364 CONCLUDING REMARKS V. CONCLUDING REMARKS Dr. C . W. Bum (I.C.I., Plastics) said: In looking a t the Discussion as a whole, and at the relations between theoretical and experimental contributions, certain things seem to me to stand out. In the first place, I am agreeably surprised a t the general agreement that a perfect crystal bounded by simple faces probably would not grow a t all. I suggested this as an inference from experimental evidence, but hardly expected i t to pass unchallenged ; actually it appears that there are theoretical grounds for expecting this to be the case. So far, theory and experiment are in accord. My other outstanding impression about the theoretical work is that much of i t is based on equilibrium considera- tions; yet crystal growth is, of course, not an equilibrium affair.I do not suggest that equilibrium considerations are irrelevant, but I think we should not assume that the conclusions from equilibrium considerations apply as they stand to actual crystal growth problems ; or, a t any rate, not to rapid growth. As they stand, they are likely to apply most closely to very slow growth. For the phenomena of rapid growth we need a dynamic theory, which treats crystal growth as a progressive event, takes into account the movements of the molecules in vapour, solution or melt, and considers how these movements influence the sites taken up on deposition and thus determine the character of the new surface on which further deposition is to take place. If we accept the thesis that perfect crystals bounded by low-index faces do not grow at any reasonable supersaturation, we are faced by the problem of accounting for the fact that crystals do actually grow, even at very low super- saturations.There are two obvious solutions; one is that real crystals are not perfect, the other is that the surfaces on which deposition occurs are not low-index surfaces ; and both these conceptions have figured in our discussions. No doubt both factors play a part in determining the rates a t which crystals grow, and we have to enquire what is their relative importance in a variety of circumstances. Turning to the experimental papers, they fall fairly sharply into two classes -those dealing with rapid growth and those dealing with extremely slow growth. The former are relevant to the industries which produce crystalline substances in large quantities and are necessarily concerned with rapid crystal growth ; the study of the rate of nucleus formation and the rate of crystal growth is directed towards maximum production and control of grain size and shape.The latter are the concern of the industries which make large perfect crystals for optical prisms or piezoelectric elements, and must necessarily grow their crystals very slowly in carefully controlled conditions. How are the industrial, experimental and theoretical aspects to be linked up ? It seems to me that i t is for problems of rapid growth from strongly super- saturated solution that a dynamic theory of crystal growth is most needed, and that since in rapid growth deposition apparently occurs on high-index surfaces a t the edges of spreading layers, the central problem is the study of the factors which keep high-index surfaces alive.On the other hand, in very slow growth from slightly supersaturated solutions there is time for high-index surfaces t o heal (that is, for the depositing molecules to go on to sites which give rise to low-index surfaces) ; in these circumstances, i t is likely that imperfections play a dominant role in controlling growth ; here, too, the theoretical approach based on equilibrium considerations is likely to be more directly applicable. Mr. P. R . Rowland (Londovt) said : The general view of the meeting seems to be that the gap between the theoretical and experimental approaches has been too wide. As a colleague To the author, the reason for this seems obvious.CONCLUDING REMARKS 365 remarked, “ The subject is still in the alchemical stage.” As an experimentalist the author feels that it is asking too much of the theoretical worker to provide even rough theories at this point of development.The information available is too meagre and the possible complications too many. However, we might have asked for guidance concerning the lines along which further work may be conducted. The author would therefore like to put forward a few opinions, though with some trepidation, since Prof. Stranski appears to have been following the course proposed and may already have forestalled them. First, the subject should be subdivided under the following headings : (i) Growth from vapour.(iii) Growth from solution. (iv) Growth by phase change in the solid state. Further subdivision according to whether the crystal is held together by ionic, homopolar, van der Waals’ or metallic forces also seems desirable. (ii) Growth from melt. Two aims should be borne in mind : (a) To provide a picture of the structures of the growing surfaces, meaning by “ picture ” the sort of information which is imparted by describing, say, methane or long conjugated chains in terms of cx bonds, etc. (b) A similar picture of the medium from which the crystal is growing, with due regard to the fact that the situation is dynamic and not static. The difficulty of supplying ( b ) will increase as we proceed from (i) above to (iii) ((iv) is a special case). In the case of growth from solution (a) and (b) may not be separable.For instance, when growing CuS0,.5H,O crystals there may be quite a large growing region, in passing through which Cu(H,O),++, SO4-- ions and water molecules gradually pass from a more or less random distribution to become units of a lattice correctly spaced and rotationally orientated. It would be difficult to say which point is the surface of the growing crystal. This picture is in fact supported by the observation that growth of good crystals from aqueous solution is only usually possible with hydrated substances, while growth from the melt seems to be the most successful way of producing really large perfect crystals. Can growth from solution be regarded as growth from a highly impure melt ? However, i t would seem wiser to start with the simplest systems (a) above.Crystallization may then be regarded as a heterogeneous reaction and it is essential that we learn as much as possible about the surface of the substrate. The author regards the technique of forming spherical single crystals and studying reactions on their surfaces as a powerful tool in the experimental study of solid surfaces. Prof. Stranski has used it to study crystal growth itself. It is suggested that progress from such beginnings may be made by carrying out work on the following lines : I . Experiments to determine the behaviour of the surface of single crystal spheres towards various reagents, e.g., the vapour of the crystal substance, adsorbates, substances of varying electronegativity, polar substances, solvents, etc.The only way to ensure a really clean surface is to heat i t in a vacuum and valuable information may be obtained by repeating some of J. K. Roberts’s work with single crystal wires. 2. Experiments with spheres a t temperatures very near their meltihg points to determine the mobility of surface layers. Growth from the vapour under these conditions, especially in cases where the gas phase could be made very dense, may give hints on the mechanisms of growth from the melt. 3 . Growth of solvated crystals from the melt may throw light on growth from s o h tion. 4. Dr. Bunn has shown how much is to be learnt by the direct observation of growing crystals. I n the electron microscope and interferometry as developed by Prof. Tolansky and his school, we now have methods which enable us to observe almost down to molecular dimensions. Though they have limitations, obvious and otherwise, the author is sure that if the attempt were made to adapt them to the study of growing crystals, a t least some confusion would be removed. The central problems could be recognized and attacked. To sum up, the theoretical physicist will only have a fair chance of getting to grips with the problem when the experimentalist has revealed what its essentials are, It is suggested that the best line of approach is to begin with a systematic study of crystal surfaces by both direct and indirect methods.