CrvstalIization J
Part 1. Transport Phenomena of Nucleation and Crystal Growth Crystallization is differentiated from other mass transfer operations
rystallization has some unique features that distinguish it from the normal mass transfer operations. For example, one of the phases frequently exists in a particulate state consisting of a “population” of highly structured particles. The number, size distribution, form, and morphology of the surface of these particles are parameters not encountered in other mass transfer operations, although they are very important in crystallization. These parameters are dependent both on diffusional resistances and on solid state phenomena and as a result, crystallization offers a broad spectrum of problems which can satisfy a variety of interests, tastes, and backgrounds of the workers in the field. Indeed, paraphrasing Laudise’s statement in ‘‘Techniques of Crystal Growth” (26A), we can classify these investigators into three groups-those who study how crystals grow, those who study how to grow crystals, and those who grow crystals. Because of varying interests of these three groups, this review has been subdivided into three parts. In Part I papers dealing with the transport phenomena involved in crystal growth and nucleation are considered. The main characteristics of these papers are usually that the crystallizing system itself is not important, that the growth of single crystals or a crystalline surface is studied, and that there is a definite separation of the nucleation and growth steps with one or the other being singled out for investigation. Papers dealing with the processes and techniques of crystallization as well as with the investigation of the operating parameters are reviewed in Part 11, to be published in November. Part I11 to be printed in December is directed toward investigators whose interests lie in the crystallizing product itself. This section is concerned with questions such as: under what conditions can a certain material be crystallized from a multicomponent system (i.e., phase equilibrium data), how crystals of a desired morphology, quality and purity can be obtained for a certain material, etc. The information carried in the papers included in this Part could be characterized as data. Because of the increasing interest in the freezing of water, the crystallization aspects of ice are treated in a separate section of Part 111. The review covers the two-year period from the Spring of 1967 to the Spring of the current year, 1969. Most, but not all, of the papers published during that period are included. Certain papers touched several aspects of crystallization and they are presented and discussed in more than one place in this review. Papers on the crystallization of polymers and on the recrystallization in a solid phase were intentionally omitted. Dissertations were also omitted.
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I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Summary of Important Trends
Growth from the melt provides a n example of a crystallization area in which results from the study of the physics of crystal growth have been used to a great extent in designing and improving techniques in crystal growth. In the past few years, the emphasis in the study of the physics of crystal growth from the melt has shifted from atomic and molecular theories of the surface attachment phenomena to studies of the influence of macroscopic phenomena such as diffusive and convective heat and mass transport in the melt. This trend has continued in the work reported in the literature in the past two years as evidenced by the number of papers dealing with topics such as morphological stability and dendritic growth, control of eutectic growth, and the influence of convection on solute distribution in a growing crystal. Extensive, careful measurements of the growth of crystal from the melt under known departures of the interface from equilibrium, to allow the testing of various theories of crystal growth, are still lacking. Some new techniques for such measurements have been suggested but they are either of limited application or ambiguous in interpretation. Of the techniques used for the production of single crystals from the melt the Czochralski or crystal pulling method continues to be the most versatile and useful. The causes and prevention of impurity bonding in crystals grown by the Czochralski method have received considerable attention and represent an area where theoretical principles have been usefully applied to practical problems of crystal growing. Zone refining continues to be adopted for the purification of more and different materials such as organic compounds. Unfortunately, there is yet to be developed a successful method of applying zone refining on a large scale. Interest in column crystallization (countercurrent contacting of melt and crystals) has continued a t about the same pace. The increased interest in the vapor growth area over the past two years is in accord with advances in the field of microelectronics. The most concentrated effort has been in the epitaxial and thin film fields with over 200 articles published. Physical vapor deposition or homogeneous condensation, chemical transport, and chemical vapor deposition have also been successfully employed to produce crystals of importance to the electronics, optical, chemical, and related industries. A number of investigators have studied the microstructure of growing or evaporating single crystal surfaces to understand better the mechanisms and phenomena occurring on the surfaces.
GREGORY D. BOTSARIS EDWARD G. DENK GUN S. ERSAN DONALD J. KIRWAN GEOFFREY MARGOLIS MAKOTO OHARA ROBERT C. REID JEFFERSON TESTER
Low-energy electron diffraction (LEED) and Auger spectroscopy are finding continued applicability in these studies. There is considerable interaction in vapor growth between physics and process of crystallization. I n contrast, growth from solution has been characterized by the absence of such interaction. Progress in the two fields-physics (Le., transport phenomena) and process--continued to follow independent and noncrossing paths. I n the field of continuous crystallization processes progress has been achieved mainly through the population theory approach, in which population balances have been applied as a n aid to the analysis of crystallizer performance. A number of interesting papers have appeared over the past two years reporting theoretical and experimental results from the application of the population theory to various systems. I n addition, extensive studies of the fluidized bed crystallizer have been reported, particularly in the Russian literature.
While population-balance studies have frequently used empirical correlations to represent the crystal growth rate, studies in the mechanism of growth have attempted to develop kinetic expressions based on physical models. The Burton-Cabrera-Frank (BCF) theory continues to be the starting point of these studies. Meaningful experimental data on crystal growth rates from solution taken under controlled conditions of supersaturation and temperature are still very scarce. The few data reported in 1967-69, point out that the BCF theory can interpret satis€actorily those results obtained a t very low supersaturations but not those obtained at high supersaturations or in the presence of impurities. The latter two cases correspond to practical situations and there are indications that they will attract considerable attention in the immediate future. A few theoretical papers have also appeared which emphasized statistical models with the probabilities of configurations deter-
PART /// Data Concerning t h e Particular System and Product
Q. Phase Equilibria R.
Production of Crystals of a Particular Compound
S.
Impurities Influencing Crystallization
1. Production of Very Pure Crystals of Particular Materials U.
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mined by free energy considerations. A definite trend toward the development of such models is evident. Workers have finally recognized the importance of secondary nucleation in crystallization from solution, and it appears that studies on secondary nucleation will be among the first to consider the combined effects of the physics and the crystal growth process. I n general, much work should be expected in the future, in topics which will bridge the existing gap between phenomena and process in growth from solution. Books and Reviews
A number of books dealing with various aspects of crystal growth have appeared since the last review (33A). Prominent among these are texts by Bamforth (3A), Strickland-Constable (&A), and Walton (43A). Strickland-Constable’s book on the kinetics and mechanism of crystallization begins with a general introduction to crystallization and continues with chapters dealing with the nucleation of liquid drops from the vapor and with the nucleation of solids. Following these are sections on the defect structure of crystals, data on growth and evaporation from the vapor, theories of crystal growth, and various topics. The chapter on the classical theories of crystal growth is especially complete and up-to-date, and it alone is enough to make this an important work. I n addition, StricklandConstable’s book is the first to treat the subject of secondary nucleation in any detail. Walton, being concerned with precipitation as opposed to crystallization, takes a somewhat different approach. His book includes chapters on nucleation, precipitation and growth kinetics, coprecipitation, surface properties, morphology, and complex precipitation systems. Like Strickland-Constable, Walton is upto-date in the coverage of his subject. Bamforth has compiled a handbook concerned with the equipment and techniques used in industrial crystallizers. He has included sections on the design and selection of a crystallizer, cooling crystallizers, vacuum crystallizers, evaporator crystallizers, reaction crystallizers, circulators and pumps, condensing and vacuum equipment, auxiliary systems and equipment, and dewatering and drying equipment. The book is a valuable source of information for anyone concerned with crystallization on a n industrial scale. Several texts translated from Russian were also released. One of these, edited by Ovsienko (32A),consists of forty papers reporting recent Soviet progress in metal physics. Other material translated from Russian include volumes 5A, 5B, 6i\, and 6B in the series of collected studies on crystal growth edited by Sheftal (38A). Many of the papers in the texts by Ovsienko and Sheftal are of particular value because of their reference to earlier Soviet work. Another Russian text recently announced will deal with crystallization from solutions (1QA). The collected papers presented at the Conference on the Solidification of Metals held a t Brighton, England in 1967 were also released (75A). Papers dealing with factors controlling as-cast macro- and microstructures, the solidification of eutectics, and the ,application of solidification theory to ingot casting were presented. An international colloquium on adsorption and crystal growth was held at Nancy, France, during June 1965. Thirty papers dealing with different aspects of adsorption and crystal growth and dissolution were read at this meeting. The collected papers are available (78A). Papers from the First (35A) and Second ( 8 A ) International Conferences on Crystal Growth held a t Boston, Mass., and Birmingham, England, respectively, were also released. More than three hundred papers dealing with virtually all aspects of crystal growth were presented a t these conferences. Among these were a number of review articles presented at the second conference. Many papers reviewing various aspects of crystal growth have also appeared recently. One of these is a survey of the research currently being conducted by the U.S. National Bureau of Standards on the growth and characterization of crystals ( 7 A ) . Among the studies in progress there are a number of investigations into the methods and theories of crystal growth, as well as several studies concerned with the properties of various materials. Sahagian (37A)has prepared an extensive, 65-page review of the growth of single crystals of more than 100 different electronically active materials. Crystals were grown by flame fusion, flux, melt, gel diffusion, low temperature solution, vapor, and hydrothermal techniques. The product crystals were examined and 88
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TABLE I-B. ADDITIONAL REFERENCES ON NUCLEATION Subject
Referencer (All Sujixed by B )
Theory of nucleation Nucleation in aqueous solutions Nucleation in a nonpolar solvent Nucleation in gels
1, 8, 13, 59, 60, 80, 86, 96, 107 72, 77 17
3 (See also Section Nb in Part 11)
Nucleation from melts Heterogeneous nucleationgeneral Nucleation from the vapor on a substrate Dynamic nucleation (cavitation) Effect of imrmrities Effect of magnetic fields Nucleation data for particular solution systems
14, 27, 22, 45-47,67, 81 30, 67, 72, 97, 705 25,26, 37, 32, 37, 39, 47, 50-53,
62, 69, 70, 73, 76, 83, 87, 104 18, 33, 34, 82
5, 58, 65 54, 64 6 (TiOz), 55 (Mg(OH)*),56 [Ca(OH)n], 66 (BaSOa), 74 (citric acid), 90 (KCl), 8Q, 7 0 7 (calcium phosphates), 94 (dimethylglyoximes), 109 (sucrose), 16, 93 (iceSee also Section U, Part 111)
characterized, and the physical properties of these crystals, their potential applications, and other pertinent information were tabulated. Jackson ( 1 6 A ) has discussed some of the recent work dealing with the fundamental aspects of crystal growth. The roles that interface kinetics, surface energy, and diffusive processes play in crystal growth are examined, and some of the recent studies conducted in these areas are reported. Kleber (20A) and Ookawa (31A) also presented reviews on the mechanisms of crystal growth. Many review papers concerned with the techniques and equipment used in crystallization processes have also appeared. Datt and Verma (6A) have attempted to use the techniques normally employed for the preparation of inorganic materials to grow organic crystals. Because organic materials have relatively weak Van der Waals forces and low degrees of hydrogen bonding, some modifications of these techniques were required. After the appropriate modifications were made, crystals were prepared by different vapor phase and solution growth techniques, and by growth from the melt. The success of these new techniques in preparing organic crystals was reported, and various potential applications for these techniques were examined. Laudise (26A)reviewed recent developments in the techniques of crystal growth. He points out the advantages of certain techniques such as crystal pulling and the use of magnetic and electric fields during melt growth. Discussions dealing with techniques for the production of large crystals by vapor growth, equipment for flux growth, and the role of water as an impurity during hydrothermal growth were given. Nassau in an extensive (68 page) paper ( 2 Q A ) conducted a general review of current crystal growth methods. Various melt, solution, and vapor phase methods, as well as solid-solid transformation techniques were reviewed, and the equipment required by each was discussed. The review has an extensive bibliography. Nitschmann (30A) has surveyed the techniques and equipment used for the production of hTaC1, (T\.THa)&Oa,KCl, azo pigments, dry ice, and in seawater desalting. Data on the nucleation, growth, and breeding of single crystals of these materials were also presented. Nucleation of Crystals
The basic thermodynamic treatment and the kinetic analysis of the nucleation process have actually changed very little since Gibbs first and later Volmer treated the subject some decades ago. A very large number of papers appear every year on the subject though. They offer modifications to the basic treatment, apply it to systems which become of importance and use sophisticated
experimental techniques for testing the classical theory of nucleation or the proposed modifications. A small number of papers will be presented in the text of this section of the review. A somewhat larger number of additional references will be classified and listed in Table 1-B. Although papers dealing with nucleation of crystals are primarily reviewed here, nevertheless a few papers treating nucleation of liquids from vapor phase will be presented because of their relevance to the general nucleation theory. Nucleation Theory a n d Test of Theory. One of the main results of the classical nucleation theory is a n equation which gives the concentration of nuclei. In 1962 Lothe and Pound considered the equation for the simplest system, i.e., liquid-droplet nucleation from vapor, and suggested that a correction factor of 1017 should be introduced in the equation. Recently, however, Bashkirov ( 4 B ) reconsidered the problem from the point of view of Brownian motion theory and concluded that such a correction factor is not needed. The fact that a debate can exist for such a large correction factor points out how difficult it is to test experimentally the values of the various parameters of the equations for homogeneous nucleation, even for the simplest system. Stein and Wegener (923) reported results from the direct measurement of the number of condensate clusters by applying a light scattering technique to a steady supersonic nozzle flow of moist air. They claim that the results point to the general validity of the classical theory as opposed to the corrected nucleation theory of Lothe and Pound. Katz and Ostermier (49B) arrived at the same conclusion for a variety of substances besides water, using a different technique (cloud chamber). Such conclusions, however, should be accepted only in a qualitative way because of the enormous dependence of nucleation rate on surface tension. Experiment and theory can be readily reconciled sometimes by assuming a different value of surface tension in the calculation. One technique in which homogeneous nucleation data from melt or solution are obtained without being masked by heterogeneous nucleation (i.e., nucleation on foreign particles) is the droplet technique. I t consists of subdividing the liquid into a great number of separated droplets. The volume of each droplet is sufficiently small, so that the suspended active foreign particles are confined to a small portion of droplets, while the remainder are free to nucleate homogeneously. This technique was suggested by Vonnegut in 1948 and is still popular with investigators. Price and Gornick (84B)presented a theoretical and computational investigation of the technique for a suspension of droplets of melt undergoing cooling a t a constant rate. A dispersion of droplets of a supersaturated solution in another solvent (ie., a n emulsion) was also investigated (700B). Nucleation of NaCl solutions was studied by making a n aerosol consisting of droplets 0.01 to 1 micron in diameter (35B). A surprisingly good agreement between experiment and theory was claimed. The classical theory, which was confined originally to isodiametric clusters (Le., spherical or cubical) and steady-state processes, was extended recently to describe formation of anisodiametric and anisotropic nuclei in isothermal and nonisothermal conditions (706B). The nucleation as a nonsteady-state process was considered also by Kashchiev (48B). I n his paper a n approximate solution of a partial differential equation derived earlier by Frenkel and Zeldovich was obtained. The case of the nucleation of a solid system, which can exist in more than one crystalline phase was considered by two papers. I n a short communication (67B), it was pointed out that in such a case the phase which is stable when the dimensions are macroscopic may be unstable when the dimensions are microscopic (nuclei); theory is thus necessary to treat this possible case. Chernov (IOB)on the other hand, dealt with the question why metastable phases may appear a t all in systems undergoing a phase
AUTHORS Robert C. Reid is Professor of Chemical Engineering at M I T , Cambridge, and Gregory D . Botsaris is Associate Professor of Chemical Engineering at Tufts University, Medford, Mass. Other coauthors are Dr. Donald J. Ktrwan, Monsanto Go., St. Louis, Mo.; Geoffrv Margolis, Assistant Professor of Chemical Engineering; Makoto Ohara, Jefferson Tester, Edward G. Denk, and Gun S. Ersan, Ph.D. candtdates in Chemical Engineering at M I T . With the exception of Dr. Kirwan, all the authors are members of the M I T - T u f t s Crystallization Study Group.
w.,
transition. H e presented a microscopic model of crystallization which actually leads to the appearance of a metastable phase. Nucleation from Supersaturated Solutions. According to the classical theory, nucleation rate, J , is given by an expression of the form J = k’exp
[- &]
where S is the supersaturation ratio, and k‘ and B are constants. However, in the treatment of industrial crystallizers (see Part II), the empirical equation
J = kSm
(IIB)
is used as a rule. Nyvlt in an interesting recent paper (78B) pointed out that equation (IIB) can be derived from (IB) by a series of approximations. He also described a n experimental technique by which the two parameters k and m can be obtained for a particular crystallizing system. The technique was applied to a number of systems including alkali halides, sulfates, and KHzPO4. Equation (IIB) was used also by Packter (79B) to correlate his nucleation data from the precipitation of sparingly soluble alkaline earth and lead salts. Nucleation theory predicts the existence of molecular clusters or embryos in supersaturated solutions. Direct evidence for the existence of embryos in supersaturated nonnucleating solutions was sought by a number of investigators. I n a recent study (43B), the difference between a n undersaturated and a supersaturated solution was examined by a measurement of their electrical conductance. The attainment of saturation was indeed characterized by a n increase of the activation energy for electrical conductance, which is a n indication of rearrangement of the molecular structures in the solution. I t should be noted, however, that the break observed in the curve log (specific conductance) us. 1/(temperature) did not always coincide with the saturation temperature. A further evidence for the existence of molecular clusters is supplied by another observation by Mullin and Leci (75B). Supersaturated solutions of citric acid kept quiescent a t a constant temperature, were found to develop concentration gradients, with the highest concentrations in the lower regions. The authors explained it by assuming segregation of the clusters under the influence of gravity. This is a very interesting observation, which needs further investigation. Nucleation theory predicts also that only embryos which attain a critical size, can become nuclei and start growing. A very interesting technique was used by Kolarov et al. ( 4 3 B ) in a n attempt to determine this critical size in supersaturated solutions of Na& 0 % 5H20. Two supersaturated solutions were separated by a porous membrane with the average pore diameter varied from 120p to 10-15 mp. Nucleation was induced in one of the solutions and no crystallization occurred in the second solution if a membrane with pore dimensions of 10-15 mp was used. This last number indicates the critical size of the nuclei in the second solution since crystallites of size smaller than 10-15 mp could not survive in that solution. Nucleation from melts. Evidence that the nucleation of metal crystals from the melt is always heterogeneous was presented by Hogan and Powell (36B). Meleshko (68B)studied the kinetics of the isothermal solidification of a betol. H e interpreted his results as indicating a n initial stage in which the heterogeneous process of nucleus formation was the dominant one and a final stage in which, after the exhaustion of the active impurities, homogeneous nucleation becomes possible. Homogeneous nucleation experiments have been used extensively for obtaining values of interfacial free energies. An independent method for determining these free energies was presented recently (23B). Substantial agreement between values obtained by the above two methods was found in the case of solidliquid interfaces of metals. Yet another study (77B)reported that homogeneous nucleation data give interfacial energy values lower than those obtained by other methods by a factor of 3/2. Heterogeneous Nucleation. Papers dealing with heterogeneous nucleation can be classified either as general references on heterogeneous nucleation, studies of nucleation from the liquid onto a substrate, studies of nucleation from the vapor onto a substrate, or investigations of the nucleation processes involved in oxidation. VOL. 6 1
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Evans (75B) observed the nucleation of ice on organic crystalline substrates. He reports that the first step in the nucleation process is the development on the substrate surface of monolayer patches of ice. This process is equivalent to the formation of a n intermediate phase because these monolayer patches were stable a t pressures as high as 1500 atmospheres-pressures a t which normal bulk ice is unstable. Anderson ( 2 B ) also studied the heterogeneous nucleation of ice, this time with clay substrates. From his results Anderson concluded that a t the ice-clay interface a mobile surface layer of unfrozen water forms. Various kinds of localized ordering are brought about in the water by the substrate, and the net effect of the substrate is to create an environment in which nuclei can form in the same way they would during homogeneous nucleation, but at much lower supercoolings. Grigson (29B) investigated the nucleation of metal films on amorphous substrates. I n this system, the first step in the nucleation process was believed to be the formation of completely disordered clusters of atoms on the substrate surface. Tiller and Takahashi (95B) have considered the contribution of the electrostatic double layer to the total interfacial free energy during heterogeneous nucleation. The double layer is something nearly all nucleation theories neglect. Tiller and Takahashi, however, found that the contribution of the double layer could be significant in the case when both the substrate and deposited material were conductors. The amount of work done in the area of nucleation from the liquid onto a substrate is quite limited. Walton, in two different studies, examined the heterogeneous nucleation of molten p dibromobenzene, p-bromochlorobenzene, and p-dichlorobenzene on cleaved alkali halide surfaces (70ZB), and the heterogeneous nucleation from solution, of alkali halides on lead sulfide, alkali halides on mica, and succinic acid on mica (703B). The latter paper (703B) is a good review on heterogeneous nucleation since, in addition to the data for the systems just mentioned, it discusses the existing theories of heterogeneous nucleation and their extensions in some detail. I n contrast with this, there are a number of studies dealing with nucleation from the vapor onto a substrate. Presumably this is because the important variables (such as the flux of crystallizing species onto the substrate) are easier to control in this type of experiment than in studies of nucleation from the liquid state. For example, seven groups of investigators (72B, 79B, 40B, 57B, 63B, 98B, 99B) studied the nucleation of gold on sodium chloride substrates. Gerasimov and Distler ( 7 9 B ) determined the nuclei density of Au crystals a t different orientations. They found that the Au crystals were likely to be positioned as local regions in (100) and (170) orientations-the directions of least misorientation between crystal and substrate. These effects were explained by the presence in NaCl of two types of long-range active centers, both of which were thought to be assemblies of point defects. I n a second paper ( 7 2 B ) , Distler expanded the scope of the investigation and observed the nucleation, both from solution and from the vapor, of PbS, CdS, Ag, and Au on NaCl and triglycine sulfate substrates. I n this latter study, nucleation was also observed to occur a t active centers. This time, however, the number of these active centers was increased by X-ray irradiation. Trofimov and Luk’yanovich (98B) also bombarded NaCl with X-rays and created F centers in the crystals. When gold was evaporated onto these substrates, the surface density of the gold nuclei was 3.5 times higher on the irradiated NaCl surfaces than o n untreated NaCl substrates. Ueda and Inuzuka (99B) exposed NaCl substrates to X-ray and electron beam radiation to create certain types of defects. They too found that this treatment greatly increased the nuclei density of gold films condensed on the surface of these crystals. Kosevich, Palatnik, et al. (57B)observed the nucleation of Au and Bi on NaCl, KC1, and KBr substrates. They reported that nucleation preferentially occurred a t color centers, attached impurities, vacancies, adsorbed surface vapors, surface deformations, and growth defects. The existing theories of heterogeneous nucleation assume that the adsorption which occurs prior to nucleation is less than a monolayer. Gretz (24B), Gretz and Pound (26B), and Sandejas and Hudson (88B) presented evidence showing that this is not necessarily so, a t least for the nucleation of Zn on W ( 2 4 B ) , Zn, Cd, Ni, and Au on W (26B),and Cd on W (88B). Another paper by Gretz (with Jackson and Hirth) deals with chemical vapor deposition (27B). The authors contrast chemical vapor deposition, in which nucleation initiates a chemical reaction, with physical vapor deposition, where nucleation initiates a phase change only. The authors also discuss the theories of hetero90
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Figure 1 . Replica electron micrograph of the (007)surface, ‘Zn’ surface, on a ZnO crystal which has been thermally etched in a He ( j o w ) atmosphere at 7200°C for 8.5 hours. Prior to the etching at this temperature, the crystal had been thermally etched in a He ( j o w ) atmosphere at l 7 0 O 0 C f o r 28 hours. Magntfication 77,000 X geneous nucleation and present some results for the chemical vapor deposition of Cr on quartz. Hruska, Hirth, and Pound (38B) in a review on recent developments in heterogeneous nucleation from the vapor, discussed the three principal mathematical and experimental treatments of heterogeneous nucleation in vapor deposition. These theories are (1) the Hruska theory which describes systems at low supersaturations where the critical nucleus contains more than 1000 atoms, (2) the classical treatment of Pound et al. for systems a t intermediate supersaturations with critical nuclei containing from 20 to 1000 atoms, and (3) the treatments of Hirth, Walton, and Rhodin which describe systems a t high supersaturations in which the critical nucleus has less than 20 atoms. Another review, this one by Sigsbee and Pound, lists (in 65 pages) the developments from 1963 to 1966 for heterogeneous nucleation in one component systems (97B). Many of the papers on heterogeneous nucleation report that minor contamination of the substrate surface, especially by oxygen, can have a profound effect on nucleation. Gillardeau, Vincent, and Oudar (ZOB), in a study of the chemical vapor deposition of fluorine on copper, noted that when the oxygen content of the fluorine was between 0.02 and O.l%, oxides rather than fluorides began forming first on the copper surface. If the oxygen content exceeded O . l % , only CuO formed. Some of the studies in the literature are investigations of the nucleation kinetics involved in oxidation. Oxidative nucleation involves a t least three phases and three components, and is a particular kind (probably the most common and most important kind) of chemical vapor deposition. Ritchie (85B) discusses the interactions in such three-component, three-phase systems. He reports that the oxide nuclei density is a function of the temperature, oxygen pressure, and substrate orientation, but that there is little correlation between the nuclei density and the dislocation sites in the substrate. The studies on the oxidation of A1 ( 7 B ) , Fe ( 9 B ) ,steel (77B), Hg-Te (85B), and W (708B) were reported.
Secondary Nucleation
Secondary nucleation refers to the production of crystal nuclei by a seed crystal. Although this phenomenon (sometimes called crystal breeding) has been recognized for many years, it is only recently that workers have begun to study the subject in any detail, Much of this recent interest has come about because of the significant role that secondary nucleation can play in determining the crystal size distribution of a typical commercial crystallizer. I n secondary nucleation processes, the conditions are almost always such that nucleation would not occur a t all if no seed crystal was present. Strickland-Constable ( 73C) has listed some of the ways in which a seed crystal could cause secondary nucleation. Secondary nuclei could come from a crystalline dust washed from the surface of the seed when it was first introduced into the system (initial or dust breeding), from pieces chipped from the seed during collisions of the seed with other crystals or with the walls of the apparatus (collision or attrition breeding), or from fragments resulting from the breaking up of a n agglomerated seed crystal (polycrystalline breeding). Other mechanisms of secondary nucleation are also proposed. The seed might grow dendritically and some of the dendrites might be broken; the seed might act as a template and cause a small, highly ordered atomic cluster to form near its surface and this cluster might somehow be swept from the surface. I t has also been suggested that secondary nucleation could occur if strong poisons (impurities) were present and if these impurities were readily taken u p by the growing crystal. Should this occur, there could be a concentration gradient of impurity in the boundary layer, and because the concentration of impurity in the boundary layer would be lower than in the bulk, spontaneous nucleation could occur in the boundary layer. According to this mechanism, the seed crystal creates a region of low impurity concentration (the boundary layer) in which spontaneous nucleation is possible. Austin (7C) suggested that the amount of breakage occurring in a crystallizer might be measured experimentally using radioactive seed crystals. Belyustin and Rogacheva (3C) studied the crystallization of MgS04. 7H20, a material which a t room temperature crystallizes in two enantiomorphic forms. They found that spontaneous nucleation (no seed present) yielded mostly left-handed crystals, and that the percentage of left-handed crystals in the product did not seem to be affected by changes in either the supersaturation or liquid velocity. When a right-handed seed was introduced, the number of product crystals, as well as the percentage of righthanded crystals in the product increased. Increases in the supersaturation and liquid velocity (with a right-handed seed present) both led to decreases in the percentage of right-handed crystals in the product. Because of this, the authors concluded that secondary nucleation was not occurring by fragmentation of the seed. Since filtration greatly retarded nucleation whether a seed crystal was present or not, Belyustin and Rogacheva proposed that secondary nucleation occurred when particles of suspended matter came in contact with the seed, became activated, and were converted into crystal nuclei. Rogacheva (72C) later suggested that certain airborne bacteria might be responsible for the fact that spontaneous nucleation yielded mostly left-handed crystals. Inyushkin and Shabalin (7C) studied the effect of liquid velocity o n the production of “parasitic” crystals in the presence of a Lis04 HtO seed. From their results in this and previous studies, they concluded that crystallization occurred by the formation of groups of molecules (blocks) near the growing crystal surface. The same authors in a later paper (8C)reported the conditions under which secondary nucleation of NaN03, Kd[Fe(CN)o] 3Hg0, and NH4H2P04 salts occurred. Lal, Mason, and Strickland-Constable (QC) investigated the secondary nucleation of various materials. For MgS04 solutions a t supercoolings greater than 4OC, dendritic breeding was observed. At lower supercoolings, different types of collision breeding occurred. This collision breeding was strongly influenced by the supersaturation, and the authors therefore concluded that if the collision breeding process was due to fragmentation of the seeds, the fragments produced had to be of a size comparable to the size of the critical nucleus for the supersaturations being used. The authors also reported that the degree of collision breeding for KCl and KBr from aqueous solutions was even higher than that for MgSOd,
--
while collision breeding of benzophenone from the melt also occurred, but a t a lower rate than for MgS04. Larson, Timm, and Wolff (70C) studied the nucleation and growth of ammonium alum and ammonium sulfate crystals in a continuous, mixed crystallizer. They found that for both materials, the predominant mode of crystal formation was by secondary nucleation, and that the extent of this secondary nucleation could be related to the supersaturation and the suspension density (which in turn can be related to the total surface area of the seed crystals present). Babayan, Isakhanyan, and Manvelyan (2C)found that seeded solutions of NaSiOs. 9Hz0 often yielded crystals containing occluded mother liquor, and that crystals containing large occlusions were prone to break up into smaller crystals. Cooke ( 4 C )reported that K4[Fe(CN)sl led to the skeletal growth of NaCl and that secondary nucleation occurred under these conditions. Randolph ( 7 I C ) proposed a mathematical model showing how secondary nucleation would affect the crystal size distribution in a mixed suspension crystallizer. The effect of secondary nucleation is always to narrow the size distribution. Expressions showing the extent of this narrowing were derived. I n summing up, it might be convenient to regard the above studies of secondary nucleation as describing either fragmentation or nonfragmentation processes (or perhaps as “apparent” or “true” secondary nucleation processes). While the various fragmentation mechanisms are relatively easy to visualize, little is known about them quantitatively, and further studies defining the extent of this kind of breeding that occurs in commercial crystallizers would be desirable. I n addition, studies aimed a t determining the mechanism (or mechanisms) by which the nonfragmentation processes occur would also be of value. Theoretical Studies in Crysial Growth GENERAL
Theoretical crystallization studies have dealt primarily with extensions of the two-dimensional, polynuclear, stepwise, or spiral models. A few papers, noted below have, however, emphasized statistical models with the probabilities of configurations determined by free energy considerations. T h e general papers published during this review period (5Da, 8Da, QDa, 15Da, 78Da)have often provided interesting perspective from kinetic and thermodynamical considerations. A well-written description of available theory and application to precipitation reaction steps was presented by Lieser (72Da). I n the nucleation theories, Vorontsova (2Da)discusses both twodimensional and multilayer nucleation for diamond-type lattices. Sumino (7QDa)has developed a theory for the growth process of deformation twins where the elementary process is considered to be a nucleation of step rings on surface dislocations. An analytical study of polynuclear growth of large crystal faces was given by Borovinskii (7Da). The interesting subject of rhythmicity in crystal growth was discussed by Sheftal (77Da). T h e subject was reviewed and theoretical and experimental work for the past 20 years was analyzed. Several reasons may be given to explain a periodic increase and decrease in growth rate with the formation of layers. Impurity adsorption is one mechanism. Sheftal also discusses the possibility of rapid surface growth leading to high surface temperatures and, therefore, a low surface supersaturation. A period of slow growth then occurs until the heat of crystallization is dissipated. T h e practical difficulty of producing perfect crystals, without layers, is emphasized. The proverbial problem of determining crystal shape in melt crystallization was treated by Oldfield, Geering, and Tiller (74Da) using a computer model. They were able to obtain a general description of the growth process considering heat and material transport, the change in melting point a t sections of high curvature, and surface kinetics. This treatment may also be useful in interpreting rate data for the growth of ice crystals in a n undercooled saline solution. I n other papers, Mutafchiev (73Da) has presented the results of a detailed study relating the roughness of a crystal surface to growth, while Gerasimenko and Lyubov (7Da)studied theoretically the nonsteady state, nonisothermal growth process. Computer simulation studies on 1-, 2-, and 3-dimensional seeds have also been published ( ~ D u )and , the importance of surface polarization to growth pointed out (3Da). Several statistical models of crystal growth are now available. VOL. 6 1
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TABLE I-D. CLASSIFICATION OF THEORETICAL PAPERS ON SOLUTION GROWTH, IMPURITY EFFECT, AND OTHERS (Dc i s to be suffixed t o all the numbers) A random walk method was suggested by Chernov (4Da)wherein particles were added and removed from kinks. Impurity effects were included. Schwoebel (16Da) and Jackson (SDa, 7 1Da) have both developed growth mechanisms wherein the process is considered to be a series of steps with a probability of attainment of any step. The more recent paper by Jackson (9Da) has unified the theory and presents a general formalism to permit the calculation of crystal growth rates from a knowledge of the configurations of the crystal surface. Rates are expressed in terms of probabilities of molecules joining or leaving a series of surface configurations. Both general and specific cases are treated. The final results are expressed in terms of free energies of the various configurations, Le., the mechanism uses a series of lowest free energy configurations as the route. THEORETICAL STUDIES OF CRYSTALLIZATION F R O M MELT
The papers are discussed in the later section on Experimental Studies of Crystallization from the Melt. T H E O R I E S ON SOLUTION GROWTH
T h e surface diffusion and volume diffusion crystal growth models developed by Burton-Cabrera-Frank (BCF) and by Chernov were compared by Bennema ( ~ D c4Dc). , He pointed out that the BCF surface diffusion model can be adapted to growth from solution, and discussed the dependence of growth rate on supersaturation that this model predicts--i.e., parabolic growth a t low supersaturations and linear growth a t high supersaturations. Kahlweit et al. (ZIDc, 37Dc) have explained the same dependence in ionic crystal growth from aqueous solution in a different way: a t lower supersaturations the rate determining step is the dehydration reaction of the ions a t the kinks, while a t higher supersaturations the controlling step is mass transfer. Brice (8Dc)developed rate expressions for the growth from perfectly and imperfectly stirred solutions ( ~ D c )and , showed the existence of a t least 6 different relations depending on interfacial structures. Other aspects of the kinetic processes highlighted were diffusionconvection growth (14Dc, 32Dc, 45Dc), diffusionless growth (44Dc), local supersaturation (76Dc, 17Dc), and solvent removal (42Dc). Studies on morphology and interfacial structure have been performed by many investigators ( IDc, 7 3 0 6 , 25Dc, 34Dc, 46Dc, 47Dc). Voronkov et al. (50Dc) considered the structure of the interface between a crystal and a n ideal solution and defined the critical temperature a t which the transition from a smooth surface to a rough one occurred, and the temperature a t which the work needed to produce a step on a smooth face becomes zero. Khamskii (23Dc) emphasized the need for additional data on the role that impurities play in determining the crystal habit and other properties. The broad effects of impurities were studied and reviewed by many investigators ( 7 IDc, 22Dc, 37Dc, 33Dc). Bertocci (5Dc) proposed a model describing the influence of time-dependent impurity adsorption on the electro-chemical deposition and dissolution of metal single crystals. Bliznakov (6Dc) suggested two types of molecules of crystallizing matter: one going through the free surface, and one going through sites occupied by impurities. H e says that the latter’s degree of coverage can be expressed by a Langmuir adsorption isotherm. The heat of adsorption of impurity was shown to be twice the value corresponding to sites on the rest of the surface for the system KBr-phenol. Sunagawa (43Dc) says that impurities interfere with the advance of growth layers (two-dimensional spreading), resulting in the formation of special surface patterns or new growth centers. The effective distribution coefficient was discussed as a function of supersaturation (49Dc),growth rate (57Dc),and impurity concentration (52Dc). Studies were made on diffusion controlled growth (ZDc, 9Dc, 78Dc, 19Dc, 36Dc); on the role of heat transfer in growth processes ( ~ D cIODc, , 18Dc, IgDc), on the temperature gradient in zone melting (72Dc, 15Dc); and on the pressure effect on growth (29Dc). Precipitation “reaction” kinetics were also reviewed (28Dc). 92
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Theory-Solution growth I , 3, 4, 7 , 8, 13, 14, 16, 17, 21, 23, 24, 25, 32, 34, 37, 42, 44, 45, 46, 47, 48, 50 Theory-Impurity effect 5,6, 11, 22, 26,31,33, 35, 38, 39,41, 43,49,51, 52 Theory-Others 2,9, 10, 12, 15, 78, 79,20,27,28,29, 30,36,40
TABLE Il-D. CLASSIFICATION OF THEORETICAL PAPERS ON VAPOR GROWTH (Dd is t o be suffixed t o all the numbers) Theory-General 5, 7, 10, 11, 17, 39, 53, 71, 72 Theory-Chemical transport and chemical vapor deposition 13, 18, 25, 26, 36, 41 Theory-Whisker growth 76, 80, 81 Theory-Epitaxy and thin films 2, 19, 24, 32, 46,47, 52, 55,56, 68, 69, 73, 74,83, 90 Theory-Morphology 1, 3, 4, 6 , 8 , 9, 12, 14, 75, 16,20, 21,22, 23,27, 28, 29, 30,31,33, 34, 35, 37, 38, 40, 42, 43, 44, 45, 48, 49, 50, 51, 54, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 70, 75, 77, 78, 79, 82, 84, 85, 86, 87, 88, 89, 91, 92
THEORETICAL ASPECTS OF VAPOR GROWTH
I n addition to the vast amount of experimental work aimed a t growing crystals with particular specifications, a number of investigations have considered the theoretical aspects of vapor-solid crystal growth. Most of the theoretical papers fall into one of the following categories:
(1) General vapor-solid growth phenomena (2) Whisker growth ( 3 ) Chemical transport and chemical vapor deposition (4) Thin films and epitaxy (Table 11-D categorizes a number of articles into the above four divisions. )
Eighteen years ago Burton-Cabrera-Frank (BCF) developed their dislocation theory of growth explaining that crystals could grow a t low supersaturations by a self-perpetuating Archimedian spiral. Most of the attention in the original BCF treatment was devoted to growth from the vapor. This theory followed chronologically the Becker-Doring-Volmer concept that a two-dimen? sional nucleus is necessary to propagate growth. Over the years many investigators have sought to test and compare these theories, and a number of cases have defended both as possible mechanisms. I n addition, several people have thought to incorporate both theories into a compound mechanism of growth. However, no completely satisfactory theory has been proposed that accounts for crystal growth over a wide range of supersaturations. Strickland-Constable ( 4 0 A ) in his book traces the theoretical development of the growth of perfect (dislocation free) crystals and imperfect crystals. He also relates several experiments to possible mechanisms of crystal growth from the vapor. Rutner (72Dd) in a recent review article discusses both condensation and evaporation theories and their development over the past ten years. Cocks, Das, et al. ( I I D d ) have investigated mechanisms of evaporation and condensation emphasizing the dependence of the evaporation or condensation coefficient on the particular plane of the single crystal being examined. They have studied morphological changes a t the surface to isolate kinetic information about condensation and evaporation processes. Jackson (39Dd) has been concerned with developing a fundamental rate equation for crystal growth. Leichkis (53Dd)did a thermodynamic analysis of crystal growth incorporating nucleation and critical size d’ependence. Chernov and Lewis (IODd) have attempted to simulate the crystallization of binary systems undergoing phase transitions on a computer and found qualitative agreement between an approximate analytical solution for the three-dimensional binary
crystal growth theory and the parameters of the computer simulation experiment. The following articles deal with the theoretical aspects of chemical transport and chemical vapor deposition (73Dd, 18Dd, 25Dd, 26Dd, 36Dd, 41Dd). Gretz and Hirth (25Dd) elaborate on how the theory of nucleation and growth processes on or near the substrate may be used to determine the rate controlling reactions. Gretz and Hirth along with Jackson (26Dd) compare chemical and physical vapor deposition in the chromium-iodine system. Schwoebel (75Dd) developed a diffusion model for filamentary crystal growth. H e states that for filamentary crystal growth to occur, there must be a mobility difference between those atoms adsorbed on one plane and those on another, and a difference between the capture mechanism a t the steps. Simmons and his associates (80Dd, 87Dd) discuss the solution of the Stefan problem for whisker growth. Those articles dealing with epitaxial and thin film growth theory are listed in Table 11-D. Kikuchi (46Dd, 47Dd) discusses the theory of nucleation and growth of a thin film in two articles. Weinstein and Wolff (9ODd) were concerned with the mechanism of epitaxy in semiconductors. They proposed that the formation and growth of thermodynamically stable epitaxial forms occur by two-dimensional nucleation where metastable forms appear with a screw dislocation mechanism controlling growth. As mentioned earlier, a growing interest in crystal morphology has been observed over the past two years. Basically, people are learning that morphology as influenced by bonding arrays, defects, temperature, etc., can be important in determining the kinetics of growth, evaporation, and dissolution. Table 11-D summarizes a number of the articles pertaining to morphology. A wide range of topics are covered. For example, Cahn (8Dd) and Hardy and Coriell(30Dd) consider the morphological stability of growing crystals while Distler and his associates (74Dd, 16Dd) discuss a dislocation free mechanism of growth. Lester and Somorjai (54Dd) point out that as the dislocation density increased they found a n increase in the evaporation rate into vacuum for NaCl single crystals. Sheftal and Magomedov (78Dd) investigated the morphological aspects of epitaxial growth of GaAs in the polar direction. Experimental Studies in Crystal Growth from Solution
\r
Kinetic Studies for Growth from P u r e Solutions. Papers in which workers attempted to explain either their results or the results of other investigators in terms of the Burton-CabreraFrank (BCF) dislocation theory or in terms of two-dimensional nucleation theory (using either mononuclear or polynuclear models) dominated this section. Bennema (17E, 78E, 79E) developed a special weighing technique to study the growth of monocrystal seeds from aqueous solutions, He used this technique to measure accurately the growth rates of potassium alum and sodium chlorate crystals a t very low supersaturations (0.003 to 1.2% and 0.003 to 0.15%, respectively) (77E, 12E, 73E, 15E). H e interpreted his results and mainly for sodium chlorate, i.e., parabolic growth a t lower supersaturations and linear growth a t higher supersaturations, as strongly supporting the surface diffusion model of the BCF theory. This theory had developed the surface diffusion model to describe growth from vapor, but Bennema adapted the model to describe growth from solution. The growth rates for alum, meanwhile, were found to be linear with the percentage supersaturation (5‘) for values of S < 1%; the growth rates deviated, however, from the linear form for higher S. Bennema and his coworkers (20E) explained this deviation from linear growth by assuming that both the polynuclear model of the two-dimensional nucleation theory and the surface diffusion model of BCF theory occurred simultaneously for S > 1%. Bennema also used the surface diffusion BCF model to interpret the data of other investigators (73E, 16E): the growth rates of sucrose crystals measured by Smythe (see 103E); the growth spiraIs on sucrose observed by Dunning et al. (see 4OE); and the growth rate of ethylenediamine tartrate crystals measured by Booth and Buckley. This second-order dependence a t lower
TABLE I-E. ADDITIONAL REFERENCES ON KINETIC AND GROWTH RATE STUDIES IN AQUEOUS SOLUTIONS CrystoNiring system
Reference
AlK(S04)z. 12Hz0 CuClz.2HzO FeS04-7Hz0 KC1 KHzP04 MgS04.7HzO NaClOa NaSiOa- 9H20 (NHdHzP04 Rochelle salt Sucrose Triglycerides
43E, 86E, 87E 72E 68E 67E, 62E 55E 7OE 46E 4E 55E 7 13E 39E, 57E 107E
supersaturations was also found for NH4H2P04 and KHzP04 (85E), for PbS04, SrS04, and BaS04, (89E), and for alkalioxalates and TlBr crystals (94E). Two-dimensional nucleation theories were supported by electrocrystallization groups. Kaishev et al. (58E) say, “the evidence of two-dimensional nucleation mechanism of growth of perfect crystal planes is provided for the first time.” Kraischew (69E) insists that electrochemical phenomena which accompany the growth of dislocation free surfaces of Ag crystals, indicate growth through two-dimensional nucleation formation. A different growth model is postulated by Russian investigators (52E) who studied LizS04.HzO growth. They reported that the growth rates pass through a maximum with increasing rotation rates of the growing crystals. At higher rotation rates, “parasite” crystals were formed and found in the bulk solution. The parasite crystals were less rapidly formed when the growing LizS04.H20 seed crystals were replaced by “identically shaped” Plexiglas models. They claim that the results support the concept that crystal growth occurs through the formation of groups of molecules or “blocks” near the growing crystal surface. Effect of Impurities or Additives o n Growth Rate. Impurities are known to affect the growth rates of crystal faces. Their main effect is retardation of growth, although there are in the literature two or three cases in which acceleration has been reported. I t is generally believed that to be effective in altering the growth on a crystal face, an impurity must adsorb to a certain extent on that particular face. There are two mechanisms mostly accepted for growth from solution. Both postulate a reduction by the adsorbed impurity, in the velocity of the growth steps moving across the crystal surface. According to one, initially proposed by Sears, the impurity is adsorbed on the growth steps and poisons the active growth sites, i.e., the kinks, and is not necessarily incorporated into the crystal, Cabrera and Vermilyea’s mechanism, on the other hand, suggests that the adsorption of the impurity takes place on the plane regions between steps. The velocity of the growth steps is reduced since they are forced to pass through the adsorbed impurity atoms and acquire a curvature. Only immobile impurities, strongly adsorbed, are effective in this mechanism. The absorbed impurities in this case are buried inside the growing crystal. A corrollary of Cabrera and Vermilyea’s theory states that for each impurity concentration there is a certain critical supersaturation below which a seed crystal will not grow a t all. A recent study (102E) aimed at testing this postulate. The existence of such a supersaturation for lead nitrate crystal in the presence of methylene blue was claimed. As with past studies, however, a doubt remains whether no growth occurred or whether the amount deposited was too small to be detected by the method used. Direct observation under a microscope, of the effect of additives on the movement of the steps on the surface of a growing crystal VOL. 6 1
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was employed by Dunning et d., in England (4OE). Continuing their work on sucrose crystallization, they used a number of oligosaccharides, and inorganic salts as additives, The main finding was that the two additives (raffinose and stachyose) which markedly affect the rate of advance (and also the shape) of the steps are adsorbed and incorporated into the crystal to a greater extent than those which do not. T h e authors described briefly a mechanism by which the adsorbed impurities retard the velocity of the steps. This mechanism has been reported by them in previous papers and is essentially a combination of Sears and CabreraVermilyea mechanisms. The results do not contradict this mechanism but a t the same time cannot be used to test it. Shichiri and Kat0 in Japan have been using the observation of the regrowth of whiskers from solutions as a means of obtaining information on the mechanism of growth and the effect of impurities on it. I n recent studies ( W E , 7OOE) the effect of Pb2+ and other heavy metal ions on the regrowth of previously grown NaCl whiskers was observed. T h e whiskers were either as grown (assumed by them as perfect crystals) or deformed. Lead in a mole ratio larger than 10-7 in solution appears to stop the growth for as-grown whiskers but it only decreases the growth in deformed whiskers. This points out that the growth rate of real crystals is determined by a coupling effect of the imperfections (which generate the steps) with the impurities (which suppress the step movement). A completely different explanation for the effect of additives is offered by Claes and Peelaers (34E). They hypothesized that impurities may affect the assumed structuredness of the water near the crystal surfaces and through this the degree of solvation of certain faces. That modifications of solvation may influence the growth rate and the habit of ionic crystals was suggested previously by Kern and his coworkers in France, and was refined further in their recent paper (22E). A highly speculative hypothesis about the effect of Pb* on the growth of KCl crystals was advanced by Glasner (44E, 4523). T h e excess of solute constituting the supersaturation was assumed to be consumed by embryo formation around each one of the lead ions in the solution. I t was further assumed that the crystals grow only by the addition of these embryos. If the latter were true, however, lead should be incorporated equally a t the (100) as well as a t the (1 11) faces which is contrary to experimental observations (29E, 65E). The change in the habit of a crystal has been used extensively in the past as a qualitative measure of the effect of impurities on the growth. Recently, however, a method for quantitative representation of the habit change by the impurities was presented by Kern’s group (23E). They represented their data on “Supersaturation-Impurity Solution Concentrations” diagrams, named morphodromes, in which well-defined areas of existence were assigned to each habit combination of the grown crystal. Kleber and Schiemann (65E) studied also the changes in the habit of NaCl crystals by PbCle impurity and correlated them to the amount of lead adsorbed and incorporated a t the (100) and a t the (111) faces. They observed the greater growth reduction in the (111) faces; also the adsorption of lead on (111) faces was more intensive than on (100) faces. The latter finding is rather strange since all previous studies, using easily detectable radioactive lead, reported no lead incorporation a t the (111) faces of NaCl. T h e above mentioned theories (Cabrera-Vermilyea and Sears) attempt to explain only haw impurities which adsorb on the face of a growing crystal affect growth. Another important question however, is why certain impurities adsorb on the crystal face and retard growth and others do not. This question has been considered by various investigators. Systems for which explanations for the adsorption have been offered on a crystal-chemical basis include Cd2+ on KC1 crystals (707E),Pb2+ on NaCl crystals (23E)and a large number of oligosaccharides on sucrose (705E). Kern summarized his ideas on the subject in a recent article in a Sovietjournal (60E). As in the past, very few studies were reported during the period covered by this review, where the emphasis was on the quantitative effect of impurities on the absolute growth rate of specific crystal 94
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
Figure 2. Thermal etching at IOOO’C of Z n O on the (007) basal plane, 40,000X
faces. Yet, such quantitative kinetic data are required in order to test the various proposed models about growth in the presence of impurities or to develop new more satisfactory ones. Reliable kinetic data on sucrose crystals, obtained under wellcontrolled conditions of constant supersaturation, temperature, liquid velocity, and impurity concentration were reported by Smythe ( 704E). Unfortunately, however, the mass deposition rates for the whole crystal and not the more meaningful individualface growth rates were recorded. A similar quantitative study was made of the effects of anionic ( I ) and cationic (11) surface active agents on the growth of the sodium triphosphate hexahydrate (Na6PaOlo.GHzO) from aqueous solution (772E). I n this study the growth rates of the various types of faces were measured independently. The results simply confirm all previous observations by Michaels and his coworkers a t M I T on the effect of surface active agents on adipic acid crystals. T h a t is: (a) selectivity of the impurity effect; for instance on (OTO) faces, growth was retarded mostly by ( I ) ; on (100) faces, however, growth is greatly reduced only by (11). Similarly, adsorption isotherms showed that ( I ) is particularly adsorbed on (OXO), and (11) on (100) faces; (b) growth rates increased more rapidly than with the second power of the supersaturation. Still no satisfactory explanation has been offered for this; (c) under certain conditions of supersaturation and additive concentration, the additive enhanced the growth rate. This is one of the very few cases where acceleration by additives has been claimed. Certain attempts to obtain a n expression relating the growth relate to impurity concentration in solution have been reported. I n 1958 Bliznakov suggested the expression
R
=
Ro
-
(Ro
- R,)O
where R is the linear growth rate at surface coverage of impurity e and impurity concentration C,, R, the growth rate at maximum coverage and ROin the absence of impurities. Assuming Langmuir adsorption and rearranging he obtained B 1 1 1-)7 1-)7,ci
1
f1-7,
where B is a constant, 7 = R/Ro and 7 , = R,/Ro. The important feature of this expression is that a plotzof 1/( 1 9 ) us. 1/Ci should give a straight line. This expression was used in two recent papers by Bliznakov (24E, 25E) to correlate successfully his data on the growth rates of potassium bromide and potassium chlorate crystals in the presence of various additives and a t different temperatures. Assuming a n
-
Arrhenius type dependence of the adsorption constant B on temperature, he also calculated a n energy quantity he termed “heat of adsorption of the impurities a t the active growth centers.” Two other investigators correlated their data by Bliznakov’s expression (42E, 108E). I t should be noted, however, that in the cases in which the above expression was verified, the impurity concentration was varied only within one order of magnitude. A different expression, however, was suggested for the system “KCl crystals/Pb2+ impurity” in which the impurity varied up to three orders of magnitude. I t was observed (29E) that the ratio S/C,O 4, where S is the percentage supersaturation, remains constant for a given growth rate. Although no theoretical justification for this has been yet presented, nevertheless it is of great practical importance. For the first time, by knowing the growth rate as a function of supersaturation for just one lead concentration, one could predict the growth rates for other lead concentrations. Impurity Incorporation. Impurities adsorbed on the surface of a growing crystal will affect not only the growth rate or the habit of the crystal but also, when buried inside the lattice, the purity of the crystal. Because of the increasing demand for pure materials in recent years, the study of the mechanism of the capture of impurities and its dependence on the conditions of growth has aroused considerable interest. An equilibrium impurity distribution coefficient, k,, can be defined as the ratio of the impurity concentration in the crystal to the concentration in solution. Although in most of the practical processes an effective (nonequilibrium) distribution coefficient is involved, a knowledge of the value of k , for a particular impuritycrystal system is desirable. I n a recent Soviet study (98E), a n empirical correlation predicting the value of k, was tested against experimental data. These data appeared to support the author’s argument that k , is determined mainly by the solubility of the impurity in the solid phase. This solubility is, in turn, determined mainly by dimensional (difference in the atom size between impurity and base element) as well as electrochemical factors (structure of valence electron shells). A number of investigators studied exclusively the incorporation of isomorphous impurities. Makarov (77E) argued that “mutual chemical indifference,” and not ionic radii size ratio is the more important factor in the case of isomorphic replacement of atoms in ionic crystals. An experimental criterion for detecting the mutual chemical indifference of a given pair of elements is the fact that no chemical compounds are formed by them during interaction in elementary state. Zhmurova et al. (119E) studied the effective distribution coefficients, k e j f , in monocrystals of various alums grown in the presence of comparatively large concentrations of isomorphous impurities (0.1 to 10%). Their results indicated that kerf does vary for the various faces; this disputes the old rule that truly isomorphous impurities fail to produce a sectorial impurity distribution in a crystal. The study was not conclusive on the question of how the capture of impurities is affected by the growth rate of the crystal. Andreev continued his studies on the distribution coefficient of impurities in various alkali halide crystals (2E, 3E). H e has been determining the impurity content of the crystal by precise measurement of the density of the crystals, by flotation in a liquid whose density was precisely known. H e claims that, because of the mm/min), the distribution slow growth (average rate: 2 X coefficient he obtained was the equilibrium one. H e did not substantiate, however, his claim with the appropriate data (diffusivity of the impurity in the crystal a t the crystallization temperature). The same author had previously determined k, for the same systems crystallizing from the melt. A comparison showed that the k , for melt growth is in general greater than k, for solution growth by one or two orders of magnitude. T h e last conclusion is also supported by two other studies (63E,64E). T h e incorporation of a dye in a crystal was correlated with data from adsorption isotherms of the dye on the crystal surface by Draganova (37E). The question of the location of the captured impurities in the crystal lattice was treated by other investigators. Buswell (31E)
TABLE I I-E. VISUAL OBSERVATION OF MORPHOLOGY O F CRYSTAL SURFACE DURING OR AFTER GROWTH (FROM SOLUTION) CryrioNizing syrfem
Re/erence
Ag Au CdIz Diamond Diphenyl Ge Gypsum KCl KHzPOi MgO Mo NaCl NaNOs PbS
26E 83E 54E, 88E 114E, 115E 38E 7 76E 47E 7773 88E, 106E 82E I16E 27E, 88E, 96E,99E, 7 76E, 117E 7 16E 36E
found segregation of impurities along dislocation lines. To explain data from X-ray topographic studies, Ikeno et al. (57E)assumed that some impurity precipitation in platelet forms occurred perpendicular to the growth direction in NaCl crystals. Melikhov (78E) discussed the various types of nonequilibrium impurity capture and also the means of identifying them. Experimental data on the incorporation of Pb2+ in KCl were presented by Botsaris et al. (28E). Their investigation confirmed in a quantitative way certain observations made in the past, more specifically that the impurity distribution coefficient crystal-tosolution, whose value is usually smaller than unity, may become larger than unity a t very low impurity concentrations in the solution. This inversion of the distribution coefficient, k e f f , provided a n explanation for the difficulty experienced in practice, in purifying certain inorganic crystals by repeated crystallizations. I n the same paper, data on the dependence of k,ff on growth rate, as well as a model of nonequilibrium capture of impurities in a growing crystal were presented. The latter was based on ideas developed in the field of crystallization from melt. A tremendous amount of theoretical and experimental work on the impurity incorporation has been done in that field. The above paper demonstrated the need for future work that will transport ideas and models developed initially for melt growth to the systems which are of particular interest to the chemical industry, Le., systems crystallizing from solutions, Visual Observations of t h e Crystal Surface d u r i n g or after Growth. Since Frank in 1949 suggested that screw dislocations play a n important role in the growth of crystals, many investigators started probing the crystal surface using refined microscopic techniques. Initially the purpose was to identify the growth spirals resulting from the screw dislocations. Later, however, the scope was broadened to include the observation of steps moving across the growing surface as well as their interaction among themselves and with imperfections. The growth steps may originate not only from a screw dislocation but presumably also from a two-dimensional nucleus. I n both cases the steps should appear to start somewhere on the surface. Certain investigators, however, claimed that the steps in a number of systems were originating a t the edges (26E). On the other hand, My1 et al. (88E) used a cinematographic technique to observe crystal growth from solutions and showed that the growth steps of NaCl in the cubic system, CdIz in the hexagonal system, and KH2PO4 in the tetragonal system, originated on the surface and neither on edges nor corners. The reports of other investigators which used visual observations of the crystal surface as a means of extracting information about the growth process are included in Table 11-E. Techniques a n d Apparatus for Study of Growth. Interferometric techniques have been used by a number of investigators VOL. 6 1
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for measuring solute concentrations and gradients in the neighborhood of a growing crystal face (46E, 53E, 72E, 773E). The first study using Rochelle salt single crystals reported that the solute concentration is greater near the center of a growing face than at the edge. The use of X-ray diffraction topography to determine the history of growth of a crystal through a determination of zoning and sectors of crystals and also defects such as dislocations, twins, etc. is discussed by Kabanovich et al. (56E). Apparatus for growing seed crystals from solution are described by t w o other Soviet studies (87E, 92E). Byrne (32E) compares the two methods of growing crystals from solution, i.e., supersaturation and evaporation, for nine inorganic materials, including Nac l o s , NaNOs, Rochelle salt, and potash alum. The problem of growing crystals of an organic material which has low solubility and is unstable in solution was attacked by Tichy ( 7 7OE). A method for growing such materials was described. Inclusion of Liquid. Crystalline material grown from solution very frequently contains liquid (solution) inclusions, which may be sometimes quite large (up to 0.5% water in large sugar crystals). The presence of these inclusions is often undesirable whether the crystals are for scientific purposes or industrial uses. It degrades many physical properties of large single crystals. I t is even suspected to contribute to caking problems. Wilcox ( 7 78E) emphasizes that, since usually crystals reject impurities during growth, inclusions may even be more rich in impurity than the mother liquor. An old mechanism-suggesting that many crystals grow initially in a dendritic form and that subsequent filling of spaces between dendrite arms is not always complete and results in inclusionswas again invoked by Kleber and Schiemann (66E)to explain their observation in NaCl crystals. Their crystals were precipitated from aqueous solutions containing CuC12. The inclusions could be easily detected because of the green color of the occluded solution. I n a recent study, however, Brooks et al. (30E) considered the above mechanism to be a n extreme case and proceeded to describe a mechanism responsible for inclusion formation even in regions of nondendritic growth. Working with ammonium dihydrogen phosphate and sodium chlorate they correlated the formation of the inclusions to the introduction of sudden step changes in supersaturation. They were able to show that inclusions are associated with certain faces, whose growth rates relative to the rates of the contiguous faces are affected by the sudden change of conditions. The sequence of events leading to occlusion is: formation of the special faces when the growth rate was slow; development of imperfections on the faces which became fast-growing when the supersaturation increased; overgrowth of the imperfections by the enlargement of adjacent slow-growing faces. A different approach is taken by a Soviet study (QE). The conditions of the origin of inclusions are discussed in terms of the model of layer growth of crystals by the advancement of steps across the surface. They conclude that the production of inclusions a t any point is governed entirely by local conditions and more specifically by the concentration gradient along the height of a step. A critical height for a step is postulated beyond which a layer of solution is trapped. Wilcox (778E)in a very interesting study reviewed first the mechanisms proposed up to now for the formation of inclusions in crystals during growth; he also described processes by which inclusions are formed after growth. Then he covered the literature dealing with techniques for removal of these inclusions. Isothermal heating, even to decrepitation was shown to be inadequate to remove all the inclusions from a crystal. Fortunately, however, gradient techniques are successful to move liquid gas and sometimes even solid inclusions through and out of crystals. For the purposes of discussion the author used the example of a temperature gradient. In this technique the result one sees externally is the movement of the inclusion, usually toward the heat source. The actual process, however, involves dissolution of the crystalline material on the high-solubility side of the inclusion, diffusion across the liquid, and precipitation on the lowsolubility side. An equation for the rate of movement of the inclusions was presented. The rates predicted by the equation 96
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
were not far from the experimental ones. Although the gradient techniques are ripe for application, a need exists for a technique to remove the inclusion from the vicinity of the crystal surface after it emerges, otherwise the impurities in the inclusion remain on the crystal surface as the solvent evaporates. The study of the liquid inclusions in crystals has not only practical but also theoretical importance. Their position and arrangement actually provide a record of the growth of the crystal. The more accurately future investigators learn to read and interpret this record, the more we will learn about the crystal growth process itself. Epitaxial Growth a n d Crystallization of Human Stones. Epitaxy is the growth of one crystal on a substrate of another, with a near geometrical fit between the respective networks which are in contact. In contrast to growth from vapor, the amount of work done in epitaxial growth from solution is rather limited. Moisar (80E)studied a process related to photography. His results on the kinetics of AgS deposition during the decomposition of thiosulfate on monodisperse AgBr crystal dispersions indicated a first order reaction a t the (111) faces. The kinetic data, however, for the deposition on the (100) faces could be correlated by an expression derived from a two-dimensional nucleation model. Workers in the field of epitaxial growth have been considering mica as an ideal substrate for studying the kinetics of two-dimensional heterogeneous nucleation using alkali halides. Detailed studies of the growth sites, however, by Dunning and Savva (4723) showed that nucleation of "11 on mica a t undercoolings of 1' to 2°C occurred a t defects on the mica surface and not through the formation of two-dimensional nuclei. Epitaxial growth was used by Distler and Kobzareva (35E) in studies of long-range surface forces of solids. The epitaxial growth of lead sulfide was carried out via intermediate amorphous plastic layers deposited on the surface of the crystal substrate (mica, silicon, quartz, etc.). The use of layers of various thicknesses (from 100A to several microns) made it possible to determine the spheres of action of the surface forces. A series of experiments on mica indicated that the morphological picture of the epitaxial growth of PbS through an intermediate plastic layer of thicknesses up to 1500A accurately repeated the corresponding picture of the epitaxy of PbS directly on a mica surface. On increasing the thickness of the intermediate layer to several thousand A, the crystallization of PbS remained broadly the same, but the orienting effect which characterizes epitaxy vanished. The above investigators hypothesized the existence of two qualitatively different types of long-range-acting local active centers on the crystal surface. The centers of the first type had an orienting effect, and under their influence epitaxial growth took place. The second type of centers, which are characterized by far larger spheres of influence, also initiated crystallization, but had no orienting effect. The investigators were also able to decorate the same surfaces with charged colloidal particles. This was interpreted by them as indicating that the above active centers are electrically active and more specifically aggregates of defects (vacancies, impurity atoms, and complexes of these). No proof is offered, however, that the same centers were involved in both types of decoration: crystallization and colloidal particle deposition. The important implication of this study is that surface processes such as adsorption, heterogeneous nucleation, and crystal growth may take place not only on the surface but also a t appreciable distances from it. According to two recent papers (74E, 75E), epitaxy from solution appears to play a very important role in the formation and growth of pathological stones in the human body, such as urinary calculi and gallstones. The author examined by X-ray diffraction a large number of stones (more than 1000) in a n attempt to determine their crystal morphology and composition and through them to conclude about the conditions of growth, to correlate with dietetic habits, etc. The common feature of many kidney and bladder stones was the existence of alternating layers of differing composition around a center nucleus. In the same study the dimensions of the networks in the occurring faces of the common stone-forming compounds were examined. I t was found that a variety of excellent fits (too many to be coincidental) are possible for epitaxial growth on a nucleus of uric acid and three other sub-
stances most frequently found in adult urinary calculi. The conclusion advanced was that deposition from a supersaturated solution of a stone-forming compound will occur a t once on a suitable seed provided that there is a n epitaxial relationship. Finding ways to prevent either supersaturation or the presence of seed is a very difficult biological problem ; however, investigating ways to prevent epitaxial deposition is a n easier experimental problem. For this reason the research trend is in the direction of finding by in vztro experiments additives retarding the growth of the stone-forming materials. The role of the organic components in the epitaxial growth of stones also remains to be defined. Effects of Irradiations a n d Fields. The number of independent variables in a crystallization process is extremely small: liquid velocity relative to crystal, supersaturation, crystallization temperature and, in unsteady-state industrial processes, the rate of supersaturation change. Introduction of additives into the solution is actually an attempt to increase the number of controllable variables. Other attempts include the use of ultrasonic and high energy radiations, and magnetic or electric fields during the growth. The effect of ultrasounds in solution crystallization has been studied in the past to some extent, especially by Soviet scientists. The conclusions were that ultrasonic radiation accelerates nucleation rates and, in certain cases, growth rates of single crystals. In investigations in which both the mass-transfer and the particle incorporation steps of the crystal growth process were studied, the latter step was found to be unaffected by the ultrasonic radiation. The mass-transfer controlled crystal growth, however, was found to be accelerated although only if a crystal was within a n antimodal plane. Two recent Russian studies (7E, 8E)are not very illuminating with regard to the fundamental effect of ultrasound on the crystallization process. I n the first the quality of crystals obtained under ultrasound irradiation was found to be poor compared to crystals grown under the same conditions but without ultrasounds. I n the other study the appearance of crystals inside aerosol drops of a supersaturated solution was observed to be more rapid when crystallization took place in an ultrasonic field. One application of ultrasounds to a crystallization process of much practical importance, i.e., scale formation on a heat exchange surface, was investigated by Sergeeva (97E). The purpose of this study was to test suggested hypotheses regarding the prevention of scale formation by ultrasonic techniques. A system consisting of KzCrz0, crystallizing from hot solutions on a cold surface was used to simulate scale formation. A motion picture camera filmed the formation of the crystalline precipitate on the cold surface of a heat-exchanger tube, in which either longitudinal or transverse standing waves were excited. Ultrasounds were observed to increase the rate of initial crystallization of K2Cr207. The study could not, however, distinguish whether the acceleration effect was on the nucleation or the growth process. The final conclusion was that ultrasonic vibrations do not prevent crystallization but simply promote the separation of the crystalline layer from the heat exchanger walls, as soon as it has achieved a critical thickness. There is conflicting evidence regarding the effects of magnetic fields on the growth rates of seed crystals. Some of the experimental results are contrary to theoretical predictions. For instance, it is difficult to understand why a magnetic field should increase the rate of deposition of diamagnetic materials like sugar or tartaric acid from their aqueous solutions as previously reported. Schieber (95E)pointed out that most of the published data report crystallization effects obtained through a reduction of the temperature. This makes the interpretation of the results very difficult. Also, none of the studies report the effects of magnetic field gradients vs. homogeneous fields. He, thus, chose to use in his study isothermal conditions and a homogeneous magnetic field. The result was a n increase of the isothermal rate of growth of the paramagnetic seed crystal, Fe(NH4)2(SO& 6 H 2 0 ; however, no measurable magnetic effect was found on the dissolution and growth of the diamagnetic A l K ( S 0 ~ ) ~ . 1 2 H z O . I t has been suspected, from the studies of the effect of high energy radiation on solid materials and on the nucleation processes in vapor-liquid phase transformations, that high-energy radiation would have a n effect on the crystallization of salts from solutions.
It was reported (7E)that saturated CuSO4 solutions when cooled and simultaneously irradiated by X-rays yielded larger and more perfect crystals, as compared with crystals from parallel runs made without irradiation. I n another qualitative study (ME),the changes in the habit and surface morphology of KHzPOl and Rochelle salt crystals grown from water solutions in the presence of X-rays, were found to be very similar to those occurring in the presence of impurities. If impurities formed by the X-rays were indeed involved, they had to be transient impurity species; no habit modification was observed when the irradiated solutions were allowed to crystallize in the absence of radiation. Formation of lattice defects in the growing crystal could also be hypothesized. Another possibility, not mentioned by the author, is that irradiation might have affected the nucleation rate and thus indirectly the supersaturation a t which the crystals grew. Gamma-rays were also used in a quantitative study involving the growth of potassium chloride seed crystals from aqueous solution under well-controlled conditions of constant temperature, supersaturation, and impurity Pb* level (27E). Linear growth rates were measured in runs made both inside and outside a yradiation field. The effect of the 7-rays (retardation) was significant only a t certain impurity concentrations. Etching of the grown KC1 crystals revealed that irradiation under certain conditions reduced the number of dislocations. A possible mechanism involving change in diffusion rates of impurity atoms in the crystal lattice was suggested by the authors to explain the results. Crystallization from solution appears to be a very complex system for the study of the effects of high-energy radiation. However, it is possible for radiation to become a valuable tool in crystal growth studies when simpler systems of growth from vapor are employed. Growth from Nonaqueous Solutions. The growth of compounds from metal solutions was recently reviewed by Luzhnaya
(76E). A number of investigations involved the growth of the following crystals from liquid gallium solution : epitaxial growth of GaAs (59E), growth of nitrogen doped GaP (709E), growth of a GaSGaP solid solution (97E)and growth of large GaP crystals (93E). Solution growth processes appear to gain importance for the growth of high melting, unstable compounds such as Gap, because the temperature of growth could be significantly lower than that of other methods. Other advantages pointed out in (93E) are the lessening of contamination from container materials and the purification that can result by the dilution of impurities in large volume of solvent. Other examples of growth from metal solutions include the growth of CdS from liquid Cd solution (50E)and &Sic from liquid Si solution (5E). Miscellaneous. Hartman (49E)reviewed the literature data on the effect of crystal structure on the morphology of a crystal and also the data on the effect of the crystallization parameters (impurities, temperature, etc.) on the crystal structure. Soviet investigators had shown theoretically in the past that the surface of a large single crystal growing from soldtion is nonisothermal and that the temperature must be higher a t the center of its faces than a t the vertexes. This was now confirmed experimentally by Kuznetsov and Kharin’s work (70E)with Rochelle salt crystals. The recrystallization of crystals suspended in a saturated solution, in other words the growth of the large crystals at the expense of the small ones, is a process of practical importance. Its kinetics was the subject of two papers (SE,67E). I n the second, the crystals were triglycerides and the progress of the recrystallization was followed by taking samples of the suspended crystals and measuring their specific area with a permeation technique. Crystal dissolution experiments are usually undertaken in order to provide, on the one hand, data on the kinetics of dissolution, and on the other hand information about the growth process. Three papers dealt with dissolution (48E,77E,9OE). The necessary requirements that must be met for obtaining smooth-interface crystal growth from solution were discussed by Tiller ( 7 77E). VOL 61
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TABLE I-F. EXPERIMENTAL STUDIES OF KINETICS AND MECHANISM OF GROWTH FROM T H E MELT. Reference
.%laterial
Trilaurin Gallium Bismuth Mercury Potassium Cadmium Rubidium Gallium Salol 1,2,4-Trichlorobenzene Tin Bismuth Lead Phosphorus Salol Salol Thymol Silicon Sodium disilicate Ice 1,2-Diphenylbenzene
Defect (screw dislocation) Two-dimensional nucleation Defect (screw dislocation) Continuous (surface roughness) Continuous (surface roughness) Continuous (surface roughness) Continuous (surface roughness) Continuous (surface roughness) ..
1
(4F) (5F)
i
(67F)
J-
Defect Defect Defect Defect Defect Defect
(33W
to continuous (screw dislocation) (screw dislocation) (screw dislocation) (screw dislocation)
1
(36F) (55F, 73F) (56F) (63C (68F)
Defect Defect
Experimental Studies of Crystallization from the Melt
Kinetics of Growth from t h e Melt. I t is now realized that an accurate description of the growth of a crystal from the melt requires the consideration of (1) the atomic or inolecular mechanism of attachment at the crystal surface and (2) of the transport of heat and mass in the bulk phases. The consideration of the interactions of these processes and the anisotropy of crystal surfaces has led to studies and theories of morphological stability and dendritic growth, eutectic formation, and solute or impurity distribution, as well as interface attachment kinetics. Jackson in a series of papers (ZGDb, 27Db, 28Db, and 2SDb) on the theory of crystal growth has emphasized the importance of the surface configuration in determining the interface attachment kinetics of crystal growth from the melt. He also noted that most quantitative data on interface kinetics for growth from the melt are of questionable reliability or are not complete enough for comparison to theory. Hillig (2ODb) considered the influence of cluster coalescence on the growth of crystals having low edge energies. Chernov (70Dp)has outlined a general theory of crystal growth taking into account the effect of both surface and bulk processes on the shape, growth rate, and impurity content of a crystal. Kirwan and Pigford (56F)presented a method, based on absolute reaction rate theory, for predicting the interface kinetics of crystals growing from pure and binary melts. Recent experimental measurements of interface kinetics for the growth of pure materials from the melt are summarized in Table I-F. Included is the apparent growth mechanism deduced from the observed kinetic law or from morphological observations. A number of new experimental techniques have been introduced in a n attempt to measure interface kinetics. Interferometry has been used in a number of cases (37F, 52F, 56F) to measure the undercooling or concentration a t the face of a growing crystal. T h e determination of interface temperatures by the technique of isenthalpic solidification is discussed in three papers (32F, 331;, 95F). I n another paper (33R)the temperatures of lead, tin, and bismuth crystals growing from the melt were measured by infrared thermometry. A theory for the measurement of atomic kinetics 98
INDUSTRIAL A N D ENGINEERING
CHEMISTRY
using Peltier heating and cooling was presented (87F). The kinetics of ice were measured by James using the thermal wave technique ( 5 0 F ) . James and Sekerka ( 5 7 F ) discussed the effect of impurities of kinetic measurements by the thermal wave technique. Temperature gradient zone refining was used in a study of the mechanism of growth of indium antimonide (43F)and silicon (63F). The use of viscous, glass-forming materials as model systems for studying interface kinetics because of the negligible heat effects was applied to sodium disilicate ( 6 8 F ) and 1,2-diphenylbenzene (39F). The effects of electric fields (30F,83F, 94F) and ultrasonic fields (3F, 868’) on crystal growth rate and orientation were investigated. Compared to pure materials, relatively little work has been done on the interface kinetics of binary systems. Chernov considered impurity incorporation in crystals from a kinetic viewpoint (9D6, 1006) and as a random walk problem ( 8 0 6 ) . Jindal and Tiller (30Db) and others ( 3 0 b , 4Db) calculated nonequilibrium distribution coefficients by the methods of nonequilibrium thermodynamics. I n another paper ( 5 W )crystallization kinetics of binary melts was treated from the absolute reaction rate theory viewpoint and the theory compared to experimental results for melts composed of salol and thymol. Measurements of growth rates in metal alloy systems were presented in two papers (74F, 75F). Baker and Cahn ( 8 F ) observed solute trapping of zinc when zinccadmium alloys were rapidly solidified. They concluded that only the theory of Chernov (9D6)could explain the results. Morphological Stability a n d Dendritic Growth. A number of papers have dealt with the interface stability of a growing crystal. Morphological instability owing to constitutional supercooling gives rise to a cellular interface under mild conditions and to a complete breakdown of the interface in the extreme. I n Table 111-D are summarized a number of theoretical papers which predict the onset of surface instability using perturbation analysis and both time-independent and time-dependent formulations of the governing equations. They consider the infiuence of different growth geometries and the effects of interface kinetics and anisotropic surface tension on stability. The stability of the interface during temperature gradient zone refining was the subject of two papers (13D6,45Db). Y u e (708F) observed the formation of a cellular interface in dilute A1-Fe alloys and compared the results to a theory of constitutional supercooling which included the effects of thermal diffusion. Cheng, Irvin, and Kyle ( 2 7 F ) observed cellular interface formation during normal freezing of a number of organic mixtures. Weinberg (102F) considered the validity of observing a decanted interface morphology to determine the degree of solute segregation within the interface. Constitutional supercooling in the presence of natural convection during crystallization of (K,Na) (Br,Cl) solid solutions was discussed by Hamalainen (44F). Hardy and Coriell (46F) measured the growth rates of
TABLE 111-8.
MORPHOLOGICAL STABILITY STUDIES Dercription
Planar interface, effect of interface kinetics Planar interface, effect of stirred melt Planar interface, combined radiative and conductive heat transfer Planar interface, time-dependent theory Sphere, effect of interface kinetics Sphere, time-dependent theory Cylinder, effect of interface kinetics Cylinder, effect of interface kinetics and surface tension anisotropy Needle crystal, effect of interface kinetics and surface tension Arbitrary shaped particle, effect of interface kinetics Arbitrary shaped particle, effect of interface kinetics and surface tension anisotropy
Reference
(49Db) (14Db) (4206) (4706) (7206) ( 4 4 06) (34Db) (I7 0 6 )
(35Db) (46Db) (6Db)
TABLE 11-F. EUTECTIC SYSTEMS FORMED BY U N I D I RECTIONAL SOL I D I FI CAT1ON System
Reference
Ag-Au-Si, C-Cr-Ni-Si LiF-NaF, Al-Zn, Al-CuAlz, Al-Ag2Al Fe-C, Ni-C, Fe-C-Si Pb-Sn A120 3-Y zA160 1 2 A1-CuA12, A1-A13Ni9, AI-Si, AI-Ge, Ag-Si Nb-NbZC, Ta-Ta& Bi-Sn, Si-Pb, Bi-T1, Bi-Ag, Bi-Zn
slightly perturbed ice cylinders and used stability theory to obtain a value for the ice-water interfacial free energy. Kotler and Tarshis (32Db, 3306) reviewed the mathematical descriptions of freely growing pure dendrites. T h e mathematics of the steady-state growth of a platelet dendrite into its undercooled melt is described in a paper by Hillig (1QDb). Another paper (38F) proposes the conditions necessary for the growth of dendrites and lamellae and compares the predictions to observations on the solidification of high purity copper. Morris and Winegard (72F) observed dendrite tip instability by using transparent organic compounds as analogs of metals. A number of Russian papers dealt with dendrite formation in the growth of semiconductor materials (48Db, 26F), particularly silicon (4OF) and germanium (42F, 78F, 79F). O’Hara, in two papers (75F, 76F), has discussed the growth of tin dendrites from the melt. T h e dendritic growth of ice from both pure water (54F, 104F) and aqueous solutions (82F)has been reported. Eutectic Solidification. The properties and uses of two-phase composite materials formed by unidirectional solidification in eutectic systems has spurred interest in the mechanisms and control of eutectic microstructures. Cooksey, Day, and Hellawell (24F)discuss the influence of growth rate, impurity content, and temperature gradient upon the reaction mechanism and the type of microstructure that results. Hunt (21Db) reviewed the more important aspects of lamellar and rod-like eutectic growth and concluded that present theories were not satisfactory for describing either the lamellar spacing or the lamellar to rod transition. I n a paper by Hunt and Jackson (ZZDb),a theory for the transition from eutectic growth to dendritic plus eutectic growth was extended to metal-like systems. Mollard and Flemings ( 4 7 0 6 ) also considered the conditions necessary for plane front growth of a eutectic alloy. By using a simple constitutional supercooling criterion, they found the extent of the eutectic range to depend upon the temperature gradient a t the interface. I n another paper (70F), Mollard and Flemings observed the breakdown of the two phase interface in the lead-tin system. A paper by Hurle and Jakeman (23Db) calculated interface stability for two classes of lamellar eutectics; those in which a t least one component exhibits faceted growth and those in which metal-like (nonfaceted) growth occurs. I n Table 11-F are presented systems in which eutectics of controlled microstructure have been produced. I n all entries in the table, unidirectional solidification was employed to produce the eutectic structure except for (28F) in which the Czochralski technique was used to observe the development of preferred orientations in the structure produced. Transport Processes i n t h e Melt. Transport of heat and mass in the melt from which a crystal is growing may occur by diffusion, by convection, or by both processes. When thermal convection can be suppressed in the melt, the heat transfer and solute distribution are governed by diffusion and are amenable to mathematical analysis. A number of papers ( IDb, 5Db, 25Db, 38Db, 39Db) consider the problem of impurity distribution by solution of the appropriate heat conduction and diffusion equations. Another paper (24Db) mathematically analyzes the influence of
temperature oscillations in the melt on the impurity distribution in the solid. I n the more usual case where convection in the melt is important, it is difficult to analyze the situation exactly. Frequently, the effect of the mass transfer processes in the melt are lumped with the solid-liquid distribution coefficient to produce a n effective distribution coefficient relating the impurity concentration in the solid to that in the bulk of the liquid. Table 111-F lists a number of systems in which effective distribution coefficients were experimentally observed. Such coefficients are dependent upon the geometry and fluid mechanical conditions in the melt as well as upon melt composition and crystal orientation. A number of papers (18F, 19F, 45F, 48F, 97F) experimentally dealt with the influence of convection on impurity distribution during horizontal solidification. Two papers (31F, 98F) showed that magnetic fields applied during the horizontal solidification of metals suppressed temperature fluctuations due to natural convection and prevented solute banding in the crystal. Another paper (23F) measured the temperature distribution and fluid flow pattern ahead of a stationary solid-liquid interface. A paper by Baralis and Perosino (IOF) observed convection induced impurity distributions during the pulling of germanium crystals by the Czochralski method. Experimental Studies of Cryslallization from the Vapor THIN FILMS AND EPITAXY
Thin-film and epitaxial technology have advanced over the past two years in proportion with continuing developments in the field of microelectronics. Epitaxy or overgrowth basically consists of depositing a layer of crystalline material on a well-defined crystallographic face of a substrate. The orientation and structure of the final layer is dependent on the nature of the substrate as well as the deposited atoms. There appear to be two basic groups of people working in the epitaxial and thin-film field: those people motivated to produce new or improve old semiconductor devices, and those interested in the phenomena and mechanism of epitaxy and thin-film growth. Chemical and physical deposition from a gas or liquid are used to obtain epitaxial and thin-film structures. Chistyakov (3OGa) has classified a considerable number of processes which result in epitaxy. For example, the sandwich method of Droducinrr eDitaxial crystals has been emphasized by a number of investiiators ( 7 12Ga, 7 IdGa, 176Ga). Most of the compounds studied over the past two years are of importance to the electronics industry. Table I-G lists some of the epitaxial systems studied according to the compound or element(s) involved, process involved, or influencing parameters. I n a recent review article Beak (17Gu) describes modern developments in semiconductors. Caveney (27Ga) discusses epitaxial growth of the electronically important 11-VI compounds. Tachi-
~
TABLE I l l - F m EFFECTIVE DISTRIBUTION COEFFICIENTS System
Reference
W in M o Divalent impurities in KC1 Cu, Ag, Ni in In Fe, Cu, Ag, in ZnS Na, Rb, Cs in KI and K F Al, P in S i Cd in Z n Numerous elements in Ge and Si Cu in A1 Fe, Ag, Sn in TlzTeg Au in T e Ag in NaCl Al, Si, Fe, Te, Bi in GaAs
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TABLE I-G.
EPITAXY AND THIN FILMS
Elernenf or compound deposited
-
Ag Alkali metal halides Alkali metal halides as substrates A1 A1 oxide A1P A1 nitride AS406
Au
Bi Bi oxide C on NaCl CdS CdSe co Cr on rocksalt Crz03 cu Fe GaAs Gal-,Al,As Ga,Int-,As GaP GdIG Ge Hg on W HgTe Ice on sodium bromate InAs InP InSb Mica as substrate MgO Mo NHJ Nb Ni Ni ferrite Ni-P Polyamides on quartz PbS PbSe PbTe PtSi Se
Si Sic Si nitride Ta T e on Cu (111) UC as substrate VdOz YIG ZnO ZnSe ZnS
References Go
57, 87, 88, 89, 97, 142, 181 105 59, 99 76 166 152 33 24 7, 12, 68, 69, 70, 85, 87, 91, 104, 125, 133, 142, 183, 190, 195, 199 149 34 43 22, 58, 73, 78, 193, 194 4, 202 139, 140, 172 38 764 91, 100, 189 131, 149, 176 35, 42, 51, 56, 61, 67, 76, 77, 93, 98, 108, 171, 112, 118, 170, 171, 174, 975, 187, 198, 207 20 7 36 39, 65, 97, 118, 121, 154 129 9, 14, 18,47,60, 106, 7 14, 144, 173, 197,204 66 6 146 128 75 102 3 130, 165 115 49 82 28, 168, 196 135 124 19
50 50 50, 117, 141 101 13, 178 2,8, 10, 17,21,32,46, 48, 52, 53,54,86,9395, 147, 153, 155, 156, 158, 162, 163, 179, 185, 186, 188,200, 206 103, 159, 182 80, 90, 203 37 5 26 55, 71, 160 7 29 161 25, 79 92, 791
Processes and equz$menl
Growth of crystalline layers Growth of amorphous films Growth of single crystal films Growth of polycrystalline films Sputtering of multilayer thin films Epitaxial growth (general) Laser evaporation to produce thin films Semiconductor growth Thin film semiconductors by eiectron beam deposition Doping semiconductors Exploding wire deposition Evaporation-diffusion-new process for epitaxy Multilayer epitaxial systems Macromolecules on quartz Sandwich method for epitaxy Vacuum deposition equipment High capacity sputtering apparatus
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
177 120, 180 63 72 40, 41, 44, 45, 83, 119, 184 205
11, 137, 151, 167 157
150 127 123 110
169 116 20, 44, 136, 167 134
References Ga
Intrinsic parnmeterr
Crystallite mobility Electric charge effect on thin metal films Formation processes in evaporated thin films Growth orientation in vapor deposition Growth habit in films grown over wires Impurity (surface active) Large scale surface perturbations Light irradiation effects Molecular processes during growth Orientation effects on impurity control Problems during deposition of optical thin films Surface defects ~~~
100
References Ga
81
726 74
84 192 7 109 163 107, 113 15 65 148 132, 143 ~~
kawa ( 184Ga) considers epitaxial technology from the standpoint of ultimate use, characteristic reactions involved, impurity introduction, typical equipment, and experimental methods. Doo and Ernst (44Ga) have reviewed epitaxial processing technology and equipment. Inuzuka (84Gu) i n a Japanese article is concerned with the formation processes involved with evaporated thin-film growth. Dorfman and Bol'shakov (45Gu)discuss the nature of epitaxy from a mechanistic standpoint. They include a phenomenological discussion of the important parameters in epitaxial growth: substrate structure, diffusion, transport reactions, dislocations, etc. A number of studies have examined the morphology of the epitaxial surface in a n effort to learn about the mechanism(s) involved. Bethge (15Ga) and Grigson (64Go) viewed surfaces undergoing epitaxy with electron microscopy and scanning electron diffraction. With the development of low energy electron diffraction (LEED) coupled with Auger emission spectroscopy as a useful tool for surface analysis, several investigators have been able to resolve microstructural and compositional aspects of surfaces undergoing epitaxy. For example, Gallon et al. (57Ga) examined silver deposition on potassium chloride with LEED and Auger spectroscopy. Also Spiegel (781Ga) studied silver film growth o n the (111) face of silicon. Takeshi, Sasaki, and Hirabayashi (185Ga)studied Si layers on the (111) Ge surface, Thomas and Francombe (188Ga) examined homoepitaxial Si layers, Palmberg, Rhodin, and Todd (742Ga) looked a t Ag and Au deposition on MgO, and Anderson, Andersson, and Marklund (5Ga) investigated T e deposition on (111) Cu. These techniques are still in the developmental stage but are indicative of advancing experimental techniques and the growth of surface physics as a separate science. PHYSICAL VAPOR TRANSPORT-HOMOGENEOUS CONDENSATION
Continued effort has been exerted in the field of physical vapor transport. Condensation from the vapor often results in a reduction of undesirable impurities in the final crystal. I t does, however, have the disadvantage that higher temperatures are required than would be for solution or melt growth. Most of the experimental work is concerned with the production of pure single crystals. Table 11-G summarizes the literature of the past two years on physical vapor growth according to the final product produced. Laudise (31Gb)briefly describes irreversible and reversible reaction techniques of vapor crystal growth for mono- and polycomponent systems. Hadamovsky and Weiss (77Gb) have proposed a method of producing single crystals of semiconductors such as GaAs whose partial pressure may exceed 1 atm a t working temperatures. Thoria single crystals have been produced by vapor deposition in a solar furnace capable of reaching 4900'K (30Gb). Jeavons and Saunders (22G6)have successfully employed a vapor growth technique to produce relatively strain-free arsenic single crystals. Vitovskii et al. (54G6) described a n improved method for producing large organic crystals in a recent Russian article. They grew crystals of hexamethylene tetramine, anthracene, and phenanthrene by rotating the crystals during deposition. Sloan (51Gb) and Jones (2366)have investigated the kinetics of anthracene growth from the vapor. Nenov and Georgieva (35G6) studied the kinetics of growth and evaporation of diphenyl by measuring morphological changes. Geguzin and Ovca ( 74Gb) discuss the kinetics of growth and evaporation of negative thread crystals. Kourilo (27Gb) presents a n excellent analytical survey of ultrahigh pressure techniques of crystal growth which includes a section on vapor phase growth.
TABLE Il-G.
PHYSICAL VAPOR TRANSPORT
Element or compound produced
References Gb
AgI AgaAsSs Anthracene Anthracene-tetracene Arsenolite
8 21 23,51 23 20 22 50 3 13 3 3 1, 2 16, 19, 33, 42, 44 42 25 18, 26, 36, 39 49 24 53
As
Au B B carbide B phosphide B arsenide C-diamond seeds CdS CdSe CsMnCls cu Eu EuS, EuSe, EuTe Fluor-Phlogopite Ge HgS HgaSzClz Hypophosphorous acid
15
7 7 38 20 40 29 34 37 59 46 57 39 4 45 25 39 32 41,48 49 30 49 20 57 49 58
I K graphites KBr KI LaB 6 Mg MgFz MoOa Nb P-black Rb RbMnClr
S Se Si Sm Tho Tm Urotropine
WOa Yb ZnO ZnS, ZnSe
11 Cancra1 topics
References Gb
Small source-substrate distances Growth of organic solids Noncentrosymmetric crystals Negative thread crystals Semiconductors Ultra-high pressure studies (survey) Electric field effects Kinetics of spontaneous transformation of a surface Micromechanism of growth of mineral salts Pure alkali metal halides Fine metal particle preparation
10 9, 54 5 74 17,47 27 28 35 43 55 56
CHEMICAL VAPOR TRANSPORT AND CHEMICAL VAPOR DEPOSITION
Chemical vapor deposition and chemical transport have seen continued use as techniques of producing single crystals. Basically, in transport reaction chemistry the desired element is reacted in one isothermal section of the crystallizer cell with iodine, chlorine, or similar carrier transport gas, which will produce a vapor VOL 61
NO. 1 0 O C T O B E R 1 9 6 9
101
compound a t that temperature. This vapor then diffuses to a different isothermal section of the cell and is deposited on a suitable substrate by a shift in the thermodynamic equilibrium created by the different temperatures. Other reactions can also be required for deposition; for example, in the production of GaAs by one process, GaI is transported and reduced with H Zin the presence of As, thereby depositing GaAs on a suitable substrate. This can be categorized as chemical vapor deposition. Some crystals can be prepared solely by chemical vapor deposition with no transporte.g., 4 BC13 CCl4 8 Hz = B4C 16 HCl(33Gc). A critical review of chemical transport reactions is presented by Nitsche (39Gc) in a German article. Nitsche’s paper includes 225 references and a discussion of more than 150 systems. Nitsche (38Gc) also presents new results on the growth of binary, ternary, and mixed crystal chalcogenides including a table of those crystals grown by the vapor transport technique during the period 196166. Magomedov, Sheftal, and Naumov (29Gc) discuss the variables that regulate supersaturation in transport reaction systems. Geary and Hough (79Gc) describe a method for continuous weight measurement by using a chemical balance to determine the rate of material transport during vapor phase growth. McDermott et al. (31Gc) have received a patent claiming a new method for producing a homogeneous single crystal of the general formula (M’,M”l-.)M, where M is a group IIIB element and M’ and M “ are group VB, one of which is P or As. Emmenegger (75Gc) has investigated ternary metal oxide growth by chemical transport. Archer et al. (2Gc) succeeded in producing single crystals of ferrite with encapsulated polycrystalline conductors. The final product consists of a ferrite single crystal with internal conduction paths running in the magnetically easy directions of the crystal, thereby producing a material suitable for computer memories. Hanak and Berman (20Gc) grew single crystals of superconducting NbsSn by simultaneous reduction of HC1-transported Nb and Sn chlorides by Hz gas a t 90O-120ODC. They hoped to increase understanding of the superconductivity of NbsSn by growing pure, single crystals, thereby avoiding grain boundaries, voids, and large concentrations of impurities, all of which can impede the superconducting properties of the pure material. Arizumi and Nishinaga (3Gc) investigated the experimental and theoretical aspects of transport growth of Ge by iodine.
+
+
TABLE I I I-G.
Element or compound produced
Alkali metal halides
B B carbide CaNbtOs CdO CdS COS2 cu Ferrite FeSz GaAs GaP GaS GaSb Ge Metal oxides MgO
+
102
INDUSTRIAL A N D ENGINEERING CHEMISTRY
74 25 6, 9, 77, 21
4 27 2 4
22, 26, 30, 43 78, 22, 28 41 48 3, 45 15, 44 32
5 50
NdTe NiO Nb06 NiS2 NbsSn Pr phosphide Se Si SiAs Si.‘\sz Sic Sip2 Tic Ti02
I 16
4 20 34
7 42 23 12 40 12 40 37 46 47
us2
VdOn
Woz, %$’os, cv w z
References Gc
73 70, 33 33
M O
o ~ ~ ~ ~ ~ i 8 ~8 4 @
1 ZnS ZnO
EVAPORATION
A few of the more pertinent articles concerning evaporation are included in this review. The comparison of evaporation and condensation (growth) processes on the surface of crystals has often been oversimplified. With improvements in experimental techniques, the comparison between evaporation and condensation phenomena can be evaluated more accurately in terms of how they are affected by crystal morphology, impurity and defect concentration, temperature, super- or undersaturation, etc. Somorjai and Lester (4Gd) have prepared a n excellent review of evaporation phenomena covering both experimental and theoretical aspects of evaporation. They also investigated the evaporation mechanism of NaCl single crystals (2Gd). Frishberg and others (7Gd) presented a paper dealing with heat transfer limitations to evaporation through the condensate layer. Rosenblatt and Lee (3Gd) measured the rate of free evaporation of arsenic. Arsenic is unusual because it undergoes a rearrangement reaction on the surface of the crystal to form As4 tetrahedra which are found in the vapor phase. This kinetic step appears to be the ratecontrolling step in the evaporation process, and accounts for the abnormally low vaporization coefficient, 01 (approximately 10-7). Most metals have a’s close to 1 (1/3 < a 5 1) which is theoretically accounted for by the surface desorption of monatomic atoms with surface diffusion providing the only major resistance to evaporation. Spiegel et ~ l (5Gd) . investigated the growth of evaporation layers of silver on silicon. Tamaki and Kuroda (7Gd) studied tungsten evaporation with a field ion microscope. Swift, Noval, and Mery (6Gd) discuss the fracturation of Ni-Cr-Cu-A1 alloys during evaporation.
CHEMICAL VAPOR DEPOSITION AND CHEMICAL TRANSPORT
6
77, 36, 49
REFERENCES Books and Reviews
"Research
(1A) Allen, H. C., Jr., on Cr stal Growth and Characterization at the National Bureau of Standards, NBS-JN-293 (1966) (Eng.). (2A) Andersen A L “Studies on Growth Mechanisms and I m erfections in Silicon Crys;als Grdhn b the Foating Zone Method,” Part I: %xt, Part 11: Illustrations, Polyteknisk Jorlag, Copenhagen, 1967. (3A) Bamforth, A. W., “Industrial Crystallization,” Macmillan, New York, 1966. (4A) Bishop, A. C., “An Outline of Crystal Morphology,” Hutchinson, London 1967. .. .
(5A) Bontinck, E.,“Crystals (Kcistallen),” Uitgeverij, Antwerp, 1967. (GA) Datt, S. C., Verrna, J. K. D., Crystal Growth of Organic Solids and Mechanisms of Single-Crystal Growth from the Melt, J.Sci. Ind. Res., 27, 11 (1968)
(End. (7A) Easterling K. E “ T h e Nucleation of Martensite in Precipitates of Iron in a Copper Matrk,” Acia Polytechnica Scandinavica, 1968. (8A) Frank F. C . Mullin, . I . B., Peiser H S. “Crystal Growth 1968 ” Supplement to’ the 3. Cryrtd Growth, Qolume’ 3-4, North-Holland huh. Co., Amsterdam, 1968. (9A) Gruber, B.,“Theory of Crystal Defects,” Academic Press, New York, 1966. (10A) Hingsamer, J., Luescher, E., Review of Inert Gas Crystals, Heh. Phyr. Acta, 41, 914 (1968) (Ger.). (11A) Hirabayshi, R., Crystal Growth and Equipment, Skinku, IO, 210 (1967) (Japan.). (12A) Hirth, J. P., Loethe, J., “Theory of Dislocations,” McGraw-Hill, New York, 1968. (13A) Hocart, R., “Crystals (Les Cristaux),” Presses Univ. France, Paris, 1968 (Fr.).
(14A) Hoselitz, J., T h e Crystals We Need, J. Crystal Growth, 3-4, 5 (1968). (15A) Iron and Steel Institute, “ T h e Solidification of Metals,” Iron and Steel Publication 110, London, 1968. (16A) Jackson, K. A,, A Review of the Fundamental Aspects of Crystal Growth, in“Crysta1 Growth,” H. Peiser, Ed., Pergamon Press, New York (1967), p 17. (17A) Jackson, K . A., “Solidification and Crystal Growth,” MacMillan, New York, 1968. (18A) Kern, M. R., “Adsorption et Croissance Cristalline,” Editions d u Centre National de la Recherche Scientifique, Paris, 1965 (Eng., Ger., Fr.). (19A) Khamskii, E. V., “Crystallization from Solutions,” Consultants Bureau, New York, 1969 (Eng.). (20A) Kleber, V., Structural Problems of Cr stal Growth, Genezis Miner. Individov Agreratou, Akad. Nauk SSSR, Inst. Mineral., &okhim. Kristallokhim. Redk. Elem., 24, (1966) (Russ.). (2lA) Knight, C. A,, “ T h e Freezing of Supercooled Liquids,” Van Nostrand, Princeton, N. J., 1967. (22A) Kozlova, 0.G., “Crystal Growth (Rost Kristallov),” Izd. Moskovsk. Univ., Moscow, 1967 (Russ.). (23A) Kraske, R. J., “Crystals of Life: T h e Story of Salt,” Doubleday, New York, 1968. (24A) Kratochvil, P., “ Crystals,” Iliffe, London, 1967 (Eng.). (25A) Laudise, R . A., “Crystal Synthesis,” Vol. I, Springer, Berlin, 1969. (26A) Laudise, R . A. Techniques of Crystal Growth, in “Crystal Growth,” H . Peiser, Ed., Pergakon Press, New York (1967) p 3. (27A) Luzhnaya, N. P., Growth from.Meta.1 Solutions, J . Crystal Growth, 3-4, 97 (1968). (28A) Moore, W. J., “Seven Solid States,” Benjamin, New York, 1967. (29A) Nassau, K., Crystal Growth Techniques, Tech. Inorg. Chem., 7, 1 (1968) (Eng.1. (30A) Nitschmann, G., Crystallization, Ver. Deut. Ingr., 107, 1419 (1965) (Ger.). (31A) Ookawa, A,, Problems of Crystal Growth, Shinku, IO, 207 (1967) (Japan.). (32A) Ovsienko, D. E., Ed., “Growth and Imperfections of Metallic Crystals,” Consultants Bureau, New York, 1968 (Eng.). (33A) Palermo, J. A,, Crystallization, INn. ENC.CHEM.,60(4), 65 (1968). (34A) Parkash, S., Lele, P. S., Crystal Growth, Chem. Age India, 18, 927 (1967) (Eng.). (35A) Peiser H . S., Ed. “Crystal Growth ” Pergamon Press, New York, 1967; (issued as 3. Phys. Chem.’Solids, Suppl. No. i). (36A) Petrov T. G., Treivus, E. B., Kasatkin, A. P., “Growing Crystals from Solutions (byrashchivanie Kristallov iz Rastvorov),” Nedra, Leningrad, 1967 (Russ.). (37A) Sahagian, C. S., Growth of Single Crystals, AD 631073 Avail. CFSTI (1966). (38A) Sheftal N. N., Ed., “Growth of Crystals,” Vol. 5A, 5B, 6A, 6B, Consultants Bureau: New York, 1968 (Eng.). (39A) Starliper A. G “Tungsten Whiskers by Vapor-Phase Growth,” U.S. Bureau of Mines, Pit;lburgh, Pa., 1968. (40A) Strickland-Constable, R. F., “Kinetics and Mechanism of Crystallization,” Academic Press, New York, 1968. (41A) Svechnikov V. N. Ed. “Phase Transformations (Fazovye Prevrashcheniya),” Nauiova DuAka, kiev, 1967 (Russ.). (42A) Walton, A. G. “Crystal Nucleation from Solution,” U S . Office of Saline Water Research aAd Development Report 263, US. Govt. Printing Office, Washington, D.C., 1967. (43A) Walton, A. G., “ T h e Formation and Properties of Precipitates,” Interscience, New York, 1967. (44A) Zief, M “Purification of Inorganic and Or anic Materials: Techniques of Fractional S;lidification,” Dekker, New York, 19f9.
Nucleation of Crystals (1B) Abraham, F. F., Pound, G. M., Re-examination of Homo eneous Nucleation Theory: Statistical Thermodynamic Aspects, J.Chem. Phys., 4f, 732 (1968). (2B) Anderson, D. M., IceNucleation, Nature, 216,563 (1967). (3B) Atkinson, R. J., Posner, A. M., Quirk, J. P., Crystal Nucleation in Fe(II1) Solutions and Hydroxide Gels, J.Inorg.Nucl. Chem., 30, 2371-81 (1968). (4B) Bashkirov, A. G., Reconsideration of Nucleation Theory, Phyr. Lett., 28, 23-4 (1968). (5B) Bischoff, J. L., Kinetics of Calcite Nucleation: Magnesium Ion Inhibition and Ionic Strength Catalysis, J.Geophys. Res., 73, 3315-22 (1968). (6B) Bobyrenko, Yu. Ya., Sheinkman, A. I., Dolmatov, Yu. D., Size of the Crystallites in T i 0 3 Nucleation Solutions in Relation to the Conditions of Their Formation, J. Appl. .. Chem. USSR, 40, 697-701 (1967). (7B) Bodson P Bouillon F Jardinier-Offergeld, M., Nucleation and Grain Growth b;Cogtrolled O;ida?ion of AI, Metalluqie, 6, 47-54 (1966) (Fr.). (8B), Chakraverty, B. K., T h e Delay in Nucleation, Colloq. Int. Centre Nut. Rcch. Scr.., 152., 373-86 (1965). (9B) Charbonnier, J. C., Bardolle, J., Mollimard, D., Nucleation Kinetics During Controlled Oxidation of Iron, Metallurgie, 7, 107-19 (1967) (Fr.). (10B) Chernov, A. A. Kinetic Phase Transitions Zh. Eksp. Teor. Fiz,, 53, 2090-8 (1967) (Russ.). [SAiet Phys.
Experimental Studies of Crystallization From The Melt (1F) Abdullaev, G. B., Mnmedov, K. P., Effect of an Elertrostatic Field on the Crystallization of Amorphous Selenium, Dokl. Akad. N a u k Azerb. SSR, 23, 10 (1967) (Russ.). (2F) Adamski, C., Bonderek, Z., Mechanism of Dendrite Crystallization, Przegi. Odlew., 17, 293 (1967) (Pol.). (3F) .4lberny, R. Turpin, M., Initial Staqes of Dendritic Solidification in IronPhosphorus All&s, Mem. Scz. Reo. M e t . , 6 5 , 591 (1968) (Fr.). (4F) Albon, N. Illingworth, D., Hull, R., Growth Mechanism of Trilaurin Crystals, J . CrystaiGrowth, 2,26 (1968). (5F) Alfinsev, G. A , , Ovsienko, D . E., Investigation of the Mechanism of Growth of Some Metallic Crystals from the Melt, J . Phys. Chem. Solzds, S~lppl.1, 757 (1967) (Russ.). (6F) Andreev G. A. Distribution of Impurities during the Crystallization of Potassium Ibdide da: Potassium Fluoride, Kristnllogrqfyn, 13, 872 (1 968) (Russ.) , (7F) Andreev, G. A,, Bureiko, S. F., Distribution of Divalent Impurities in the Crystallization of KCl from the Melt, Soviet Physics-Solid Stole, 9, 58 (1967). (8F) Baker J. C. Cahn, J. W., Solute Trapping by Rapid Solidification, Acta M e t . , 17,’575 (lj69). (9F) Balandin G. F Semenov B. I . Hydrodynamic Fluxes Near the Crystallization Front, kir. M h . .Metoldued., i5, 380 (1 968) (Russ.). (10F) Baralis G. Perosino M. C. Convection-Induced Impurity Distribution During Ge;maLium Crysth Pullin;, J . Crystal Gmmth, 3, G5l (1968). (11F) Barthel, J., Eichler, K., Effect of Laminated Inclusion of Fnrei n Elements in Zone Melting on the Effective Distribution Coefficients, Krist. #ech., 2, 205 (1967) (Ger.). (12F) Bares H. E. Wald F. Weinstein, M., Controlled Solidification of Metal Matrix Cbmposites UtilikniMonovariant Eutectic Reactions, J . M a t l . Sci.,4, 25 (1969). (13F) Borisov, V. T., Temperature at the Growth Front of a Mercury Crystal, “Growth of Crystals,” 3, 135, Consultants Bureau, New York, 1962. (14F) Borisov, V. T., Dukhin, A . I., others, T h e Growth Kinetics of Metal Crystals, “Growth of Crystals,” 5A, 67, Consultants Bureau, Kew York, 1968. (15F) Borisov, V. T., Dukhin, A. I., others, Kinetics of Crystallisation and Mechanism of Crystal Growth in Metallic Systems, J. Crystal Growth, 3, 663 (1 968), (16F) Borisov V. T. Golikov I. N., Matveev, Y u . E., Kinetics and Mechanism of Growth of dallium’Crystals,’K~istollogro~ya, 13,876 (1968) (Russ.). (17F) Bri ham, R . .T., Purdy, G . R., Kirkaldy, J. S., Unidirectional Solidification of Fe-C, d - C , and Fe-C-Si Eutectics, J . Phys. Chem. Solids, Suppl. 1, 161 (19G7). (18F) Carruthers, J. R., Thermal Convection in Horizontal Crystal Growth, J. Crystal Growth, 2, 1 (1968).
(19F) Carruthers J R Winegard W. C Thermal Convection and Solute Segregation during Hdriionyal M e l t i n i and solidification, J . Phys. Chem. Solids, Suppl. 1, 645 (1967). (20F) Chase A. B Habit Changes and Growth Mechanisms of Inz03 Grown from PbO-B20;Melts:J. Amer. Cer. SOL.,51, 507 (1968). (21F) Chcng, C . S., Irvin, D. A,, Kyle, B. G., Normal Freezing of Eutectic Forming Organic Mixtures, A.I.Ch.E. J., 13, 739 (1967). (22F) Chernov, A. A,, Khadzhi, V. E., Trapping of Colloidal Inclusions in the Growth of Quartz Crystals, J . Crystal Growth, 3, 641 (1968). (23F) Cole G . S. Temperature Measurements and Fluid Flow Distribution Ahead of Solid-Liquid interfaces, Trans. M e t . Soc. A Z M E , 239,1287 (1967). (24F) Cookse D. J. S. Day M G. Hellawell A. T h e Control of Eutectic Microstructures, Y i P h y s . Chim. Soiids;Su&. 1, 151 (i96j). (25F) Dashevskii M . Ya. Poterukhin, A. N. Growth Mcchanism and Impurity Distributions df Doped ’Indium Antimonidb Dendrites, Zrv. Akad. Nauk SSSR, Neorp. Mater., 4, 1478 (1968) (Russ.). (26F) Dem’yanov, E. A,, Smirnov, V. V., Stroitelev S. A. Growth of Lamellar and Dendritic Crystals During Mass Crystallization,’Znorg. hater., 4, 1245 (1968). (27F) Deo P. G. Sharma S . D. Impurity Substructures and Dislocations in MeltGrown drystall, J . Phys.’Chem. kolids,Suppl. 1, 665 (1967). (28F). Double, D. D., Truelove, P., Hellawell, A,, T h e Dcvclopment of Preferred Orientations in Eutectic Alloys, J . Crystal Growth, 2, 191 (1968). (29F) Faust J. W. Jr. Crystal Growth Utilizing the Twin Plane Re-entrant Edge Mechanisk, J . $fiys.’Chem. Solids,Suppl. 1, 183 (1967). (30F) Fischer D. Oriented Growth of Anthracene Crystals in an Electric Field, Mater. Res. hull.’, 3, 759 (1968) (Ger.). (31F) Flemings M. C., Utech, H . P., Miksch, E. S., Effect of Fluid Flow on Solidification Struckre, U . S.Gout. Res. Develop. Rept., 41,72 (1966). (32F) Frieman, S. W., Hench, L. L., Kinetics of Crystallization in LizO-Si02 Glasses, J . Amer. Cer. Soc., 51, 382 (1968). (33F) Gauthcrie, M., Apparatus for Studying Crystalline Growth from Liquid States, Rev. Phys. ApPl., 3, 131 (1968) (Fr.). (34F) Gerasimenko V. S . , Lyubov, B. Ya Theory of the Method for the Experimental Determinition of the Growth Ra;e of Metallic Crystals as a Function of Sunercoolina, Kristolloqrafya, 1 2 , 840 (1967) (Russ.) . .. (35F) Glicksman M. E . Schaefer R. J. Comments on Theoretical Analyses of Isenthalpic Solihificatidn, J , Crystal G r o d h , 2, 239 (1968). (36F) Glicksman M . E. Schaefer R. J Investigation of Solid/Liquid Interface Temperatures Gia Isedhalpic Soiidifica‘hon, ibid., 1,297 (1967). (37F) Goldsztaub S Gautherie M. Two Methods for Determining the Temperature Gradient Neay a Crystal GroGth from a Molten Bath, Silicates Znd., 32, 291 (1967) (Fr.). (38F) Graf, L., Scheiner, L., Crystal Growth in Phase Nonequilibrium Conditions. Conditions for Formation of Dendrites and Lamellas, Z . Metallk., 58, 271 (1967) (~--..,. G P Y ). (39F) Greet, R . J. Solidification Kinetics of 1,2-Diphenylbenzene, J . Crystal Growth, 1, 195 (19k7). (40F) Grishin, V. P., Shashk, Yu. M., Molecular Growth-Rate Constant of Silicon Dendrites, Inorg. Mater, 4, 1252 (1968). (41F) Guasti M . V. Munoz, E., Separation of Silver in Single Crystals of NaCl, Rev. Mew. his., 14, i 7 (1965) (Span.). (42F) Gubenko A. Ya. Influence of the Conditions of Growth on the Limit of Alloying of GLrmaniuk Crystals, Znorg. Mater., 4, 371 (1968) (Russ.). (43F) Hamaker, R. W., White, W. B., Mechanism of Single-Crystal Growth in InSb Using Temperature-Gradient Zone Melting, J . Appl. Phys., 39, 1758 (1968). (44F) Hamalainen, M., Constitutional Supercooling in the Presence of Convection Cells, J . CrystalGrowth, 1, 125 (1967). (45F) Hamalainen M Segre ation of Impurities in Molten Salts Induced by Cellular Convectjon and its Effect on Crystal Growth, ibid., 2,131 (1968). (46F) Hardy S . C., Coriell, S . R., Morphological Stability and the Ice-Water Interfacial Free Energy, ibid., 3, 569 (1968). (47F) Hess S. von Kujawa R. Effect of an Ultrasonic Field on the Segregation Behavior’ of ’Gold in T e l l h i m during Normal Solidification, Krist. Tech., 2, 89 (1967) (Ger.). (48F) Hurle, D. T. J., Thermo-hydrodynamic Oscillations in Liquid Metals: the Cause of Impurity Striations in Melt-Grown Crystals, J . Phys. Chem. Solids, .C,,hhl 1 . 659 119671. --rr.. -~ (49F) Ibaraki, M., Okamoto, T., Effe5t of the Solute Content on the Dendritic Structure in Columnar Crystals of Blnary Alloy, Nippon Kznroku Cakkaishi, 31, 450 (1967) (Japan.). (5OF) James, D., Solidification Kinetics of Ice, J . Phys. Chem. Solids, Suppl. 1, 767 (1967). (5117) James D. W Sekerka, R. F., T h e Effect of Impurities on Solidification Kinetics Measure; by the Thermal Wave Technlque, J . Crystal Growth, 1, 67 (1967). ( 5 2 ~ )Johnston, D. C., Witt, A. F., Gatos, H. C . , I m urity Heterogeneities and Multiple-Beam Interferometry, J . Electrochem. Soc., 1 1 8 438 (1968). (53F) Kerr, H . W., Winegard, W. C., Eutectic Solidification, J . Phys. Chem. Solids, Suppl. 1, 179 (1967). (54F) Ketcham W. M., Hobbs, P. V., T h e Preferred Orientation in the Growth of Ice from t i e Melt, J . Crystal Growth, 1, 263 (1967). (55F) Kirtisinghe D . Morris, P. J. Strickland-Constable, R. F., Retardation of the Rate of Growti of’Salol Crystalh in Capillary Tubes, J . Crystal Growth, 3, 771 -~ (1968). (5GF) Kirwan D. J Pigford R. L., Crystallization of Pure and Binary Melts, A.Z.Ch.E. J.: 15, 422 (1969): (57F) Klokman V. R . Coprecipitation of Radioactive Isotopes with Isomorphous and Nonisom&ohoua Carriers, Crystallizing from a Melt, Soviet Rndiochem., 9, 528 (1967)~(Russ.).’ (58F) Kozielski, M. M., Distribution of Iron, Coppcr, and Silver Impurities in Zinc Sulfide Single Crystals Grown from the Melt, Phys. Status Solidi,31, K9 (1969). (59F) Krupkowski, A. Dendritic Crystallization of Binary Alloys and Migration of Atoms during Homdgenizing, Arch. Hutn., 12, 343 (1967) (Pol.). (60F) Laird, J. A,, Bergeron, C. G., Interface Temperature of a Crystallizing Melt, ‘ J . Amer. Cer. Soc., 51, 60 (1968). (61F) de Leeuw, den Bouter, J. A,, Heertjes, P. M., Determination of the Surface ~ ~ m n e r n t ~ iof r eCrvstals Growina from Melts under Unidirectional Coolina.
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-7
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I
(62F) Lemky F. D. Salkine M.J T h e Growth and Properties of Carbide Whisker Reinforced’Refradtory Mitals fr;m the Melt, J . Phys. Chem. Solids, Suppl. 1, 171 (1967). (63F) Lozovskii, V. N Nikolaeva E. A. Study of thc Mechanism of Silicon Crystallization from ‘[he Melt b; Zone ’Meltin with Temperature Gradient, T i . Novocherkassk. Politekh. znst., 170, 49 (1967) b u s s . ) . From Ref. Zh., Fiz,, A 1968, Abstr. 3A648. (64F) Lyubov, B. Ya. Evaluation of the Su ercooling at the Phase Interface during Crystallization, “Giowth of Crystals,” 5 1 , 80, Consultants Bureau, New York, 1968. (65F) Mamedov, K . P., Nurieva, Z. D., Crystallization Mechanism of Selenium, Sou. Phv.-Crvstalloerabhv. 12. 605 (1968). , . (66F) Mavlonov Sh. Karimov S Se regation of Iron Silver and Tin in the Growth of Si; le drystals of ?l*?ea from a Melt by ;he Czdchralski Method, Znorg. M a t . , 4, to69 (1968) (Russ.). (67F) Mazhul M. M., Voitovich S . M. Effect of Ultrasonic Cavitations on the Growth Rat; of a Solid Phase frbm a Bit01 Melt, Vetsz. Akad. Navuk. Belarus, S S R , Ser. Fir.-Mat. Navuk, 3, 120 (1968) (Russ.). (68F) Meiling, G. S . Uhlmann, D. R . Crystallization Kinetics of Sodium Disilicate, J . Phys. Che6. Solids, Suppl. 1,747 (1967). (69F) Mekhtieva, S . I., Abdinov, D . Sh., Aliev, G. M., Kinetics of Selenium Crystallization, Znorg. Meter., 4, 259 (1968) (Russ.). (70F) Mollard, F. R.,Flemings, M. C., Growth of Composites from the Melt. 11, Trans. Met.Soc. A I M E , 239, 1534 (1967). (71F) Morizane, K., Witt, A. F., Gatos, H. C., Impurity Distribution in Single Crystals. IV. Growth Characteristics and I m urity Incor oration during Facet Growth, J . Eleclrochem. Soc.: Solid State Science, f15, 747 (196%). (72F) Morris, L. R., Winegard, W. C., Dendrite T i p Instability, J . Crystal Growth, 1, 245 (1967). (73F) Morris, P. J. Kirtisinghe D. Strickland-Constable R F. Retardation of the Growth of Salbl Crystals frbm h e Melt in Capillary Tkbes, idid., 2, 97 (1968). (7$7) Nikonova, V. V., Formation of Pseudoprimary Crystals in Eutectic Alloys, Growth of Cr stals ” 5 4 92 Consultants Bureau New York 1968. (75F) O’Hara, Cokrol.
(17Gc) Fochs, P. D., George, W., Augustus, P. D., Growth of Cadmium Sulfide Single Crystals of Controlled Composition from the Vapour Phase, J . Crystal Growth, 3-4, 122 (1968). (18Gc) Frosch, C. J., The Growth and Do ing of Single Crystal GaP Needles by an Open-Tube Wet Hydrogen Process, J . P i y s . Chem. Solids, Suppl., 1,305 (1967). (19Gc) Geary D A. Hough J. M Thermal Balance for Measuring Transport During Vapbr Phas; Crystaf Grow&, J . Crystal Growth, 2, 113 (1968). (20Gc) Hanak, J. J., Berman, H. S., T h e Growth of Sin le Crystals of NbsSn by Chemical Transport, J . Phys, Ckem. Solids, Suppl., 1, 249 71967). (21Gc) Hildisch, L., Nonstoichiomctry of CdS Crystals Grown by Different Methods, J . Crystal Growth, 3-4, 131 (1968). (22Gc) Hoss, P. A , , Murray, L. A,, Rivera, J. J., T h e Close-Spaced Growth of Degenerate P-Ty e GaAs, Gap, and G a (Asz, Pi-Z) by ZnClz Transport for Tunnel Diodics, J? Electrochem. SOC.,115, 553 (1968). (23Gc) Ing, S. W., Jr., Chang, Y . S., Haas, W., Vapor Grown SiAs Crystals, J . Electrochem. SOC.,114, 761 (1967). (24Gc) Jeffes, J. H. E., Alcock, C. B., T h e Production of Refractory Crystals by Vapor Transport Reactions, J . Mater. Sci.,3, 635 (1968). (25Gc) Konak, C., Hoschl, P., others, Preparation, and Electrical and Optical Properties of CdO Crystals, J . Pkys. Chem. Solids, Suppl., 1 , 341 (1967). (26Gc) L a icrre A G Wolfson R G., Juleff, E. M., Anomalous Unconstrained Crystal $row& oi &AS, ibid., 301. (27Gc) Latiere, H . J., Progressive Development by Layers of Copper Whiskers, Metoux (Corros.-Ind.),41 (489), 217 (1966) (Fr.). (28Gc) Luther, L. C., Growth of Zn-Doped Gallium Phosphide by Water Vapor Transport Method, J . Electrochem. Soc., 116, 374 (1969). (29Gc) Magomedov, Kh. A , , Sheftal, N . N., Naumov, A. S., Supersaturation in Crystallization by Chemical Transport Reactions, Krist. Tech., 3 , 31 (1968) (Ger.). (30Gc) Manasrvit, H. M., Single Crystal GaAs on Insulating Materials, Appl. Phys. Lett., 12, 156 (1968). (31Gc) McDermott, P. S. Maniey G. W., others A Method of Producing a Homogeneous Single Cryhal, Brit. )Patent 1,087,268’(Cl. C Olg), 18 Oct. 1967. (32Gc) Met, J. E., Pulliam, G . R., Chemical Vapor Deposition of Single-Crystal Metal Oxides. I . M g O on MgO, J . Phys. Chem. Solids, Suppl., 1, 333 (1967). (33Gc) Mierze’ewska-A penheimer, S., Niemyski, T., Vapor-Phase Crystallization of Boron andBoron &bide, ibid., p 229. (34Gc) Mironov, K. E., A Transport Reaction for the Growth of Praseodymium Phosphide, J . Crystal Growth, 3-4, 150 (1968). (35Gc) Nickl, J., Growing Whisker Crystals, Ger. Patent 1,255,092 (121. B Olj), 30 Nov. 1967. (36Gc) Nielscn K F Growth of Z n O Single Crystals by the Vapor Phase ReacGrowth, 3-4, 141 (1968). tion Method,’J. Cr&l (37Gc) Niemyski T. Piekarczyk W The Growth of Rutile (TiOz) Single Crystals by Chemical T i a d p o r t with TkCI4; J . Crystal Growth, 2, 177 (1968). (38Gc) Nitschc, R., Crystal Growth by Chemical Trans ort Reactions IV. New Results on the Growth of Binary, Ternary, and M i x e l Crystal Chalcogenides, J . Phyr. Chem. Solids, SupFl., I , 215 (1967). (39Gc) Nitsche, R., Crystal Growth from the Gas Phase by Chemical Transport Reactions, Fortschr. Miner., 44, 231 (1967) (Ger.). (40Gc) Pearcc, M. L., Marek, R. W., Formation of Silicon and Titanium Carbides by Chemical Vapor Deposition, J . Amer. Cer. Soc., 51, 84 (1 968). (41Gc) Rustamov P. G. Mardakhaev B. N Growing of Some Gallium Sulfides Single Cr stals krom kaseous Phase: Izv. ‘hkad. Nauk SSSR, Neorg. Mater., 3, 575 (1967y (Russ.). (42Gc) Salli I V. Fal’kevich E. S. others Growth of Silicone Single Crystals from the dasPhahe, Kristallog;afrya, 15, 499 (i967) (Russ.). (43Gc) Shcftal, N. N., Magomedov, K h . A., Growth Rate of Crystalline Layers of Gallium Arsenide in the Iodide Process, Soviet Physics-Crystallogruphy,12, 129 (1967). (44Gc) Shiskalov, N. A,, Nayarova, R. I., Orientating Influence of Ag Crystals upon the Growth of Surface Oxides, Bull. USSR Diu.Chem. Sci.,3, 496 (1967). (45Gc) Silvcstri, V. J., Growth Rate and Surface Morphology Studies in the GeCla-HzSystem, J . Electrochem. Soc., 116, 81 (1969). (46Gc) Smith, P. K., Cathcy, L., T h e Preparation and Electrochemical Resistance of Single Crystals of P-USe, J . Electrochem. Soc., 114, 973 (1967). (47Gc) Takei, H., Va or Phase Crystallization of Vanadium Oxide by Hydrolysis of Vanadium Oxychforide, Jap. J . Appl. Phys., 7 , 827 (1968). (48Gc) Von der Meulen, Y . J., Growth Properties of GaSb, T h e Structure of Residual Acceptor Centers, J . Phys. Chcm. Solids,28, 25 (1967). (49Gc) Wcavcr, E. A,, Vapor-Phase Growth of Zinc Oxide Single Crystals, J . Crystal Growth, 1, 320 (1967). (50Gc) Zinchenko, K. A,, Yaremhash, E. I., others, Growing of Neodymium Telluride Single Cr stals b the Gas-Transport Reaction Method, Izv. Akad. NaukSSSR, Neorg. d t e r . , 3, 1 9 (1967) (Russ.). EVAPORATION (1Gd) Frishberg, I. V., Mikulinskii, A. S., Chctin, F. E., Sublimation Limited by Heat Transfer Through a Layer of Condensate, T r . Inst. Met., Saerdlovsk, 11, 54 (1966) (Russ.). (2Gd) Lester J. E. Somorjai G A Eva oration Mechanism of Sodium Chloride Single Cryitals, J : Chem. Phis., 49, ‘i940 8968). (3Gd) Rosenblatt, G. M . , Lee, P. K., Rate of Vaporization of Arsenic Single Crystals and the Vaporization Coefficient of Arsenic, ibid., p 2995. (4Gd) Somorjai, G. A., Lester, J. E., Evaporation Mechanism of Solids, Progr. Solid State Chem., 4, 1 (1967). (5Gd) S e g e l , K., Niedermayer, R., Maycr, H., Structure and Growth of Thin Silver vaporation Layers on Atomically Pure Silicon (1 11) Surfaces, Kunnachr. Akod. Wiss. Goettingen, Sammelh., 2 (9-24), 103 (1966) (Ger.). (6Gd) Swift R A. Nova1 B. A. Mery K. M . Fracturation of Ni-Cr-Cu-Ai Alloys During Vkcuum’Evapo;ation,’J. Va&n Sci.’ Tech., 5 , 79 (1968). (7Gd) Tamaki, S., Kuroda, T., Field-Eva oration of Tungsten in Field Ion Microscope, Jap. J . Appl. Phys., 7 , 1202 (19687.
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