R. BECKER 61 GENERAL PRINCIPLES OF CRYSTAL GROWTH BY PAUL H. EGLI AND S. ZERFOSS Received 18th March, 1949 Certain facts of crystal growth have been observed with sufficient regularity to justify their being regarded as general principles. Some are familiar and will be mentioned only briefly for the sake of coherence. Others, equally significant, have received scant attention. A systematic consideration of this total body of facts should provide the background for extending the theories of crystallization. Classifying the principles of crystal growth in a completely logical fashion is impossible because of the manner in which they are interrelated. Accordingly, some repetition will be necessary and the significance of certain experiments will require discussion in connection with several phases of the general problem.Nucleation Nucleation is discussed as the first phase of the problem because it is the initial step in the overall process of crystallization ; but most of the factors that control nucleation apply in the same manner to growth, and can be discussed more conveniently in that connection. Moreover, the important facts of nucleation are well known and need only to be described briefly.62 GENERAL PRINCIPLES OF CRYSTAL GROWTH (I) The rate of nuclei formation increases with supercooling. Tammann and others1 demonstrated that in melts the nucleation rate reaches a maximum and decreases with further supercooling as diffusion becomes the controlling factor. In solutions such a maximum is difficult to measure and probably does not usually occur.(2) An incubation period is recognized in growth from melts during which nucleation cannot be measured. In solutions, even when seeded, a metastable region of supersaturation is also recognized within which nucleation cannot be measured. Numerous investigators have found, in the phase diagram, well-defined regions with sharp boundaries beyond which nucleation was observable, and it seems reasonable to conclude that under certain con- ditions the rate of nucleation in solution increases extremely rapidly with a small increase in supersaturation. The “ metastable region ” principle is widely employed in the control of industrial crystallization processes and is a useful concept which will be referred to without apology even though the behaviour is more properly described as a rate phenomenon.(3) The extent of the incubation period (or metastable region of super- saturation) can be changed appreciably by slight changes in composition of the system. It is particularly important to note that the metastable region can be greatly increased beyond that of a pure solution by the addition of small amounts of certain additives. This little-explored phenomenon i s well substantiated for numerous compounds and will be further described in subsequent sections dealing with growth factors. (4) The incidence of nucleation depends on the previous history of the system. The evidence supporting the existence of superheatability of nuclei appears overwhelming. The work of Tammann and others1 with organic melts and with metals would seem sufficiently convincing, but the matter is still disputed.The fact that .increasing the amount and time of superheating a system reduces the incidence of nucleation during subsequent supercooling is apparently accepted, but the opponents of the concept of superheated nuclei offer an alternative explanation-that it is insoluble impurities and not nuclei of the principle solid phase which the superheat destroys. This is an important argument in view of the fact that superheat in solids is not predicted in the lattice dynamics of Born or by the theories of melting as recently discussed by Mayer. Accepting the experimental results as evidence of superheated nuclei would also appear- to be somewhat out of harmony with Frenkel’s concept of nuclei formation from embryo. This question is difficult to settle by investigation of solution systems because of the experimental difficulties of observing the early stages of nucleation. Efforts have been made at the Naval Research Laboratory to obtain reliable data by means of heat effects, Tyndall effects, small- angle scattering of X-rays, etc.-all with little success.Qualitatively,. however, it was the general conclusion of the several chemists concerned with growth of numerous crystals from solution that the existence of super- heated nuclei was verified by their experiments on the preparation of saturated solutions. This work is mentioned because in solution systems an explanation based on impurities is extremely unlikely. The reagents were prepared with great care, and in several instances any remaining impurities were in amounts less than those detectable by ordinary analytical techniques.(5) Nucleation is induced by the presence of foreign bodies and by agitation of the system. These well-known facts deserve to be listed in Tammann, Aggregatzustande (Leipzig, 1922). * Frenkel, Kinetic Theory of Liquids (Oxford Univ. Press, 1946).PAUL H. EGLI AND S. ZERFOSS 63 view of the frequent statements that nucleation always occurs for these reasons, or even stronger, that nucleation can never occur without such assistance. Again, these are difficult statements to disprove completely by experiment. Crystal Growth Almost all the phenomena of crystal growth-inclusion of impurities, habit modification, the genesis of twins and flaws-can be resolved into problems of growth rate under certain conditions.Accordingly the growth principles are presented, for the most part, on this basis. There are certain important phenomena, however, for which the rate aspect is not a convenient viewpoint, and which thus necessitate a more complete description. (I) Growth rate increases with increasing supersaturation (or supercooling) and with agitation. The ramifications of these facts are too well known to require elaboration except perhaps noting that diffusion is remarkably constant in all water solutions, and also that normally a moderate amount of agitation is sufficient to eliminate diffusion as a controlling factor. (2) Different faces of a single crystal (under the same degree of super- saturation and agitation) grow at different rates. The rules governing this significant feature of the growth process have been the subject of refinement throughout the history of crystal re~earch.~ In general, crystals possess faces of low indices because of the differential bonding along the few principal directions within the lattice.This idea can be restated in terms of growth toward a minimum free surface energy. (3) The difference in the growth rate of various faces becomes smaller as the overall rate is increased. This long-recognized fact has been demon- strated in a sufficient number of systems and under a sufficient variety of conditions that it can be safely regarded as a general rule. (4) Flawed surfaces grow more rapidly (under the same degree of super- saturation and agitation) than corresponding surfaces without detectable faults.This is meant to apply to twin boundaries, veils, lineage, mosaic structure and presumably any other type of large-order defect. Elaboration of this point is helpful in explaining why defects are propagated and frequently induce additional defects during subsequent growth. At growth rates appreciably below the maximum which can be supported for good growth certain types of flaws lose their rate advantage and may be healed over. ( 5 ) The maximum rate at which good growth can be obtained on a particular surface (the “ critical ” rate) decreases as the size of that surface increases. This highly significant fact has apparently received little attention, but the supporting data appear convincing.Yamamoto demonstrated the phenomenon very clearly with NaCl on a microscopic scale. Investigations at the Naval Research Laboratory, particularly by A. A. Kasper, showed similar results for NH,H,P04 grown under a variety of conditions and the effect has been observed qualitatively in the growth of numerous other crystals. The existence of a “critical” rate dependent on size would appear to lead to the conclusion that in practice there is a limit in size to which a good single crystal of each compound can be grown. Experience would appear to bear this out. The possibility is also predicted that there will be crystals in which zones developed by growth of certain faces will invariably be bad whereas adjoining zones may grow well, and that the volume of poor material could be reduced or eliminated by reducing on the seed the size 3 Wells, Phil.Mag., 1946, 37, 184. Buerger, Amer. Miner., 1947, 32. 593. Yamamoto, Sci. Pafiers. Inst. Physic. Chem. Res., 1939, 35, 228.64 GENERAL PRINCIPLES OF CRYSTAL GROWTH of the face which grows poorly (in NaBrO, use a 1x0-cut seed rather than 1x1-cut seed). It is suggested that this principle must also be more clearly recognized in crystallization theory. Presumably in an ideal system in which growth could be maintained at an infinitely slow rate the limit on size would disappear, but it is also possible that the necessary rate would be below that induced by normal fluctuations at equilibrium. Further implications of this feature of the growth process will be discussed in connection with the general problem of growth from the viewpoint of supersaturation. (6) The critical growth rake in solution systems increases with increasing temperature.This may also be true for any system with two or more components when temperature is a variable. Discussion of this point is necessary because of frequent statements that crystals contain more defects when grown at high temperatures. It is an accepted fact that as the temperature of a crystal increases, whether grown at a high temperature or heated after growth, the number and activity of atomic-scale defects increase. This applies, however, only to vacancies and dislocations of single ions or atoms and does not pertain to large-scale order. In fact, the increased activity with temperature, particularly at the surface, tends to improve the large-scale perfection of the structure during the growth process 2 ; experimentally, it has been found that increasing temperature favours the formation of perfect textures over the formation of spontaneous nuclei or the various types of large-scale flaws.In addition to the foregoing list, there is a rarely mentioned feature of the growth process which deserves considerable discussion. No one has yet offered a satisfactory answer to the basic question of why some com- pounds crystallize readily and others very poorly ; and yet there are some striking facts on which to base such a discussion. The first point to be noted is that in aqueous solution systems compounds which grow readily are all quite soluble. In general, slightly soluble compounds are grown with great difficulty, and highly soluble compounds are grown with great ease.This correlation is far from perfect, however, SO that simple solubility is not a sufficient specification for good crystal growth, and it is necessary to consider the state of association. Some evidence indicates that the critical rate for a given surface increases with increasing association of solute. This is first a statement in harmony with the familiar expression of theory-that the growth rate depends on the difference in the chemical potentials of a particle on the crystal surface and of one in the fluid phase. But the statement also implies something more-namely, that increasing association increases the advantage to formation of a perfect structure relative to the formation of flaws or spontaneous nuclei.The implications of these statements can be more readily discussed in terms of supersaturation than from a strict rate viewpoint. As previously discussed in connection with nucleation, this viewpoint is not a rigorous approach in terms of the kinetics of the rate process, but is a valuable concept for the sake of clarity. The problem then becomes one of determining the range of super- saturation which will induce only perfect growth, the additional degrees of supersaturation which will induce flawed growth of various types and, finally, the degree of supersaturation which will induce spontaneous nuclei. The amount of supersaturation which will induce perfect growth, lineage, etc., is of course dependent on the configuration of each crystal surface availa- ble for growth.For the purposes of this discussion, however, this factor can be neglected by assuming that each crystal has some face which is relatively favourable for growth so that the supersaturation required for that growth is small relative to that required for spontaneous nuclei and is somewhat This also has been demonstrated.PAUL H. EGLI AND S. ZERFOSS 65 less than required to initiate a flaw. On this basis compounds which are difficult to crystallize are those which form spontaneous nuclei with very small degrees of supersaturation so that the range which will induce growth but not flaws is vanishingly small. Easily grown crystals are those for which nuclei form only with considerable supersaturation so that there is a large range in which only perfect growth is obtained.Returning to the original assertion that ease of growth increases with increasing association of the solute, it is desirable to consider the supporting evidence from the supersaturation viewpoint. Quantitative data are difficult to obtain because of the difficulty of measuring and rigorously describing the quality of a crystal, but even more because of the lack of quantitative data regarding the amount of association of various salts in highly concen- trated solutions. Acceptable evidence is thus by necessity limited to obvious gross effects, but several compounds can be discussed for which the growth behaviour clearly supports the viewpoint expressed. NaCl is a typical example of a compound which is soluble but highly dissociated in solution, and experience indicates that NaCl is virtually impossible to grow into a perfect crystal at any reasonable rate from pure solution.It forms copious nuclei with very small degrees of supersaturation. HIO, is typical of compounds known to be highly associated in solution. Nuclei form only with considerable supersaturation, and large, perfect crystals are easily grown. Also typical of the associated solutes which support supersaturation and form crystals readily are a large number of hydrated salts. Additional significant evidence was demonstrated by growing benzil from water solution and various organic solvents. Growth was difficult in every solvent except benzene ; from this related environment nuclei were formed only with considerable supersaturation and growth was excellent.Thus all the available evidence appears to be in harmony, but additional data are desirable. Significant information can be derived from the remarkable effect of small concentrations of foreign ions. The growth of several dozens of compounds has been markedly improved by the addition of “ impurities” to the solution. A typical case is NaCl which grows with great difficulty from pure solution but which grows readily from a solution containing Pb. The obvious effect is to greatly increase the range of supersaturation within which spontaneous nuclei do not form. Yamamoto obtained data for several compounds and this work has been extended a t the Naval Research Labora- tory to many solution systenrs.The same phenomenon has also been demonstrated there in the growth of alkali halides from a melt and has been reported by one competent investigator to apply in growth by flame fusion. The rules for selecting the most effective additive are not yet entirely obvious. Heavy metal, multivalent ions in concentrations of less than 0.01 mol-% are frequently the best choice, though small concentrations of anything that, if present in larger amounts, would modify the habit appear to be helpful. If concentrations beyond the optimum are used, the habit is modified, flaws are induced and spontaneous nuclei occur more readily than from pure solution. When properly used, however, this is a very powerful tool. In one case, for example, it made possible the formation of a compound which cannot be precipitated from pure solution ; K,MnCl, can be formed only by the addition of Pb++ to the solution. In a practical sense, the phenomenon is extremely valuable for increasing the efficiency of growth processes for single crystals and has in addition promising applications in industrial crystallization of fine chemicals.From a scientific viewpoint it promises to contribute valuable clues to the overall problem of nucleation and growth. Space does not permit thoroughly justifying the choice of the foregoing C66 GENERAL DISCUSSION factors as being the most significant to interpretation of the overall problem. Obviously many interesting facts have been completely neglected. Habit modification, oriented overgrowths , inclusion of impurities and similar fields of research contribute valuable information but for the most part appear to be less directly necessary for consideration as part of the primary process of crystallization. The points which are discussed can hardly be ignored in even a qualitative theory that is to be of any value. The concept of a critical growth rate dependent on the size of the surface and the extent of association in the fluid phase, for example, appears to be a basic factor in the process. It is hoped that discussion in this manner of a rather loose body of facts may point out more clearly than would a neat mathematical expression the status of our present knowledge and the direction most profitable for future research. Crystal Section, Naval Research Laboratory, Washington, D.C.