Crystal growth

Abstract: Parts I and II deal with the theory of crystal growth, parts III and IV with the form (on the atomic scale) of a crystal surface in equilibrium with the vapour. In part I we calculate the rate of advance of monomolecular steps (i.e. the edges of incomplete monomolecular layers of the crystal) as a function of supersaturation in the vapour and the mean concentration of kinks in the steps. We show that in most cases of growth from the vapour the rate of advance of monomolecular steps will be independent of their crystallographic orientation, so that a growing closed step will be circular. We also find the rate of advance for parallel sequences of steps. In part II we find the resulting rate of growth and the steepness of the growth cones or growth pyramids when the persistence of steps is due to the presence of dislocations. The cases in which several or many dislocations are involved are analysed in some detail; it is shown that they will commonly differ little from the case of a single dislocation. The rate of growth of a surface containing dislocations is shown to be proportional to the square of the supersaturation for low values and to the first power for high values of the latter. Volmer & Schultze’s (1931) observations on the rate of growth of iodine crystals from the vapour can be explained in this way. The application of the same ideas to growth of crystals from solution is briefly discussed. Part III deals with the equilibrium structure of steps, especially the statistics of kinks in steps, as dependent on temperature, binding energy parameters, and crystallographic orientation. The shape and size of a two-dimensional nucleus (i.e. an ‘island* of new monolayer of crystal on a completed layer) in unstable equilibrium with a given supersaturation at a given temperature is obtained, whence a corrected activation energy for two-dimensional nucleation is evaluated. At moderately low supersaturations this is so large that a crystal would have no observable growth rate. For a crystal face containing two screw dislocations of opposite sense, joined by a step, the activation energy is still very large when their distance apart is less than the diameter of the corresponding critical nucleus; but for any greater separation it is zero. Part IV treats as a ‘co-operative phenomenon’ the temperature dependence of the structure of the surface of a perfect crystal, free from steps at absolute zero. It is shown that such a surface remains practically flat (save for single adsorbed molecules and vacant surface sites) until a transition temperature is reached, at which the roughness of the surface increases very rapidly (‘ surface melting ’). Assuming that the molecules in the surface are all in one or other of two levels, the results of Onsager (1944) for two-dimensional ferromagnets can be applied with little change. The transition temperature is of the order of, or higher than, the melting-point for crystal faces with nearest neighbour interactions in both directions (e.g. (100) faces of simple cubic or (111) or (100) faces of face-centred cubic crystals). When the interactions are of second nearest neighbour type in one direction (e.g. (110) faces of s.c. or f.c.c. crystals), the transition temperature is lower and corresponds to a surface melting of second nearest neighbour bonds. The error introduced by the assumed restriction to two available levels is investigated by a generalization of Bethe’s method (1935) to larger numbers of levels. This method gives an anomalous result for the two-level problem. The calculated transition temperature decreases substantially on going from two to three levels, but remains practically the same for larger numbers.

Abstract: The purpose of this article is to describe the basic physical processes involved in the nucleation and growth of thin films of materials on solid surfaces. In this introduction the three modes of crystal growth which are thought to occur on surfaces in the absence of interdiffusion are described, and the relationships between the thermodynamics of adsorption and the kinetics of crystal growth are explored in general terms. This is followed by a brief review of atomistic nucleation theory, explaining the relations of such theories to experimental observables. In the next three sections, recent experimental examples of these three growth modes are given, which are interpreted where possible in terms of nucleation and growth theory. The last section discusses observations on the shapes of growing crystallites and the relation of such observations to nucleation and surface diffusion processes.

Abstract: This report introduces briefly some concepts and materials on crystal growth presented by Dr. Zhen-yu Zhang from the Oak Ridge (TN) National Laboratory, and Dr. En-ge Wang from the Institute of Physics, Chinese Academy of Sciences, in a session on crystal growth at the first Chinese-American Frontiers of Science Symposium. Crystal growth involves a variety of research fields ranging from surface physics, crystallography, and material sciences to condenser mater physics. Though it has been studied extensively more than 100 years, crystal growth still plays an important role in both theoretical and experimental research fields, as well as in applications. For example, how to growth ideal high Tc superconductor crystal has become an dominant subject both for testing of superconductor theories and physical properties. Furthermore, carbon 60 and carbon nano-tubes have opened a new field to both condensed mater physics and chemistry. From the recent discoveries in high Tc superconductors and C60, which brought the Nobel prize to the pioneer researchers in this field, one can understand the importance of crystal growth today. As the development of scientific instruments and analytical methods, such as x-rays, electron microscopy, NMR, and scanning tunneling microscopy continues, research on crystal growth and structure characterization has entered an atomic level, which makes it possible for further understanding of the physical, chemical, and other properties of the structure nature of various crystals. Especially for the crystals with low dimension and nano-structures, such as carbon nanotubes, blue-light emitting GaN thin films, and magnetic multilayers with giant magneto-resistance, their abnormal properties that have great potential in application can be understood only with the knowledge of structure at the atomic level. Moreover, a further improvement of crystal quality also depends on the structure characterizations. Based on its importance described above, crystal growth had been chosen as one of the topics …

Abstract: Crystals are generally considered to grow by attachment of ions to inorganic surfaces or organic templates. High-resolution transmission electron microscopy of biomineralization products of iron-oxidizing bacteria revealed an alternative coarsening mechanism in which adjacent 2- to 3-nanometer particles aggregate and rotate so their structures adopt parallel orientations in three dimensions. Crystal growth is accomplished by eliminating water molecules at interfaces and forming iron-oxygen bonds. Self-assembly occurs at multiple sites, leading to a coarser, polycrystalline material. Point defects (from surface-adsorbed impurities), dislocations, and slabs of structurally distinct material are created as a consequence of this growth mechanism and can dramatically impact subsequent reactivity.