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Recently developed semiempirical potential energy functions for the Ga-As-Si and Ga-As-Al systems have been applied here to determine the excess formation energy for GaAs clusters on GaAs(00-1), AlAs(00-1), Si(001), and one atomic layer As-covered Si(001) substrates as a function of cluster size and cluster shape by the Monte Carlo technique. Pyramidal type ledges on the GaAs clusters are found to be the favored ledge for the first three layers while an inverted-pyramidal type ledge is also favored in certain cases for the As1/Si(001) substrate. Cluster formation at ledges is compared with cluster formation on a flat terrace for the Si(001) and the As1/Si(001) substrates.

Colloid stability theory has been applied to protein crystallization and predicts a narrow range of conditions under which crystals can be grown without the agglomeration of protein molecules (colloids) in the bulk solution. It also predicts a critical electrolyte concentration above which agglomeration will always occur. Using this theory, the rapid protein agglomeration occurring during Schlieren experiments as well as a terminal crystal size effect in a fixed container were explained. Following this concept, the supposed 'terminal' crystal size has been at least doubled.

Semiempirical potential energy functions have been utilized for a variety of calculations in the Ga-Al-As system. Surface energies have been calculated for several orientations of GaAs. Ledge energies for the GaAs (0 0 -1) (As-terminated) surface show long-range interaction effects with the ledge energy increasing with spacing. GaAs (001)/AlAs (001) superlattices have been simulated for a range of interlayer spacings with the excess interfacial energy per interlayer increasing from 5 erg/sq cm at an interlayer spacing of 1 molecular layer (5.8 A) to 50 erg/sq cm at an interlayer spacing of 18 molecular layers (103.8 A).

Both strip and triangular clusters, composed of 2 -1 -1 line ledges, have been simulated on the Si (111) surface. The long-range ledge-ledge interaction and the surface stress tensor distribution have been evaluated for these two pill-box geometries using a semiempirical potential-energy function that incorporates both two-body and three-body contributions. The consequences of the ledge-ledge interaction on two-dimensional nucleation for Si (111) has been evaluated as a function of Si adatom supersaturation and shown to differ significantly from conventional theory, where such interaction is neglected.

Using a computer simulation technique with a semiempirical potential, a Si crystal was cleaved along the (111) plane. The pi-bonded chain structural features of the Si(111) cleavage surface are observed and found to be a consequence of the dynamics of this cleavage process and seem not to be influenced by the final energetics.

A direct and convenient method is presented for deriving expressions which equate any thermodynamic state function to averages of specific dynamical functions and their fluctuations over the classical microcanonical distribution. Specific expressions are obtained for a variety of thermodynamic quantities. The effect of various entropy definitions on the results are assessed, and the latter are compared to previous work in the literature. The derived formulas are applied to the analysis of molecular-dynamics computer simulations.

Most geometric modeling systems use either polynomial or rational functions to represent geometry. In such systems most computational problems can be formulated as systems of polynomials in one or more variables. Classical elimination theory can be used to solve such systems. Here Cayley's method of elimination is summarized and it is shown how it can best be used to solve the curve/curve intersection problem. Cayley's method was found to be a more straightforward approach. Furthermore, it is computationally simpler, since the elements of the Cayley matrix are one variable instead of two variable polynomials. Researchers implemented and tested both methods and found Cayley's to be more efficient. Six pairs of curves, representing mixtures of lines, circles, and cubic arcs were used. Several examples had multiple intersection points. For all six cases Cayley's required less CPU time than the other method. The average time ratio of method 1 to method 2 was 3.13:1, the least difference was 2.33:1, and the most dramatic was 6.25:1. Both of the above methods can be extended to solve the surface/surface intersection problem.

All the investigations which were performed employed in one way or another a computer simulation technique based on atomistic level considerations. In general, three types of simulation methods were used for modeling systems with discrete particles that interact via well defined potential functions: molecular dynamics (a general method for solving the classical equations of motion of a model system); Monte Carlo (the use of Markov chain ensemble averaging technique to model equilibrium properties of a system); and molecular statics (provides properties of a system at T = 0 K). The effects of three-body forces on the vibrational frequencies of triatomic cluster were investigated. The multilayer relaxation phenomena for low index planes of an fcc crystal was analyzed also as a function of the three-body interactions. Various surface properties for Si and SiC system were calculated. Results obtained from static simulation calculations for slip formation were presented. The more elaborate molecular dynamics calculations on the propagation of cracks in two-dimensional systems were outlined.

Report on study of solute segregation and interface stability during crystal growth describes new theoretical model for crystal growth from melt. Report also describes experiments in crystal growth by controlled-gradient freezing and by pulling from melt (Czochralski growth).

Adequate computer methods, based on interactions between discrete particles, provide information leading to an atomic level understanding of various physical processes. The success of these simulation methods, however, is related to the accuracy of the potential energy function representing the interactions among the particles. The development of a potential energy function for crystalline SiO2 forms that can be employed in lengthy computer modelling procedures was investigated. In many of the simulation methods which deal with discrete particles, semiempirical two body potentials were employed to analyze energy and structure related properties of the system. Many body interactions are required for a proper representation of the total energy for many systems. Many body interactions for simulations based on discrete particles are discussed.

The general aim of this investigation was to study interface stability and solute segregation phenomena during crystallization of a model system. Emphasis was to be placed on direct observational studies partly because this offered the possibility at a later stage of performing related experiments under substantially convection-free conditions in the space shuttle. The major achievements described in this report are: (1) the development of a new model system for fundamental studies of crystal growth from the melt and the measurement of a range of material parameters necessary for comparison of experiment with theory. (2) The introduction of a new method of measuring segregation coefficient using absorption of a laser beam by the liquid phase. (3) The comparison of segregation in crystals grown by gradient freezing and by pulling from the melt. (4) The introduction into the theory of solute segregation of an interface field term and comparison with experiment. (5) The introduction of the interface field term into the theories of constitutional supercooling and morphological stability and assessment of its importance.

A molecular dynamics technique based upon Lennard-Jones type pair interactions is used to investigate time-dependent as well as equilibrium properties. The case study deals with systems containing Si and O atoms. In this case a more involved potential energy function (PEF) is employed and the system is simulated via a Monte-Carlo procedure. This furnishes the equilibrium properties of the system at its interfaces and surfaces as well as in the bulk.