GENERAL INTRODUCTION ON CRYSTAL GROWTH BY W. E. GARNER Received 3rst January, 1949 In the earlier investigations the two aspects of the growth of crystals, the initiation of crystallization and the rate of growth, were developed independently. It is now realized that each plane of atoms or molecules added to the crystal may involve a fresh initiation of crystallization, and that the rate of crystallization is dependent on the rate of nucleation on the crystal surface. This means that in the fundamental treatment of crystal growth, the two sections are inseparable, and this has been recognized in the grouping of papers for this Discussion. In this introduction, which is mainly historical, the gradual evolution of the present outlook is indicated. Interest in this field has been accentuated by important applications in industry and a brief survey of these applications is included.Initiation of Crystallization. Throughout the nineteenth century there n7as much interest in the crystallization of supersaturated solutions, for example, of solutions of Glauber’s salt, magnesium sulphate, vitriols, etc. Boisbaudron found that spontaneous crystallization took place only in strongly supersaturated solutions and de Coppet, by cooling solutions, determined the limits of solubility at which spontaneous crystallization begins. Ostwald developed the idea of a metastable zone on the solubility diagram showing the limits within which no crystal nuclei could form spontaneously. This theory proved to be of considerable practical importance at the time in explaining some of the phenomena of precipitation and of Liesegang rings. Much attention was paid to the limiting size of particle needed to start crystallization in the metastable zone, and rough estimates gave a minimum size of 10-~-10-~~ g.The thermodynamic criteria developed by Willard Gibbs in 1878 which were applicable to this problem were not very early appreciated, with the result that for a long period the approach to the subject was empirical in character. Tammann’s work on the initiation of crystallization in undercooled organic liquids and inorganic glasses was of the greatest significance and settled many doubtful points. By making counts of nuclei under controlled condi- tions, he showed that the formation of nuclei obeyed the laws of probability and that the maximum probability occurred a t temperatures 4oo-12o0 below the melting point, where the liquids begin to lose their mobility and show marked changes in viscosity.There was a zone of about zoo, below the melting point, where nuclei formation was very slow, which corresponded to the metastable zone found with supersaturated solutions. Tammann showed that nuclei could be formed in this zone if the observer would wait long enough for them. He thought, however, that there might be a metastable region a few tenths of a degree below the melting point, due to an increase in solubility resulting from a decrease of particle size. He also found that the rate of nuclei formation became very slow in the glassy state of under- cooled liquids, where the viscosity was very high.Tammann considered that since the formation of a nucleus was a very rare event, a large number of molecules must meet under limiting condi tions o 78 GENERAL INTRODUCTION ON CRYSTAL GROWTH velocities, orientation and direction of movement, before a nucleus can be formed. The process was so complicated that any simple relations between the probabilities and the stabilities of the forms produced were not to be expected. He concluded that Ostwald’s Law of Stages was not universally applicable. Willard Gibbs showed that a spherical particle of phase 11, p = p”, was in The equilibrium with a continuous phase I, $ = p’, when r = II equilibrium is, however, unstable, for if r is slightly reduced, the particle will decrease in size and finally disappear, and if it be slightly extended it will grow until phase I completely disappears.The work done in the creation of a partide of phase I1 in phase I is always positive up to the value of y = pfl - - p” so that phase I is stable with respect to nuclei formation so long as r is of such magnitude for the surface tension equation to apply. It will break down as r approaches molecular dimensions and 9’’ > p’. It would be expected, therefore, that for an undercooled liquid there would be a metastable region for phase I , where spontaneous nuclear formation could not occur, and a metastable limit below which the system became labile owing to r approaching molecular dimensions. Haber employed the Thomson equation , 2 0 P -$‘* 2cr T, - TI 2aM ~ -- Ts - r Q 4 in a theoretical examination of the crystallization of supercooled liquids.T, is the melting point, T, the melting point of a nucleus of radius r, G the interfacial energy, Qs the heat of crystallization, p the density of the solid phase, and M the molecular weight. He postulated a Spurenschmelxpunkt as the melting point of the smallest ordered aggregate, which determined the temperature of the metastable limit. These considerations of Gibbs and Haber will, however, be modified if there be taken into account the local fluctuations of energy which occur in any fluid and which have been demonstrated in the phenomena of critical opalescence. These local fluctuations will facilitate the formation of nuclei and render the metastable limit less sharp, although the conception of a metastable zone is still of some practical value.Rate of Growth. Tammann’s researches on the crystallization of super- cooled liquids show that the rate of crystallization is very slow down to about 30” below the melting point, increasing to a maximum which is often flat, and falling off as the viscosity increases to that of a glass. The maximum for the rate of crystallization lies at higher temperatures than for nucleation. The low values just below the melting point are due to the slow removal of heat of Crystallization. Tammann concludes that the rate is at its maximum when the temperature of the melt is where To is the melting point, qo the heat of crystallization, and cm the mean specific heat. Surface Flow. Studies of the growth of crystals from the gaseous phase indicate that the flow of molecules over the surfaces of the crystals plays an important role in the rate of crystallization.Volmer and Estermann showed that mercury crystals formed from the vapour consist of very thin flat plates, and that the rate of extension of the main faces can only be accounted for if the molecules colliding over the whole surface of the crystal are available for the growth of the very small areas at right-angles to the basic planes. This requires that the surface flow of a molecule during its = ‘0 - qo/c?nJW. E. GARNER 9 tifetime on the surface is of considerable magnitude. The work of Becker and of Taylor and Langmuir on adsorbed czsium on tungsten, and of Bosworth on potassium on tungsten, at temperatures where the evaporation of the adsorbed atoms is low, shows that the atoms undergo activated diffusion along the surface.For czsium the number of sites covered during the lifetime is at least xo8. Also, Newman has demonstrated that activated diffusion occurs on the surface of heated sodium chloride crystals. The experiments of Volmer and Adikari on the surface flow of benzophenone on glass and of Xowarski on $-toluidine over a crystal of the same substance illustrate the same principle. The extension of this principle to crystallization from supersaturated solutions and from undercooled melts is unavoidable, since in general the work required to move a molecule or ion along the surface is less than that to transfer it to the liquid phase. The Repeatable Step. The energies required to remove ions or mole- cules of sodium chloride from the surface of a crystal into the gaseous phase have been calculated by Kossel and Stranski for the corner, edge and various surface positions.Homopolar lattices have been dealt with similarly by the same authors and by Becker and Doring. The difference between the energies for the various sites is sufficiently great to have an important bearing on the kinetics of crystal growth. In building up a plane of atoms on the surface of a crystal, the greatest energy is liberated at the repeatable step of an uncompleted edge of a covered area. The energy evolved on adsorption on such sites is approx- imately the same as that resulting from embedding the atom half-way in the crystal. The process of crystallization on surfaces large compared with the atomic diameter consists mainly in the repetition of the ' repeatable step.' The adsorption of atoms singly on the plane surface is much less strong than at the repeatable step. Over part of the range of temperatures for which atoms are firmly held at the repeatable step, those on the main surface are readily desorbed.The surface molecules, however, travel by surface flow considerable distances before they evaporate, and therefore it is to be expected that in favourable circumstances the whole surface of the crystal will act as a collecting ground for the repeatable step. Two-dimensional Nuclei. The rate of evaporation is greatest if the adsorbed molecules are held singly on the surface and least when held at a repeatable step on a two-dimensional nucleus, the size of which is above a critical value.In the building-up of new crystal planes, the average time taken to complete a two-dimensional nucleus of this critical size may be considerably greater than that required to complete the plane of molecules by a succession of repeatable steps. Volmer, for iodine crystals growing from vapour, concludes that the formation of the two-dimensional nucleus is such a rare event that the probability of its occurrence determines the velocity of crystallization. Crystals grow the more regularly the lower the supersaturation. At high supersaturations polymolecular sheets are built up, giving a series of steps on the faces of crystals which can be detected by interference colours (Marcellin, Perrin, Kowarski) .These phenomena are of frequent occurrence and are of special interest. Stranski, studying the growth of polished spherical surfaces, shows that the planes with high indices of even simple lattices give uneven surfaces during growth, built up of steps of various heights. It should, however, be borne in mind that some of these phenomena may be due to the discontinuities caused by polishing. It is clear, however, that the mechanism of crystal growth, with complex molecules from strongly super- saturated solutions, can become an involved problem. Phenomena makeI0 GENERAL INTRODUCTION ON CRYSTAL GROWTH their appearance which have not been unambiguously elucidated. It is possible that some of these may be due to Smekal, Zwicky or other types of discontinuity, as suggested by Frank.However, under the simplest condi- tions, with low supersaturation, the conception of the formation of two- dimensional nuclei aided by surface flow may prove to be adequate for the calculation of rates of growth. Crystal-Crystal Interface. The nuclei formation in solid phases obeys similar temperature relationships to supercooled melts, giving maxima at temperatures considerably below the melting point. Volume changes on crystallization, producing cracks, are, however, an added complication. Nuclei formation in processes which are accompanied by gas evolution are one step more complicated, but the phenomena obey the same general rules. In a number of cases in which gas evolution occurs, the activation energy is approximately the same as the thermodynamic heat for the process, which implies a close fit between the lattices of the two phases and a very close coupling between the disappearance of the old and the building-up of the new lattice.This may well be the case, in favourable circumstances, for the growth of one crystal phase out of another. The need for large crystals free from flaws for spectroscopy, piezoelectric measurements and the various purposes of the electrical industry cannot be met from the diminishing natural resources, nor do these give a sufficient variety. This has led to researches on the methods of accurate control of crystallization from the vapour phase, the melt, from supersaturated solutions and by hydrothermal processes at high pressures simulating those in nature.In the natural processes whereby crystals are formed in the earth’s crust, an infinitude of time is available for the manufacture, but on the industrial scale the time available makes it necessary to work at higher supersaturations, where irregularities are the more likely to occur in t h e crystallization processes. The control of crystal shape and size by the addition of surface active substances is a requirement in many industries. In the explosives industry particles with as nearly spherical shape as practicable are advantageous from the point of view of flow properties, bulk density, pelleting properties, etc. It is also possible in cases where two solid modifications are produced to prevent the formation of the unstable modification by the use of suitable additaments. The control of particle size distribution is also important in the manufacture of materials used as the basis of products with good plasticity.The tendency of hygroscopic substances to cake can often be reduced by paying attention to crystal shape, choosing that shape which gives a minimum of contacts between the grains. The surface agents may operate by adsorption on one set of faces, either reducing or preventing growth, as is found by the use of certain dyestuffs. These agents may operate by retarding all growth except in one direction, thereby giving spherulitic growths. The detailed mechanism by which they act is not yet elucidated, although it can readily be seen from current ideas on crystal growth that the effects of adsorption at the repeatable step would have important consequences. There are many processes in which crystallization is the final stage, giving the product its essential properties. Such are the manufacture of cements, bricks, ceramics, etc. Although in these cases the crystallization process is often accompanied by chemical change, the mechanism involves the nucleation by crystals and the growth of crystals such as occurs for the simpler processes, and their study will benefit by the development of the fundamental theory of cryst a1 growth. Practical Applications. The University, Bristol.