Perfect crystal

About: Perfect crystal is a research topic. Over the lifetime, 1112 publications have been published within this topic receiving 30992 citations.

The Growth of Crystals and the Equilibrium Structure of their Surfaces

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.

Principles of Solidification

Abstract: Solidification, in the sense used in this context, is the process by which a liquid is transformed into a crystalline solid. In crystal growth the solid that forms first is solvent rich as distinct from crystallisation, in which the crystals that are formed are solute rich. It is not always possible to make a clear distinction. Solidification is important as the process employed in the widely used process of casting, in all its forms from large ingots of steel to small crystals of silicon. While in principle it would seem simple to convert a homogeneous liquid into an equally homogeneous perfect crystal, this is extremely difficult, if not impossible to achieve in practice. Thorough understanding requires that the process be studied at various levels, which can be conveniently described as the angstrom level, the micron level and the centimetre level.

Long-range Finnis–Sinclair potentials

Abstract: Finnis–Sinclair potentials are developed for computer simulations in which van der Waals type interactions between well separated atomic clusters are as important as the description of metallic bonding at short range. The potentials always favour f.c.c. and h.c.p. structures over the b.c.c. structure. They display convenient scaling properties for both length and energy, and a number of properties of the perfect crystal may be derived analytically.

Development of new interatomic potentials appropriate for crystalline and liquid iron

Abstract: Two procedures were developed to fit interatomic potentials of the embedded-atom method (EAM) form and applied to determine a potential which describes crystalline and liquid iron. While both procedures use perfect crystal and crystal defect data, the first procedure also employs the first-principles forces in a model liquid and the second procedure uses experimental liquid structure factor data. These additional types of information were incorporated to ensure more reasonable descriptions of atomic interactions at small separations than is provided using standard approaches, such as fitting to the universal binding energy relation. The new potentials (provided herein) are, on average, in better agreement with the experimental or first-principles lattice parameter, elastic constants, point-defect energies, bcc–fcc transformation energy, liquid density, liquid structure factor, melting temperature and other properties than other existing EAM iron potentials.

Point defects in semiconductors

Abstract: In introductory solid-state physics texts we are introduced to the concept of a perfect crystalline solid with every atom in its proper place. This is a convenient first step in developing the concept of electronic band struc ture, and from it deducing the general electronic and optical properties of crystalline solids. However, for the student who does not proceed further, such an idealization can be grossly misleading. A perfect crystal does not exist. There are always defects. It was recognized very early in the study of solids that these defects often have a profound effect on the real physical properties of a solid. As a result, a major part of scientific research in solid-state physics has, ' from the early studies of "color centers" in alkali halides to the present vigorous investigations of deep levels in semiconductors, been devoted to the study of defects. We now know that in actual fact, most of the interest ing and important properties of solids-electrical, optical, mechanical- are determined not so much by the properties of the perfect crystal as by its im perfections."