Our understanding of the basic processes of crystal growth has meanwhile reached the level of maturity at least in the phenomenological concepts. This concerns for example the growth of pure crystals from a low-density nutrient phase like vapor or dilute solution with various aspects of pattern formation like spiral and layer growth, facetting and roughening, and the stability of smooth macroscopic shapes, as well as basic mechanisms of impurity incorporation in melt growth of (in this sense) simple materials like silicon or organic model substances. In parallel the experimental techniques to quantitatively ana lyze the various growth mechanisms have also reached a high level of reproducibility and precision, giving reliable tests on theoretical predictions. These basic concepts and appli cations to experiments have been recently reviewed by one of us (A. A. C. ) in "Modern Crystallography III. Crystal Growth" (Springer Series on Solid State Sciences, 1983). It has to be emphasized, however, that for practical applications we are still unable to quantitatively calculate many important parameters like kinetic coefficients from first principles. For mixed systems such as complex oxides, solutions and systems with chemi cal reactions, our degree of understanding is even lower. As a few examples for present achievements we note that experiments with vapour and molecular beam condensation of alkali halides confirmed the qualitatively predicted mechanisms of screw dislocations and two-dimensional nucleation for layer-growth.

Volumes 11 and 12 contain the papers read at the Fourth All-Union Conference on Crystal Growth in Tsakhkadzor, September 17-22, 1972; this volume contains papers on crystal growth from melts, from low-temperature solutions, hydrothermal solutions, and hot solutions, and also from the gas state, including processes involving reactions. In addition, there are papers on crystal perfection in relation to conditions of formation and the effects of electric and mag netic fields on crystallization. These papers reflect researches directed to the development and industrial production of perfect crystals required for advanced techniques in solid-state physics and chemistry, as well as for other purposes such as novel materials. There are many different scientific and technical problems in producing large perfect single crystals, and advances in this area made in the USSR and elsewhere are reflected in the papers in both volumes. On the one hand, any particular defective structure in a crystal originates from some mechanism and growth conditions; in particular, inclusions are trapped on account of the physicochemical parameters of the melt, the surface processes, and the sta bility of the growth front under particular crystallization conditions. Further, impurity trap ping is decisively influenced by the surface kinetics, growth-front stability, composition and structure of the boundary layer, any complexes present in the liquid, and (of course) the crys tallochemical relationships between the impurity and the crystal.

The Growth of Crystals series was begun in 1957 by A. V. Shubnikov and . N. N. SheftaP with the publication of the first volume. which contained the proceedings of the First All-Union Conference on Crystal Growth. The initiative and considerable efforts of the principal editor of the entire series. N. N. Sheftal', and his assistants led over the next 15 years to the publica tion of ten volumes which have assumed a leading position among the numerous books on crys tal growth. It has become traditional in this series to adopt a broad approach to crystal growth problems, and this approach is continued in Volumes 11 and 12, which are composed mainly of papers presented at the Fourth All-Union Conference on Crystal Growth in Tsakhkadzor. September 17-22, 1972. These papers, presented by both Soviet and foreign workers, deal with crystal growth processes. growth methods. and crystal perfection. Many of the papers reflect the tendency for our knowledge of crystallization processes to become increasingly more fundamental. with emphaSis on quantitative treatments. There are some extremely difficult problems in this approach. especially when the requirements of practical uses are envisaged. and many of these are discussed in various ways in these two volumes. These topics include detailed theoretical and experimental analysis of cooperative phenomena in crystallization. with emphasis not only on statistical thermodynamics but also statistical kinetics. This approach involves research on the structure and properties of phase boundaries. including the composition and structure of surface layers in liquids.

Early in this century, the newly discovered x-ray diffraction by crystals made a complete change in crystallography and in the whole science of the atomic structure of matter, thus giving a new impetus to the development of solid-state physics. Crystallographic methods, pri marily x-ray diffraction analysis, penetrated into materials sciences, mol ecular physics, and chemistry, and also into many other branches of science. Later, electron and neutron diffraction structure analyses be came important since they not only complement x-ray data, but also supply new information on the atomic and the real structure of crystals. Electron microscopy and other modern methods of investigating mat ter-optical, electronic paramagnetic, nuclear magnetic, and other res onance techniques-yield a large amount of information on the atomic, electronic, and real crystal structures. Crystal physics has also undergone vigorous development. Many re markable phenomena have been discovered in crystals and then found various practical applications. Other important factors promoting the development of crystallog raphy were the elaboration of the theory of crystal growth (which brought crystallography closer to thermodynamics and physical chem istry) and the development of the various methods of growing synthetic crystals dictated by practical needs. Man-made crystals became increas ingly important for physical investigations, and they rapidly invaded technology. The production . of synthetic crystals made a tremendous impact on the traditional branches: the mechanical treatment of mate rials, precision instrument making, and the jewelry industry."