Xtl Growth

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REV IMS

Chemistry and Crystal GrowthJ iirg Hulliger

Dedicated to Professor H ams Thomas Arend on the occasionof his 70th birthduy

Single-crystal materials, along withother formsof condensed matter (ceram-ics, polymers, liquid crystals, etc.) arefundamental to modern technology. Thebasic research and production of newmaterials with tailored solid-statephysical properties therefore necessitatenot only chemical synthesis but also theproduction of single crystalsof a partic-

ular morphology (either bulk or thinlayer crystals) and well-defined crystaldefects (doping). In this review, an at-tempt is made to broaden the traditionalsynthetic concept of chemistry to theprocess of single-crystal synthesis. Themethods of the resulting approach,which takes into account the specificproperties of solid materials, are dis-

cussed and illustrated by experimentalset-ups for the solution of a range ofproblems in chemical crystallization.Also included is recent work on thegrowing of single crystals of high-tem-perature superconductors, organic non-linear optical compounds, and proteins.

1. IntroductionSolve et Coagula!]

1.1. Chemistry and Crystal Growth: The Evolution andSignificanceof CrystallizationThe endeavor to transform liquid and gaseous substances intothe solid, pure state, thereby immobilizing them (coagulation),permeates the wholeof chemistry, from the early uncertain at-tempts of the alchemists[.21to present day methods of purifica-tion and crystal growth (Fig. ) . [ 3 9 4 1 Coagulation, in the modernsense, means the bonding of atoms, ions, and molecules to formsupramolecular solid-state structures.[51 Therefore, the forma-tion of crystal nuclei of molecular substances would seem to bean ideal case of molecular self-organization,[61n which the gen-eration of a multiplicity of system-determined morphologicalforms can be interpreted, for example, within the framework ofpattern formation theory.[]In the courseof the development of chemistry, chemists havebeen primarily concerned with the synthesis of low molecularweight and macromolecular substances and the building upofextended solid-state structures, basically by molecular accre-tion. This led to the fact that crystal nucleation and growth

[*] Prof. Dr. J. HulligerEidgenossische Technische HochschuleInstitut fur Qudntenelektmn;kNew address:lnstitut fur anorganische, analytische und physikalische Chemie der UniversitdtFreiestrdsse 3, CH-3012 Bern (Switzerland)Telefax: Int. code +(31) 631-3993

...remained virtual areasof darkness on the map of the chemicalknowledge.] Somewhat belatedly, great interest in supra-molecular chemistry became apparent very recently. This hasbeen strongly motivated, for example, by the development offunctional solid materials (for molecular electronics,[91 or sen-sors,[lol and for applications based on their mechanical andother properties[]). Traditionally, however, the physical prop-erties of single-crystal materials (e.g., cooperative phenomenasuch as magnetism,[2] ferroelectricity,[31 or superconduc-tivity,[I4]etc) did not occupy the center of interest. In this con-text Luttringhaus The more chemistry ex-panded, the more the chemist concerned himself with chemicalreactions, and the less with the state of his substances. I n partic-ular, he entrusted the study of crystals to crystallographers orstructural physicists.When the anisotropy of physical phenomena in single crystalswas discovered, the peculiarities of their physical properties,however, became a topic of physics. The Neumann Principleenabled an increasing number of properties represented by ten-sors to be qualitatively classified by point symmetry groups.[l61The direction of solid-state physics had been pointed towardsthe high tech age by important discoveries including the tech-nologies of high frequencies, semiconductors, magnetic storage,and lasers, and by the physics of solid phases characterged bynonlinear properties. This could not have been contemplatedwithout experiments with increasingly complex single crystals.The necessary crystal growth technique had taken its place inthe fied of crystal physics alongside crystallography and exper-imental mineralogy.Significantly, the above passage can be found in the introduc-tion to general laboratory practice (crystallization) in Volume1of the textbook Methoden der Organischen Chemie (Houben-

Angen. Chem. Int. Ed. E nd 1994, 33. 143-162 0 VC H Verl agsgesel l schaf t mbH. 0-69451 Wei nhei m1994 0570-0833/94jO202-0l43 10.00+,2510 143


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REVIEWS J. Hulligerture.[I7- Nevertheless, crystallization, in the conventionalchemical sense, is merely a useful laboratory technique eventoday, whereas crystal growth in the true sense, that is, thescience of producing large single crystals for a particular pur-pose, is a topic mainly found in the fieldof physics research. Aglance at the many general chemistry textbooks available todayreinforces this impression (Scheme1).On average, the subjectof

Scheme1. References to crystal growth in chemical textbooks: 60 recent generaltextbooks of organic, inorganic, and physical chemistry were searched for referencesto crystallization, recrystallization, and crystal growth (191. The histogram showsthe frequency of these references. S =number of pages on crystallization (K);n =number of books: out of approximately 43000 pages, about 50 pages coveredthis theme ( cK % 0.12%). If the cy value is compared with the corresponding valueof 50 oldorganicchemistry textbooks, the value of cK today is considerably smaller.

crystallization forms only about 0.1% of the total.[g1 Themajority of current chemistry textbooks do not describe it at all,nor do they describe the solid-state properties of the interestingtypesof materials mentioned above. (The review of well-knownchemical journals (1968- 1991) gives a similar picture.) Com-pared with textbooks written 20-40 years ago, the relativeamount of space devoted to the special science of crystallizationhas clearlv decreased. One can onlv assume that the situationFig. 1. Crystallization in the course of time. Top: Salt production in the Middle

Ages [2c]: evaporation and crystall ization of vitriol; bottom: Advanced crystalgrowth of large, highly pure crystals of KH,PO, for optical frequency doubling [4].

with respect to chemistry be improved;how-ever, in a recent summary of views on the themeIsEverythingO.K. with Solid-state Chemistry?[zo1 t is stated: .. thereis no textbook on solid-state chemistry adequate for modern

We~l);[ ~]rystallization had not become a theme of modern science...,[z01and the reviewer summarizes the results of anchemistry. Obviously, crystallization processes have always opinion poll involving50 specialists in solid-state chemistry:played an important role in chemistry, and crystallization has I t is high time to recognize that besides classical chemistry,been exhaustively described in the older chemical litera- which deals with individual molecules and atoms or ions,

J urg Hulliger was born in 1953 in Zurich. He studied chemistry at the E TH , Zurich, andgraduated in physical chemistry. H e took his Doctorate at the anorganisch-chemisches Institutder Universitat Zurich under Prof. J . H. Ammeter. After spending a year at the PennsylvaniaState University, he succeeded Prof. H . Arend at the E TH , Zurich, at the Institut f ur Fest-korperphysik (later Quantenelektronik). There, between 1987 and 1993, he led a group work-ingoncrystalgrowth. In 1993, he accepted the offer of a Professorship at the Institut ur anor-ganische, analytische und physikalische Chemie der Universitat Bern. H is research fields are:chemistry, crystal growth, andphysical properties of inorganic and organic solid materials, andthe development of special methodsfor the synthesis of crystals and for the in situ characteriza-tion of crystal growth.

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REVIEWSrystal Growththere exists chemistry where chemical transformation has acollective character. This chemistry cannot be equated withclassical chemistry nor extrapolated from it.t201In the case of solid-state chemistry, the collective character ofthe process which leads to the formation of complex solids isstressed, but, even in this connection, the general importance ofprocesses and mechanisms of crystal growth and their charac-terization by instrumental analysis have not been mentioned.

Wehave to say, with no exaggeration: solid-state properties (asconsidered by physics) in association with crystal growth (syn-thesis of single crystals-as distinct from molecular synthesisorthe usual kind of synthesis of solid materials) has not been theconcern of chemistry, or has only been on the fringe.On the other hand, how are developments progressing in thefield of materials research (see, for example, the recently found-ed (1988) ournal Advanced M aterials, VCH, orpapers in I ssuesand Opportunities i n Materials Research[ ]) whose success de-pends to a large extent on the contribution from chemical syn-thesis? The concept of crystal engineering was given an identityafter 1945 by von Hippel,rzzland in its further development(Hahn,Iz31 Kitaigorod~ki ,~~~]rend,[25] Willet,[z61F. Hul-liger,[] Kaldis,[z81 eiserowitz et al.,[291Schmidt,[301McBrideet a1.,[311Desiraj~,[~I tter,[331 agan et a1.,[61etc.) is to be re-garded as a solid-state analogue of molecular engineering, thewell-known system of synthesis. One of the great challenges ofmodern chemistry thus concerns the reinforcing of ways ofthinking about supramolecular structures and developing meth-ods for their construction, in particular the synthesis of single-crystal materials with tailored physical properties (see Tablesin refs. [3, 341).In this context, a new topochemical subject known asnanochemi~try~~~]eserves special attention (see, for example,O~i n[ ~~] ) .hus, a series of methods of extremely wide applica-tion are available to the modern grower of crystals, enabling thetargeted construction of solid-state structuresormolecular syn-theses, impossible by the classical route. These include (in addi-tion to the possibilities discussed by O ~i n, [ ~~]nd the fullerenesyntheses) molecular beam epitaxy (MBE),[3 metal-organicchemical vapor deposition (MOCVD), chemical beam epitaxy(CBE)[381 VD, or plasma-assisted deposition techniques, theLangmuir-Blodgett process,t391and special applications oftopochemi~try.[~~~here is also an analogy between the mecha-nistic concepts of molecular synthesis and controlled crystalliza-tion. Kahr et al.t311, or example, have compared the productionof true growth locations of a crystal nucleus with the startingpoint of a radical chain reaction (see Section2.1). The termchemospecificity in crystallization corresponds to the selectivechoice of a particular guest molecule, regiospecificity is shownby alteration of crystal habit, and stereospecificity in the spatialdistribution of crystal defects.Modern achievements in synthetic chemistry such as super-conducting oxides,[411magnetically-ordered organicor organo-metallic compounds,[4z1ullerenes and their andorganic, strongly nonlinear, optical compounds[441areof inter-est for their distinctive solid-state physical properties. The de-tailed investigation of these subjects requires well-defined singlecrystals, and, increasingly, also epitaxial thin films. In general,a detailed investigation of the physical properties of a new sub-stance discovered by classical synthesis is only possible after

single-crystal samples of known real structure have been pre-pared. Single crystals, epitaxial thin films, and fibers made froman increasingly large number of different compounds are todayundeniably a part of the fundamental research into materialscience and technology. Here, where success largely depends onan interdisciplinary method of thought and work, the elucida-tion of complex plans of materials research requires the inter-linking of chemistry and physics. The modern science of crystalgrowth is active in the promising areas in which chemistry andphysics overlap, that is, where growth processes are investigat-ed, and special methods for producing solid single crystals, epi-taxial layers, and fibers with tailored properties are developed.To quote but one example: Materials are really the key tonew solid-state lasers (Chai).[451 ollowing the first phase ofdevelopment of solid-state lasers in the1960sand 1970s, a morevigorous search for other matrix lattices has recently been start-ed,[461which, along with high power short wavelength semicon-ductor laser diodes, has the main aim of producing tunable lightsources and up-conversion systems.[471 his involves, for ex-ample, the crystal growth of fluorides (LiYF,, KYF,, etc.) andoxides (silicates, garnets, etc.) as well as fluoride glasses.[481From todays viewpoint, the basic question for chemists is towhat extent chemistry should integrate solid-state propertiesand single-crystal synthesis as one of its new leitmotifs intoresearch and teaching in the future.Single crystals play a decisive role not only in the context ofcomplex materials research. Single-crystal X-ray structuralanalysis still represents the definitive proof of structure for thechemist. The discussion of molecular and other properties de-pends upon it, especially for a comparison with structures calcu-lated from quantum chemistry.Based on this outline, two subjects are dealt with in the fol-lowing sections: 1)an introductory description for the chemistof the basic principles of crystallization and crystal growth fromthe modern viewpoint (see especially refs. [3, 34, 49]), and 2) apractical discussion of methods which can contribute to pro-gress in mass crystallization (on the laboratory scale), or theproduction of small single crystals (for structural investiga-tions), and the preparation of larger single crystals (for the in-vestigation of the physics of the solid state).

1.2. From Crystallizationto SingleCrystal GrowthCrystallization is one of the most perfect

purijication operations ...I blI n practice, crystallization was, for organic chemistry, one ofthe most effective methods of purifying substances for a longtime, especially for the separation of enantiomers (resolutionofracemates). With the development of chromatography andother methods of separation (including chiral stationaryphases), crystallization itself lost some importance as a labora-tory technique, which must be the main reason why it is nottreated at all in the newer textbooks of general chemistry, oratleast only briefly, although methods for the preparation of smallsingle crystals or polycrystalline materials, mainly for completecrystal structure analysis by X-rayorneutron diffraction, have

remained in use.Anpew. Ckem. I n r . Ed. Engl . 1994. 33, 143-162 145


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REVIEWS J. HulligerThe special techniques summarized in Scheme 2, for whichcrystallization processes were developed or used, have attainedimportance in chemical research and technology. Industrialcrystallization is undoubtedly most important.[501Because of

1. Industrial crystall ization [ 50- 53]Salesof a) polycrystalline bulk materials in which each product is estimated toexceed lo6t per year, for example, NaCI, urea, sugar, or zeolite Linde A withlo5 per year [54]; b) single-crystal production of elements (e.g., Si with nodislocations: lo4 t per year) 1551and compounds (e.g., cubic stabilized ZrO,:300 t per year) [56](about 8000new crystal structures per year)and natural products

2. Determination of structures of crystals and molecules3. Separation, purification, and purity determinationof fine chemicals, pigments,4. Racemate separation and determinationof absolute configurations [29,5715. Crystallization of macromolecular substances (proteins, polymers) [58, 5916. Measurement of physical properties by spectroscopic and other physical

methods7. Biocrystall ization (also in the medical field: osteoporosis (see ref. [3]: kidneystones and gall stones)) [60]8. Synthesis under topochemical control [40, 611(e.g., cracking catalysts based on zeolites [54])

Scheme2. Areas where crystallization processes are important in chemical researchand technology.

the necessity for quality control of bulk production, as wel asa technically feasible user-friendly crystal morphology[51s2 1and defined particle size distribution of agglomerates,[531 heprocess control system must be based on extensive knowledge ofthe mechanisms of nucleation and growth for a given hydro-dynamic regime and set of surface-active agents (crystal habitmodifiers[621). In the industrial production of mainly largesingle crystals with defined real structure, extremely pure start-ing materials are required on the one hand, and veryclosely controlled crystal growth technology on the other( ~ i ~ ,),[2.4.55.631

Fig. 2. Special technology (edge-defined film-fedgrowth) for the economic production of siliconsolar cells. Eight- or nine-sided thin-walled singlecrystals, several meters long, are obtained from themolten material by crystal pulling [63].

In the laboratory, the elucidation of structure has had to takesecond place in view of the demand for small single crystals(linear dimensionsd less than one mm); about8000new crystalstructures per year currently result either from the purificationof various compounds or the separation of racemates. As amore detailed discussion of all recent relevant fields would gofar beyond the scope of this article, the reader is referred to therecent literature on this subject in some cases.To recapitulate, most types of chemical crystallization can bedivided into three classes, which differ in the method used:a) large-scale production of small crystals, b) crystallization ofindividual single crystals (dless than one mm), and c) growth ofsingle crystals (1mm5 d 51 m). As modern materials researchand crystal growth are oriented towards the same stages of the

processes, this classification will be used for the planning ofSection 3. That is to say, for newly synthesized compounds, thedesired solid-state properties are at first investigated with poly-crystalline (for example, ceramic) and small single-crystalsamples, and are then optimized (see Scheme 3) by developingspecific methods of crystal growth (bulk, thin film, and fibersingle crystals). From the viewpoint of materials research, theusual synthetic methods at this point give way to methods ofsingle-crystal growth to achieve the desired solid-state proper-ties.

applicat ionof chemistryto thestudyof materials

determination

applicat ionsScheme3. Chemistry and crystal growth: interlinkingof the processes in materialsscience including single-crystal synthesis.

In view of the continually increasing number of initially poor-ly characterized compounds, the question of simple but effectivestrategies of crystallization arises. A cost estimate (man-yearsinvestments) based on response theory (Tiller, 1991)[491shows that the implementation of the black box assumption(a current view of crystal growth!) leads to an art-based tech-nology (crystal growth=a collection of recipes) based on themultidimensional parameter spacej +k, wherej =the numberof materials and k =the number of experimental parameters,whereas a system approach, which always presupposes somesort of prestructuring clustering, leads to a science-basedtechnology (strategies for proceeding with a minimum of ex-periments). A proposed plan for an intelligently organized labo-ratory crystallization process is discussed from a practical pointof view in Sections3.2 and 3.3. This contains the exploratorymethods of crystallization and the advanced methods ofsingle-crystal growth.All methods must be termed exploratory when they syste-matically use a phenomenological approach with a minimum ofexperimental work, for example, by the deliberate use of self-regulating mechanisms. In many cases, crystals produced in afirst stage are used as nuclei in a second stage of advancedcrystal growth. The so-called temperature-difference method ofsolution growth (see Section 3.2) should be regarded as a simpleexample of a science-based technology. Here it should bementioned that H. T. Arend contributed greatly to the researchand development work on exploratory strategies of crystalliza-tion during the course of his activity as a crystal grower at theEidgenossische Technische Hochschule (ETH), Zurich.In the future, the electronic storage and handling of dataconcerning methods and materials should provide the chemist

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REVIEWSrystal Growthwith a database, in which the knowledge about crystallization isstored (computer knowledge base for ~rystallization[~~]).first attempt at this has been in existence since 1990,[641and it isto be hoped that its usefulness and shortcomings will becomeapparent through continual use. However, data systems willcertainly not be able to replace the specialist in the foreseeablefuture. If a problem is too difficult for the crystal growth expertto solve, existing electronic strategies will also fail. The expertthen falls back on his intuition and far more wide backgroundknowledge.[641 There is another electronic data bank thatstores information on the crystallization of biological macro-molecule~.[ ~~~his contains data on more than 1000 crystallineforms of over 600 biological macromolecules. The use of thiswhen attempting systematic protein crystallization (e.g. suc-cessive automated grid searches) is discussed by Weber.LS8]

In addition to the electronic media, it should not be forgottenthat a rich experienceof the solution of crystallization problemsexists, for example, in the older organic chemical literature. Thiscan now be extended in a methodical manner. 9 18]

This article hasso far been aimed at throwing some light onthe significanceof crystallization in chemistry, and preparingthe reader for the specific nature of the later part of the discus-sion which describes experiments in modern crystal growth. Af-ter a general outline of the theory (Section 2), a very practicallyoriented systematic approach is set out in Section 3. In Sec-tion 4, the crystal growth of three classes of materials of topicalinterest is briefly discussed.

2. Fundamentalsof Crystal Growth2.1. Energetics and K inetics of Nucleationand Volume Growth

A crystal is nothing but a large molecule.Van Vleck[661Crystallization leads to the buildup of supraatomic and

supramolecular ordered states, whose microscopic real structureand macroscopic morphology are determined by energetic,kinetic, and transport (mass and heat) mechanisms; thus,lattice components are attached. This means that, as a nonequi-librium process of a heterogeneous system (AG(N -+C)=G, - G, Tequilibrium),he struc-ture-forming self-organization of the components (Fig.3) takesplace in the supercooled or supersaturated state in severalstages,t871eading to a reaction principle (with a part played bymolecular recognition mechanisms) whose elementary steps, in-finitely repeated, lead to themacromolecular crystal. Homo-geneous nucleation and crystal growth can be described in anal-ogy to chemical reactions according to Scheme 4.t4996a] As anillustration of stepwise buildup by nucleation, Figure 3 showsstructures calculated from quantum mechanics of associates andclusters (Na+(NaCI),) up to the formation of a first NaClordered structureof a unit cell (gasIn the classical capillary approximation, the transition ofsmall molecular agglomerates to clusters (C) of increasing sizeleads to the formation of a phase boundary surface (outer sur-face), for which the cluster formation energy AGc consists of avolume and surface area term. For a nucleus. assumed to be

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REVIEWSd

Fig. 3. Quantum-mechanical calculation of the stepwise development of structuresleading to the formation of an NaCl lattice cell structure (from ref. [87a] withadditions from the author). a) Small aggregates; b) cluster formation; c) transitionto an NaCl lattice structure unit; d) first unit cell.

spherical, in solution, AG,[531 is described by Equation (a),where the cluster radius r* [Eq. (b)] represents the critical size,and AG,* [Eq. (c)] represents the activation energy to overcomethe critical size of the nucleus. The molar volume of the clusteris represented by v; IJ =( X-XJ X, represents the relative su-persaturation,[] X, represents the equil ibri um concentration, yrepresents the interface surface energy per unit area, and k, isthe Boltzmann constant.4n3G, =AGc(r) =-- 3 [k,Tln (a+)]/v +4nr2y

r* =2vy/[k,Tln(a +I)]AG,*=16nv2y3/[3k~T2n2(a+ )]

The transition into growth of macroscopic crystals (Reac-tions 3and4 in Scheme4) can take place by energy f luctuationsin the system; thus, r* and AG,* are overcome.1) Formation of associates from monomerA

A C A ~2A,A, +A A,...2) Buildup of clusters

A ,+A A n+i.. .(coalescence of clusters also possible)

3) Formation of critical nucleusA: and its growthAm- ,f A ZI? A:A: f A Am+

4) Molecular accretion on macroscopic crystal surfaces (Q)Q f A ZIZ! QA

Scheme4. Reaction schemeforhomogeneous nucleation (see text).

AccordingtoLarson et al.,[8g1 onsideration of surface curva-ture anisotropy (for example, by the attachment of clusters tomacroscopic surfaces) leads to a thermodynamic stabilization ofsmall clusters with r


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REVIEWSrystal Growth( v is linearly dependent on a). Detailed ofR(a)andu(a) on, for example, KH,P04, have shown consider-able deviations from the expected parabolic relationship forsmall values of a, attributed to the effect of foreign materials.Above a critical supersaturation valuea , the growth velocityRincreases considerably (suppression of growth for a small devia-tion from equilibrium). This shows once again the importanceof prior purification of materials before mechanisms of crystal-lization can be investigated and interpreted. Because specificimpurities are active down to the ppm level, this presents no easytask for preparative and analytical chemistry. This helps to un-derstand why, in some cases, even when seed nuclei are used andthe supercooling and/or supersaturation is relatively large(AT,o),no crystal growth, or very slow crystal growth is ob-served. From general experience with solid materials of varioustypes, it can be said that the problems of chemical crystallizationare not with the crystal growth, but with the nucleation. Thishappens in many systems where nucleation takes place at a highdegree of supersaturation, so that the volume growth proceedstoo quickly. Separate production of seed nuclei for a later crys-tallization process is therefore to be recommended.

Foreign materials can reduce the rate of accretion, even with-out adsorption onto growth-active locations. When k,


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REVIEWS J. Hulliger

Fig. 5. I n situ observation (see furnace inFig. 4) of epitaxial growth of dark blueKTa,. .Nb,O, crystals on a KTaO, suh-strate from K F flux at 920 "C after 10mn(110) orientation with macroscopicallyrough growth surface [95]. Crucible diame-ter0=8mm.

Three phase diagrams (T ,X, at constant p ) are shown sche-matically in Figures6 and 7 to help in understanding the laterdiscussion of the crystal growth of many substances: 1) The

I II 111T

TL M

1 1

XA x, X A AB xB xA XBFig.6. ( T , X ) Phase diagram for two-component systems (A/B) as a basis for:solution growth of B (I ; see also Fig. 7); the melt growth or flux growth of acongruently melting compound AB (11); the growth of mxed crystals A,. .B, (111).L : liquid phase, E: eutectic point; T,,, Ts: melting points of solvent and of suh-stance AB, respectively.

two-component system A/B without formation of solid solu-tions, as a basis for solution growth from dilute or concentratedsolution, 2) the melting diagram for crystal growth of a congru-ently melting compound AB from the pure melt or from theself-fluxing mixture (incongruently melting compounds are usu-

tT

metastable

. zone Solvent: crystaline substance

+solid solventx%Ma"c=0 AX xwtlslnm =1

x +Fig. 7. Phase diagram(T ,X ) of solution growth, showing optimum crystall izationzone(AT ,AX) , and metastable region of supersaturation and of superheating. Theregion of freezing of the solvent is shown on the left of the diagram (see Sec-tions 3.1.1 and4. T,,, T,: melting points of solvent and substanceS, respectively;T,: eutectic temperature.

ally obtained from nonstoichiometric melt solutions, that is anexcess of one of the components (self-fluxing mixtures)), and 3)the two-component system forming solid solutions A,- xBx,which requires special techniques for growing macroscopic ho-mogeneous mxed crystals. The diagram illustrating the mostcommonly used solution growth method (Fig. 7) is discussed inmore detail: In the A/B system (no solid solutions), to enable aswide a range of T (largest value of A T ) on the solubility curveto be utilized practically, the eutectic temperature T, should bereached at a low concentration of Xsubctance.elow the liquiduscurve and adjacent to it, there is a metastable state, such thatwhen this is crossed, spontaneous nucleation takes place. In themetastable region of the phase diagram, the reactions ofScheme 4 take place. These reactions havesofar been very littleinvestigated experimentally. A complex array of processes andconditions determine the width (AT ) of this important zone.These include cooling velocity, hydrodynamic state, concentra-tion of dissolved and undissolved foreign substances, type ofsolvent and extent of solvation, dwell times, etc. In the case ofmass crystallization (see Section 3.1), the attempt should bemade to cause nucleation in the system without too large a stepbeyond the metastable zone. If seed nuclei are used, it is advan-tageous to superheat the system, and then to keep it alwayswithin the metastable zone, so that controlled growth is thenpossible without the formation of secondary nuclei.

With regard to the classification of crystallization processesto be described later, it should be said that if crystallization isregarded as a phase change of a system of one or more compo-nents, this leads to a systematization of the general methods(L a~dise,['~]rend["'I). Sections3 and 4 give more details ofindividual processes.

2.3. Morphology as a PropertyGrowth processes lead not only to the formation of the real

structure of a crystalline solid (which largely determines itsphysical properties), but also to the creation of a morphology,which determines the real structure by means of the growthmechanisms of the individual faces, and also creates additionalproperties. The scale of this effect extends to large three-dimen-sional crystals with specific crystal habit, two-dimensional epi-taxial thin films, one-dimensional fiber crystals or whiskers, and"zero-dimensional'' "quantum dots". For about 15years, meth-ods of two-dimensional crystallization (liquid-phase epitaxy(LPE), MBE, and MOCVD) have enabled functional semicon-ductor structures to be pr~duced.[~'~11 Homo- and heteroepi-taxy increasingly includes other classes of materials such asoxides (ABO, ferroelectric materials,[98. magneto-optic gar-nets['021), and even organic compounds. Also in the area ofthree-dimensional crystals, process control of the morphologyhas become important. The Stephanov process,['031 for ex-ample, enables crystals of sapphire and LiNbO, in the form ofplates, tubes, and other shapes to be pulled. Silicon single crys-tals for solar cells have recently been produced with a profile inthe form of a thin-walled polygon (seeFig. 2).[631

In industrial mass crystallization and general crystal growth,those molecular processes are of interest which lead to the for-mation of a specific growth morphology. Here, the distinction

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Crystal Growth REVIEWSmust be made between mechanisms for pure substances andthose influenced by surface-active[(hkf)-specificor site-specific]foreign materials. For pure substances, the morphology is deter-mined by stabilitylinstability criteria in the crystal-nutrient in-terface (CNI), and is essentially controlled kinetically. Depend-ing on the extent of supersaturation and on the mass and heatflow, polygonal, hopper-shaped, dendri ti ~,~~~]nd irregular(even fractal)['' growth is observed (Fig. X).[721

Fig. 8. MonteCarlo simulations of growth in two dimensions as a mathematicalfunction of the driving potential (from [72]). a) Polygonal surface growth,b) transition to hopper-shaped growth, c) dendritic growth, d) irregular growth.

In general, the end morphology of a faceted crystal is deter-mined by the slowest growing faces. The theory of Hartman andPerdok can be used to predict flat crystal surfaces ("periodicbond chains", so-called PBC vectors;['041 or new developmentssee ref. [85]),according to which, the(hkf) aces with the lowestenergy of attachment of a growth layer show the lowest facegrowth rateR.

Even small concentrations (ppm) of suitable foreign sub-stances can influence growth, for example, by molecular recog-nition mechanisms, and can retard rapidly growing surfaces.With the synthesis of tailored additives ("habit modifiers"), theformation of a desired crystal habit or form of agglomerates isrealized in industrial crystallization,[52.2b1enabling the proper-ties of a large number of products in powder form to be con-trolled (purity, bulk density, dissolution rate, etc.). The activityof foreign substances is deduced experimentally from the formof the function R(a,Xforeign Here, it is certain that insitu atomic force microscopy will yield interesting results withinthe next few years.[781As well as the effect of the foreign sub-stance onR, the effect on the nucleation rateJ is of practical aswell as theoretical interest. The majority of the well-known crys-tallization problems in organic synthetic chemistry must tosome extent be caused by small or large amounts of mainlyunknown foreign substances.

Considerable progress in the understanding of molecularrecognition processes achieved during the last decade,[29*have, according to Davey et al., had the result that "tailor-made additives for the control of specific processes are now a

3. Experimental Methodsof CrystallizationCrystal growth is a science and an art. The scientists'

role in the crystal growth process is that of anassistant who helps molecules to crystallize.Most molecules, after al l, are very good at growingcrystals. The scientific challenge is to learnhow to intervene in the process in order to improvethe fi nal product.E tter [' 51

Following the classification made in Section 1, the techniquesof mass crystallization and of true methods of crystal growth(exploratory and advanced) are treated separately. We shalltherefore collate the crystallization techniques described in thechemical literature, briefly discuss them, and hence elucidate thebasic principles of the most commonly used process of solutioncrystallization. The obvious consequences for methods of masscrystallization on the laboratory scale are set out in Sections 3.1and 3.2.Asexamples of bulk growth, three crystal growth pro-cesses are described in Section 3.3. These are used in materialsresearch into molecular substances for nonlinear optics.

3.1. Mass Crystallization on the Laboratory ScaleThe processes listed in Sections 3.1.1-3.1.5 are described in

the extensive literature on industrial crystallization[50*06] andchemical laboratory practice :[15*17."

3.1.1. Crystallization f romSolutionCrystallization from solutions has mainly two aims: the isola-tion of a solid, which was synthesized in solution, and the step-

wise purification of a soluble solid. Isolation: Crystallization isachieved by 1. complete, usually rapid (isothermal) evaporationof the solvent (rotary evaporator); 2. partial or complete, usual-ly slow (isothermal) evaporation of the solvent (crystallizingdishes, open to the atmosphere or in a desiccator); 3. slow orrapid reduction of the temperature of a saturated solution (with-out evaporation); 4. freezing of the solvent; 5. precipitation bythe (isothermal) addition of reactive components or solventcomponents to reduce solubility (addition by diffusion or withstirring); 6.salting out by the (isothermal) addition of a strongelectrolyte; 7. spray drying by rapid evaporation of the solventby pressure reduction (flash evaporation); 8. freeze drying; 9.electrocrystallization; 10. molten salt synthesis (at high temper-ature~);['~']1. hydrothermal synthesis.['081

Here, in practice, crystallization is essentially performed morerapidly than with single-crystal growth, the purity of the sub-stances obtained is rather less, and the crystallized material of-ten shows inclusions of solvent. Success depends greatly on thechoice of solvent,['091 and on the nature of the impuritiespresent. Van der Sluis et al.["ol have used statistical analysismethods to determine which solvent molecules are preferentiallyincluded in the crystal lattices of known organic compounds:water to 61%, dichloromethane to 6%, benzene to 5 % ,methanol to 4%, acetonitrile to 2%,and dimethyl sulfoxide to

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REVIEWS J. Hulliger0.5%. These figures indicate the proportion of the structuresthat can include solvent molecules or form solvates. It shouldalso be noted that the concentration and frequency of the inclu-sions are strongly dependent on the growth conditions (kineticeffects, see Section 2.1), which are usually not discussed in thisconnection.Even if the aim of the crystallization is the isolation of acompound, the principle applies that the material should bepurified by other methods before crystallization, and analysisfor trace elements or molecules for control purposes should beincluded.If a compound needs to be purified in a stepwise manner, thiscan be achieved by crystallization with rejection of motherliquor or by fractional crystallization with reuse of motherliquor.3.1.2. Crystall ization from the Melt

Crystals that form from molten substances can be obtainedby zone melting carried out one or more times, by Bridgmantechniques or by solidification of a supercooled melt. Whereassolution processes cover almost the entire range of classesofmaterials, melt crystallization is restricted to those that are ther-mally stable in the liquid state at their melting point, and wherechemically inert vessels are available (a problem with high-tem-perature superconductors, see Section 4.2). Zone melting hasbeen of great importance for the purification of thermally stablematerials for a long time." ' I Bridgman techniques have beenapplied in many cases.[34]3.1.3. Crystallization from the Gas Phase

Crystals form from the gaseous state by 1. sublimation anddesublimation in a vacuum or in a gas flow, 2. chemical trans-port, 3. reactive deposition from the gas phase (chemical vapordeposition CVD). Quantitative crystallization from the gasphase is usually of limited application due to the low vaporpressure of the component being transported. With semicon-ductor materials (Si, ZnSe, ZnS, Sic, etc.), CVD is an importantprocess.3.1.4. Crystallization in the Solid State

Crystals form likewise from solids by 1. recrystallization, 2.devitrification (slow crystallization of supercooled organic andinorganic glasses),3. reactive solid-state diffusion and ceramicsynthesis, 4. sol-gel syntheses of ceramic materials.["21The crystallization of the so-called oils of organic compounds(glassy, high viscosity condensed phases), which is often de-scribed as difficult, is here discussed in more detail. The funda-mental investigations of Tammann have led to the formulationof rules for the nucleation behavior of organic melts (see Sec-tion 2).['5 , ' According to these, for complex molecular materi-als, the temperature T, of the maximum rate of nucleus forma-tion J can be considerably below the temperature TG of themaximum rate of crystal growth. As exemplified by glycerine,this difference can be as much as 65K in exceptional cases.[341It is generally known that many organic melts that are thermallyfairly stable (benzophenone, salol, benzil, etc.) can be strongly

supercooled,['13]without producing growth nuclei within a rea-sonably short time. As the nucleation rate J is n general reducedby dissimilar dissolved materials, prior purification and traceanalysis are of the greatest importance, and active impuritiesmust be limited to the ppm concentration range. To bring aboutthe crystallization of analytically pure, stable, but difficult tonucleate supercooled melts (see ref. [15], therein Fig. 1,2), thesamples are preferentially heated above the melting point, slow-ly supercooled(1Kmin-' to 1K h-'), and repeatedly subjectedto temperature cycling at temperatures just below the meltingpoint (5-20 K ), so that the oily substance does not completelyharden in the supercooled region (insufficient diffusion, Eq. (d),Section 2.1). Slow heating and cooling, with periods of constanttemperature (hours to days), at various temperatures (inductionperiods) can be helpful in finding the regions for TNand T,,which sometimes do not overlap. For most real systems (ma-terial +its surroundings), heterogeneous nucleation is moreprobable than homogeneous nucleation. Therefore, purificationof the melts should only involve the removal of dissolved impu-rities. The introduction of a matrix with a similar lattice struc-ture can lead to crystallization by heteroepitaxial processes.Forother induction possibilities (e.g., by ultrasound), see refer-ences[18, SO].3.1.5. Crystalli zation by the Formation of Derivatives

Several organic compounds crystallize better 1. as salts (alkalimetal or ammonium salts), 2. as hydrochloride, 3. as metal-salt complex, 4. as molecular compounds (diastereomeric reac-tion partners for racemate separation), or 5. as inclusion com-pounds." 14J3.1.6. Basic Principles of Chemical Crystallizationfrom Solution

Although many methods are available, for most newly syn-thesized substances, only crystallization from solution (temper-ature reductionor evaporation) s used. (For a critical review ofcrystallization from solutions and melts, see Matz.["]) The fur-ther development of efficient and versatile laboratory methodsof solution crystallization that take advantage of establishedknowledge of nucleation and growth mechanisms are thereforestill important for synthetic chemistry.If one wishes to obtain crystals from solution efficiently, thefollowing points should be taken into consideration:Choice of a chemically stable two-component or multicom-ponent system without formation of solid solutions and witha eutectic temperature TEfor small values of Xsubstanceseephase diagram in Fig. 7; solvents: see refs. [34, 1091).Exclusion of components that inhibit nucleation and growth(which may include solvents).Suitable concentration range for crystallization:~5 wt%5Xsubstance30 wt% (for systems showing goodnucleation properties, superheating for a short period at5-20 K above saturation temperature is recommended;otherwise not). When growing large single crystals, theXsubstanceoncentration should be as high as possible.The optimum nucleation and growth temperatures (in par-ticular for molecular crystals) are usually considerably below

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REVIEWSrystal Growththe melting point of the pure material, and considerablyabove the eutectic temperature or the melting point of thepure solvent.

5) After successful nucleation (N) at TN0). The

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REVIEWS J . Hulligergas flow through the evaporation chamber should be reduced atthe same time. It is recommended that the first crystals shouldbe almost completely redissolved in the solution, so that theycan then be allowed to grow slowly as has been described. Theremoval of small crystals (dz 0.1-0.3 mm) requires great care.A thin-walled capillary can be used with a mechanical means ofapplying reduced pressure (with fine adjustment), so that thesmall crystal brings with it a minimal amount of solution. Thenutrient phase and the crystal are then ejected into a large vol-ume of preheated liquid in which the crystallized compound isless soluble (only for stable hydrates and solvates). After a smallamount of etching of the crystal, it is again picked up andtransferred to the absorbent base of a preheated container,which also serves for the removal and slow cooling of the crys-tal. Meanwhile, the growth of the remaining crystals continuesfairly undisturbed. The other crystallization methods also re-quire an equal amount of care. In general, isothermal evapora-tion is the preferred choice if i3X,,,,,,,,,/aT 0) of the polar twofold axis; see Fig.21). Use: measurement of nonlinearoptical and electro-optical effects[169].

tion of deviations from the1:1 distribution of D and L crystals("chiral symmetry breaking""'']) as the mobility of secondarynuclei is here much reduced.Temperature-difference method (Fig. 12):This system has awide application spectrum (provided that 5 5XsubsIance30 wt%, dX,,,,,,,,,/dT >O['z21) . The separately saturated solu-

A 5

w 4Fig. 12. Crystallization by the temperature-difference ( AT ) process (from [122],modified). Arrangement for the observation of spontaneous crystallization orgrowth upon nuclei. 1: Thermostatically controlled air bath. 2: T-controlled A1block inclined at angle a =10- 30" ( AT =T, -T, =I - 5 K) . 3: Glass vessel withrectangular center section [I 231and screw lid,4:Cold light illumination. 5: Obser-vation by binocular microscope. 6: Supply of solid phase. 7: Flow due to thermalconvection. 8: Holder for seed crystal (eccentrically mounted) for seed-growth ex-periments.

tion at T, is placed in the glass vessel (with a small excess of solidphase at the bottom), so that, in the temperature gradientAT =Tl - T,


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Crvstal Growth REVIEWSvessels can be placed in conventionally heated cabinets fittedwith the appropriate equipment. As indicated, crystallizationcan also be carried out by using seed nuclei. The small crystalsshould be removed in the manner described. Typical crystalliza-tion times can be several weeks. As this process operates afterreaching a stationary state of constant supersaturation, it canalso be used to produce macroscopic homogeneous single crys-tals of solid solutions.[1221

(a slow precipitation reaction), in general using inward diffusionof components that reduce solubility or change pH (substanceexample:[1241, ee Fig. 15). It is also possible to work with thehelp of a

AFig. 13. Crystallization matrix forthe determination of optimumgrowth conditions; on they axis thetemperature differenceAT is variedand on thex axis the solvent is varied.Series arrangement using sampletubes in a matrix [123}PR,, (i: AT ,j : solvent) in a heated cabinet [1221. F ,~,5. Gel growth ofsilverperio-The temperatures of the blocks date by pH reduction (AgNO,,(shown by dashed lines) are individu- H,~o,, and sodium silicate gel),

tograph): AgJO, [124].ally controlled, sothat a constantAT( i )with respect to the ambient temperature (i.e. yellowcrystals: A~H,Io,, red-of the heated cabinet) s obtained. The blocks have several holes (numbered)forthe brown crystals (black in pho-sample tubes PR,,. AT influences the supersaturation and flow velocity.

r .__. . ._ . .__. . . . ._ .______@ @ @ @ @i @ @ @ @ @i @ @ @ @ @

___ ___ __ ._ _ _ ._ ._ _ _ _ __ ___ _r _ _ _ . _ _ . _ _ . . _ . . _ _ _ _ _ _ _ _ _ _

__............~._________r . _ _ _ _ _ _ _ _ . _ _ _ . . _ - _ _ _ _ _ __

__ _.._._._..__ .__ __ __ __ __

Melt growth in capillaries may be used if, for example, onlysmall amounts of material are available. The cylindrical crystal-lizates formed can be used for X-ray work, either together withthe capillary (Lindemann glass) orafteretching,A modern ap-plication of melt growth in glass capillaries is in the productionof nonlinear optical organic fibers ( ~ i ~ ,6),[126l

Based On many years Of (Arend, with awide range of classes of substances, the chance of Success ofcrystallization with the ATmethod is over90%. It is possible toextend the process to large crystals['22a1 nd to the use of hightemperatures (approximating to hydrothermal in subcriticalpressure ranges).

The isothermal diffusion method (Fig. 14) also has a wideapplication spectrum, and the "sitting-drop'' version of this isreported to be most successful.[1151 lso included here is gelcrystallization by counter-current diffusion of two components

Fig. 16. Modern application of melt growth in glass capillaries. Fiber single crystalof 4-( N, N- di methyl amno) - 3-acetamdoni t robenzeneDAN). Internal diameter=6 pm.With DAN fibers,a high efficiency was obtainable in optical frequency dou-bling experiments (Nd:YAG, 1064nm) (Kerkoc et al. [126]).

Fig. 14. Crystallization by isothermal diffusion a) "sitting drop" method. I :Precip-itating agent, 2: control of evaporation rate, 3: plate with hollowsfor receiving thedrops (see also commercial products for protein crystall ization); b) diffusionthrough a membrane. 1 :Membrane,2/3: solution/precipitating agent;c) two typesof diffusion in the ge (see also[34,117]) :mostly unidirectional diffusion into the ge(left-hand diagram1:precipitating agentorsecond component)orcounter-currentdiffusion (right-hand diagram3,4: components A and B in solution), 2: ge withcrystallizing substance, 5 : initially pure gel.

Sublimation and Desublimation (Fig. 17): In addition to thewell-known variations of gas-phase crystallization, the tech-nique of controlled evaporation from Knudsen cells should bementioned here.['"] This system (Fig. 17) can be used for crys-tallization by forming derivatives, but particularly for produc-ing macroscopically homogeneous solid solutions (other pro-cesses are given in ref. [34]and by Karl[''11).

Possible processes for crystal growth by using chemical trans-port reactions are described in the well-known work ofSchafer."

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Fig. 17. Growth from the gas phase by con-trolled evaporation from Knudsen cells [127].(T , , T,: cell temperatures, T 3: temperatureofdeposition (cold finger). Suitable for the growthof mxed crystals A, .B, by separate evapora-tion of A(T,) and B(T,), and for low tempera-tures (unstable compounds). 1: Inlet or outletfor heating liquid.2: Connections for coolant. 3:To high vacuum pump with cold trap. 4:Knud-sen cells sealed with O-rings. 5: Supply of solidphase. ti: Aperture for controlled evaporationrate at cell pressurep ( T ) .

The hydrothermal crystallization process involves consider-able Moret has developed a small apparatus forexploratory work (Fig. 18),[1301which was used in reactivecounter-current diffusion experiments for forming single crys-tals of a series of compounds, including NiFe,O,, KFeF,,Te40g, PbCu,O,, Cu,I,. The construction of autoclaves, ingeneral, is described by Laudise et al.;[1311he hydrothermalsynthesis of inorganic substances by Rabenau.['O8I

(Ed~.),['~~lilke et al.,[341Arend et al. (Ed~.) ,[~~'lnd Hurleet al. (E~s.).[ '~~]Three processes will be described in more detail. These arecurrently used for growing single crystals of nonlinear opticalmolecular crystals. Their applicability to other classes of com-pounds depends on specific properties which cannot be dis-cussed in general terms.3.3.1. Crystallization from Slightly SupercooledOrgani c Melts

Under certain conditions, the strong tendency of organicmelts to supercool (Section 3.1.4) can be successfully used forthe synthesis of single crystals of cm3 dimensions, and for mak-ing single crystals that are almost perfect crystallographically.For this, pure materials are required that are sufficiently ther-mally stable for long periods (days or weeks). These are melted,preferably degassed, superheated (10-20 K), slightly super-cooled ( A T =0.1-2 K), and can then be crystallized by thecomplete immersion of a seed crystal. Scheffen-Lauenroth et al.and Klapper" 371 have recently demonstrated the usefulness ofthis method with salol, benzophenone, and benzil. Using equip-ment similar to that shown in Figure 19 (left), a strongly nonlin-ear optical compound (COANP: 2-cyclo-octylamino-5-nitro-pyridine) could be crystallized (Fig. 19 right)." 381 Crystal

1 1Fig. 18. Schematic diagram of ahydrothermal reactor for the synthesis of AB bycounter-current diffusion of the starting materials A and B through a dia-phragm (1).Miniaturized, easily operated equipment for the synthesis and single-crystal growth of small crystals is described by Moret 11301. (Reactor dimensions:/ zz 15cm, internal diameter % 0.7cm; see also [lOS]).

This discussion of the practical aspects of exploratory crystalgrowth is deliberately not oriented towards particular classes ofsubstances, but has attempted to propose a developable range ofbasic equipment whose design must be optimized in individualcases. The classification of processes according to substances isbased only on distinctions such as low melting point, high melt-ing point, stability/instability, etc. The substance-based ap- Fig. 19. Left: Crystall ization from a supercooled melt (Hulhgeretal. [138]). 1 Seedpreach,which corresponds more with thought, crystal (completely immersed: crystal pulling also possible). 2: Isother-has not proved useful in crystal growth. Chemically unimpor- mally heated melt. 3: Glass vessel with water cooling. 4: Heating for gas atmo-tantdifferences in the structure ofthe moleculesor in associated sphere. 5 : Pt-100control thermocouple. 6:Vacuum hood. 7: Equipment for movingseed crystal (translation or rotation). 8: Inert gas inlet. 9: Red glass (protectionimpurities can affect crystal growth disproportionately, and can against short wave light). 10: Polarizer, analyzer. and cold light illumination (IRinfluence the choice of process decisively. The present approach filter not shown). Right: COANP single crystals (1 mm thick platelets) produced byshould provideuseful guidelines and shouldenable crystalliza- crystal growth from slightly supercooled melts by complete immersionof the seedcrystal [138]. Growth time: 1-2 weeks. Application: frequency doubling experi-tion to be carried out by the most adequate means as the last ments and measurement ofelectro-optical effect11691.synthesis step. It should also lead to an improvement in thereproducibility of crystallization results in the majority of cases.

3.3. Discussion of Modern M ethodsofAdvanced Chemical CrystallizationA fairly complete overview of advanced methods used todaycan be obtained from the following articles: Gilman (Ed.)," 321

Pamplin L audi~e,[~~llwell et a1.,[961Dryburgh et al.

pulling from a slightly supercooled melt produced cm3-sizesingle crystals of COANP which had not been obtainable byother methods." 391Moreover, the same growth method has ledto the discovery of the first purely organic photorefractive crys-tal.[1393401The investigation of the physical state (vitreous stateand cluster formation) of supercooled COANP melts is de-scribed by Kind et al.[l4'] Crystal growth from supercooledmelts has at least two important advantages over normal meth-

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REVIEWSrystal Growthods (zone melting and Bridgman technique ' : The growingcrystal is surrounded only by the liquid phase (as well as by theseed holder), and the growth takes place under virtually isother-mal conditions.

3.3.2. Crystallizationby I sothermal Evaporationwith ResaturationThe principle of controlled isothermal evaporation and resat-uration has attractive advantages compared with temperature-

reduction methods. This method is 1) possible whenaXsubstance/aT50 and for relatively small values of Xsubstance;)single-crystal synthesis is possible when the evaporation temper-ature is constant and as low as necessary (unstable compounds).Bosch etal.1'421nd Hesse et al.1'431crystallized alkali metalhyperoxides, peroxides, as well as ozonides from liquid ammo-nia by this technique. Fuith et al.['441discussed the design of theapparatus shown in modified form in Figure 20 (and the growthof, for example, sulfate crystals). This apparatus is also used bythe present author for organic compounds.

Fig.20. Crystal growth by isothermalevaporation (arrangement placed in athermostatically heated water bath)with resaturation (Fuith et al. [144],modified). 1: Seed crystal. 2: Solutionwith hydrostatic equilibration. 3: Nu-trient material. 4: Cold finger (ther-mostat or Peltier element) for conden-sation of solvent. 5: Rotationalmovement of crystal (for relativelyrapid growth).

3.3.3. Crystal Growth in Laminar F lowby Lowering the Temperature of a Sol uti on

Convection phenomena or other uncontrolled flow condi-tions in the nutrient phase can reduce the width of themetastable areaof supercooling1681 nd lead to the formationofundesired growing crystal surfaces (defect formation and mor-phological instabilities).rgl. 451 The hydrodynamic state of thesystem is more easily controlled by a directed, almost laminarflow over a seed nucleus (stationary or intermittently rotated,Fig. 21). Furthermore, thorough mixing is ensured by the care-ful selection of the method of propelling the solution. In somecases, growth rate by the solution process is considerably in-creased at increased flow velocities (several cms- '). This hasbeen used for the relatively rapid growth of very large crystalsof KH,P04 (see Fig. l).[1461lso, in cases of strongly anisotrop-ic growth, the directed flow improves deposition on slowlygrowing surfaces. This should have many small-scale applica-tions. At the present time, the author is crystallizing nonlinearoptical compounds, such as 2- (N- (~ -prol i nol )- 5-ni tr opyri di ne(PNP) (Fig. 11) and4- di methyl amno- N- met hyl - st i l bazoni ump-tosylate (DAST: oneof the strongest electro-optical organiccompounds known today) by this method.

Fig. 21. Crystal growth by lowering the temperature(arrangement placed in a temperature-controlled ,water bath) under smooth fluid flow: 1:Seed crystalin a zone with almost laminar flow.2: Diaphragmorglass spheres (disturbance of stream lines). 3: Cone(smoothing and compressionof the flow).4:Propul-sion heix (Delrin). - l Ocm+4. Progress in the Single-Crystal Growthof M aterials of Topical I nterest4.1. Special L iterature Information

A wide-ranging review of developments in the crystal growthof approximately 2000 compounds is available in the latest edi-tion (1988) of the highly regarded standard work of Wilke andBohm (349-pages index of materials information and litera-t~re).[~~Inother compendium will be available in 1993, namelythe first handbook of crystal growth, including the newer meth-ods and materials (MBE, MOCVD, superconductors, proteins,et~.).['~~]urrent work (e.g., CA selects, "crystal growth", etc.)is reported in theJ ournal of Crystal Growth,which also publish-es the reports of the conferences held by the ICCG (Internation-al Conferences on Crystal Growth) that take place every 3-4years. Journals of national speciality groups[1471 ay alsobeofinterest, since they publish listsof grown crystals (special mate-rials), and name indexes from time to time.

4.2. High-Temperature Superconductors: OxocupratesUp to three or four years ago oxocuprates werea class of chemical compounds no more remarkablethan countless others.Mii l ler-B~schbaurn"~~~

With the discovery of the relatively high transition tempera-ture of La, -xBaxCu04,1'491he superconductivity of severaloxides WbO, SrTiO, (doped), LiTi,04 (T ,=13.7 K),BaPb,Bi, - xO, (T,=13 K), known for quite a long time] be-came the center of interest of solid-state science virtuallyovernight.[41*5O1 Where is the challenge of growing crystals ofthis typeof material?

It was soon realized that for La, - M,CuO, (M =Ba,Sr)andthe related compounds of Y-Ba-Cu-0, Bi-Ca-Sr-Cu-0, Tl-Ca-Ba-Cu-0, etc., the controlled three- and two-dimensional crys-tal growth (see Section 2.3) of the oxocuprates requires detailedknowledge of the stability regions (primary crystallizationfields) of incongruently melting substances within a pseudo-ternary or pseudo-quaternary phase diagram, including oxygenpressure, so that the pure compounds can be crystallized from

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REVIEWS J. Hulligernonstoichiometric melt solutions.[' l a] The determination ofphase diagrams and the crystal growth itself are made moredifficult by complex reaction equilibria that are established ki-netically slowly.[' 2 1 Moreover, the Ba-Cu-0 liquid phase hasextremely corrosive properties, which require the developmentof resistant crucible materials:['531 Corrosion of the crucible isthe most basic problem for crystal growth of the highT,super-conductors" (Changkang" 51a1). The determinationof the phasediagram of YBCO has given very variable results (Fig. 22).[' 5 2 e 1Also, the use of foreign fluxing agents, in analogy to the usualprocess of flux growth, gives mainly negative results. Watanabehas tested nearly 100 flux compositions at various tempera-tures," 54a1 and concludes: "The present results suggest that amore extensive and detailed search for a suitable flux may beworthwhile: but there may be no suitable (apart fromself-fluxing[' 54bl).

Fig.22 Graphic design or the key to YBCO crystallization? Primary crystalliza-tion fieldsfrom theresults of several authors (from [152e]).

Nevertheless, mm-size single crystals were occasionally pro-duced. However, the still-awaited breakthrough in oxocupratecrystal growth depends on: 1) the chemical stability of liquidphases towards crucible materials yet to be developed[' ' 1(coldcrucible processes are conceivable), 2) knowledge of the phasediagram (T ,X i ,p )and of the purity of the phases (effects ofimpurities), 3) the establishment of equilibrium (oxygen pres-sure) and the homogenization of the liquid phase (mixing, su-perheating), 4) the control of growth kinetics within themetastable region of supercooling. The solution of the crucibleproblem is of the greatest importance, and not only from thepractical point of view: side reactions disturb the equilibrationof the oxocuprate, sothat relatively narrow existence and stabil-ity regions change continuously during phase diagram or crystalgrowth work.Even if all these problems were solved (including problems ofphase changes during cooling), large oxocuprate crystals maysoon be of minor importance technologically; this does not ap-ply to epitaxial and polycrystalline thin films. In this area, aswell as LPE,[' 551 gas-phase techniques['561 have mainly beenused, including laser ablation,[' 5 7 1 RF sputtering," 5 8 1MBE,['591MOCVD, and even sol-gel techniques. This has stim-ulated developments in the epitaxy of other oxides, for example,in ferroelectricity.['O'l Just as the epitaxy of other materials(semiconductors and magneto-optic garnets) was achieved in a

similar way, a parallel development of substrate crystals is re-quired for thin film growth of oxocuprates.[1601The known hurdles in three- and two-dimensional crystalgrowth of oxocuprates reveal themselves primarily as a chemicalproblem, and high-temperature and solid-state chemistry will beable to contribute greatly to its solution. In conclusion, it maybe mentioned that advances have been made in the last 12 yearsin the crystal growth of organic superconductors (ambient pres-sure, T,(max) =11.4 K).['61,'621 The future may well havesome big surprises in store directly stemming from the mergingof these two worlds of chemistry (alkali metal-C,,, . . . ?). 11631Areal challenge for crystal synthesis!

4.3. Nonlinear Optical Molecular CrystalsSpecial donor-substituted and acceptor-substituted n-elec-tron systems[441 how optical frequency doubling or an electro-optical effect in crystals. These effects have appreciably higheror comparable values compared with those observed with inor-ganic substances known for a long time, such as LiNb03,['641KNb0,,['651 KH,PO, (see Fig. l).[", 66 1During the past 15 years, about 300 more or less stronglyhyperpolarizable organic compounds were rediscovered formodern optics. Some of these were modified existing com-pounds and some were newly synthesized ("molecular and crys-tal engineering"), and were investigated as single orLangmuir-Blodgett (LB) 1671and in the form of poledpolymers.['681 In frequency doubling experiments with theNd:YAG laser (A, =1064nm), for three-['38.'691and one-di-mensional crystals['26* 01(see Figs. 16, 19right), efficiencies ofover 25%producing green light were reached. Reviews of com-pounds, crystal growth, and optical characteristics have been

published by Zyss et al.[44a1 nd in reference[171].In three-dimensional crystal growth, it was necessary to workmainly with solutions (and gels) for stability reasons.['201By themethod of temperature reduction and isothermal evaporation,cm3-sized crystals were produced of MBANP (a-(a-methyl-benzyl amn0)-5-ni tropyri di ne), [ ' ~~ ~POM (methyl-3-nitro-4-pyridine-1-oxide)," la] NPP ( N- (4-ni tr ophenyl )- (~ ~)- prol i -n~l ),[ '~'~INP,['721 DAST,['731 and other compounds. Meltgrowth was used only infrequently (for example, for rn-dini-trobenzene, rn-nitroaniline, methyl - (2, 4- di ni t rophenyl ) - amno-2-pr0panoate,['~"] COANP,['381 and DAN,['261), where thebest conditions for obtaining the desired optical quality shouldbe provided by slow growth from the homogeneously super-cooled melt (seeSection 3.3.1).In analogy to other topical subjects, interest in two-dimen-sional crystallization is also increasing. With the achievement ofgrowing pm-thick crystal platelets[' 741 in a smooth (sometimeswedge-shaped) fissure, development is clearly proceeding in thedirection of heteroepitaxy from the gas phase (MBE)." 751Faced with the wide variability of organic compounds, thesalient question is not what can be achieved but whether theclass of materials shows sufficient long-term stability after in-corporation into an optical component. I t is wel known that theoptical damage threshold of organic compounds is lower thanwith oxides or semiconductors. Also, in this field, a furtherchemically interesting task presents itself, namely, to find hyper-

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REVIEWSrystal Growthpolarizable systems that are significantly more stable photo-chemically and thermally than the amino- orhydroxy- and ni-tro-orcyano-substituted n-electron systems that have been usedfor a long time. Here, the resulting nonlinearity would be ex-pected to be less, which reduces one of the important advantagescompared with oxides. However, for electro-optical use, organiccrystals and thin films of significantly more stable compoundsshould have a chance (a general discussion of application areasis given in [176]). The newly discovered photorefractive effectsin organic crystals are even less researched.[401

4.4. Protein CrystallizationMany protein crystallographers believe that thegrowth ofprotein crystals is much more complicatedthan the growth of inorganic crystalsRosenberger 71

The fact that it has taken so long to produce proteins whosecrystals have sufficiently good diffraction properties (Bernaland Crowfoot, 1934).. is undoubtedly partly due to preju-dice... (Luttringhaus[]) although the crystallization ofhemoglobin was first reported in 1840 (McPherson, historicalreview). 781

From the modern point of view, it is generally accepted that,as regards nucleation and growth behavior, proteins do notdiffer in principle from lower molecular weight sub-stance~.[~.9J Some differences arise from the biological originof the samples and the fact that a protein crystal contains 30-80 vol YOcombined water. Hence, crystallization is carried outfrom water (TI 0C), usually after adding a controlled quan-tity of a precipitating agent [(NH,),SO,, 2-methyl-2,4-pentane-diol, polyethylene glycol, e t ~. [ ~~.801]o that, for a given totalsystem, the solubility behavior of the protein becomes a criticalparameter of the process. When salts are used, the solubilitydecreases with increasing ionic strength. Although solubilityproperties have been widely researched, there is still no modelthat can explain what takes place when the type of precipitatingagent or its concentration is changed. According to Sieker,[1801experiments on 70 proteins produced crystals with a60YOsuc-cess rate, although crystals of a quality good enough for X-raystructural analysis could be produced from only 70% of thecrystallizable samples after further development of the crystal-lization techniques used.

The main difference in behavior compared with lower molec-ular weight substances is that a higher degree of supersaturation(az 5-20) is often necessary, together with a long inductionperiod (lysozyme: 1-200 days depending on the concentrationsof protein and NaCI).[81 Because of the molar volume, r* isapproximately 500 times as large for proteins as for lowermolecular weight substances. For some years, induction periodshave been investigated with dynamic light scattering, leading toconclusions about the diffusion and size of the scattering cen-ters. This method could also be used diagnostically to establishthe effectiveness of precipitation agents. 791

Work on the growth kinetics of macroscopic protein crystalshas led to the conclusion that the rate-determining step dependson processes on the growth surface. The measured growth rates

Rare of the order of a few cm per day. In comparison withtypical R values for other solution growth processes, proteincrystals do not grow appreciably more slowly. On the otherhand, at the molecular level, the mass transfer rate is approxi-mately times less1116b] a recent discussion of growthmechanisms is given by Weber[581).One of the remaining prob-lems in the mechanistic investigation lies with the poor repro-ducibility of the data. Apart from the effects of impurities (in-cluding bacteria), this is certainly associated with the slowestablishment of complex equilibria (folds and water inclusions,etc.). However, the use of the atomic force microscopy (AFM)method by Durbin et a1.[821 howed that the well-known BCF(see Section 2) mechanism[80] for low molecular weight ma-terials is in fact also valid for protein crystals.

Experimental methods of protein crystallization have beendescribed by many 6b, 179s In analogy tothe methods described in Section3, the following are available:1. Isothermal diffusion, a) over the gas phase (5-50 pL,hanging or sitting drop method-the commonest), b) byusing a membrane, c) in a gel (hanging drop),[831and d) bydiffusion across the interface between the protein solutionand the precipitant solution, and 2. temperature reduction(rare).

In addition to the literature mentioned previously, four con-ference reports Crystal Growth o Biological Macromolecules(1985, 1987, 1989, 1992) are worthy of note.[841

5. Summary and Future ProspectsI t has become increasingly evident in the last f ewyearsthat scientific aspects of crystal growth haveattracted the attention of physicists, chemists,

metallurgists, ceramists, materials scientists,mineralogists, geologists, as well as a small number ofbiologists, and that a substantial number of thesepeople regard crystal growth as their special field ofcompetence and interest.Although these lines were written 25 years ago, large areas of

synthetic chemistry have not yet adopted crystal growth as apossible special method of synthesis for building supramolecu-lar structures with specific physical properties. Nevertheless, thedevelopment of a large number of single-crystal materials sincethe general upsurge in solid-state physics and materials sciencehas shown the way towards the possibility of a chemistry thatencompasses both the classical synthesis of new compounds andthe formation of single-crystal phases with interesting proper-ties. As well as giving an account of interdisciplinary coopera-tion and the theoretical side of the science of crystal growth,it seemed to me that the central topic was a discussion ofrecent developments in the systematic practical solution ofcrystallization problems. Here, the distinction has beenmade between exploratory methods, which are as simple andself-regulating as possible, and advanced methods of crystalgrowth. Crystallization is no longer an outdated laboratorytechnique for the chemist, but a modern and novel method ofcarrying out chemical syntheses in new areas of materials re-search.

Angeu. Chem. I n t . Ed. Engl. 1994, 33, 143-162 159


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REVIEWS J. HulligerI should l ike to thank my colleagues Hermann Wuest, MarcelEhrensperger, Lucien Pauli, Dr. Roland Gutmann, Dr. PrimozKerkoc, and Dr. Bohuslav Bfezina (P rague) or their collabora-tion in the development of a large number of methods of crystalgrowth. M y special thanks are due to Prof. Dr. Dr . hc HannsArend, who introduced me to crystal growth and who has given megreat support ever since. The E TH Zurich and the Swiss NationalScience Foundation are acknowledged for financial support.

Received: October 5, 1992 [A 926 IE]German version: Angew. Chem. 1994, 106,151Translated by R. G. Leach, Basingstoke, UK

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Crystal Growth REVIEWS[63] Mobil Solar Energy Corporafion brochure1992). Billerica, MA 01821-3980,[64] P. van der Sluis, A. M. F. Hezemans, J. K roon, J . Cr yst. Growth 1991, I O N ,[65] G. L. Gilliland. J . Crvst. Growth 1988, 90, 51 -59.[66] J. H. Van Vleck. Theory of Electric and Magnetic Susceptibilities, Oxford[67] A. M . Stoneham,Theory ofDefects n Solids (E lectronic Structure of Defects[68] A. Neuhaus. Chem. Ing. Tech. 1956,28, 155-161.[69] H. Watanabe. T. Mizutani, A. Usui. Semicond. Semimet. 1990, 30, 1-52.[70] Wiss.Z. Tech. Univ. Dresden 1988, 37, 179-282; G. W. Cullen, C. C. Wang,Heteroepitaxial Semiconductorsfor Semiconductor Devices, Springer, Berlin,1978; R. A. McKee, F. J. Walker, J. R. Comer, E. D. Specht, D. E. Zelmon,Appl. P h w L ett. 1991, 59, 782-784; J. S. Harris, J. N. Eckstein, E. S. Hell-man, D. G. Schlom,J . Cr yst. Growth 1989, 95, 607-616; J. Kwo, ibid. 1991,

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