lead to autophagy through the upregulation of microtubule-associated proteins 1A/1B light chain 3B (LC3-II) and Beclin-1 expression ( Fig. 4 ).

Role of nanobacteria in stone formation. The nanobacteria may induce ROS production through the JNK/p-JNK signaling induction, may decrease mitochondrial membrane potential and promote cell apoptosis through the downregulation of Bcl-2 expression and the upregulation of Bax expression. Additionally, nanobacteria may lead to autophagy through the upregulation of LC3-II and Beclin-1 expression. ROS, reactive oxygen species; LC3-II, microtubule-associated proteins 1A/1B light chain 3B.

According to currently available findings in the literature, NB are localized in high concentrations in kidneys, excreted in urine, are isolated from RPs and the majority of renal stones, and play the role of the initiator, by favoring nucleation and crystal formation. Continued investigations are required, in order to solve the controversy of whether NB are living or non-living, as well as the mechanisms through which NB induce calcification and stone formation.

Intestinal microbiota

The intestinal microbiome, which has been a recent area of wide interest, has been reported to play a role in both the pathogenesis and prevention of kidney stone disease ( 87 , 98 - 100 ). Oxalobacter formigenes is the most well-studied Gram-negative anaerobic bacterium that degrades oxalate in the intestinal tract and has potential probiotic characteristics for the prevention of CaOx kidney stone formation.

In a pilot study, Stern et al ( 101 ) investigated the distinct differences in the gut microbiome of nephrolithiasis patients, as compared with patients without kidney stone formation. Their results demonstrated that the genus Bacteroides were 3.4-fold more abundant in the kidney stone group, while the genus Prevotella were 2.8-fold more abundant in the non-stone control group. A 24 h urine analysis revealed that the genus Eubacterium was inversely associated with oxalate levels and the genus Escherichia trended to an inverse correlation with citrate level ( 101 ). However, the potential causative role of pre-existing dysbiosis of gut microbiome in kidney stone disease is still unclear, and the association of urinary oxalate excretion and oxalate-degrading bacteria abundances remain limited ( 87 , 98 , 102 , 103 ).

Both absorptive and secretory pathways for oxalate have been identified in the proximal and distal segments of the colon, regulated by neuro-hormones that direct net oxalate level. Thus, it has been suggested that intestinal tract participates significantly in oxalate balance and subsequent oxalate homeostasis ( 104 - 106 ). The intestinal tract is also where oxalate-degrading bacteria tend to reside, particularly Oxalobacter formigenes , which requires a strict anaerobic environment to survive. One hypothesis for the role of the microbiome in the prevention of kidney stone has been that specific functional bacteria, such as the oxalate-degrading bacteria (such as Oxalobacter formigenes , Bifidobacterium sp. Porphyromonas gingivalis and Bacillus sp.) in human gut and intestinal tract, which use oxalate as their carbon energy source and thrive in the presence of the oxalate anion, exhibit growth inhibition in the CaOx crystallization in the kidney ( 102 , 107 , 108 ) ( Fig. 5 ).

Role of oxalate-degrading bacteria in stone formation. Oxalate-degrading bacteria use oxalate as a carbon energy source and thrive in the presence of the oxalate anion, reduce urinary oxalate level and exhibit growth inhibition in the calcium oxalate crystallization in the kidney.

The activity of oxalate-degrading bacteria mediates extra-renal elimination of oxalate in the intestines and has a significantly impact on the homeostatic levels of oxalate in plasma and urine ( 109 ). This activity exhibits a strong association with the occurrence of CaOx stone formation.

6. Immune response to urinary crystals

Macrophage accumulation and macrophage-related inflammation or anti-inflammation is the main immune response alteration observed in kidney stone disease, which has been widely reported to play a crucial role in renal CaOx crystal formation ( 110 ).

Firstly, the recruited macrophages could promote the development of COM crystals via the interaction of CD44 with OPN and fibronectin (FN) ( 111 ), which are upregulated in renal tubular cells induced by crystals. Secondly, macrophages have been evidenced to secrete various mediators via classical secretory pathways that cause renal interstitial inflammation ( 112 , 113 ), particularly macrophage inhibitory protein-1, monocyte chemoattractant protein-1 and interleukin-8 (IL-8) ( 112 ). These chemokines consequently enhance the recruitment of various immune cells, including monocytes, macrophages, neutrophils, dendritic cells and T-cells into the inflammatory locale ( 114 , 115 ). Several studies have demonstrated that macrophage-derived exosomes following COM exposure are involved in kidney stone pathogenesis ( 112 , 113 , 116 ). A set of proteins in COM-treated macrophage exosomes were previously identified as proteins involved mainly in immune processes, including T-cell activation and homeostasis, Fcγ receptor-mediated phagocytosis, interferon-γ (IFN-γ) regulation and cell migration ( 112 ). Additionally, infiltrated monocytes could differentiate into different macrophage subtypes with a wide range of clinical manifestations, presentations and histological phenotypes ( 110 , 117 ), display protective or pathogenic activities in kidney stone development ( 110 ).

Increasing evidence has revealed that M1/M2-macrophage differentiation plays an important role in renal CaOx crystal formation ( 111 , 115 , 118 - 120 ). However, whether M1 macrophage-mediated inflammation that contributes to stone formation will initiate stone promoters and reduce stone inhibitors remains controversial. Khan et al ( 58 ) demonstrated that M1 macrophages could cause acute tissue injury, which was associated with crystal deposition and RP formation. Conversely, Taguchi et al ( 121 ) concluded that there was no association between renal dysfunction and increased crystal deposition, based on their observation that no changes were observed in urinary variables in lipopolysaccharide (LPS)-induced M1 macrophage-mediated acute renal injury. M2 anti-inflammatory macrophages can phagocytize and degrade CaOx kidney stone fragments through a clathrin-dependent mechanism ( 110 , 113 , 115 , 120 , 121 ) ( Fig. 6 ).

Immune response to urinary crystals. Macrophage accumulation and macrophage-related inflammation or anti-inflammation is the main immune response alteration observed as a result of kidney stone formation. M1 macrophages are important effectors of CaOx stone formation, while M2 macrophages could prevent CaOx inflammatory damage through crystal phagocytosis. CaOx, calcium oxalate.

Given the critical role of immune-response in CaOx crystal formation and development, the immunotherapy approach has been proposed to prevent stone recurrences in certain individuals through the modulation of the immune response, in order to degrade CaOx crystals and thus prevent stones from developing ( 122 ). However, investigations into immunotherapeutic targets for kidney stone disease are urgently required.

7. Conclusion and future perspectives

In the present review article, emerging concepts of mechanisms contributing to stone formation were summarized, by reviewing novel insight into kidney stone disease related-metabolic risk factors, receptors, promoters and inhibitors, through the examination of the roles of immune-response, microbiome and sex hormones in stone formation and development. The pathophysiology of kidney stone disease cannot be completely explained by crystallization processes alone. However, due to current limitations in research, there are still some research areas in kidney stone formation that remain poorly understood, and were not been discussed herein. Future comprehensive studies are mandatory to further elucidate the mechanisms of the microbiome and immune response in kidney stone formation, in order to develop novel prophylactic and therapeutic approaches.

Acknowledgments

Funding statement.

The present study was supported by the National Natural Science Foundation of China (grant no. 81802566), and Shenzhen Science and Technology Program (Basic Research Project, grant no. JCYJ20180228163919346).

Availability of data and materials

Authors' contributions.

ZW and YZ prepared and drafted the manuscript. ZW obtained funding for the study, and drafted and revised the manuscript. QD, JZ and HL assisted in obtaining data for the review article, drafted the manuscript and provided critical revision of the manuscript for intellectual content. ZW and HL confirm the authenticity of all the raw data. All authors have read and approved the final manuscript.

Ethics approval and consent to participate

Patient consent for publication, competing interests.

The authors declare that they have no competing interests.

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Global projections of macroeconomic climate-change damages typically consider impacts from average annual and national temperatures over long time horizons 1 , 2 , 3 , 4 , 5 , 6 . Here we use recent empirical findings from more than 1,600 regions worldwide over the past 40 years to project sub-national damages from temperature and precipitation, including daily variability and extremes 7 , 8 . Using an empirical approach that provides a robust lower bound on the persistence of impacts on economic growth, we find that the world economy is committed to an income reduction of 19% within the next 26 years independent of future emission choices (relative to a baseline without climate impacts, likely range of 11–29% accounting for physical climate and empirical uncertainty). These damages already outweigh the mitigation costs required to limit global warming to 2 °C by sixfold over this near-term time frame and thereafter diverge strongly dependent on emission choices. Committed damages arise predominantly through changes in average temperature, but accounting for further climatic components raises estimates by approximately 50% and leads to stronger regional heterogeneity. Committed losses are projected for all regions except those at very high latitudes, at which reductions in temperature variability bring benefits. The largest losses are committed at lower latitudes in regions with lower cumulative historical emissions and lower present-day income.

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Projections of the macroeconomic damage caused by future climate change are crucial to informing public and policy debates about adaptation, mitigation and climate justice. On the one hand, adaptation against climate impacts must be justified and planned on the basis of an understanding of their future magnitude and spatial distribution 9 . This is also of importance in the context of climate justice 10 , as well as to key societal actors, including governments, central banks and private businesses, which increasingly require the inclusion of climate risks in their macroeconomic forecasts to aid adaptive decision-making 11 , 12 . On the other hand, climate mitigation policy such as the Paris Climate Agreement is often evaluated by balancing the costs of its implementation against the benefits of avoiding projected physical damages. This evaluation occurs both formally through cost–benefit analyses 1 , 4 , 5 , 6 , as well as informally through public perception of mitigation and damage costs 13 .

Projections of future damages meet challenges when informing these debates, in particular the human biases relating to uncertainty and remoteness that are raised by long-term perspectives 14 . Here we aim to overcome such challenges by assessing the extent of economic damages from climate change to which the world is already committed by historical emissions and socio-economic inertia (the range of future emission scenarios that are considered socio-economically plausible 15 ). Such a focus on the near term limits the large uncertainties about diverging future emission trajectories, the resulting long-term climate response and the validity of applying historically observed climate–economic relations over long timescales during which socio-technical conditions may change considerably. As such, this focus aims to simplify the communication and maximize the credibility of projected economic damages from future climate change.

In projecting the future economic damages from climate change, we make use of recent advances in climate econometrics that provide evidence for impacts on sub-national economic growth from numerous components of the distribution of daily temperature and precipitation 3 , 7 , 8 . Using fixed-effects panel regression models to control for potential confounders, these studies exploit within-region variation in local temperature and precipitation in a panel of more than 1,600 regions worldwide, comprising climate and income data over the past 40 years, to identify the plausibly causal effects of changes in several climate variables on economic productivity 16 , 17 . Specifically, macroeconomic impacts have been identified from changing daily temperature variability, total annual precipitation, the annual number of wet days and extreme daily rainfall that occur in addition to those already identified from changing average temperature 2 , 3 , 18 . Moreover, regional heterogeneity in these effects based on the prevailing local climatic conditions has been found using interactions terms. The selection of these climate variables follows micro-level evidence for mechanisms related to the impacts of average temperatures on labour and agricultural productivity 2 , of temperature variability on agricultural productivity and health 7 , as well as of precipitation on agricultural productivity, labour outcomes and flood damages 8 (see Extended Data Table 1 for an overview, including more detailed references). References  7 , 8 contain a more detailed motivation for the use of these particular climate variables and provide extensive empirical tests about the robustness and nature of their effects on economic output, which are summarized in Methods . By accounting for these extra climatic variables at the sub-national level, we aim for a more comprehensive description of climate impacts with greater detail across both time and space.

Constraining the persistence of impacts

A key determinant and source of discrepancy in estimates of the magnitude of future climate damages is the extent to which the impact of a climate variable on economic growth rates persists. The two extreme cases in which these impacts persist indefinitely or only instantaneously are commonly referred to as growth or level effects 19 , 20 (see Methods section ‘Empirical model specification: fixed-effects distributed lag models’ for mathematical definitions). Recent work shows that future damages from climate change depend strongly on whether growth or level effects are assumed 20 . Following refs.  2 , 18 , we provide constraints on this persistence by using distributed lag models to test the significance of delayed effects separately for each climate variable. Notably, and in contrast to refs.  2 , 18 , we use climate variables in their first-differenced form following ref.  3 , implying a dependence of the growth rate on a change in climate variables. This choice means that a baseline specification without any lags constitutes a model prior of purely level effects, in which a permanent change in the climate has only an instantaneous effect on the growth rate 3 , 19 , 21 . By including lags, one can then test whether any effects may persist further. This is in contrast to the specification used by refs.  2 , 18 , in which climate variables are used without taking the first difference, implying a dependence of the growth rate on the level of climate variables. In this alternative case, the baseline specification without any lags constitutes a model prior of pure growth effects, in which a change in climate has an infinitely persistent effect on the growth rate. Consequently, including further lags in this alternative case tests whether the initial growth impact is recovered 18 , 19 , 21 . Both of these specifications suffer from the limiting possibility that, if too few lags are included, one might falsely accept the model prior. The limitations of including a very large number of lags, including loss of data and increasing statistical uncertainty with an increasing number of parameters, mean that such a possibility is likely. By choosing a specification in which the model prior is one of level effects, our approach is therefore conservative by design, avoiding assumptions of infinite persistence of climate impacts on growth and instead providing a lower bound on this persistence based on what is observable empirically (see Methods section ‘Empirical model specification: fixed-effects distributed lag models’ for further exposition of this framework). The conservative nature of such a choice is probably the reason that ref.  19 finds much greater consistency between the impacts projected by models that use the first difference of climate variables, as opposed to their levels.

We begin our empirical analysis of the persistence of climate impacts on growth using ten lags of the first-differenced climate variables in fixed-effects distributed lag models. We detect substantial effects on economic growth at time lags of up to approximately 8–10 years for the temperature terms and up to approximately 4 years for the precipitation terms (Extended Data Fig. 1 and Extended Data Table 2 ). Furthermore, evaluation by means of information criteria indicates that the inclusion of all five climate variables and the use of these numbers of lags provide a preferable trade-off between best-fitting the data and including further terms that could cause overfitting, in comparison with model specifications excluding climate variables or including more or fewer lags (Extended Data Fig. 3 , Supplementary Methods Section  1 and Supplementary Table 1 ). We therefore remove statistically insignificant terms at later lags (Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ). Further tests using Monte Carlo simulations demonstrate that the empirical models are robust to autocorrelation in the lagged climate variables (Supplementary Methods Section  2 and Supplementary Figs. 4 and 5 ), that information criteria provide an effective indicator for lag selection (Supplementary Methods Section  2 and Supplementary Fig. 6 ), that the results are robust to concerns of imperfect multicollinearity between climate variables and that including several climate variables is actually necessary to isolate their separate effects (Supplementary Methods Section  3 and Supplementary Fig. 7 ). We provide a further robustness check using a restricted distributed lag model to limit oscillations in the lagged parameter estimates that may result from autocorrelation, finding that it provides similar estimates of cumulative marginal effects to the unrestricted model (Supplementary Methods Section 4 and Supplementary Figs. 8 and 9 ). Finally, to explicitly account for any outstanding uncertainty arising from the precise choice of the number of lags, we include empirical models with marginally different numbers of lags in the error-sampling procedure of our projection of future damages. On the basis of the lag-selection procedure (the significance of lagged terms in Extended Data Fig. 1 and Extended Data Table 2 , as well as information criteria in Extended Data Fig. 3 ), we sample from models with eight to ten lags for temperature and four for precipitation (models shown in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ). In summary, this empirical approach to constrain the persistence of climate impacts on economic growth rates is conservative by design in avoiding assumptions of infinite persistence, but nevertheless provides a lower bound on the extent of impact persistence that is robust to the numerous tests outlined above.

Committed damages until mid-century

We combine these empirical economic response functions (Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) with an ensemble of 21 climate models (see Supplementary Table 5 ) from the Coupled Model Intercomparison Project Phase 6 (CMIP-6) 22 to project the macroeconomic damages from these components of physical climate change (see Methods for further details). Bias-adjusted climate models that provide a highly accurate reproduction of observed climatological patterns with limited uncertainty (Supplementary Table 6 ) are used to avoid introducing biases in the projections. Following a well-developed literature 2 , 3 , 19 , these projections do not aim to provide a prediction of future economic growth. Instead, they are a projection of the exogenous impact of future climate conditions on the economy relative to the baselines specified by socio-economic projections, based on the plausibly causal relationships inferred by the empirical models and assuming ceteris paribus. Other exogenous factors relevant for the prediction of economic output are purposefully assumed constant.

A Monte Carlo procedure that samples from climate model projections, empirical models with different numbers of lags and model parameter estimates (obtained by 1,000 block-bootstrap resamples of each of the regressions in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) is used to estimate the combined uncertainty from these sources. Given these uncertainty distributions, we find that projected global damages are statistically indistinguishable across the two most extreme emission scenarios until 2049 (at the 5% significance level; Fig. 1 ). As such, the climate damages occurring before this time constitute those to which the world is already committed owing to the combination of past emissions and the range of future emission scenarios that are considered socio-economically plausible 15 . These committed damages comprise a permanent income reduction of 19% on average globally (population-weighted average) in comparison with a baseline without climate-change impacts (with a likely range of 11–29%, following the likelihood classification adopted by the Intergovernmental Panel on Climate Change (IPCC); see caption of Fig. 1 ). Even though levels of income per capita generally still increase relative to those of today, this constitutes a permanent income reduction for most regions, including North America and Europe (each with median income reductions of approximately 11%) and with South Asia and Africa being the most strongly affected (each with median income reductions of approximately 22%; Fig. 1 ). Under a middle-of-the road scenario of future income development (SSP2, in which SSP stands for Shared Socio-economic Pathway), this corresponds to global annual damages in 2049 of 38 trillion in 2005 international dollars (likely range of 19–59 trillion 2005 international dollars). Compared with empirical specifications that assume pure growth or pure level effects, our preferred specification that provides a robust lower bound on the extent of climate impact persistence produces damages between these two extreme assumptions (Extended Data Fig. 3 ).

Estimates of the projected reduction in income per capita from changes in all climate variables based on empirical models of climate impacts on economic output with a robust lower bound on their persistence (Extended Data Fig. 1 ) under a low-emission scenario compatible with the 2 °C warming target and a high-emission scenario (SSP2-RCP2.6 and SSP5-RCP8.5, respectively) are shown in purple and orange, respectively. Shading represents the 34% and 10% confidence intervals reflecting the likely and very likely ranges, respectively (following the likelihood classification adopted by the IPCC), having estimated uncertainty from a Monte Carlo procedure, which samples the uncertainty from the choice of physical climate models, empirical models with different numbers of lags and bootstrapped estimates of the regression parameters shown in Supplementary Figs. 1 – 3 . Vertical dashed lines show the time at which the climate damages of the two emission scenarios diverge at the 5% and 1% significance levels based on the distribution of differences between emission scenarios arising from the uncertainty sampling discussed above. Note that uncertainty in the difference of the two scenarios is smaller than the combined uncertainty of the two respective scenarios because samples of the uncertainty (climate model and empirical model choice, as well as model parameter bootstrap) are consistent across the two emission scenarios, hence the divergence of damages occurs while the uncertainty bounds of the two separate damage scenarios still overlap. Estimates of global mitigation costs from the three IAMs that provide results for the SSP2 baseline and SSP2-RCP2.6 scenario are shown in light green in the top panel, with the median of these estimates shown in bold.

Damages already outweigh mitigation costs

We compare the damages to which the world is committed over the next 25 years to estimates of the mitigation costs required to achieve the Paris Climate Agreement. Taking estimates of mitigation costs from the three integrated assessment models (IAMs) in the IPCC AR6 database 23 that provide results under comparable scenarios (SSP2 baseline and SSP2-RCP2.6, in which RCP stands for Representative Concentration Pathway), we find that the median committed climate damages are larger than the median mitigation costs in 2050 (six trillion in 2005 international dollars) by a factor of approximately six (note that estimates of mitigation costs are only provided every 10 years by the IAMs and so a comparison in 2049 is not possible). This comparison simply aims to compare the magnitude of future damages against mitigation costs, rather than to conduct a formal cost–benefit analysis of transitioning from one emission path to another. Formal cost–benefit analyses typically find that the net benefits of mitigation only emerge after 2050 (ref.  5 ), which may lead some to conclude that physical damages from climate change are simply not large enough to outweigh mitigation costs until the second half of the century. Our simple comparison of their magnitudes makes clear that damages are actually already considerably larger than mitigation costs and the delayed emergence of net mitigation benefits results primarily from the fact that damages across different emission paths are indistinguishable until mid-century (Fig. 1 ).

Although these near-term damages constitute those to which the world is already committed, we note that damage estimates diverge strongly across emission scenarios after 2049, conveying the clear benefits of mitigation from a purely economic point of view that have been emphasized in previous studies 4 , 24 . As well as the uncertainties assessed in Fig. 1 , these conclusions are robust to structural choices, such as the timescale with which changes in the moderating variables of the empirical models are estimated (Supplementary Figs. 10 and 11 ), as well as the order in which one accounts for the intertemporal and international components of currency comparison (Supplementary Fig. 12 ; see Methods for further details).

Damages from variability and extremes

Committed damages primarily arise through changes in average temperature (Fig. 2 ). This reflects the fact that projected changes in average temperature are larger than those in other climate variables when expressed as a function of their historical interannual variability (Extended Data Fig. 4 ). Because the historical variability is that on which the empirical models are estimated, larger projected changes in comparison with this variability probably lead to larger future impacts in a purely statistical sense. From a mechanistic perspective, one may plausibly interpret this result as implying that future changes in average temperature are the most unprecedented from the perspective of the historical fluctuations to which the economy is accustomed and therefore will cause the most damage. This insight may prove useful in terms of guiding adaptation measures to the sources of greatest damage.

Estimates of the median projected reduction in sub-national income per capita across emission scenarios (SSP2-RCP2.6 and SSP2-RCP8.5) as well as climate model, empirical model and model parameter uncertainty in the year in which climate damages diverge at the 5% level (2049, as identified in Fig. 1 ). a , Impacts arising from all climate variables. b – f , Impacts arising separately from changes in annual mean temperature ( b ), daily temperature variability ( c ), total annual precipitation ( d ), the annual number of wet days (>1 mm) ( e ) and extreme daily rainfall ( f ) (see Methods for further definitions). Data on national administrative boundaries are obtained from the GADM database version 3.6 and are freely available for academic use ( https://gadm.org/ ).

Nevertheless, future damages based on empirical models that consider changes in annual average temperature only and exclude the other climate variables constitute income reductions of only 13% in 2049 (Extended Data Fig. 5a , likely range 5–21%). This suggests that accounting for the other components of the distribution of temperature and precipitation raises net damages by nearly 50%. This increase arises through the further damages that these climatic components cause, but also because their inclusion reveals a stronger negative economic response to average temperatures (Extended Data Fig. 5b ). The latter finding is consistent with our Monte Carlo simulations, which suggest that the magnitude of the effect of average temperature on economic growth is underestimated unless accounting for the impacts of other correlated climate variables (Supplementary Fig. 7 ).

In terms of the relative contributions of the different climatic components to overall damages, we find that accounting for daily temperature variability causes the largest increase in overall damages relative to empirical frameworks that only consider changes in annual average temperature (4.9 percentage points, likely range 2.4–8.7 percentage points, equivalent to approximately 10 trillion international dollars). Accounting for precipitation causes smaller increases in overall damages, which are—nevertheless—equivalent to approximately 1.2 trillion international dollars: 0.01 percentage points (−0.37–0.33 percentage points), 0.34 percentage points (0.07–0.90 percentage points) and 0.36 percentage points (0.13–0.65 percentage points) from total annual precipitation, the number of wet days and extreme daily precipitation, respectively. Moreover, climate models seem to underestimate future changes in temperature variability 25 and extreme precipitation 26 , 27 in response to anthropogenic forcing as compared with that observed historically, suggesting that the true impacts from these variables may be larger.

The distribution of committed damages

The spatial distribution of committed damages (Fig. 2a ) reflects a complex interplay between the patterns of future change in several climatic components and those of historical economic vulnerability to changes in those variables. Damages resulting from increasing annual mean temperature (Fig. 2b ) are negative almost everywhere globally, and larger at lower latitudes in regions in which temperatures are already higher and economic vulnerability to temperature increases is greatest (see the response heterogeneity to mean temperature embodied in Extended Data Fig. 1a ). This occurs despite the amplified warming projected at higher latitudes 28 , suggesting that regional heterogeneity in economic vulnerability to temperature changes outweighs heterogeneity in the magnitude of future warming (Supplementary Fig. 13a ). Economic damages owing to daily temperature variability (Fig. 2c ) exhibit a strong latitudinal polarisation, primarily reflecting the physical response of daily variability to greenhouse forcing in which increases in variability across lower latitudes (and Europe) contrast decreases at high latitudes 25 (Supplementary Fig. 13b ). These two temperature terms are the dominant determinants of the pattern of overall damages (Fig. 2a ), which exhibits a strong polarity with damages across most of the globe except at the highest northern latitudes. Future changes in total annual precipitation mainly bring economic benefits except in regions of drying, such as the Mediterranean and central South America (Fig. 2d and Supplementary Fig. 13c ), but these benefits are opposed by changes in the number of wet days, which produce damages with a similar pattern of opposite sign (Fig. 2e and Supplementary Fig. 13d ). By contrast, changes in extreme daily rainfall produce damages in all regions, reflecting the intensification of daily rainfall extremes over global land areas 29 , 30 (Fig. 2f and Supplementary Fig. 13e ).

The spatial distribution of committed damages implies considerable injustice along two dimensions: culpability for the historical emissions that have caused climate change and pre-existing levels of socio-economic welfare. Spearman’s rank correlations indicate that committed damages are significantly larger in countries with smaller historical cumulative emissions, as well as in regions with lower current income per capita (Fig. 3 ). This implies that those countries that will suffer the most from the damages already committed are those that are least responsible for climate change and which also have the least resources to adapt to it.

Estimates of the median projected change in national income per capita across emission scenarios (RCP2.6 and RCP8.5) as well as climate model, empirical model and model parameter uncertainty in the year in which climate damages diverge at the 5% level (2049, as identified in Fig. 1 ) are plotted against cumulative national emissions per capita in 2020 (from the Global Carbon Project) and coloured by national income per capita in 2020 (from the World Bank) in a and vice versa in b . In each panel, the size of each scatter point is weighted by the national population in 2020 (from the World Bank). Inset numbers indicate the Spearman’s rank correlation ρ and P -values for a hypothesis test whose null hypothesis is of no correlation, as well as the Spearman’s rank correlation weighted by national population.

To further quantify this heterogeneity, we assess the difference in committed damages between the upper and lower quartiles of regions when ranked by present income levels and historical cumulative emissions (using a population weighting to both define the quartiles and estimate the group averages). On average, the quartile of countries with lower income are committed to an income loss that is 8.9 percentage points (or 61%) greater than the upper quartile (Extended Data Fig. 6 ), with a likely range of 3.8–14.7 percentage points across the uncertainty sampling of our damage projections (following the likelihood classification adopted by the IPCC). Similarly, the quartile of countries with lower historical cumulative emissions are committed to an income loss that is 6.9 percentage points (or 40%) greater than the upper quartile, with a likely range of 0.27–12 percentage points. These patterns reemphasize the prevalence of injustice in climate impacts 31 , 32 , 33 in the context of the damages to which the world is already committed by historical emissions and socio-economic inertia.

Contextualizing the magnitude of damages

The magnitude of projected economic damages exceeds previous literature estimates 2 , 3 , arising from several developments made on previous approaches. Our estimates are larger than those of ref.  2 (see first row of Extended Data Table 3 ), primarily because of the facts that sub-national estimates typically show a steeper temperature response (see also refs.  3 , 34 ) and that accounting for other climatic components raises damage estimates (Extended Data Fig. 5 ). However, we note that our empirical approach using first-differenced climate variables is conservative compared with that of ref.  2 in regard to the persistence of climate impacts on growth (see introduction and Methods section ‘Empirical model specification: fixed-effects distributed lag models’), an important determinant of the magnitude of long-term damages 19 , 21 . Using a similar empirical specification to ref.  2 , which assumes infinite persistence while maintaining the rest of our approach (sub-national data and further climate variables), produces considerably larger damages (purple curve of Extended Data Fig. 3 ). Compared with studies that do take the first difference of climate variables 3 , 35 , our estimates are also larger (see second and third rows of Extended Data Table 3 ). The inclusion of further climate variables (Extended Data Fig. 5 ) and a sufficient number of lags to more adequately capture the extent of impact persistence (Extended Data Figs. 1 and 2 ) are the main sources of this difference, as is the use of specifications that capture nonlinearities in the temperature response when compared with ref.  35 . In summary, our estimates develop on previous studies by incorporating the latest data and empirical insights 7 , 8 , as well as in providing a robust empirical lower bound on the persistence of impacts on economic growth, which constitutes a middle ground between the extremes of the growth-versus-levels debate 19 , 21 (Extended Data Fig. 3 ).

Compared with the fraction of variance explained by the empirical models historically (<5%), the projection of reductions in income of 19% may seem large. This arises owing to the fact that projected changes in climatic conditions are much larger than those that were experienced historically, particularly for changes in average temperature (Extended Data Fig. 4 ). As such, any assessment of future climate-change impacts necessarily requires an extrapolation outside the range of the historical data on which the empirical impact models were evaluated. Nevertheless, these models constitute the most state-of-the-art methods for inference of plausibly causal climate impacts based on observed data. Moreover, we take explicit steps to limit out-of-sample extrapolation by capping the moderating variables of the interaction terms at the 95th percentile of the historical distribution (see Methods ). This avoids extrapolating the marginal effects outside what was observed historically. Given the nonlinear response of economic output to annual mean temperature (Extended Data Fig. 1 and Extended Data Table 2 ), this is a conservative choice that limits the magnitude of damages that we project. Furthermore, back-of-the-envelope calculations indicate that the projected damages are consistent with the magnitude and patterns of historical economic development (see Supplementary Discussion Section  5 ).

Missing impacts and spatial spillovers

Despite assessing several climatic components from which economic impacts have recently been identified 3 , 7 , 8 , this assessment of aggregate climate damages should not be considered comprehensive. Important channels such as impacts from heatwaves 31 , sea-level rise 36 , tropical cyclones 37 and tipping points 38 , 39 , as well as non-market damages such as those to ecosystems 40 and human health 41 , are not considered in these estimates. Sea-level rise is unlikely to be feasibly incorporated into empirical assessments such as this because historical sea-level variability is mostly small. Non-market damages are inherently intractable within our estimates of impacts on aggregate monetary output and estimates of these impacts could arguably be considered as extra to those identified here. Recent empirical work suggests that accounting for these channels would probably raise estimates of these committed damages, with larger damages continuing to arise in the global south 31 , 36 , 37 , 38 , 39 , 40 , 41 , 42 .

Moreover, our main empirical analysis does not explicitly evaluate the potential for impacts in local regions to produce effects that ‘spill over’ into other regions. Such effects may further mitigate or amplify the impacts we estimate, for example, if companies relocate production from one affected region to another or if impacts propagate along supply chains. The current literature indicates that trade plays a substantial role in propagating spillover effects 43 , 44 , making their assessment at the sub-national level challenging without available data on sub-national trade dependencies. Studies accounting for only spatially adjacent neighbours indicate that negative impacts in one region induce further negative impacts in neighbouring regions 45 , 46 , 47 , 48 , suggesting that our projected damages are probably conservative by excluding these effects. In Supplementary Fig. 14 , we assess spillovers from neighbouring regions using a spatial-lag model. For simplicity, this analysis excludes temporal lags, focusing only on contemporaneous effects. The results show that accounting for spatial spillovers can amplify the overall magnitude, and also the heterogeneity, of impacts. Consistent with previous literature, this indicates that the overall magnitude (Fig. 1 ) and heterogeneity (Fig. 3 ) of damages that we project in our main specification may be conservative without explicitly accounting for spillovers. We note that further analysis that addresses both spatially and trade-connected spillovers, while also accounting for delayed impacts using temporal lags, would be necessary to adequately address this question fully. These approaches offer fruitful avenues for further research but are beyond the scope of this manuscript, which primarily aims to explore the impacts of different climate conditions and their persistence.

Policy implications

We find that the economic damages resulting from climate change until 2049 are those to which the world economy is already committed and that these greatly outweigh the costs required to mitigate emissions in line with the 2 °C target of the Paris Climate Agreement (Fig. 1 ). This assessment is complementary to formal analyses of the net costs and benefits associated with moving from one emission path to another, which typically find that net benefits of mitigation only emerge in the second half of the century 5 . Our simple comparison of the magnitude of damages and mitigation costs makes clear that this is primarily because damages are indistinguishable across emissions scenarios—that is, committed—until mid-century (Fig. 1 ) and that they are actually already much larger than mitigation costs. For simplicity, and owing to the availability of data, we compare damages to mitigation costs at the global level. Regional estimates of mitigation costs may shed further light on the national incentives for mitigation to which our results already hint, of relevance for international climate policy. Although these damages are committed from a mitigation perspective, adaptation may provide an opportunity to reduce them. Moreover, the strong divergence of damages after mid-century reemphasizes the clear benefits of mitigation from a purely economic perspective, as highlighted in previous studies 1 , 4 , 6 , 24 .

Historical climate data

Historical daily 2-m temperature and precipitation totals (in mm) are obtained for the period 1979–2019 from the W5E5 database. The W5E5 dataset comes from ERA-5, a state-of-the-art reanalysis of historical observations, but has been bias-adjusted by applying version 2.0 of the WATCH Forcing Data to ERA-5 reanalysis data and precipitation data from version 2.3 of the Global Precipitation Climatology Project to better reflect ground-based measurements 49 , 50 , 51 . We obtain these data on a 0.5° × 0.5° grid from the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) database. Notably, these historical data have been used to bias-adjust future climate projections from CMIP-6 (see the following section), ensuring consistency between the distribution of historical daily weather on which our empirical models were estimated and the climate projections used to estimate future damages. These data are publicly available from the ISIMIP database. See refs.  7 , 8 for robustness tests of the empirical models to the choice of climate data reanalysis products.

Future climate data

Daily 2-m temperature and precipitation totals (in mm) are taken from 21 climate models participating in CMIP-6 under a high (RCP8.5) and a low (RCP2.6) greenhouse gas emission scenario from 2015 to 2100. The data have been bias-adjusted and statistically downscaled to a common half-degree grid to reflect the historical distribution of daily temperature and precipitation of the W5E5 dataset using the trend-preserving method developed by the ISIMIP 50 , 52 . As such, the climate model data reproduce observed climatological patterns exceptionally well (Supplementary Table 5 ). Gridded data are publicly available from the ISIMIP database.

Historical economic data

Historical economic data come from the DOSE database of sub-national economic output 53 . We use a recent revision to the DOSE dataset that provides data across 83 countries, 1,660 sub-national regions with varying temporal coverage from 1960 to 2019. Sub-national units constitute the first administrative division below national, for example, states for the USA and provinces for China. Data come from measures of gross regional product per capita (GRPpc) or income per capita in local currencies, reflecting the values reported in national statistical agencies, yearbooks and, in some cases, academic literature. We follow previous literature 3 , 7 , 8 , 54 and assess real sub-national output per capita by first converting values from local currencies to US dollars to account for diverging national inflationary tendencies and then account for US inflation using a US deflator. Alternatively, one might first account for national inflation and then convert between currencies. Supplementary Fig. 12 demonstrates that our conclusions are consistent when accounting for price changes in the reversed order, although the magnitude of estimated damages varies. See the documentation of the DOSE dataset for further discussion of these choices. Conversions between currencies are conducted using exchange rates from the FRED database of the Federal Reserve Bank of St. Louis 55 and the national deflators from the World Bank 56 .

Future socio-economic data

Baseline gridded gross domestic product (GDP) and population data for the period 2015–2100 are taken from the middle-of-the-road scenario SSP2 (ref.  15 ). Population data have been downscaled to a half-degree grid by the ISIMIP following the methodologies of refs.  57 , 58 , which we then aggregate to the sub-national level of our economic data using the spatial aggregation procedure described below. Because current methodologies for downscaling the GDP of the SSPs use downscaled population to do so, per-capita estimates of GDP with a realistic distribution at the sub-national level are not readily available for the SSPs. We therefore use national-level GDP per capita (GDPpc) projections for all sub-national regions of a given country, assuming homogeneity within countries in terms of baseline GDPpc. Here we use projections that have been updated to account for the impact of the COVID-19 pandemic on the trajectory of future income, while remaining consistent with the long-term development of the SSPs 59 . The choice of baseline SSP alters the magnitude of projected climate damages in monetary terms, but when assessed in terms of percentage change from the baseline, the choice of socio-economic scenario is inconsequential. Gridded SSP population data and national-level GDPpc data are publicly available from the ISIMIP database. Sub-national estimates as used in this study are available in the code and data replication files.

Climate variables

Following recent literature 3 , 7 , 8 , we calculate an array of climate variables for which substantial impacts on macroeconomic output have been identified empirically, supported by further evidence at the micro level for plausible underlying mechanisms. See refs.  7 , 8 for an extensive motivation for the use of these particular climate variables and for detailed empirical tests on the nature and robustness of their effects on economic output. To summarize, these studies have found evidence for independent impacts on economic growth rates from annual average temperature, daily temperature variability, total annual precipitation, the annual number of wet days and extreme daily rainfall. Assessments of daily temperature variability were motivated by evidence of impacts on agricultural output and human health, as well as macroeconomic literature on the impacts of volatility on growth when manifest in different dimensions, such as government spending, exchange rates and even output itself 7 . Assessments of precipitation impacts were motivated by evidence of impacts on agricultural productivity, metropolitan labour outcomes and conflict, as well as damages caused by flash flooding 8 . See Extended Data Table 1 for detailed references to empirical studies of these physical mechanisms. Marked impacts of daily temperature variability, total annual precipitation, the number of wet days and extreme daily rainfall on macroeconomic output were identified robustly across different climate datasets, spatial aggregation schemes, specifications of regional time trends and error-clustering approaches. They were also found to be robust to the consideration of temperature extremes 7 , 8 . Furthermore, these climate variables were identified as having independent effects on economic output 7 , 8 , which we further explain here using Monte Carlo simulations to demonstrate the robustness of the results to concerns of imperfect multicollinearity between climate variables (Supplementary Methods Section  2 ), as well as by using information criteria (Supplementary Table 1 ) to demonstrate that including several lagged climate variables provides a preferable trade-off between optimally describing the data and limiting the possibility of overfitting.

We calculate these variables from the distribution of daily, d , temperature, T x , d , and precipitation, P x , d , at the grid-cell, x , level for both the historical and future climate data. As well as annual mean temperature, \({\bar{T}}_{x,y}\) , and annual total precipitation, P x , y , we calculate annual, y , measures of daily temperature variability, \({\widetilde{T}}_{x,y}\) :

the number of wet days, Pwd x , y :

and extreme daily rainfall:

in which T x , d , m , y is the grid-cell-specific daily temperature in month m and year y , \({\bar{T}}_{x,m,{y}}\) is the year and grid-cell-specific monthly, m , mean temperature, D m and D y the number of days in a given month m or year y , respectively, H the Heaviside step function, 1 mm the threshold used to define wet days and P 99.9 x is the 99.9th percentile of historical (1979–2019) daily precipitation at the grid-cell level. Units of the climate measures are degrees Celsius for annual mean temperature and daily temperature variability, millimetres for total annual precipitation and extreme daily precipitation, and simply the number of days for the annual number of wet days.

We also calculated weighted standard deviations of monthly rainfall totals as also used in ref.  8 but do not include them in our projections as we find that, when accounting for delayed effects, their effect becomes statistically indistinct and is better captured by changes in total annual rainfall.

Spatial aggregation

We aggregate grid-cell-level historical and future climate measures, as well as grid-cell-level future GDPpc and population, to the level of the first administrative unit below national level of the GADM database, using an area-weighting algorithm that estimates the portion of each grid cell falling within an administrative boundary. We use this as our baseline specification following previous findings that the effect of area or population weighting at the sub-national level is negligible 7 , 8 .

Empirical model specification: fixed-effects distributed lag models

Following a wide range of climate econometric literature 16 , 60 , we use panel regression models with a selection of fixed effects and time trends to isolate plausibly exogenous variation with which to maximize confidence in a causal interpretation of the effects of climate on economic growth rates. The use of region fixed effects, μ r , accounts for unobserved time-invariant differences between regions, such as prevailing climatic norms and growth rates owing to historical and geopolitical factors. The use of yearly fixed effects, η y , accounts for regionally invariant annual shocks to the global climate or economy such as the El Niño–Southern Oscillation or global recessions. In our baseline specification, we also include region-specific linear time trends, k r y , to exclude the possibility of spurious correlations resulting from common slow-moving trends in climate and growth.

The persistence of climate impacts on economic growth rates is a key determinant of the long-term magnitude of damages. Methods for inferring the extent of persistence in impacts on growth rates have typically used lagged climate variables to evaluate the presence of delayed effects or catch-up dynamics 2 , 18 . For example, consider starting from a model in which a climate condition, C r , y , (for example, annual mean temperature) affects the growth rate, Δlgrp r , y (the first difference of the logarithm of gross regional product) of region r in year y :

which we refer to as a ‘pure growth effects’ model in the main text. Typically, further lags are included,

and the cumulative effect of all lagged terms is evaluated to assess the extent to which climate impacts on growth rates persist. Following ref.  18 , in the case that,

the implication is that impacts on the growth rate persist up to NL years after the initial shock (possibly to a weaker or a stronger extent), whereas if

then the initial impact on the growth rate is recovered after NL years and the effect is only one on the level of output. However, we note that such approaches are limited by the fact that, when including an insufficient number of lags to detect a recovery of the growth rates, one may find equation ( 6 ) to be satisfied and incorrectly assume that a change in climatic conditions affects the growth rate indefinitely. In practice, given a limited record of historical data, including too few lags to confidently conclude in an infinitely persistent impact on the growth rate is likely, particularly over the long timescales over which future climate damages are often projected 2 , 24 . To avoid this issue, we instead begin our analysis with a model for which the level of output, lgrp r , y , depends on the level of a climate variable, C r , y :

Given the non-stationarity of the level of output, we follow the literature 19 and estimate such an equation in first-differenced form as,

which we refer to as a model of ‘pure level effects’ in the main text. This model constitutes a baseline specification in which a permanent change in the climate variable produces an instantaneous impact on the growth rate and a permanent effect only on the level of output. By including lagged variables in this specification,

we are able to test whether the impacts on the growth rate persist any further than instantaneously by evaluating whether α L  > 0 are statistically significantly different from zero. Even though this framework is also limited by the possibility of including too few lags, the choice of a baseline model specification in which impacts on the growth rate do not persist means that, in the case of including too few lags, the framework reverts to the baseline specification of level effects. As such, this framework is conservative with respect to the persistence of impacts and the magnitude of future damages. It naturally avoids assumptions of infinite persistence and we are able to interpret any persistence that we identify with equation ( 9 ) as a lower bound on the extent of climate impact persistence on growth rates. See the main text for further discussion of this specification choice, in particular about its conservative nature compared with previous literature estimates, such as refs.  2 , 18 .

We allow the response to climatic changes to vary across regions, using interactions of the climate variables with historical average (1979–2019) climatic conditions reflecting heterogenous effects identified in previous work 7 , 8 . Following this previous work, the moderating variables of these interaction terms constitute the historical average of either the variable itself or of the seasonal temperature difference, \({\hat{T}}_{r}\) , or annual mean temperature, \({\bar{T}}_{r}\) , in the case of daily temperature variability 7 and extreme daily rainfall, respectively 8 .

The resulting regression equation with N and M lagged variables, respectively, reads:

in which Δlgrp r , y is the annual, regional GRPpc growth rate, measured as the first difference of the logarithm of real GRPpc, following previous work 2 , 3 , 7 , 8 , 18 , 19 . Fixed-effects regressions were run using the fixest package in R (ref.  61 ).

Estimates of the coefficients of interest α i , L are shown in Extended Data Fig. 1 for N  =  M  = 10 lags and for our preferred choice of the number of lags in Supplementary Figs. 1 – 3 . In Extended Data Fig. 1 , errors are shown clustered at the regional level, but for the construction of damage projections, we block-bootstrap the regressions by region 1,000 times to provide a range of parameter estimates with which to sample the projection uncertainty (following refs.  2 , 31 ).

Spatial-lag model

In Supplementary Fig. 14 , we present the results from a spatial-lag model that explores the potential for climate impacts to ‘spill over’ into spatially neighbouring regions. We measure the distance between centroids of each pair of sub-national regions and construct spatial lags that take the average of the first-differenced climate variables and their interaction terms over neighbouring regions that are at distances of 0–500, 500–1,000, 1,000–1,500 and 1,500–2000 km (spatial lags, ‘SL’, 1 to 4). For simplicity, we then assess a spatial-lag model without temporal lags to assess spatial spillovers of contemporaneous climate impacts. This model takes the form:

in which SL indicates the spatial lag of each climate variable and interaction term. In Supplementary Fig. 14 , we plot the cumulative marginal effect of each climate variable at different baseline climate conditions by summing the coefficients for each climate variable and interaction term, for example, for average temperature impacts as:

These cumulative marginal effects can be regarded as the overall spatially dependent impact to an individual region given a one-unit shock to a climate variable in that region and all neighbouring regions at a given value of the moderating variable of the interaction term.

Constructing projections of economic damage from future climate change

We construct projections of future climate damages by applying the coefficients estimated in equation ( 10 ) and shown in Supplementary Tables 2 – 4 (when including only lags with statistically significant effects in specifications that limit overfitting; see Supplementary Methods Section  1 ) to projections of future climate change from the CMIP-6 models. Year-on-year changes in each primary climate variable of interest are calculated to reflect the year-to-year variations used in the empirical models. 30-year moving averages of the moderating variables of the interaction terms are calculated to reflect the long-term average of climatic conditions that were used for the moderating variables in the empirical models. By using moving averages in the projections, we account for the changing vulnerability to climate shocks based on the evolving long-term conditions (Supplementary Figs. 10 and 11 show that the results are robust to the precise choice of the window of this moving average). Although these climate variables are not differenced, the fact that the bias-adjusted climate models reproduce observed climatological patterns across regions for these moderating variables very accurately (Supplementary Table 6 ) with limited spread across models (<3%) precludes the possibility that any considerable bias or uncertainty is introduced by this methodological choice. However, we impose caps on these moderating variables at the 95th percentile at which they were observed in the historical data to prevent extrapolation of the marginal effects outside the range in which the regressions were estimated. This is a conservative choice that limits the magnitude of our damage projections.

Time series of primary climate variables and moderating climate variables are then combined with estimates of the empirical model parameters to evaluate the regression coefficients in equation ( 10 ), producing a time series of annual GRPpc growth-rate reductions for a given emission scenario, climate model and set of empirical model parameters. The resulting time series of growth-rate impacts reflects those occurring owing to future climate change. By contrast, a future scenario with no climate change would be one in which climate variables do not change (other than with random year-to-year fluctuations) and hence the time-averaged evaluation of equation ( 10 ) would be zero. Our approach therefore implicitly compares the future climate-change scenario to this no-climate-change baseline scenario.

The time series of growth-rate impacts owing to future climate change in region r and year y , δ r , y , are then added to the future baseline growth rates, π r , y (in log-diff form), obtained from the SSP2 scenario to yield trajectories of damaged GRPpc growth rates, ρ r , y . These trajectories are aggregated over time to estimate the future trajectory of GRPpc with future climate impacts:

in which GRPpc r , y =2020 is the initial log level of GRPpc. We begin damage estimates in 2020 to reflect the damages occurring since the end of the period for which we estimate the empirical models (1979–2019) and to match the timing of mitigation-cost estimates from most IAMs (see below).

For each emission scenario, this procedure is repeated 1,000 times while randomly sampling from the selection of climate models, the selection of empirical models with different numbers of lags (shown in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) and bootstrapped estimates of the regression parameters. The result is an ensemble of future GRPpc trajectories that reflect uncertainty from both physical climate change and the structural and sampling uncertainty of the empirical models.

Estimates of mitigation costs

We obtain IPCC estimates of the aggregate costs of emission mitigation from the AR6 Scenario Explorer and Database hosted by IIASA 23 . Specifically, we search the AR6 Scenarios Database World v1.1 for IAMs that provided estimates of global GDP and population under both a SSP2 baseline and a SSP2-RCP2.6 scenario to maintain consistency with the socio-economic and emission scenarios of the climate damage projections. We find five IAMs that provide data for these scenarios, namely, MESSAGE-GLOBIOM 1.0, REMIND-MAgPIE 1.5, AIM/GCE 2.0, GCAM 4.2 and WITCH-GLOBIOM 3.1. Of these five IAMs, we use the results only from the first three that passed the IPCC vetting procedure for reproducing historical emission and climate trajectories. We then estimate global mitigation costs as the percentage difference in global per capita GDP between the SSP2 baseline and the SSP2-RCP2.6 emission scenario. In the case of one of these IAMs, estimates of mitigation costs begin in 2020, whereas in the case of two others, mitigation costs begin in 2010. The mitigation cost estimates before 2020 in these two IAMs are mostly negligible, and our choice to begin comparison with damage estimates in 2020 is conservative with respect to the relative weight of climate damages compared with mitigation costs for these two IAMs.

Data availability

Data on economic production and ERA-5 climate data are publicly available at https://doi.org/10.5281/zenodo.4681306 (ref. 62 ) and https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5 , respectively. Data on mitigation costs are publicly available at https://data.ene.iiasa.ac.at/ar6/#/downloads . Processed climate and economic data, as well as all other necessary data for reproduction of the results, are available at the public repository https://doi.org/10.5281/zenodo.10562951  (ref. 63 ).

Code availability

All code necessary for reproduction of the results is available at the public repository https://doi.org/10.5281/zenodo.10562951  (ref. 63 ).

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Acknowledgements

We gratefully acknowledge financing from the Volkswagen Foundation and the Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ) GmbH on behalf of the Government of the Federal Republic of Germany and Federal Ministry for Economic Cooperation and Development (BMZ).

Open access funding provided by Potsdam-Institut für Klimafolgenforschung (PIK) e.V.

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All authors contributed to the design of the analysis. M.K. conducted the analysis and produced the figures. All authors contributed to the interpretation and presentation of the results. M.K. and L.W. wrote the manuscript.

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Extended data figures and tables

Extended data fig. 1 constraining the persistence of historical climate impacts on economic growth rates..

The results of a panel-based fixed-effects distributed lag model for the effects of annual mean temperature ( a ), daily temperature variability ( b ), total annual precipitation ( c ), the number of wet days ( d ) and extreme daily precipitation ( e ) on sub-national economic growth rates. Point estimates show the effects of a 1 °C or one standard deviation increase (for temperature and precipitation variables, respectively) at the lower quartile, median and upper quartile of the relevant moderating variable (green, orange and purple, respectively) at different lagged periods after the initial shock (note that these are not cumulative effects). Climate variables are used in their first-differenced form (see main text for discussion) and the moderating climate variables are the annual mean temperature, seasonal temperature difference, total annual precipitation, number of wet days and annual mean temperature, respectively, in panels a – e (see Methods for further discussion). Error bars show the 95% confidence intervals having clustered standard errors by region. The within-region R 2 , Bayesian and Akaike information criteria for the model are shown at the top of the figure. This figure shows results with ten lags for each variable to demonstrate the observed levels of persistence, but our preferred specifications remove later lags based on the statistical significance of terms shown above and the information criteria shown in Extended Data Fig. 2 . The resulting models without later lags are shown in Supplementary Figs. 1 – 3 .

Extended Data Fig. 2 Incremental lag-selection procedure using information criteria and within-region R 2 .

Starting from a panel-based fixed-effects distributed lag model estimating the effects of climate on economic growth using the real historical data (as in equation ( 4 )) with ten lags for all climate variables (as shown in Extended Data Fig. 1 ), lags are incrementally removed for one climate variable at a time. The resulting Bayesian and Akaike information criteria are shown in a – e and f – j , respectively, and the within-region R 2 and number of observations in k – o and p – t , respectively. Different rows show the results when removing lags from different climate variables, ordered from top to bottom as annual mean temperature, daily temperature variability, total annual precipitation, the number of wet days and extreme annual precipitation. Information criteria show minima at approximately four lags for precipitation variables and ten to eight for temperature variables, indicating that including these numbers of lags does not lead to overfitting. See Supplementary Table 1 for an assessment using information criteria to determine whether including further climate variables causes overfitting.

Extended Data Fig. 3 Damages in our preferred specification that provides a robust lower bound on the persistence of climate impacts on economic growth versus damages in specifications of pure growth or pure level effects.

Estimates of future damages as shown in Fig. 1 but under the emission scenario RCP8.5 for three separate empirical specifications: in orange our preferred specification, which provides an empirical lower bound on the persistence of climate impacts on economic growth rates while avoiding assumptions of infinite persistence (see main text for further discussion); in purple a specification of ‘pure growth effects’ in which the first difference of climate variables is not taken and no lagged climate variables are included (the baseline specification of ref.  2 ); and in pink a specification of ‘pure level effects’ in which the first difference of climate variables is taken but no lagged terms are included.

Extended Data Fig. 4 Climate changes in different variables as a function of historical interannual variability.

Changes in each climate variable of interest from 1979–2019 to 2035–2065 under the high-emission scenario SSP5-RCP8.5, expressed as a percentage of the historical variability of each measure. Historical variability is estimated as the standard deviation of each detrended climate variable over the period 1979–2019 during which the empirical models were identified (detrending is appropriate because of the inclusion of region-specific linear time trends in the empirical models). See Supplementary Fig. 13 for changes expressed in standard units. Data on national administrative boundaries are obtained from the GADM database version 3.6 and are freely available for academic use ( https://gadm.org/ ).

Extended Data Fig. 5 Contribution of different climate variables to overall committed damages.

a , Climate damages in 2049 when using empirical models that account for all climate variables, changes in annual mean temperature only or changes in both annual mean temperature and one other climate variable (daily temperature variability, total annual precipitation, the number of wet days and extreme daily precipitation, respectively). b , The cumulative marginal effects of an increase in annual mean temperature of 1 °C, at different baseline temperatures, estimated from empirical models including all climate variables or annual mean temperature only. Estimates and uncertainty bars represent the median and 95% confidence intervals obtained from 1,000 block-bootstrap resamples from each of three different empirical models using eight, nine or ten lags of temperature terms.

Extended Data Fig. 6 The difference in committed damages between the upper and lower quartiles of countries when ranked by GDP and cumulative historical emissions.

Quartiles are defined using a population weighting, as are the average committed damages across each quartile group. The violin plots indicate the distribution of differences between quartiles across the two extreme emission scenarios (RCP2.6 and RCP8.5) and the uncertainty sampling procedure outlined in Methods , which accounts for uncertainty arising from the choice of lags in the empirical models, uncertainty in the empirical model parameter estimates, as well as the climate model projections. Bars indicate the median, as well as the 10th and 90th percentiles and upper and lower sixths of the distribution reflecting the very likely and likely ranges following the likelihood classification adopted by the IPCC.

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Kotz, M., Levermann, A. & Wenz, L. The economic commitment of climate change. Nature 628 , 551–557 (2024). https://doi.org/10.1038/s41586-024-07219-0

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Received : 25 January 2023

Accepted : 21 February 2024

Published : 17 April 2024

Issue Date : 18 April 2024

DOI : https://doi.org/10.1038/s41586-024-07219-0

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