Milisavljevic and Wu BMC Mat (2020) 2:2 https://doi.org/10.1186/s42833-020-0008-0 BMC Materials

REVIEW Open Access Current status of solid‑state single crystal growth Iva Milisavljevic and Yiquan Wu*

Abstract 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-efectiveness and simplicity in terms of processing. Moreover, the SSCG technique has enabled the fab- rication 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 prin- ciples 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 materi- als fabricated via the solid-state single crystal growth technique and their properties. Keywords: Single crystal, Solid-state single crystal growth, SSCG, Mixed control mechanism, Microstructural evolution

Introduction Single crystals have found extensive use in optical, elec- A need for single crystal fabrication tronic, optoelectronic, and other applications. Specif- Single crystals are one of the most important groups of cally, single crystal semiconductors are one of the most materials due to their continuous, uniform, and highly- widely researched and used materials. Tese materials ordered structure which enables them to possess unique have been applied for various electronic and optoelec- properties. In many aspects, single crystal materials can tronic devices and components, such as light-emitting be found to be advantageous over polycrystalline materi- diodes (LEDs), photodetectors, wide-bandgap devices, als, and many properties which are found in single crys- high-power lasers, consumer electronics, and more tals cannot be replicated in polycrystals [1]. Currently, [2, 3]. For example, current computer chip production even with the technological developments of advanced is not possible without high-quality single crystal sili- polycrystalline materials which are designed for specifc con (Si) wafers [4]. Due to their outstanding optical and applications, the electrical, optical, thermal, mechanical, electronic properties, single crystals of III–V semicon- and other properties of single crystals still remain supe- ductors, such as GaAs, GaN, InP, InAs, and others, are rior. For these reasons, it is not surprising that single an integral part of devices for application in fber-optic crystals, and the methods for their fabrication, are a topic communication, wireless and satellite communication, of interest among many researchers. solid-state lighting, and more [2]. Te importance of sin- gle crystal alumina, also known as sapphire, as well as *Correspondence: [email protected] yttrium aluminum garnet (YAG), for laser materials has Kazuo Inamori School of Engineering, New York State College also been demonstrated through numerous applications. of Ceramics, Alfred University, 2 Pine Street, Alfred, NY 14802, USA Sapphire has been used in the electronics industry both

© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativeco​ ​ mmons.org/licen​ ses/by/4.0/​ . The Creative Commons Public Domain Dedication waiver (http://creativeco​ mmons​ .org/publi​ cdoma​ in/​ zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. Milisavljevic and Wu BMC Mat (2020) 2:2 Page 2 of 26

as a passive substrate material and active device (e.g. sil- Growth from melt is the most commonly used method icon-on-sapphire); likewise, it is used for rocket domes, and is based upon the solidifcation and crystallization optical data storage, radiation detection, LED devices, of a melted material. Te Czochralski and Bridgman optical windows, and other applications [5]. On the other methods are the two most utilized melt-growth tech- hand, YAG single crystals, and especially ­Nd3+-doped niques. Te Czochralski method (Cz) is, for example, YAG, are known for their important application in solid- very important for the production of single crystals for state laser devices, such as waveguide lasers [6] and single electronic and optical applications, such as silicon and crystal fbers for high-power lasers [7], as well as scintil- germanium single crystals, as well as some fuoride and lation crystals, and others. Piezoelectric single crystal oxide single crystals [13]. Single crystal growth from melt materials, which were initially developed and utilized allows for the fabrication of large single crystals of excel- as transducers for sonar devices and medical ultrasonic lent quality in a relatively short time when compared to diagnostic devices, have also been applied in sensors, other growth techniques [14]. However, the melt-growth actuators, medical transducers, energy harvesters, and technique shows some disadvantages as well, such as dif- more [8, 9]. As it can be seen, single crystal materials are fculties in maintaining a stable temperature during the capable of covering a wide variety of applications, which crystal growth and in achieving very high melting points range from scientifc- and research-related to daily life. for some materials, achieving chemical homogeneity, Another important use of single crystal materials is as especially in the case when multiple elements are present substrates for flms of diferent materials; this enables a in the system, reactivity of the melted material with the whole new collection of applications. Single crystals can crucible, and high costs of production and equipment. be used not only as a mechanical support or a surface Unlike the melt-growth technique, in which the mate- at which layer or layers of materials are being deposited rial is melted frst, the solution-growth technique but can also act as a single crystal seed during epitaxial involves the dissolution of the material to be crystallized growth [10], when the deposited flm takes on orientation within a suitable solvent or fux (e.g. PbO, PbF­ 2, ­Bi2O3, of the substrate, and sometimes even a lattice structure. ­Li2O, Na­ 2O, K­ 2O, KF, ­P2O5, etc.) [13, 15]. Out of all the Likewise, the fabrication of single crystal epitaxial flms solution-growth techniques, high-temperature solution- on various substrates, which are a vital part of a wide growth, also known as fux-growth, has been the most range of devices for electronic, optoelectronic, magneto- utilized technique for the fabrication of single crystals optic, and many other applications, although very chal- thus far. Tis technique is especially convenient for mate- lenging, is an important goal in the thin flm industry due rials that incongruently melt or when melt-growth tech- to the numerous advantages of single crystal flms [11]. niques cannot be applied. Te main advantage of this As technological development increases, the need for technique is that the crystals are grown below their melt- high-quality single crystal materials, both in bulk and in ing temperatures and the growth of the crystal occurs thin flms, grows simultaneously. Te availability of vari- spontaneously through nucleation or crystallization on a ous single crystal materials has enabled the development seed. On the other hand, the crystal growth rates for the of a new generation of electronic, optical, optoelectronic, solution-growth method are much slower than that of and other devices. However, growth of high-quality sin- the melt-growth method and the presence of fux ions is gle crystals, with stable and reproducible quality, low unavoidable in the crystal. Growth of single crystals via defect density, with various chemical compositions and the fux method has found many important applications sometimes even extreme thermodynamic properties is in the production of single crystal materials such as gar- still one of the greatest challenges today [12]. Further- nets, various laser crystals, including borates, ­LiNbO3, more, techniques which are currently used for growing BaTiO­ 3, ­BaB2O4, and more complex systems such as single crystals experience many processing-related dif- ­Sr Ba Nb O , ­Pb Ba Nb O , and others [13]. 1−x x 2 6 1−x x 2 6 fculties despite the technological advancements made Vapor-phase growth is the third method of growing throughout the years [13]. Terefore, a high demand single crystals, although it is more commonly applied for various single crystal materials has imposed a need to the fabrication of thin single crystals flms on sub- for improving the growth techniques that are currently strates than bulk single crystals. Te growth of single used as well as developing new, alternative single crystal crystals through the vapor phase can be accomplished growth techniques. via a sublimation process, reaction in the gas phase and transport reaction, such in the case of chemical vapor Conventional techniques of single crystal growth transport (CVT) and, physical vapor transport (PVT) Currently, there are three general approaches for the [16]. Compared to the melt-growth method, the vapor- growth of bulk inorganic single crystals: growth from growth method utilizes lower processing temperatures melt, solution and vapor phase. which result in a signifcantly higher quality crystal due Milisavljevic and Wu BMC Mat (2020) 2:2 Page 3 of 26

to avoidance of incorporating impurities, structural and the mass production of single crystals for various exist- compositional uniformities, and phase transitions. On ing as well as new applications [22]. Te technique uti- the other hand, the low growth and transport rates in lizes conventional sintering equipment, such as simple the vapor to the interface, associated with the low tem- furnaces, which cost notably less than the equipment for perature, make this technique less favorable when com- conventional single crystal growth [23]. For comparison, pared to the other two growth techniques. However, a furnace for Cz growth of sapphires can cost between this technique is still used if neither one of the other two $400,000 and $1,000,000 [14], while regular furnaces can techniques is applicable for the growth of single crystals, cost at least an order of magnitude less. Furthermore, the which is the case in, for example, SiC single crystals [15]. more complex the composition is, the harder it becomes to fabricate a single crystal using the conventional single New technique for single crystal fabrication crystal growth route, due to chemical inhomogeneities, Another pathway for growing single crystals which has the presence of elements that melt incongruently, volatil- recently received attention within the research commu- ity of certain elements, and so on. Terefore, solid-state nity, is through the solid-state conversion of polycrystal- single crystal growth has been found to be promising and line materials to single crystals. Tis method is based on applicable to many diferent systems, especially systems a phenomenon which can be observed in many systems, with complex chemical compositions. Net-shape pro- known as abnormal grain growth (AGG). duction, when compared to cutting and shaping from Solid-state single crystal growth was frst observed and the single crystal boules grown conventionally [14], is studied in metals as a possible alternative to very difcult another advantage in cost-efectiveness of single crys- and expensive procedures used to fabricate metal single tals produced by solid-state growth since it reduces the crystals. Most of the research on single crystal conver- number of machining steps after the growth process and sion in metals date to the middle of the last century and even allows for growth of more complexly-shaped single include the reports on single crystals of Fe, Mo, W, and crystals. other metals [17–19]. Later on, in the early 1980s, apply- Tis review article will provide an overview of the cur- ing the same principles observed in the metal systems, rent status of techniques utilized for the solid-state con- Matsuzawa and Mase [20, 21] performed research on version of single crystals (here, solid-state single crystal the growth of single crystals from various polycrystal- growth (SSCG) will be used with the same meaning) and line oxide materials, including ferrites, garnets, and spi- the principles behind them, including AGG, boundary nels. Tey demonstrated that single crystal growth using migration, and microstructural evolution. Also, recent the solid-state conversion approach, which was reserved reports on the solid-state conversion of single crys- only for metals at the time, could also be applied to more tals in diferent systems will be summarized and the complex materials’ systems. Furthermore, many issues most important fndings highlighted. Te review will associated with conventional single crystal growth tech- be concluded with a discussion on some of the biggest niques, such as heating at high temperatures, maintain- challenges of the SSCG technique, followed by a brief ing compositional uniformity, contamination from the summary and a future outlook. crucibles, etc., were avoided during the solid-state single crystal growth and performed with much lower produc- Solid‑state conversion of single crystals tion costs. In the years that followed, most of the research from polycrystals focus was on ­BaTiO3 and Pb(Mg1/3Nb2/3)O3‒PbTiO3 sys- tems, however, still in a limited number. In recent years, solid-state single crystal growth (SSCG) Although it was observed for the frst time decades ago, has emerged as a promising alternative technique for solid-state single crystal growth can still be considered growth of single crystals through a conversion process to be a relatively new technique since it did not receive in polycrystalline materials. Tis technique, which ofers signifcant attention from the research community until numerous advantages over conventional single crys- recently once more work had been done. Due to con- tal growth techniques, is based on the occurrence of siderable advancements made in nanotechnologies and AGG in polycrystals. More precisely, SSCG technique sintering technology that have enabled the fabrication of is developed around what is known as a “mixed control high-quality ceramics, interest in solid-state single crystal mechanism” [24] of grain boundary migration as well as growth from polycrystals has been renewed. Solid-state principles of microstructural evolution. Te mixed con- single crystal growth has been shown to be an efective trol mechanism can be used as a general guiding princi- and simple technique for obtaining single crystals with ple for suppressing growth and controlling the growth of lower capital costs associated with production equip- single crystals from polycrystalline materials, which are ment and components, which could potentially allow for the key requirements for SSCG. Milisavljevic and Wu BMC Mat (2020) 2:2 Page 4 of 26

In this section, the phenomenon of abnormal grain model was necessary to more clearly explain the phe- growth will be briefy explained and discussed. Further- nomenon of AGG. more, the mixed control mechanism of grain boundary Recently, a “mixed control mechanism” was proposed migration and the principles of microstructural evolu- to explain AGG and other types of grain growth behav- tion will be presented and explained. However, for more ior; this further enabled the defnition of the principles of details on the mixed control mechanism and the related evolution of the microstructure in polycrystalline materi- phenomena, the reader is strongly encouraged to refer to als [23, 27]. the research articles of Dr. Kang and his associates who developed the mixed control mechanism and have con- Mixed control mechanism ducted extensive research work in this feld. Te classical understanding of the mechanisms of AGG, which were mentioned in the previous section, provide Abnormal grain growth (AGG) explanation for grain boundary migration which is based In general, there are two diferent types of grain growth on atomistic difusion. Tese models, however, can only which can be observed during sintering. One, known be applied to some specifc cases; for this reason, the as normal grain growth (NGG), involves a uniform rate mixed control mechanism, which is a more universal of grain growth via thermally activated grain boundary model, was suggested to explain diferent grain growth migration which results in a uniformly developed micro- behaviors. Te mixed control mechanism has its roots in structure with respect to the sintering time (stationary the theories of crystal growth and experimental obser- grain growth). Te other type of grain growth is non- vations and explains the phenomenon of grain bound- normal grain growth (non-NGG) and instead follows a ary migration considering the atomic structure of grain non-stationary grain growth [23]. AGG is a type of a non- boundaries; this has not been taken into account in clas- NGG and is referred to as the grain growth where a cer- sical grain growth theory [24]. tain number of grains experience a much faster growth Tere are two diferent types of grain boundaries which rate than the neighboring grains in the matrix. Such can be identifed by diferences in structure. One is a growth may signifcantly change a grain size distribu- rough (round) grain boundary which exhibits an atomi- tion, leading to broadening or even a bimodal grain size cally disordered structure, and the other is faceted grain distribution. With extended annealing time, the abnor- boundary, whose interface is smooth and atomically mal grains gradually increase in size by consuming the ordered. In some recent studies [27–31], it was observed surrounding matrix grains until they impinge upon each that the type of grain boundary has the most signifcant other. Tis lowers the driving force for further growth infuence on the occurrence of AGG. While rough grain of abnormal grains and they usually stop growing at this boundaries were observed to result in NGG, faceted stage [25]. grain boundaries were more likely to undergo AGG (or In general, AGG is a phenomenon which is not favora- some other non-normal type of grain growth) [24, 32]. ble during materials processing since the presence of In other words, the presence of faceted grain boundaries abnormally grown grains may have a negative efect on in the system can be regarded as a prerequisite for AGG. microstructure development, and therefore on the physi- Such a phenomenon was explained by diferences in the cal properties of materials. Te appearance of AGG has grain boundary mobilities of rough and faceted bounda- been observed in many diferent systems both ceramic ries with regard to the driving force for grain boundary and metallic. Many authors have tried to explain the migration [33]. occurrence of AGG, suggesting diferent mechanisms In the case of rough interfaces, grain boundary and models, however, the underlying reasons for AGG migration has been shown to have a direct relationship are still under debate [26]. Generally, the following phe- with respect to the driving force for the grain growth. nomena have been suggested as the possible causes of Because of their atomically disordered structures, AGG: (a) the presence of second phases, pores or impuri- rough interfaces allow for a large number of attach- ties (b) high anisotropy of the interfacial energy and grain ment sites for atoms, which then enables a high rate of boundary mobility, and (c) the presence of a thin liquid interfacial reactions. Since the migration kinetics are flm at the grain boundary which facilitates grain bound- governed by the slowest process, in the case of rough ary mobility [23, 24]. As explained in [23], in all of the grains, the difusion, as the slowest process, will be the aforementioned phenomena, it was originally thought rate-determining process for grain boundary migra- that AGG was a result of atomic difusion across the tion [26]. On the other hand, for faceted grains, the grain boundary. However, neither of these models could experimental results have shown that the grain growth explain, nor be entirely applied to all of the systems which is controlled by either interface reaction (attachment of were studied thus far. Terefore, another explanation or atoms from one grain to an adjacent grain) or atomic Milisavljevic and Wu BMC Mat (2020) 2:2 Page 5 of 26

difusion across the grain boundary, depending on 4. Stagnant grain growth (SGG) occurs when which process is slower. Furthermore, it has been dem- Δgmax ≪ Δgc. onstrated that there is a relationship between the grain boundary migration of faceted interfaces and the driv- In systems with faceted grain boundaries, the growth of ing force being non-linear [33–35]. faceted grains is governed by the difusion process when Each individual grain in the polycrystalline matrix the driving force for growth is larger than the critical possesses its own driving force for grain boundary driving force. On the other hand, when the driving force migration and the maximum driving force for grain is smaller than the critical, the growth rate is signifcantly growth (Δgmax) is defned by the average grain size and smaller than that by difusion and is led by the inter- grain size distribution [24]. In addition, the maximum face reaction instead [32]. Such non-linear grain growth driving force is assigned to largest grain in the grain behavior with respect to the driving force is therefore population and increases with decreasing average grain said to be mixed controlled by either a difusion or inter- size as well as broadening of the grain size distribution face reaction, as illustrated in Fig. 1. [27]. Another important parameter in grain growth is AGG, which is the focus of the SSCG method, occurs the critical driving force (Δgc) for grain growth which in systems with faceted grain boundaries. For an efcient depends mainly on the type of grain boundary interface solid-state single crystal conversion, it is preferred that and can be changed by varying the temperature, atmos- the growth of grains within a polycrystalline matrix be phere, oxygen partial pressure, and presence of dopants negligible (with Δgmax lower than Δgc), while the growth [24, 28–30]. of one or a small number of grains (acting as single According to Kang et al. [24], the ratio between crystal seeds) is promoted. For the latter case, the driv- Δgmax and Δgc determines the type of the grain growth ing force should be larger than the critical driving force and can even help to further predict and explain the (Δgc) in order for the grains to begin experiencing AGG. microstructure development. Additionally, the authors For such growth conditions, and in order for single crys- explained that there are, in general, four diferent grain tal conversion to occur, it is necessary to have a well- growth behaviors which can be observed depending on balanced ratio between Δgmax and Δgc [23]. Te average the magnitude of Δgmax and Δgc and their relation [24, grain size and grain size distribution signifcantly impact 36]: Δgmax and, as a consequence, the ratio between the maxi- mum and the critical driving force, as shown in Fig. 1. 1. Normal grain growth (NGG), which is a stationary Similarly, a variation in Δgc, afected by the change in grain growth for which Δgc = 0 (presented with a the grain boundary structure, will also impact the micro- dashed line in Fig. 1). structural development. 2. Pseudo-normal grain growth, when 0 < Δgc ≪ Δgmax. Te predictions set by the mixed control mechanism on 3. Abnormal grain growth (AGG) occurs when microstructural evolution can be demonstrated best by Δgc≤ Δgmax. observing the efects of a change in Δgmax under constant Δgc, or vice versa. For example, in the experiments of Jung et al. [37], when Δgc was kept constant, Δgmax could be manipulated by changing the initial particle size of the powder sample. As a result, the fne-grained BaTiO­ 3 sample exhibited AGG, while the same sample, but with coarser particles, underwent SGG due to diferences in Δgmax. Such an observation confrms the predictions presented in Fig. 1. Conversely, when Δgc was varied, dif- ferent scenarios could be observed depending on which parameter was afecting the grain boundary structure. A relationship between the change in oxygen partial pres- sure and the degree of faceting of grain boundaries is one of the best examples of how this parameter can afect the grain boundary structure and therefore lead to AGG; several studies conducted in which ­BaTiO was used as Fig. 1 Schematic illustration of the mixed control mechanism of 3 grain growth: (left) Mixed control mechanism of grain growth for a model system support this [28, 29, 37]. Other param- grains with rough and faceted grain boundaries; (right) Schematic of eters that can afect the grain boundary structure (e.g. two systems with diferent microstructures due to the diference in doping, temperature and sintering atmosphere) have also Δgmax [24] been investigated [28, 30, 33, 38, 39], and can be seen as Milisavljevic and Wu BMC Mat (2020) 2:2 Page 6 of 26

an additional endorsement to the concept of the mixed conversion) of the single crystal material from the poly- control mechanism. crystals through a controlled AGG process as well as in Furthermore, some experimental studies have con- the crystallographic direction of the seed crystal. Figure 3 frmed that even diferent crystallographic directions will depicts the process of conversion where the small matrix experience diferences in migration kinetics in systems grains are being consumed by a large single crystal seed. with faceted grain boundaries [33, 35, 40]. Under some Te same principle is used for the fabrication of single experimental conditions, the migration in certain crystal- crystals from melt, except in this case, heating well above lographic directions was even completely omitted [35]. the melting temperature is necessary and, also, other According to the authors of the studies, the presence of issues associated with this processing method are dif- the critical driving force for grain boundary migration, cult to avoid. Furthermore, single crystals can be grown Δgc, which varied with crystallographic planes, was the using the “seed-free method” via prior nucleation of the reason for this discrepancy in results. Such observa- seed crystal in the polycrystalline matrix by applying a tions are consistent with the assumptions of the mixed temperature gradient or by adding a dopant material [23]. control mechanism and are further evidence that the Tis method does not require embedding of the single microstructural development in the systems with faceted crystal seed in the polycrystalline matrix as in the case of 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 tech- nique was actually based on this phenomenon [41]. Fur- thermore, 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 sin- gle crystal seed of a similar crystalline structure with the matrix material which is either embedded in the poly- crystalline 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. Te seed and the green body are both sintered at a temperature which is below the melt- Fig. 3 Cross-section of the Nd:YAG single crystal grown by SSCG ing point of the crystal. Tis enables the formation (or method [42]

Fig. 2 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] Milisavljevic and Wu BMC Mat (2020) 2:2 Page 7 of 26

the seeding method, but the principle of the single crystal PMN–35 mol% PT single crystal using the same method conversion is the same. which the previously mentioned group of authors used in Although the SSCG method has given very good their study. During preparation of the matrix material, a results thus far, there are still certain aspects which need specifc amount of PbO was mixed in. Following the sin- to be considered and which could be limiting, such as tering of PMN with the PT single crystal embedded in the choice of the seed crystal, density of polycrystalline the material, the compact was annealed at 1150 °C for matrix, size distribution of the grains, structural match- 10 h. During annealing, PbO was in a liquid phase, which, ing between the seed crystal and matrix, and control of according to the authors, had a signifcant impact on the the interface [41]. So far, the SSCG has been successfully single crystal growth inside the polycrystalline matrix. applied to only a limited number of systems which mainly Te authors also showed that as the single crystal bound- include oxides and piezoelectric ceramic materials. ary migrated through the polycrystalline matrix, PbO as Te following section of this paper will provide an the second phase accumulated at the triple points in the overview of the results which have been reported on sin- matrix and remained entrapped in a form of spherical gle crystal growth via the SSCG technique. inclusions in the grown crystal. In 2003, another group of authors reported [45] a Current developments on solid‑state single crystal study on the same material which included seeding of growth the PT single crystal in the PMN matrix with a small Pb‑based piezoelectric materials amount of liquid PbO, added to the matrix to increase Solid-state conversion of single crystals has recently been the grain boundary mobility. In this study, the authors proved to be a very successful way to produce piezo- used a vacuum hot-pressing furnace following cold iso- electric single crystals for commercial usage. For exam- static pressing of the green pellets to obtain the com- ple, single crystals such as Pb(Mg1/3Nb2/3)O3–PbTiO3 pact. Tey observed a clear boundary between the single (PMN–PT) and Pb(Mg1/3Nb2/3)O3–Pb(Zr,Ti)O3 (PMN– crystal and polycrystal area. But what is more important, PZT) are now produced by the SSCG method, while the they observed a notable diference between the samples conventional methods include growth via Bridgman or in which the liquid PbO was not added and when it was fux methods. By using the fux-method, it is difcult to included in the matrix. A small amount of the liquid PbO obtain single crystals of size and quality required for the increased the single crystal growth constant by nearly commercial usage. Another issue associated with this 100 times. method is that it causes vaporization of the toxic PbO A common issue which was observed in all the previ- substance. With the Bridgman method it is hard, on the ously mentioned studies was that the grown single crys- other hand, to achieve compositional uniformity within tals contained a signifcant number of pores as well as a the growing crystal. Te SSCG technique, therefore, has PbO second phase entrapped inside the structure. Tis appeared as a very promising and efective method for negatively afected the properties of the single crystals. production of lead-based piezoelectrics. An interesting observation made by Kim [45] was that the single crystal seed orientation had a great infuence PMN–PT on the elimination of the PbO liquid phase from the Single crystals of some relaxor-based ferroelectrics, such grown single crystal. as Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN–PT) exhibit supe- Despite the issues related with the growth of PMN– rior properties compared to polycrystalline forms of the PT single crystals in laboratory conditions, this type of same composition. Especially important are PMN–PT material was successfully fabricated by scaling-up the materials with 35 mol% of PbTiO­ 3 added because of their SSCG process for commercial purposes. It is interest- potential application as electromechanical devices. A ing to mention that by the SSCG method, it is possible possibility to grow a single crystalline PMN–PT material to grow both undoped and doped (e.g. Fe, Mn) PMN–PT by the SSCG method was recognized many years ago. In single crystals with very high quality and excellent dielec- 1998, Li et al. [43] used a method of embedding a ­PbTiO3 tric and piezoelectric properties [47]. Recently, growth of (PT) single crystal into polycrystalline Pb(Mg1/3Nb2/3) undoped and Mn-doped 71PMN–29PT high-quality sin- O3 (PMN), to grow PMN–PT single crystals. A powder gle crystals using the SSCG method were reported [46], with a single crystal was cold isostatically pressed and in which excellent piezoelectric and electromechanical then sintered and annealed under pressureless condi- properties of both single crystals were demonstrated. tions in a range of temperatures. Te authors were able With such results, these materials, and especially Mn- to observe distinct boundaries between the grown sin- doped single crystal, could be utilized as high-power gle crystal area and polycrystal grains of matrix mate- piezoelectric transducers in sonars and medical devices. rial. Khan et al. [44] reported a solid-state growth of the In this study, undoped and Mn-doped (Mn–PMN–PT) Milisavljevic and Wu BMC Mat (2020) 2:2 Page 8 of 26

Fig. 4 Polished surfaces of 71PMN–29PT single crystals grown by SSCG method: (left) undoped and (right) Mn-doped [46]

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 sam- ple [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 benefcial for obtaining a high-density product at the end. Lim et al. [49] published their investigation on a ternary system comprised of BiScO­ 3–Pb(Mg1/3Nb2/3)O3–PbTiO3 (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)O3 (BZT) into Fig. 5 Schematic of experimental procedure for fabrication of PMN– the matrix compact. Te authors used four diferent PT single crystals by SSCG method [48] fuxes ­(Bi2O3, ­LiBiO2, PbO/LiBiO2 and PbO/Bi2O3) in which they tried to grow single crystal BS–PMN–PT. Te fuxes were added with the intention of enhancing the material transfer by forming a liquid phase during sin- PMN–PT single crystals were fabricated by Ceracomp tering. What they observed was that the PbO/Bi2O3 fux Co., Ltd. from South Korea (Fig. 4), which has become enabled growth of the BS–PMN–PT single crystal from well-known for their production of high-quality piezo- BZT single crystal, while other fuxes were inefcient, electric single crystals via the SSCG method. In another which indicated that the BZT single crystal was chemi- study, Mn–PMN–PT single crystals were grown into cally stable against the PbO/Bi2O3 fux. very thin plates (< 0.2 mm) which enabled them to show high stability and piezoelectric performance which is suitable for high frequency composites, medical ultra- PMN–PZT sound probes, non-destructive testing devices, and fex- Along with the PMN–PT single crystal relaxor ferroelec- ible devices applications [9]. tric, Pb(Mg1/3Nb2/3)O3–PbZrO3–PbTiO3 ternary system, Company Ceracomp Co. also introduced a method for or shorter Pb(Mg1/3Nb2/3)O3–Pb(Zr,Ti)O3 (PMN–PZT), obtaining PMN–PT single crystal ceramics by seeding is a very important material which has numerous appli- with a BaTiO­ 3 single crystal. Figure 5 presents a sche- cations in areas such as ultrasonic transducers and matic for obtaining such materials via the SSCG method. actuators due to its large piezoelectric coefcient and high electromechanical coupling factors in areas such as Milisavljevic and Wu BMC Mat (2020) 2:2 Page 9 of 26

medical. Traditionally, these types of single crystal mate- SSCG method they were able to obtain high-quality sin- rials were grown via the fux method or the Bridgman gle crystals (Fig. 6) which exhibited good piezoelectric method which were found to be costly and usually result- properties, among which Mn-doped PMN–PZT was ing in chemical inhomogeneity of the grown crystals. shown to be the most promising. Zhang et al. [50] demonstrated single crystal growth of Until now, the SSCG technique was shown to be the PMN–PZT by means of the SSCG technique. Te matrix only method to produce large relaxor-PZT single crystals, compact containing ­Pb3O4, ­MgNb2O6, ­ZrO2, and ­TiO2 such as PMN–PZT, of diferent ratios of Pb(Mg1/3Nb2/3) was prepared by mixing and pressing of the raw materials O3 (PMN), PbZrO­ 3 (PZ) and PbTiO­ 3 (PT). Te change of into pellets, sintering in the range from 1100 to 1200 °C, PMN/PZ/PT ratios has a signifcant infuence on mate- followed by hot isostatic pressing of the ceramics. BZT rials’ piezoelectric and dielectric properties [47]. Also, single crystal plates were used as seed crystals for single because of the PZ component in the PMN–PZT system, crystal growth during the SSCG process. Te density of which exhibits incongruent melting behavior, and PbO such obtained PMN–PZT single crystals was found to be which is very volatile, PMN–PZT single crystal has been greater than 99% of the theoretical density. Te authors successfully produced only by the SSCG technique so far. further investigated the electromechanical and piezoelec- An interesting report which was done by Hwang et al. tric properties of the fabricated PMN–PZT single crys- [22] in 2015 demonstrated the possibility of fabricating tals and showed that single crystals grown by the SSCG thin flm PMN–PZT single crystals by the SSCG method method exhibited properties which were greater than the used for the fabrication of a high-performance energy previously investigated PMN–PT single crystals. harvester material. Te authors used a BZT single crystal Further investigation on PMN–PZT single crystals seed plate to attach it to the surface of the polycrystalline obtained by the SSCG method was extended to doping of ceramic during the SSCG process. Afterwards, they were the same with manganese (Mn), iron (Fe), or even indium able to take the thin single crystal PMN–PZT flm from (In). In 2017, researchers from the Sunmoon University the glass substrate and transfer it to the plastic substrate in South Korea, in collaboration with the Ceracomp Co., without making any damage to the material. A schematic presented their study in which they doped single crystal illustration of the whole process is presented in Fig. 7. PMN–PZT with Mn [8]. In this study, the authors used three diferent generations of piezoelectric single crys- Pb‑free piezoelectric materials tal materials (PMN–PT - frst, PMN–PZT - second, and Conventionally, piezoelectric single crystals have been Mn-doped PMN–PZT - third generation) obtained by produced via the fux or the Bridgman method. As pre- the SSCG method in order to compare the properties of viously mentioned, these methods require high-tempera- each to one another. Te preparation of the single crys- ture treatment for the melting of the raw materials which tals included attachment of the BZT single crystal as can, at the end, create chemical inhomogeneity and, a seed crystal, after primary sintering. By applying the more importantly, evaporation of highly toxic substances,

Fig. 6 Three generations of piezoelectric single crystals grown by the SSCG method [8] Milisavljevic and Wu BMC Mat (2020) 2:2 Page 10 of 26

Fig. 7 Flexible PMN–PZT thin flm 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 flm on plastic substrate [22]

such as lead. In the last few decades, the question of envi- growth of the single crystal by the seeding method and ronmental and health issues concerning the production the other can be referred to as the “seed-free” method for of the lead-based piezoelectric single crystal materials the growth of single crystals. has been raised. As the growing market demand for these materials is rising more and more each year, a develop- KNN‑based single crystals grown by seeding method In ment of lead-free piezoelectric ceramics and single crys- the study conducted on obtaining single crystal KNN via tals which will be able to replace lead-based piezoelectric the SSCG method, Fisher et al. [52] used a <110> KTaO3 materials became necessary. single crystal as a seed crystal which was found similar to Tis paper will review the two most studied lead-free KNN in terms of the unit cell parameters. Te single crys- piezoelectric ceramic materials which were proven to tal was embedded into the powder matrix and, following be able to be fabricated by the SSCG technique. Te two this, the green body was prepared by uniaxial pressing lead-free piezoelectric materials which will be presented and subsequent cold isostatic pressing. Te authors’ goal here belong to the KNaNbO­ 3 (KNN) lead-free family and was to investigate the infuence of the applied pressure on the ­(Na1/2Bi1/2)TiO3–BaTiO3–(K1/2Na1/2)NbO3 (NBT– the quality and porosity of the grown KNN single crystal. BT–KNN) family of single crystals. Tey determined that certain loading pressures had sig- nifcant impacts on the porosity of the grown single crys- KNN‑based lead‑free single crystals tals. Te single crystal obtained by heat treatment under KNaNbO3 (KNN), a lead-free piezoelectric material has applied pressure in a hot pressing furnace in comparison attracted a lot of attention in the past decade because of to the sample heat-treated under pressureless conditions its desirable properties as a piezoelectric and dielectric, experienced a much smaller number and size of the pores, and a potential to replace lead-based piezoelectric ceram- demonstrating the crucial role of pressure in obtaining a ics and single crystals. KNN has a perovskite structure high-density single crystal KNN. Te SEM images pre- and exhibits three phase transitions, at around 160 °C sented in Fig. 8 depict interfaces between single crystal from rhombohedral to orthorhombic phase, at around seed and grown single crystal, and grown single crystal 200 °C from orthorhombic to tetragonal phase, and at and the polycrystalline matrix in the samples prepared in 420 °C from tetragonal to cubic phase [51]. Of impor- pressureless and pressure-assisted conditions. tance regarding this material is that it undergoes AGG Benčan et al. [53] investigated the single crystal growth during sintering after the temperature reaches a certain of KNN and Li, Ta-doped KNN by the SSCG method. critical point, which in turn decreases its piezoelectric Teir preparation method for the green compacts was properties. On the other hand, such behavior is impor- similar to the work of Fisher et al. Tey also used ­KTaO3 tant in terms of the growth of the single crystal material as a seed crystal due to its compatibility with KNN. Te by the SSCG method. authors demonstrated that the single crystal growth in Two diferent approaches have been recognized so far the hot press furnace is advantageous over the conven- which can be used for the fabrication of single crystal- tional furnace. Tey explained that in the conventional line KNN by the SSCG method. One approach utilizes furnace, the growth of single crystal, matrix grains, and Milisavljevic and Wu BMC Mat (2020) 2:2 Page 11 of 26

Fig. 8 SEM images of KNN single crystal grown by SSCG method in: a, b conventional furnace, and c, d hot pressing furnace [52]

densifcation are all happening simultaneously, which which resulted in interfacial reactions that signifcantly might be a reason for the high number of pores left afected the crystal growth rate, but only up to a certain trapped inside the single crystal. Another point they threshold. Also, the authors observed a high number of made was on the infuence of the addition of the sintering pores, which is the result of the fast movement of the aid (in their case, K­ 4CuNb8O23) on single crystal growth. interface between the growing single crystal and matrix Te sintering aid was shown to be helpful when 2 mol% grains which tend to increase in size as the growth of was added because it allowed the growth of the matrix the crystal continues [54]. grains to some extent, after which the driving force for Although the SSCG method was found promising for the single crystal remained constant, allowing the crys- growth of the lead-free piezoelectric single crystals, one tal to grow under extended annealing time. On the other of the biggest problems associated with this method is hand, a smaller amount of sintering aid (0.5 mol%) was in the high porosity of the end product. Uwiragiye et al. found to cause a reduction of the single crystal and [51] reported in their study on 0.96(K0.48Na0.52)NbO3– matrix grain growth rates. 0.03(Bi0.5(Na0.7K0.2Li0.1)0.5)ZrO3–0.01(Bi0.5Na0.5)TiO3 in Similarly, Yang et al. [54] studied the single crystal which they used a ­KTaO3 seed crystal with <110> ori- growth mechanism by the SSCG method on a KNN- entation, that the piezoelectric properties of the grown based piezoelectric material doped with lithium. Sin- single crystal could be enhanced if the porosity of the tering of the matrix material with a buried single crystal could be reduced. Tey observed that the poros- crystal seed of ­KTaO3 was performed in the presence ity increases with distance from the seed crystals and of a sintering aid, ­MnO2. Te results demonstrated that that the pores are irregular in both shape and size. the addition of the sintering aid created a liquid phase Milisavljevic and Wu BMC Mat (2020) 2:2 Page 12 of 26

KNN‑based single crystals grown by seed‑free AGG mechanism. Te authors used a sol-gel route for method Using a single crystal seed to instigate conver- the powder preparation, and they were able to grow sion of the polycrystalline matrix grains to a single crystal single crystals of KNN as big as 3 mm by sintering for with a desired crystallographic direction can be achieved 2 h at 950 °C. by the SSCG method. However, despite the difculties Later on, Jiang et al. [57] showed in their study on KNN associated with controlling the growth process, the qual- that it is possible to obtain a high-quality single crystal 3 ity of the grown crystal is also afected by the seed crystal. KNN of perovskite structure (11 × 9 × 3) mm via the Terefore, a seed-free method of growing single crystals SFSSCG method through a relatively simple and low cost by the SSCG method has been proposed. Tis method is route. Tey observed that single crystal grains tend to known as the seed-free solid-state single crystal growth, form a structure with a self-assembled arrangement, with or SFSSCG. preferred orientation and layer stacking along the growth In 2007, Zhen and Li reported their study on growth of direction. Tey also performed a systematic study on the single crystals in KNN and (Li­ 0.04K0.44Na0.52)(Nb0.85Ta 0.15) efects of sintering aid content (LiBiO­ 3), as well as sinter- O3 (LKNNT) ceramic materials prepared and sintered ing time and temperature on crystal growth. Figure 10 in a conventional way, without seed crystals [55]. Te presents the results of their systematical study on crys- authors were able to observe a small number of coarse tal growth kinetics, where the growth of large grains was grains which experienced AGG in both samples. While triggered under certain conditions. In the same year, Ahn the distribution of these grains was somewhat random et al. [58] reported self-growth of a centimeter-sized sin- in KNN, the distribution of grains in LKNNT was more gle crystal of 0.985(K1/2Na1/2)NbO3–0.015Ba(Cu1/3Nb2/3) ordered. An interesting phenomenon which the authors O3 (KNN–BCuN) by the SFSSCG method. Te authors observed was that the abnormal grains had a core–shell prepared a KNN polycrystalline powder in a conven- structure, as can be seen in Fig. 9a. Diferent structural tional way, with the addition of ­Ba2+ ions aimed to + features of the core and shell grains could be observed, compensate for the loss of ­Na ions due to ­Na2O vola- but both regions showed to belong to a single crystal tilization during the liquid phase sintering, and CuO as grain. Another interesting observation was how the core sintering aid which is known to form a liquid phase at grains maintained their original grain size; this could not high temperatures. Te authors were able to observe the be explained using classical grain growth theory. Te self-growth of giant grains which were single crystals, as authors proposed a schematic explanation for the core– shown in Fig. 11. Tey also stressed the importance of the shell structure formation (Fig. 9b). But despite the AGG, CuO addition because it had a vital role in the stimula- the ceramic materials exhibited good piezoelectric and tion of AGG. Although the giant single crystal of KNN– dielectric properties, showing that the SFSSCG method BCuN contained a signifcant number of pores, it showed could be a promising technique for the single crystal excellent piezoelectric properties and was found to be a growth. promising candidate for piezoelectric sensors and energy Following Zhen and Li, many other authors reported harvesting devices. Another important beneft presented successful fabrication of KNN-based single crystals by the authors was that the SFSSCG method was approx- through the SFSSCG method. In 2010, Wang et al. [56] imately 100 times faster than the SSCG method. reported single crystal growth of KNN by utilizing the

Fig. 9 A core–shell structure in KNN: a SEM micrograph; b schematic diagram showing procedure for formation of the core–shell structure [55] Milisavljevic and Wu BMC Mat (2020) 2:2 Page 13 of 26

Fig. 10 KNN samples with LiBiO­ 3 sintering aid, sintered under diferent temperature and time regimes [57]

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 ceram- ics by the SFSSCG method [62]. Tey determined that the amount of ­Ba2+ (donor ion) in the system had a sig- nifcant role in AGG, and therefore on the growth of the single crystal. Te authors came up with equations with which they were able to calculate, and in that way pre- dict, how much of each ion is present or substituted in Fig. 11 Variation of sizes of KNN–BCuN single crystals with sintering temperature grown by seed-free SSCG method [58] the system. Teir calculations showed a good ft 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. In the years following, there have been many difer- Later on, Jiang et al. [41] proposed a crystal growth ent reports on single crystal growth in KNN-based method in their latest work which could qualitatively ceramics by using the SFSSCG method in which the explain the SFSSCG mechanism in KNN-based ceram- authors achieved improvements in piezoelectric prop- ics. As they pointed out, the AGG at which the SFSSCG erties of the grown crystals. Yang et al. [59] reported model is based on should no longer be regarded as improved piezoelectric properties in their self-grown abnormal, but normal since the process of grain growth single crystal of ­(K0.45Na0.55)0.96Li0.04NbO3. Another is now understood much better, and in that way better group reported CaZrO­ 3-doped KNN-based single controlled, at least in case of KNN-based materials. crystals [60] grown by the SFSSCG method, which showed improved piezoelectric and dielectric proper- ties as well. In 2017, Hao et al. [61] reported their study NBT‑based lead‑free single crystals on the efects of diferent ratios of sodium and potas- Another group of promising lead-free piezoelectric sium in KNN on the growth of the single crystal by the ceramics which were found to be able to be converted SFSSCG method. Tey summarized their results in a to single crystal materials are ­(Na1/2Bi1/2)TiO3 or NBT- composition-temperature phase diagram at which they based materials. Tese materials may be presented with showed that the growth of the single crystal KNN is a general formula (Na­ 1/2Bi1/2)TiO3–BaTiO3–(K1/2Na1/2) NbO3 or shorter NBT–BT–KNN. NBT–BT–KNN single Milisavljevic and Wu BMC Mat (2020) 2:2 Page 14 of 26

crystals are traditionally fabricated via the fux or the for the growth of single crystals of practical sizes, can Bridgman method, but both methods introduce the dif- be overcome. Tey fabricated NBT–BT single crystals fculties of getting the crystals to have uniform chemical by using a SrTiO­ 3 seed crystal embedded in the ceramic compositions due to the volatility of Na- and Bi-oxides. powder compact, which had a certain degree of porosity Tis further creates difculties in obtaining single crys- and density inhomogeneity, but still exhibited good pie- talline NBT–BT–KNN with desired piezoelectric prop- zoelectric properties. In 2016, Gürbüz et al. [67] reported erties. Te SSCG method, therefore, appeared as a their comparative study between NBT–BT single crystals promising technique for obtaining such single crystal grown by SSCG, which included both the conventional materials. and spark plasma sintering (SPS) methods. Te authors In one of the earliest reported studies on the applica- demonstrated a signifcant diference in porosity between tion of the SSCG method for the conversion of polycrys- the single crystals obtained using these two sintering talline NBT‒BT‒KNN to single crystal, Park et al. [63] techniques. Tey achieved 99% of the theoretical density successfully grew an NBT–BT–KNN single crystal from of the grown single crystal for the sample sintered by SPS conventionally prepared ceramic powder. In their experi- for 5 min at 950 °C, while conventional sintering in air mental work, this group used a SrTiO­ 3 single crystal seed for 2 h at 1130 °C produced a single crystal with 96% of of <110> orientation embedded in a ceramic powder to the relative density. Te same result was in favor to SPS initiate single crystal growth during a 50-h annealing sintering when the dielectric properties were measured, period at a temperature of 800 °C. Te grown single crys- which demonstrated that SPS might be an efcient tech- tal exhibited good piezoelectric properties which were nique for fabrication of NBT-based single crystals by the comparable to those of other lead-free single crystals. SSCG method, providing high relative densities and low Te same group of authors continued their research on alkaline evaporation. the same material [64] and 2 years later reported their In literature, reports can also be found on NBT-based fnding that the KNN content in NBT–BT–KNN had a single crystals grown by the SSCG technique which used signifcant efect on the piezoelectric properties of NBT– other alkali earth perovskites, such as ­CaTiO3 and ­SrTiO3. BT–KNN single crystals. Along with that, they were able For example, in 2016, Lee et al. [68] reported for the to demonstrate that the SSCG method was a prospec- frst time a single crystal 0.8(Na1/2Bi1/2)TiO3–0.2SrTiO3 tive method for growth of NBT–BT–KNN single crystals grown by the SSCG method, which was grown from the with high performance, which could replace Pb(Zr,Ti) ­SrTiO3 single crystal as a seed crystal. Te grown single O3 for actuator applications. In the same year, the afore- crystal exhibited high porosity. Le et al. [69] afterward mentioned group of authors presented their results on reported growth of 0.75(Na1/2Bi1/2)TiO3–0.25SrTiO3 sin- NBT–BT–KNN single crystals by seeding with a ­SrTiO3 gle crystal using the same approach. Tey investigated single crystal [65]. Tey fabricated a highly dense NBT– the dependence of growth of the single crystal and matrix BT–KNN single crystal with signifcant improvements grains on sintering time and temperature, and showed in its piezoelectric properties, which were higher than that the results could be explained with the mixed con- that of any previously reported ceramics or single crystal. trol mechanism of microstructural evolution [23]. Te high relative density (96.6%) of a grown crystal was Later on and for the frst time ever, a diferent group achieved by creating a layered structure which was com- of authors reported on a fabricated 0.96(Na1/2Bi1/2) posed of pre-sintered ceramic pellets between which a TiO3–0.04CaTiO3 single crystal [70] via conversion of the seed crystal was positioned, followed by a 30-h annealing polycrystalline powder matrix to a single crystal, in pres- period at 900 °C in air. Tis method enabled the authors ence of SrTiO­ 3 as a seed crystal. Te grown single crystal to fabricate a single crystal which had a notably smaller showed improved ferroelectric and piezoelectric proper- number of pores, which typically remain entrapped in ties compared to its polycrystalline ceramic counterpart. the powder compact. Another group of NBT-based piezoelectric single crys- Ferroelectric materials tals which will be covered by this review pertains to the Ferroelectric oxides are a class of perovskite-type materi- solid solution of ­(Na1/2Bi1/2)TiO3 (NBT) with alkali earth als which exhibit spontaneous electrical polarization that perovskite-type materials ­(CaTiO3, ­SrTiO3 and ­BaTiO3). can be oriented in the presence of an external electric Te solid solution system (Na­ 1/2Bi1/2)TiO3–BaTiO3 feld. Also, these materials possess other properties such (NBT–BT) was found to be a promising environmentally as piezoelectricity and pyroelectricity and may have large friendly, lead-free piezoelectric material. In the study on dielectric constants which are important for actuator NBT–BT single crystals obtained by the SSCG method, and sensor applications. ­BaTiO and Ba(Zr Ti )O or 3 x 1−x 3 Moon et al. [66] demonstrated that the common problem Ba(Zr,Ti)O3 (BZT) are some of the most important fer- associated with the insufcient AGG, which is important roelectric oxides and, thus, will be covered in this review. Milisavljevic and Wu BMC Mat (2020) 2:2 Page 15 of 26

BaTiO single crystals 3 electrical conductivity compared to the ceramic ­BaTiO3 One of the biggest issues in the fabrication of the ­BaTiO3 due to the absence of grain boundaries, which act as elec- single crystals lies in its hexagonal-tetragonal transition trical barriers, and less oxygen vacancies, which have a which occurs at 1430 °C and prevents the growth of a sin- direct infuence on the difuse dielectric anomaly. gle crystal ­BaTiO3 from a stoichiometric melt. Although Later on, Jung et al. [37] investigated grain growth the ­BaTiO3 single crystal can be obtained from, for exam- behavior in BaTiO­ 3 with a small excess of ­TiO2 during ple, a BaTiO­ 3–SrTiO3 congruent melt, or by the fux- sintering in air with and without pre-sintering in ­H2 envi- method if the transition temperature is below 1430 °C, ronment. Te authors provided a theoretical explanation these methods are somewhat complicated. [71] In 1994, to the infuence of the oxygen partial pressure on AGG. Yamamoto and Sakuma [71] reported that a single crystal Tey explained that pre-sintering in ­H2 atmosphere for of ­BaTiO3 can be grown via the SSCG method by utiliz- a long time led to an increase in the average grain size ing the previously observed phenomenon of AGG in this which in turn suppressed AGG during air sintering. In type of material which occurs in the presence of a small this way, the authors demonstrated that by increasing the excess of TiO­ 2. Te authors observed a non-uniform initial average grain size in the polycrystalline matrix, it grain size distribution as well as AGG following anneal- is possible to suppress AGG by reducing driving force for ing of the seeded ceramic compact at a temperature of the growth of the faceted grains below the critical value. 1300 °C. Although the size and quality of the single crys- Although ferroelectric oxides such as ­BaTiO3 represent tals could not be successfully controlled and there was a very important group of materials with mainly elec- a resulting high porosity, this study did show that SSCG tronic applications, there have not been many reports could be a promising method for the fabrication of sin- on SSCG of BaTiO­ 3 single crystals recently. Most of the gle crystals. A few years later, Yoo et al. [72, 73] reported recent studies on SSCG of BaTiO­ 3 were carried out by growth of ­BaTiO3 single crystals without the presence of Ceracomp Co. which is now utilizing this method for a seed crystal. Te authors used previous observations the commercial production of BaTiO­ 3 single crystals. in which ­BaTiO3 experienced AGG in the presence of a In one of their publicly available technical reports [48], small amount of SiO­ 2, which is similar to what Yamamoto they mentioned that the number density of the abnor- and Sakuma [71] had used in their work. In their experi- mally grown grains in ­BaTiO3 can be controlled during mental work, Yoo and co-workers prepared an SiO­ 2 the SSCG, thus implying that this method can be used for slurry which they dropped on top of the surface of a poly- conversion of single crystals from polycrystalline ceram- crystalline green body of ­BaTiO3. Tis enabled the forma- ics (Fig. 12a). Tey also determined that this method tion of the <111> fast-growing twin lamellae inside the can be utilized for the fabrication of transparent ­BaTiO3 polycrystalline ­BaTiO3 during sintering, which continued single crystals (Fig. 12b) and even layered Mn-, Cr-, and to grow without limitation. According to the authors, Ce-doped ­BaTiO3 single crystals (Fig. 12c) with compo- the structure of the twin lamellas of the BaTiO­ 3 enabled sitional gradients. In the same report [48], Lee presented easier grain growth when compared to two-dimensional the study on BaTiO­ 3 single crystals obtained by the SSCG nucleation. Also, they concluded that the formation of method doped with various ions (Ca, Ce, Zr, La, Nb, Nd, the twins was facilitated by the presence of liquid ­SiO2. Cr, Co, Fe, Mg, and Mn). All these ions were successfully Te same authors also observed in [73] that there was doped into ­BaTiO3 and then converted into a single crys- greater success in forming single crystalline ­BaTiO3 tal. Lee pointed out in his report that for obtaining high- in the presence of liquid ­SiO2 than in ­TiO2. Further- quality transparent single crystals via the SSCG method, more, Lee et al. [74] continued to investigate the AGG it is crucial to increase the density of the polycrystalline and formation of <111> twins of BaTiO­ 3 in the presence ceramics and reduce porosity before conversion of the of ­TiO2. Te authors observed at temperatures higher single crystal, which can be done in a hot press (Fig. 12d). than the eutectic (1360–1370 °C), a phenomenon which they called secondary abnormal grain growth (SAGG). BZT single crystals According to them, the grains which experienced SAGG Ba(Zr,Ti)O3 (BZT) polycrystalline ceramics have recently all contained twins, and, at the previously described tem- found a wide range of applications as piezoelectric mate- perature range, had grown without any limitation in size. rials, especially due to their lead-free nature and the envi- In their study on difuse dielectric anomaly in ­BaTiO3, ronmental concerns which are imposed by the usage of Kang and co-workers [75, 76] fabricated a ­BaTiO3 single lead-containing piezoelectric materials such as Pb(Zr,Ti) crystal with <100> direction by the SSCG method. Tey O3 (PZT). As it has been mentioned previously, single obtained a single crystal that was entirely free of grain crystal materials show better dielectric, piezoelectric boundaries after sintering for 200 h at 1360 °C. Also, they and many other properties compared to polycrystal- showed that the single crystal had a signifcantly higher line ceramics of the same composition. Terefore, Milisavljevic and Wu BMC Mat (2020) 2:2 Page 16 of 26

Fig. 12 SSCG growth of ­BaTiO3 single crystals: a control of the number density of abnormal grains; b transparent BaTiO­ 3; c Mn-, Cr-, and Ce-doped ­BaTiO3 single crystal with compositional gradient; d highly dense transparent BaTiO­ 3 single crystal obtained using a hot press [48] development of technology which will be able to replace and dielectric loss more than nine times smaller than the lead-containing ferroelectrics and piezoelectrics has BZT polycrystalline ceramic, as well as an electrome- become necessary. chanical coupling factor greater than of PZT ceramics. Te addition of Zr in a ­BaTiO3 matrix was dem- In his earlier studies, Lee [47] also obtained BZT onstrated to reduce the transition temperature from single crystals by seeding a BZT ceramic com- the cubic to tetragonal phases as well as increase the pact. He was able to observe an obvious boundary transition temperatures between the tetragonal and between a grown <100> single crystal with a size of 3 orthorhombic, and orthorhombic and rhombohedral (50 × 50 × 10) mm and polycrystalline matrix, as shown phases. If the orthorhombic or rhombohedral phase is in Fig. 13a. Another thing Lee pointed out was that the stabilized at room temperature, then the single crystal SSCG method allowed for the fabrication of more com- BZT shows good piezoelectric properties [47]. Due to plex shapes compared to the conventional single crystal their incongruent melting, BZT single crystals are hard growth techniques. One of the examples given by him to obtain by any conventional single crystal growth tech- is shown in Fig. 13b, which represents a ring-shaped nique (fux, Bridgman, etc.). Terefore, SSCG method single crystal obtained from a polycrystalline ceramic, has been introduced as a promising technique for growth which was uniaxially pressed, sintered, and later attached of high-quality BZT single crystals. In their study on to a single crystal seed which enabled a single crystal the dielectric and piezoelectric properties of BZT sin- conversion. gle crystals, Lee and associates [77] were able to grow a rhombohedral BZT single crystal by the SSCG method. Al‑based oxide materials Tey prepared a single crystal by seeding a pre-sintered Al2O3 and ­MgAl2O4 single crystals polycrystalline ceramic compact with a BaTiO­ 3 seed crys- Polycrystalline alumina is an important industrial mate- tal and sintering it for 100 h. Since the sintering and sin- rial that is used in various application, one of which being gle crystal conversion were performed at temperatures sodium vapor lamps [78]. Terefore, sintering this mate- lower than the melting temperature, a homogeneous rial is an important process for obtaining many difer- chemical composition was obtained for the single crys- ent products. Fortunately, the majority of the problems tal. Furthermore, the authors showed that the SSCG- associated with the usage of polycrystalline alumina can grown <001> BZT single crystal had a piezoelectric be overcome by instead using single crystal alumina, also charge constant which was more than six times higher known as sapphire. Milisavljevic and Wu BMC Mat (2020) 2:2 Page 17 of 26

Fig. 13 Growth of a <100> and b a ring-shaped BZT single crystal by SSCG method [47]

Te solid-state conversion of single crystals from Similar to the previous study, Tompson et al. [81] polycrystals has appeared to be a promising technique investigated the infuence of localized surface co-doping which can be used for large-scale production of sin- with ­SiO2 on the single crystal conversion of Al­ 2O3. Te gle crystal alumina. Tis method utilizes a well-known co-doping with SiO­ 2 was done prior to sintering, which phenomenon that is related to AGG, which occurs in enabled AGG and conversion of the polycrystalline polycrystalline ­Al2O3 during heat treatment. Moreover, matrix from the outside to the inside of the ceramic tube there are many reports which discuss other interesting sample as soon as the heat treatment started (Fig. 15a, phenomena in which AGG can be induced in the pres- b). Teir study demonstrated that it is indeed possible to ence of CaO or ­SiO2 in alumina, or suppressed in the obtain nearly transparent single crystals of Al­ 2O3 by the presence of MgO [79–81]. Te efects of CaO and ­SiO2 SSCG method (Fig. 15c), with low porosity, high density, in alumina can be explained by the formation of a liquid and good physical and optical properties. An interesting phase during sintering which acts as a driving force for conclusion the authors made was that the SiO­ 2 co-dopant grain growth through the formation of straight and fac- did not directly afect the densifcation of the converted eted grain boundaries. On the other hand, the presence single crystal sapphire. In the early stages, ­SiO2 initiated of MgO was observed to suppress AGG by coarsen- conversion by removing the grain boundaries, which ing of the grain boundaries. All of the aforementioned consequently provided a pathway for fast densifcation. observations were later used in studies with the goal of In the years that followed, through a series of stud- developing a new approach for ­Al2O3 single crystal fab- ies on controlled AGG in alumina in presence of MgO, rication - SSCG. CaO and SiO­ 2, Dillon and Harmer tried to explain the In one of the earliest studies, Scott et al. [80] investi- phenomenon of single crystal conversion. Tey pro- gated the possibility of the conversion of polycrystalline posed a mechanism of single crystal conversion via the ­Al2O3 to single crystal sapphire without going through SSCG method in alumina which involved rapid difusion the melting process of the material. Tey sintered ­Al2O3 through an intergranular flm of 10–20 nm thickness at with an amount of MgO which was enough to suppress the grain boundaries [82]. Tey also emphasized that AGG during sintering. Once they allowed grains to grow the diferent grain boundary structures in alumina have up to 20–30 μm in average (NGG), through a careful con- a direct infuence on the grain boundary kinetics, which trol of the sintering temperature, they managed to insti- they used to explain the conversion process [83–85]. gate the AGG despite the presence of MgO in the matrix. While the previously mentioned authors investigated Te high temperature of 1880 °C which they applied the SSCG of MgO-doped alumina by controlling AGG in was sufcient to promote AGG by inhibition of various the presence of ­SiO2 or CaO, the following authors uti- dragging forces for boundary movement. Tey observed lized the SSCG approach to grow single crystals by the very high velocities of grain boundary migration which conversion of epitaxial flm on substrates. Te conversion reached as high as 1 cm/h. As a result, the authors of epitaxial flms is a potential method for the fabrication obtained a centimeter-sized single crystal sapphire con- of patterned single crystal substrates for various applica- verted from the polycrystalline ­Al2O3 (Fig. 14). tions [86]. Milisavljevic and Wu BMC Mat (2020) 2:2 Page 18 of 26

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 ­Al2O3 matrix and the grown single crystal [80]

Fig. 15 Optical micrographs of the single crystal ­Al2O3 (sapphire) grown via the SSCG method: a, b cross-section of single crystal sapphire grown from polycrystalline ­Al2O3; c translucent single crystal sapphire doped with MgO and ­SiO2 [81]

Park and Chan [87] reported their study on the epi- similar investigation, but instead of single crystalline taxial growth of single crystal alumina on a surface of substrate, they used a polycrystalline MgAl­ 2O4 spinel. sapphire which could be utilized to obtain a pristine sap- Tis approach can be considered analogous to the SSCG phire surface when a high-quality surface fnish is neces- method which has been discussed thus far. Te authors sary (e.g. for substrate material for high-power blue LEDs used a wet-chemical method to prepare a sol-gel for spin- and laser diodes). A thin flm of Al was deposited by mag- coating of the ­MgAl2O4 ceramic polycrystalline surface. netron sputtering onto sapphire disks, after which a two- After this step, the coated samples were heat-treated at stage sintering was applied, frst to oxidize the Al flm at diferent temperatures. Te authors demonstrated that at moderate temperatures and then to induce the growth 1400 °C, the coating was converted into an epitaxial layer of a single crystal at high temperatures by consumption by the growth of substrate grains and their correspond- of the oxide layer grains by the single crystal substrate. ing absorption of the grains in the coating. A few years Furthermore, Browne et al. [88] conducted a somewhat later, Dutta et al. [86] reported on a spin-coated sapphire Milisavljevic and Wu BMC Mat (2020) 2:2 Page 19 of 26

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 poros- ity. But, a uniform conversion of the sol-gel coating was observed at the coating-sapphire interface.

YAG​ 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. Te importance of Nd:YAG single crystals as Fig. 16 Micrograph showing surface of the grown single crystal YAG laser materials has been covered elsewhere. Te work of by SSCG method [89] Ikesue has confrmed that it is possible to obtain a sin- gle crystal of high quality that is nearly pore-free using a fabrication method which is signifcantly diferent from Other oxide materials conventional growth methods. Te authors used a solid- state reaction method for the fabrication of an Nd:YAG Aside from Al-based oxides and YAG, there are also polycrystalline powder, which was then pressed into a some reports on attempts to grow single crystalline compact and sintered under vacuum. A seed crystal of materials of other oxide materials by the SSCG method. YAG which was grown by the Cz method was placed Such reports which investigated the feasibility of the on the top surface of the ceramic Nd:YAG and then sin- growth of single crystals of the apatite-type of oxide tered together in the range of 1700–1800 °C. Tis ena- ionic conductors were given by Nakayama et al. In 2013, bled the continuous growth of grains, which starts in the they reported on the growth of single crystals of hex- single crystal region and heads towards the polycrystal- agonal apatite-type ­La9.33Si6O26 [90] by seeding with a line grains. Te authors observed abrupt abnormal grain single crystal of the same composition grown by the Cz growth at the single crystal-polycrystal interface, where method. As in the previous studies involving the SSCG the surface energy of the seed crystal was low enough method, the authors observed an abrupt motion of the compared to the surface energy of the polycrystals to grain boundary from the seed crystal with a low sur- consume the smaller polycrystalline grains. Continu- face energy to a polycrystalline area with higher surface ous absorption of the smaller grains by the single crystal energy due to the seed crystal consuming the smaller, instigated a rapid grain boundary movement towards the fne grains. In the same year, the authors reported on rest of the polycrystalline region which at the end created another study on apatite-type oxide ­La9.33Ge6O26 [91] a Nd:YAG single crystal. grown as a single crystal by the SSCG method. Com- A few years later, the infuence of the diferent stoichio- pared to the previous, ­La9.33Ge6O26 exhibited much less conductive anisotropy. metries of Y­ 2O3 and Al­ 2O3 on the solid-state conversion of polycrystalline YAG to a single crystal was investi- In 2016, Fisher et al. [92] reported on the growth of gated by Bagayev et al. [89]. In their study, the authors a ­BaFe12O19 single crystal via the SSCG method. Te used a <111> polished YAG single crystal as a seed crys- authors prepared the samples by cold isostatic pressing tal which they placed on the surface of the polycrystal- the polycrystalline powder with a seed crystal which line ceramic YAG. A micrograph of the thermally etched was buried inside the powder compact, following heat surface of the grown crystal which is entirely free of treatment. Te authors used a mixed control mecha- grain boundaries is shown in Fig. 16. Te authors also nism model of grain growth [23] to explain the single observed that the single crystal growth rates were highly crystal conversion in the system being studied. Tey temperature dependent and were faster in samples with observed a signifcant temperature infuence on the porosity of the grown ­BaFe O single crystal as well excess ­Al2O3. Te highest achieved growth velocity was 12 19 0.15 mm/h. Additionally, the authors did not observe any as on the number of abnormally grown grains. Once diferences in the growth rates between the Nd-doped the number of abnormal grains had become high, the and the undoped YAG. growth of the single crystal stopped. Milisavljevic and Wu BMC Mat (2020) 2:2 Page 20 of 26

In more recent reports, Kappenberger et al. [93] conducted by this group by adjoining two pieces of the reported on the growth of a single crystal LaFeAsO via polycrystalline ceramic to a single crystal seed from both the SSCG method. LaFeAsO belongs to the family of high sides with the assistance of ethyl silicate as an adhesive. temperature iron-based superconductors, which have After this step, they annealed the sandwiched samples in considerable c-axis growth of the {1111} family of planes. the ­N2–O2 atmosphere where they could observe AGG of Tis type of material is very difcult to obtain via con- the polycrystalline material which lead to single crystal ventionally used single crystal growth techniques such as conversion. Although the authors proved that the SSCG the fux-method; therefore, the report of Kappenberger method can be used for the fabrication of Mn–Zn ferri- et al. has introduced a promising route for the fabrica- tes, the Bridgman method is still widely used [23]. tion of single crystals within this family of materials. Te authors grew LaFeAsO single crystal from polycrystalline powder in the presence of a Na-As powder which turned Electric feld‑assisted single crystal growth into a liquid phase at around 550 °C during annealing, So far, this review has discussed solid-state single crys- difused into the pores of the polycrystalline compact and tal conversion from a polycrystalline matrix either by promoted crystal growth. A schematic representation of the seeding method or by the control of AGG inside the steps for growth of LaFeAsO single crystals via the the ceramic during heat treatment (seed-free method). SSCG method is presented in Fig. 17. It was shown that But reports are also available which discuss single crys- this method is successful for obtaining large single crys- tal growth in the presence of an externally applied elec- tals with considerable growth along the c-axis, with high tric feld. Liu et al. [96] investigated the infuence of an quality as well as good physical properties. applied electric feld on single crystal conversion of Yb:Sr5(PO4)3F from a seed crystal buried in the polycrys- Mn–Zn ferrite talline matrix during spark plasma sintering (SPS). It was In literature, studies can also be found on the growth of thought that the applied direct current (DC) feld during single crystal ferrites via the SSCG. Te earliest report, SPS had an infuence on the grain boundary potential, which dates back to 1985, was done by Tanji and associ- and therefore on the activation energy for grain boundary ates [94]. Conventionally, Mn–Zn ferrites were produced motion. Te authors showed that pressureless SPS sinter- via the Bridgman method. Tese were, therefore, costly ing might be used for single crystal growth from poly- and difcult to obtain. Te authors applied the SSCG crystalline material at temperatures and times which are method, and by seeding the polycrystalline Mn–Zn fer- signifcantly lower than usual for the material being used. rite matrix with the single crystal seed, they were able to In another study [97], the same authors used a ­Sr5(PO4)3F successfully grow Mn–Zn ferrite single crystals. A few polycrystalline powder which was sintered via SPS with years later, a diferent group reported on a study regard- the addition of NaF as a sintering aid and a single crys- ing the same material, but, in comparison to the previous tal seed embedded in the powder, and annealed further study, they tried to explain the infuence of diferent sin- at the same temperature. Te authors investigated the tering additives on single crystal conversion of Mn–Zn infuence of the DC electric feld on grain growth and ferrite via the SSCG method [95]. Te experiment was noted that the DC feld retarded the grain growth dur- ing post-sintering treatment, but induced grain boundary migration; this was benefcial for solid-state single crystal conversion. In a diferent study, a group of researchers which were led by Chen [98] performed an investigation on the infu- ence of a DC electric feld on the AGG in KNN. Te authors observed that the samples which were sintered under an applied non-contact electric feld exhibited obvious grain growth and even exhibited AGG when compared to those sintered without a DC feld. Also, the application of the electric feld had a positive efect on the densifcation of KNN due to the formation of a liquid phase that could enhance mass transport. Te authors pointed out that the observed behavior of the mate- rial when put under an applied electric feld could be an Fig. 17 Schematic showing SSCG process for obtaining LaFeAsO advantageous approach for the solid-state conversion of single crystals [93] polycrystalline KNN to a single crystal. Milisavljevic and Wu BMC Mat (2020) 2:2 Page 21 of 26

Challenges of SSCG issues related to this technique which are not yet well Te challenges associated with current (conventional) understood to be fully controllable. So far, this method technologies for the growth of single crystals may be has been successfully applied to the commercial pro- overcome by the solid-state conversion of single crys- duction of high-quality piezoelectric single crys- tals. At the moment, however, there are a few important tals, such as ­BaTiO3, BZT, PMN–PT, and more, while challenges that should be overcome frst. Control of the other types of materials still present problems when microstructure development during the conversion pro- produced via the SSCG method. Terefore, the most cess of the polycrystalline material is the most impor- important next step is to provide an even stronger tant and most challenging part of the SSCG method [23]. theoretical background for the SSCG technique, which Although the proposed mixed control mechanism [24] would extend the current knowledge and understand- has made a signifcant contribution towards explaining ing of the microstructure control and the mechanisms and better understanding of the single crystal conver- associated with solid-state single crystal conversion. sion phenomenon, especially in certain piezoelectric, Tis would, consequently, help to overcome some of ferroelectric, and a few other materials systems, there is the challenges mentioned in the previous section and still an insufcient amount of data and overall knowledge push the SSCG technique towards commercialization about the SSCG method, which would allow for it to be as an alternative, or in some cases, a unique technique more commercially utilized. Porosity in the single crys- [23] for the fabrication of single crystals. tals grown via the conversion process is another impor- So far, only a few groups have conducted research on tant issue associated with the SSCG method. Te quality solid-state conversion of single crystals; although these of the grown single crystal, and, in that way, its properties investigations have been thorough, they have only been and the intended application, are greatly afected by the conducted on a limited number of materials. Most of the porosity. investigations have been focused onto ferroelectric and At the moment, the sizes of the single crystals grown piezoelectric materials, and a few other oxide materials, in the laboratory conditions via the SSCG method are however, it is expected in the future for studies to expand limited to the scale of at most few centimeters. Growth onto other types of materials. Table 1 summarizes some of larger single crystals, comparable in size to the ones of the relevant results presented in this paper. It contains obtained via the conventional single crystal growth tech- information such as single crystal growth conditions, size niques, is necessary in order for SSCG to become a com- of the grown single crystals, some important parameters mercially used technique. or properties measured by the authors, or the authors’ Because of the inability to fully control the growth and observations, and potential applications. Until now, the development of single crystals during conversion, as most of the single crystals grown by the SSCG method well as other aspects, the SSCG technique is still con- involved growth from a single crystal seed, which was strained to a small number of systems, and the large-scale placed either on top of the polycrystalline matrix or production is somewhat limited. embedded within the matrix. For example, Ikesue et al. [42] showed that YAG single crystal, which is a very important material for diferent optical applications, can Summary and future outlook be fabricated via the SSCG seeding method. However, Solid-state single crystal conversion (SSCG) has been the selection of suitable single crystal seeds is another shown to be a promising technique for the growth of common issue associated with the SSCG method. For- single crystal materials from all of the investigations tunately, some authors were able to grow single crystals presented thus far. Te SSCG method ofers many without the use of seed crystals, which can even poten- advantages over conventional single crystal growth tially reduce the production cost for the price of the seed techniques, such as Bridgman, fux, Cz, and others. crystals that can sometimes be very expensive. Tis fab- Among the strongest advantages of the SSCG method rication route has been very successful for various com- are the low fabrication costs, processing simplicity, mercially grown lead-free piezoelectric single crystals of and applicability of the method to the growth of single centimeter-scale range [56–58]. Te SSCG technique is crystals of complex compositions with a high degree still in its developing stage, so it is projected that more of chemical uniformity. However, there are still many research work will be available in the future. Milisavljevic and Wu BMC Mat (2020) 2:2 Page 22 of 26 [ 8 ] [ 46 ] [ 59 ] [ 63 ] [ 65 ] [ 72 ] [ 60 ] [ 52 ] [ 58 ] [ 49 ] [ 48 ] Refs. [ 45 ] applications (sonar trans - medical ultrasonic ducers, ultrasonic motors) devices, transducers piezoelectrics piezoelectrics tions piezoelectrics energy harvestingenergy devices - tem at elevated operated peratures for militaryfor and medical application High-power piezoelectric High-power piezoelectric High-performance Pb-free Replacement for Pb-based Replacement for High-stroke actuator applica - – – Pb-free replacement for PZT PZT for replacement Pb-free Piezoelectric sensors and Piezoelectric Electromechanical devicesElectromechanical – Application Transducers and actuators Transducers - m Q kV/cm; Vm/N = 689 pC/N; = 488 pC/N = 0.67% and = 6.3

− 3 C 33 33 E = 850 ‒ 1100 pC/N d d max

= 0.57% and pm/V

­ S 33 ­ d max 1050 pm/V at 7 kV/mm 1670 pm/V at 4 kV/mm µm/h ­ S ‒ PT ceramics , tan δ - 50% decrease, , tan δ - 50% decrease, 145 °C; ­ = 967 = =

432 °C; ­ 391 °C; ­ 33 - 150% increase, and ­ - 150% increase, 96.9%; = 131 × 10 * 33 * 33 * 33 =

­ d C

> 0.9; = =

, d d 500% increase compared to to compared 500% increase PMN d KNN: cantly reduced (from 100 to 100 to (from cantly reduced hot pressing 1 ‒ 2 µm) by migration of ions between migration the seed and grown single crystal ­ E high-density single crystal PbO up to 3 vol.%; decrease decrease 3 vol.%; up to PbO than 3 larger of k with PbO vol.% = 33 T 3 RT C C 33 k k > 200 K T T (001)-oriented NBT ‒ BT ρ - signif size and pore Porosity Good chemical stability, no Good chemical stability, T Chemically homogeneous, Chemically homogeneous, g Key parameters Key with increase of Increase of k with increase 3 3 3 3 3 ­ mm ­ mm ­ mm 5) 5) ­ mm ­ mm 2) 8) 0.8) mm) × 15 × 30 × 5 × 6 × 3 1.5 cm 1890 µm 500–1000 μm (6 2 cm > 1.5 inch (~ 38 1.3 cm (6 (3 Crystal size (15 – (30 - as sintering aid 23 fux and embed - green body; green sinter 3 3 O 8 O 2 to compensate for the for compensate to 3 loss ­ BaTiO + slurry dropped (additive) CuNb 2 4 ing in air (1370 °C, 80 h) and embedded seed ded seed 15 h) ics, then annealing at high ics, temperatures MPa, then (975 °C, 2 h, 50 MPa, with 1100 °C, 100 h, 50 MPa) ­ K embedded seed (950 °C, 10 min), then anneal - ing in air (900 °C, 30 h) with seed on top ­ Na on CuO as sintering aid and CuO ­ BaCO ceramics with seed on top PbO/Bi MPa), (880 ‒ 900 °C, 30 min, 20 MPa), then annealing in air (1150 °C, 0 ‒ 10 h) ics, then annealing at high ics, temperatures Sintering in air (1080 °C, 10 h) Sintering in air (1090–1115 °C, SiO Hot pressing to obtain ceram - to Hot pressing Two-step sintering in hot press sintering in hot press Two-step Sintering (800 °C, 50 h) with of ceramics Pre-sintering Sintering (1120 °C, 2 h) with Growth conditions Growth Heat treatment of pre-sintered of pre-sintered Heat treatment Annealing (1050 °C, 100 h) with Hot pressing in excess PbO PbO in excess Hot pressing Hot pressing to obtain ceram - to Hot pressing 3 3 3 3 ­ KTaO ­ SrTiO ­ SrTiO No seed No seed No seed (110) BaTiO (110) (110) No seed Seed BZT (110) BZT (001) PMN–PT BZT 3 3 NbO NbO 0.04 0.5 Li K 0.5 0.96 ) ‒ PZT 0.55 ‒ Na 3 3 Na ‒ PT ‒ PT ‒ PT ‒ PMN 0.45 KNN PMN CaZrO NBT ‒ BT KNN BaTiO NBT ‒ BT KNN KNN ‒ BCuN Formula (K Mn BS–PMN–PT PMN Undoped and Mn-doped PMN Summary representing some of the relevant reports on the growth of single crystals via the SSCG method of single crystals reports via the SSCG on the growth some of the relevant Summary representing Pb-free piezoelectricsPb-free Ferroelectrics 1 Table Category Pb-based piezoelectrics Milisavljevic and Wu BMC Mat (2020) 2:2 Page 23 of 26 [ 86 ] [ 93 ] [ 77 ] [ 80 ] [ 90 ] [ 42 ] Refs. , transition , transition RT ­ T substrates ductor Patterned single crystalPatterned - supercon High-temperature Actuators, sensors, transducers sensors, Actuators, – – Solid-state lasers Solid-state Application - K; = 145

nm/s; k ( r - S , electromechanical coupling factor;, electromechanical coupling , maximum strain; ρ, relative density; ρ, relative , maximum strain; η, optical slope ­ T /(N s) nm/s 33 − 2 3 k Vm/N max − 1 ­ m S

~ 950 pC/N, − 3 33 − 10 ­ d = 5 × 10 127 K and = 4 × 10 0.85, = cm/h; average

= 41 × 10 =

63% (2.4 at. % Nd:YAG) 33 SDW 33 plane) ­ g grain boundarygrain mobil - ity ~ 2 × 10 ­ k ­ T linear behavior of mag - linear behavior netization as a function of feld magnetic allel to the c -axis allel to was ~ 100 times higher than the perpendicular = k ~ 1.5 (001)-oriented BZT: Splitting of two transitions at Conductivity component par η k ( c -plane) Key parameters Key 3 3 ­ mm ­ mm 5) , electromechanical quality factor; ­ 0.4) m , efective piezoelectric coefcient; ­ piezoelectric coefcient; , efective Q * 33 × 25 × 3 up to 30 cm up to (25 – 3 ‒ 5 mm up to 2 µm thicknessup to Crystal size (2 - , coercive electric feld; ­ , coercive C E atmosphere atmosphere 2 H , piezoelectric voltage coefcient; d , piezoelectriccoefcient; voltage 33 g (1880 °C) with MgO as sinter ing aid annealing for 100 h with annealing for seed on top (1500 °C, 2 h), then annealing (1725 °C, with seed on top 2 h) vacuum (1550 °C, 3 h), then annealing in vacuum flm sample in air (1025 °C, 18 h) Na-As as sintering aid Na-As (1080 °C, 200 h) Sintering in ­ Pre-sintering of ceramics, then of ceramics, Pre-sintering of ceramics in air Pre-sintering Pre-sintering of ceramics in Pre-sintering Heat-treating of spin-coated Heat-treating Growth conditions Growth Sintering of ceramics with 26 O 6 , structural temperature transition Si S ­ T 9.33 3 ­ La , Curie temperature; ­ temperature; , Curie C ­ T No seed (001) (111) YAG; (110) YAG; ​ (100) YAG c -sapphire Seed No seed BaTiO , piezoelectric charge constant; tan δ, dielectric, piezoelectric constant; loss; ­ charge 33 d 26 O 6 flm Si 3 3 O O 9.33 2 2 ​ Nd:YAG Formula Al Al LaFeAsO La BZT , dielectric ­ constant; T 3 , temperature of emergence of the spin-density of emergence wave; , temperature SDW (continued) ­ T temperature between rhombohedral and tetragonal phases; and tetragonal rhombohedral between temperature 1 Table Category in the reference not provided was the information that "–" denotes Sign K constant; k , growth Al-based oxides Other oxides efciency; Milisavljevic and Wu BMC Mat (2020) 2:2 Page 24 of 26

Abbreviations 12. Fornari R. Electronic materials and crystal growth. In: Fornari R, editor. AGG​: abnormal grain growth; BS–PMN–PT: BiScO3–Pb(Mg1/3Nb2/3)O3–PbTiO3; Single crystals of electronic materials: growth and properties. Cambridge: BZT: Ba(Zr,Ti)O3; CVT: chemical vapor transport; Cz: Czochralski method; Woodhead Publishing; 2019. p. 1–3. DC: direct current; KNN: KNaNbO3; KNN–BCuN: 0.985(K1/2Na1/2)NbO3– 13. Müller G, Friedrich J. Crystal growth, bulk: methods. In: Bassani G, Liedl 0.015Ba(Cu1/3Nb2/3)O3; LED: light-emitting diode; LKNNT: (Li0.04K0.44Na0.52) G, Wyder P, editors. Encyclopedia of condensed matter physics. Oxford: (Nb0.85Ta0.15)O3; NBT: (Na1/2Bi1/2)TiO3; NBT–BT: (Na1/2Bi1/2)TiO3–BaTiO3; NBT– Elsevier Ltd; 2005. p. 262–74. BT–KNN: (Na1/2Bi1/2)TiO3–BaTiO3–(K1/2Na1/2)NbO3; NGG: normal grain growth; 14. Carter CB, Norton MG. Growing single crystals. Ceramic materials. New PMN: Pb(Mg1/3Nb2/3)O3; PMN‒PT: Pb(Mg1/3Nb2/3)O3–PbTiO3; PMN‒PZT: York: Springer; 2007. p. 507–26. Pb(Mg1/3Nb2/3)O3–Pb(Zr,Ti)O3; PT: PbTiO3; PVT: physical vapor transport; PZ: 15. Dhanaraj G, Byrappa K, Prasad V, Dudley M. Springer handbook of crystal PbZrO3; PZT: Pb(Zr,Ti)O3; SAGG​: secondary abnormal grain growth; SEM: scan- growth. Berlin: Springer; 2010. ning electron microscope; SFSSCG: seed-free solid-state single crystal growth; 16. Dhanasekaran R. Growth of semiconductor single crystals from vapor SGG: stagnant grain growth; SPS: spark plasma sintering; SSCG: solid-state phase. In: Dhanaraj G, Byrappa K, Prasad V, Dudley M, editors. Springer single crystal growth; YAG:​ yttrium aluminum garnet. handbook of crystal growth. Berlin: Springer; 2010. p. 897–935. 17. Chen NK, Maddin R, Pond RB. Growth of molybdenum single crystals. Acknowledgements JOM. 1951;3:461–4. The authors gratefully acknowledge the NSF CAREER Grant (1554094) for 18. Hughes FL, Levinstein H, Kaplan R. Surface properties of etched tungsten funding this research. The authors also thank Professor Suk-Joong L. Kang from single crystals. Phys Rev. 1959;113(4):1023–8. Korea Advanced Institute of Science and Technology for his suggestions on 19. Bailey DJ, Brewer EG. Method for solid state growth of iron single crystals. this paper. U.S. Patent 3,694,269. 1972. 20. Matsuzawa S, Mase S. Method for producing a single crystal of ferrite. U.S. Authors’ contributions Patent 4,339,301. 1982. Both IM and YW discussed the review structures and wrote the paper. Both 21. Matsuzawa S, Mase S. Method for producing a single crystal. U.S. Patent authors read and approved the fnal manuscript. 4,402,787. 1983. 22. Hwang G-T, Yang J, Yang SH, Lee H-Y, Lee M, Park DY, et al. A reconfgur- Funding able rectifed fexible energy harvester via solid-state single crystal grown National Science Foundation (NSF). PMN–PZT. Adv Energy Mater. 2015;5:1500051. 23. Kang SJL, Park J-H, Ko S-Y, Lee H-Y. Solid-state conversion of single Availability of data and materials crystals: the principle and the state-of-the-art. J Am Ceram Soc. Not applicable. 2015;98(2):347–60. 24. Kang SJL, Ko S-Y, Moon S-Y. Mixed control of boundary migration Competing interests and the principle of microstructural evolution. J Ceram Soc Jpn. The authors declare that they have no competing interests. 2016;124(4):259–67. 25. Kang SJL. Sintering: densifcation, grain growth and microstructure. Received: 9 September 2019 Accepted: 6 January 2020 Oxford: Elsevier; 2005. 26. Fisher JG, Kang SJL. Strategies and practices for suppressing abnor- mal grain growth during liquid phase sintering. J Am Ceram Soc. 2018;102(2):717–35. 27. Kang SJL. Boundary structure-dependent grain growth behavior in References polycrystals: model and principle. Mater Sci Forum. 2013;753:377–82. 1. DeBarr AE. The applications of single crystals. Contemp Phys. 28. An S-M, Kang SJL. Boundary structural transition and grain growth behav- 1961;2(6):409–22. ior in ­BaTiO3 with ­Nd2O3 doping and oxygen partial pressure change. 2. Dutta PS. Bulk growth of crystals of III–V compound semiconductors. In: Acta Mater. 2011;59(5):1964–73. Bhattacharya P, Fornari R, Kamimura H, editors. Comprehensive semicon- 29. Jung Y-I, Choi S-Y, Kang SJL. Efect of oxygen partial pressure on grain ductor science and technology. Amsterdam: Elsevier Science; 2011. p. boundary structure and grain growth behavior in ­BaTiO3. Acta Mater. 36–80. 2006;54(10):2849–55. 3. Frank-Rotsch C, Dropka N, Rotsch P. III Arsenide. In: Fornari R, editor. 30. Jung SH, Kang SJL. Repetitive grain growth behavior with increasing Single crystals of electronic materials: growth and properties. Cambridge: temperature and grain boundary roughening in a model nickel system. Woodhead Publishing; 2019. p. 181–240. Acta Mater. 2014;69:283–91. 4. Kearns JK. Silicon single crystals. In: Fornari R, editor. Single crystals of 31. Moon K-S, Kang SJL. Coarsening behavior of round-edged cubic grains in electronic materials: growth and properties. Amsterdam: Elsevier Ltd; the ­Na1/2Bi1/2TiO3–BaTiO3 system. J Am Ceram Soc. 2008;91(10):3191–6. 2019. p. 5–56. 32. Kang SJL, Lee M-G, An S-M. Microstructural evolution during sin- 5. Tatartchenko VA. Sapphire crystal growth and applications. In: Capper tering with control of the interface structure. J Am Ceram Soc. P, editor. Bulk crystal growth of electronic, optical and optoelectronic 2009;92(7):1464–71. materials. West Sussex: Wiley; 2005. p. 299–338. 33. An S-M, Yoon B-K, Chung S-Y, Kang SJL. Nonlinear driving force–veloc- 6. Huber G, Kränkel C, Petermann K. Solid-state lasers: status and future. J ity relationship for the migration of faceted boundaries. Acta Mater. Opt Soc Am B. 2010;27(11):B93–105. 2012;60(11):4531–9. 7. Délen X, Piehler S, Didierjean J, Aubry N, Graf T, Balembois F, et al. 250 W 34. Kang SJL. Liquid phase sintering. In: Fang ZZ, editor. Sintering of single-crystal fber Yb:YAG laser. Opt Lett. 2012;37(14):2898–900. advanced materials. Cambridge: Woodhead Publishing Ltd.; 2010. p. 8. Oh H-T, Lee J-Y, Lee H-Y. Mn-modifed PMN–PZT [Pb(Mg1/3Nb2/3)O3–Pb(Zr, 110–29. Ti)O3] single crystals for high power piezoelectric transducers. J Korean 35. Lee M-G, An S-M, Jung S-H, Kang SJL. Migration enhancement of faceted Ceram Soc. 2017;54(2):150–7. boundaries by dislocation. J Asian Ceram Soc. 2013;1(1):95–101. 9. Oh H-T, Joo H-J, Kim M-C, Lee H-Y. Thickness-dependent properties of 36. Kang SJL, Jung Y-I, Jung S-H, Fisher JG. Interface structure-dependent undoped and Mn-doped (001) PMN-29PT [Pb(Mg1/3Nb2/3)O3–29PbTiO3] grain growth behavior in polycrystals. In: Molodov DA, editor. Microstruc- single crystals. J Korean Ceram Soc. 2018;55(3):290–8. tural design of advanced engineering materials. Weinheim: Wiley; 2013. p. 10. Herman MA, Richter W, Sitter H. Epitaxy: physical principles and technical 299–322. implementation. Berlin: Springer; 2004. 37. Jung Y-I, Choi S-Y, Kang SJL. Grain-growth behavior during stepwise 11. Brune H. Epitaxial growth of thin flms. In: Wandelt K, editor. Surface and sintering of barium titanate in hydrogen gas and air. J Am Ceram Soc. interface science: solid–solid interfaces and thin flms. New York: Wiley; 2003;86(12):2228–30. 2014. p. 421–91. 38. Lee B-K, Chung S-Y, Kang SJL. Control of {111} twin formation and abnor- mal grain growth in ­BaTiO3. Met Mater Int. 2000;6(4):301–4. Milisavljevic and Wu BMC Mat (2020) 2:2 Page 25 of 26

39. Fisher JG, Choi S-Y, Kang SJL. Abnormal grain growth in barium titanate 60. Song J, Hao C, Yan Y, Zhang J, Li L, Jiang M. Enhanced piezoelectric doped with alumina. J Am Ceram Soc. 2006;89(7):2206–12. property and microstructure of large CaZrO­ 3-doped ­Na0.5K0.5NbO3-based 40. Jung S-H, Kan SJL. An explanation for the formation of polyhedral abnor- single crystal with 20 mm over. Mater Lett. 2017;204:19–22. mal grains in single-phase systems. Scr Mater. 2014;82:49–52. 61. Hao CY, Gu ZF, Cheng G, Li L, Zhang JW, Song JG, et al. Composition 41. Jiang M, Han S, Zhang J, Song J, Hao C, Deng M, et al. Large-scale grain design and electrical property of a pure ­KxNa1 xNbO3 single crystal growth in the solid-state process: from ‘‘abnormal” to ‘‘normal”. J Cryst fabricated by the seed-free solid-state crystal growth.− J Mater Sci: Mater Growth. 2018;483:258–64. Electron. 2017;28(24):18357–65. 42. Ikesue A, Aung YL, Yoda T, Nakayama S, Kamimura T. Fabrication and 62. Rahman A, Cho K-H, Ahn C-W, Ryu J, Choi J-J, Kim J-W, et al. A composi- laser performance of polycrystal and single crystal Nd:YAG by advanced tion design rule for crystal growth of centimeter scale by normal sinter- ceramic processing. Opt Mater. 2007;29(10):1289–94. ing process in modifed potassium sodium niobate ceramics. J Eur Ceram 43. Li T, Scotch AM, Chan HM, Harmer MP. Single crystals of Pb(Mg1/3Nb2/3) Soc. 2018;38(4):1416–20. O3–35 mol% PbTiO­ 3 from polycrystalline precursors. J Am Ceram Soc. 63. Park J-H, Lee H-Y, Kang SJL. Solid-state conversion of ­(Na1/2Bi1/2)TiO3– 1998;81(1):244–8. BaTiO3–(K1/2Na1/2)NbO3 single crystals and their piezoelectric properties. 44. Khan A, Meschke FA, Li T, Scotch AM, Chan HM, Harmer MP. Growth Appl Phys Lett. 2014;104(22):222910. of Pb(Mg Nb )O –35 mol% PbTiO­ single crystals from (111) 64. Park J-H, Kang SJL. Solid-state conversion of (94 x)(Na Bi )TiO – 1/3 2/3 3 3 − 1/2 1/2 3 substrates by seeded polycrystal conversion. J Am Ceram Soc. 6BaTiO3 x(K1/2Na1/2)NbO3 single crystals and their enhanced converse 1999;82(11):2958–62. piezoelectric− properties. AIP Adv. 2016;6(1):015310. 45. King PT, Gorzkowski EP, Scotch AM, Rockosi DJ, Chan HM, Harmer 65. Ko S-Y, Park J-H, Kim I-W, Won S-S, Chung S-Y, Kang SJL. MP. Kinetics of {001} Pb(Mg1/3Nb2/3)O3–35 mol% ­PbTiO3 single Improved solid-state conversion and piezoelectric properties of crystals grown by seeded polycrystal conversion. J Am Ceram Soc. ­90Na1/2Bi1/2TiO3–5BaTiO3–5K1/2Na1/2NbO3 single crystals. J Eur Ceram Soc. 2003;86(12):2182–7. 2017;37(1):407–11. 46. Oh H-T, Joo H-J, Kim M-C, Lee H-Y. Efect of Mn on dielectric and piezo- 66. Moon KS, Rout D, Lee HY, Kang SJL. Solid state growth of Na­ 1/2Bi1/2TiO3– electric properties of 71PMN-29PT [71Pb(Mg1/3Nb2/3)O3–29PbTiO3] BaTiO3 single crystals and their enhanced piezoelectric properties. J Cryst single crystals and polycrystalline ceramics. J Korean Ceram Soc. Growth. 2011;317(1):28–31. 2018;55(2):166–73. 67. Gürbüz M, Ayas E, Dogan A. Sintering of ­94Na0.5Bi0.5TiO3–6BaTiO3 with 47. Lee H-Y. Development of high-performance piezoelectric single SPS and conventional methods for crystal growth. J Ceram Process Res. crystals by using solid-state single crystal growth (SSCG) method. In: 2016;17(1):36–40. Ye Z-G, editor. Handbook of advanced dielectric, piezoelectric and fer- 68. Lee D, Vu H, Sun H, Pham TL, Nguyen DT, Lee J-S, et al. Growth of roelectric materials: synthesis, properties and applications. Cambridge: ­(Na0.5Bi0.5)TiO3–SrTiO3 single crystals by solid state crystal growth. Ceram Woodhead Publishing Ltd.; 2008. p. 158–72. Int. 2016;42(16):18894–901. 48. Lee H-Y. Technical report on “development of n- and p-type doped 69. Le PG, Jo G-Y, Ko S-Y, Fisher JG. The efect of sintering temperature and perovskite single crystals”. Air Force Research Laboratory—AF Ofce of time on the growth of single crystals of 0.75 (Na­ 0.5Bi0.5)TiO3–0.25 ­SrTiO3 Scientifc Research (AFOSR)/IOA; 2017. by solid state crystal growth. J Electroceramics. 2018;40(2):122–37. 49. Lim JB, Zhang S, Lee H-Y, Shrout TR. Solid state crystal growth of 70. Sun H, Fisher JG, Moon S-H, Tran HT, Lee J-S, Han H-S, et al. Solid-state- ­BiScO3–Pb(Mg1/3Nb2/3)O3–PbTiO3. J Electroceram. 2012;29(2):139–43. growth of lead-free piezoelectric (Na­ 1/2Bi1/2)TiO3–CaTiO3 single crystals 50. Zhang S, Lee S-M, Kim D-H, Lee H-Y, Shroutz TR. Electromechanical and their characterization. Mater Sci Eng B. 2017;223:109–19. properties of PMN–PZT piezoelectric single crystals near morphotropic 71. Yamamoto T, Sakuma T. Fabrication of barium titanate single crystals by phase boundary compositions. J Am Ceram Soc. 2007;90(12):3859–62. solid-state grain growth. J Am Ceram Soc. 1994;77(4):1107–9. 51. Uwiragiye E, Farooq MU, Moon S-H, Pham TL, Nguyen DT, Lee J-S, et al. 72. Yoo Y-S, Kang M-K, Han J-H, Kim H, Kim D-Y. Fabrication of BaTiO, single High performance lead-free piezoelectric 0.96(K048Na052)NbO3–0.03[Bi crystals by using the exaggerated grain growth method. J Eur Ceram Soc. 0.5(Na07K0.2Li0.1)0.5]ZrO3–0.01(Bi0.5Na0.5)TiO3 single crystals grown by 1997;17(14):1725–7. solid state crystal growth and their phase relations. J Eur Ceram Soc. 73. Yoo Y-S, Kim H, Kim D-Y. Efect of ­SiO2 and ­TiO2 addition on the exagger- 2017;37(15):4597–607. ated grain growth of BaTiO­ 3. J Eur Ceram Soc. 1997;17(6):805–11. 52. Fisher JG, Bencan A, Kosec M. Growth of dense single crystals of potas- 74. Lee H-Y, Kim J-S, Hwang N-M, Kim D-Y. Efect of sintering temperature sium sodium niobate by a combination of solid-state crystal growth on the secondary abnormal grain growth of BaTiO­ 3. J Eur Ceram Soc. and hot pressing. J Am Ceram Soc. 2008;91(5):1503–7. 2000;20(6):731–7. 53. Benčan A, Tchernychova E, Uršič H, Kosec M, Fisher J. Growth and 75. Kang BS, Choi SK. Difuse dielectric anomaly of BaTiO­ 3 in the temperature characterization of single crystals of potassium sodium niobate by range of 400–700 °C. Solid State Commun. 2002;121(8):441–6. solid state crystal growth. In: Lallart M, editor. Ferroelectrics—material 76. Kang BS, Choi SK, Park CH. Difuse dielectric anomaly in perovskite-type aspects. Rijeka: InTech; 2011. p. 87–108. ferroelectric oxides in the temperature range of 400–700 °C. J Appl Phys. 54. Yang J, Yanga Q, Lia Y, Liuc Y. Growth mechanism and enhanced electri- 2003;94:1904. cal properties of ­K0.5Na0.5NbO3-based lead-free piezoelectric single 77. Lee J-Y, Oh H-T, Lee H-Y. Dielectric and piezoelectric properties of “lead- crystals grown by a solid-state crystal growth method. J Eur Ceram Soc. free” piezoelectric rhombohedral Ba(Ti0.92Zr0.08)O3 single crystals. J Korean 2016;36(3):541–50. Ceram Soc. 2016;53(2):171–7. 55. Zhen Y, Li J-F. Abnormal grain growth and new core-shell structure in 78. Wei GC, Rhodes WH. Sintering of translucent alumina in a nitrogen- (K, Na)NbO3-based lead-free piezoelectric ceramics. J Am Ceram Soc. hydrogen gas atmosphere. J Am Ceram Soc. 2000;83(7):1641–8. 2007;90(11):3496–502. 79. Park CW, Yoo DY. Efects of ­SiO2, ­CaO2, and MgO additions on the grain 56. Wang C, Hou Y-D, Ge H-Y, Zhu M-K, Yan H. Growth of ­(Na0.5K0.5)NbO3 growth of alumina. J Am Ceram Soc. 2000;83(10):2605–9. single crystals by abnormal grain growth method from special shaped 80. Scott C, Kaliszewski M, Greskovich C, Levinson L. Conversion of polycrys- nano-powders. J Eur Ceram Soc. 2010;30(7):1725–30. talline ­Al2O3 into single-crystal sapphire by abnormal grain growth. J Am 57. Jiang M, Randall CA, Guo H, Rao G, Tu R, Gu Z, et al. Seed-free solid- Ceram Soc. 2002;85(5):1275–80. state growth of large lead-free piezoelectric single crystals: (Na­ 1/2K1/2) 81. Thompson GS, Henderson PA, Harmer MP. Conversion of polycrystalline NbO3. J Am Ceram Soc. 2015;98(10):2988–96. alumina to single-crystal sapphire by localized codoping with silica. J Am 58. Ahn C-W, Lee H-Y, Han G, Zhang S, Choi S-Y, Choi J-J, et al. Self-growth Ceram Soc. 2004;87(10):1879–82. of centimeter-scale single crystals by normal sintering process in 82. Dillon SJ, Harmer MP. Mechanism of ‘‘solid-state’’ single-crystal conversion modifed potassium sodium niobate ceramics. Sci Rep. 2015;5:17656. in alumina. J Am Ceram Soc. 2007;90(3):993–5. 59. Yang J, Zhang F, Yang Q, Liu Z, Li Y, Liu Y, et al. Large piezoelec- 83. Dillon SJ, Harmer MP. Multiple grain boundary transitions in ceramics: a tric properties in KNN-based lead-free single crystals grown by case study of alumina. Acta Mater. 2007;55(15):5247–54. a seed-free solid-state crystal growth method. Appl Phys Lett. 84. Dillon SJ, Harmer MP. Relating grain-boundary complexion to 2016;108(18):182904. grain-boundary kinetics I: calcia-doped alumina. J Am Ceram Soc. 2008;91(7):2304–13. Milisavljevic and Wu BMC Mat (2020) 2:2 Page 26 of 26

85. Dillon SJ, Harmer MP. Relating grain boundary complexion to 93. Kappenberger R, Aswartham S, Scaravaggi F, Blum CGF, Sturza MI, Wolter grain boundary kinetics II: silica-doped alumina. J Am Ceram Soc. AUB, et al. Solid state single crystal growth of three-dimensional faceted 2008;91(7):2314–20. LaFeAsO crystals. J Cryst Growth. 2018;483:9–15. 86. Dutta S, Kim TB, Krentz T, Vinci RP, Chan HM. Sol–Gel-derived single- 94. Tanji S, Matsuzawa S, Wakatsuki N, Soejima S. A magnetic head of Mn–Zn crystal alumina coatings with vermicular structure. J Am Ceram Soc. ferrite single crystal produced by solid–solid reaction. IEEE Trans Magn. 2011;94(2):340–3. 1985;21(5):1542–4. 87. Park H, Chan HM. A novel process for the generation of pristine sapphire 95. Hirota K, Satomi M, Matsuyama K, Kugimiya K. The solid state single surfaces. Thin Solid Films. 2002;422(1–2):135–40. crystal growth from Mn–Zn ferrite polycrystal with additives. Mater Res 88. Browne D, Li H, Giorgi E, Dutta S, Biser J, Vinci RP, et al. Templated epitaxial Bull. 1990;25(12):1453–9. coatings on magnesium aluminate spinel using the sol-gel method. J 96. Liu Y, Li Y, Wu Y. Low-temperature crystal growth of Yb:Sr5F(PO4)3 without Mater Sci. 2009;44(5):1180–6. evident thermal runaway. J Am Ceram Soc. 2017;100(6):2402–6. 89. Bagayev SN, Kaminskii AA, Kopylov YL, Kotelyanskii IM, Kravchenko VB, 97. Liu Y, Wu Y. Electric feld-enhanced solid-state conversion of ceramic Luzanov VA. Single crystal growth in YAG ceramics of diferent stoichiom- ­Sr5(PO4)3F to crystals. J Am Ceram Soc. 2016;99(11):3561–8. etry. Opt Mater. 2013;35(4):757–60. 98. Chen K, Jiao Y, Zhao Y, Gao Y, Zhang X, An L. Non-contact electric feld- 90. Nakayama S, Ikesue A, Higuchi Y, Sugawara M, Sakamoto M. Growth enhanced abnormal grain growth in ­(K0.5Na0.5)NbO3 ceramics. Ceram Int. of single-crystals of apatite-type oxide ionic conductor from sintered 2017;43(15):12343–7. ceramics by a seeding method. J Eur Ceram Soc. 2013;33(2):207–10. 91. Nakayama S, Sakamoto M. Preparation of apatite-type ­La9.33Ge6O26 single-crystal from sintered ceramics by a seeding method and its oxide Publisher’s Note ionic conduction. Solid State Ion. 2013;253:47–52. Springer Nature remains neutral with regard to jurisdictional claims in pub- 92. Fisher JG, Sun H, Kook Y-G, Kim J-S, Le PG. Growth of single crys- lished maps and institutional afliations. tals of ­BaFe12O19 by solid state crystal growth. J Magn Magn Mater. 2016;416:384–90.

Ready to submit your research ? Choose BMC and benefit from:

• fast, convenient online submission • thorough peer review by experienced researchers in your field • rapid publication on acceptance • support for research data, including large and complex data types • gold Open Access which fosters wider collaboration and increased citations • maximum visibility for your research: over 100M website views per year

At BMC, research is always in progress.

Learn more biomedcentral.com/submissions