Farid F. Abraham

On the thermodynamics, structure and phase stability of the nonuniform fluid state

Abstract This study is based on a simple and straightforward generalization of the van der Waals theory for the thermodynamics and structure of a nonuniform fluid postulated almost one century ago. The relationship of this generalized van der Waals theory to the currently popular perturbation theory for liquid-vapor surfaces is demonstrated. An application of this theory to the description of the Lennard-Jones fluid interface near the triple point is reported, and comparisons of the predictions with numerical Monte Carlo experiments are made. The generalized van der Waals theory is then used to study infinitesimal density fluctuations and their relation to the stability of the single phase fluid state and critical opalescence. Theories for describing nonequilibrium density variations in a fluid are discussed with particular emphasis on the diffusion approximation. Theoretical predictions using the generalized diffusion equation are presented and compared with a numerical molecular dynamics simulation of a Lennard-Jones fluid quenched into the unstable region of the phase diagram (spinodal decomposition). Finally, a formal statistical mechanical theory for nonuniform fluids is presented and related to the van der Waals type theories.

Bond and strain energy effects in surface segregation: An atomic calculation

A model for predicting the surface segregation of solute in very dilute binary solid alloys is developed. The two main factors contributing to the driving force for segregation are the bond strength ratio ϵ∗ and size ratio σ∗ for the solute atom in the solvent matrix. These differences are accounted for implicity by considering various solid solution systems in bulk and surface configurations and by minimizing the total potential energy of the systems (0 K) through atomic relaxation consistent with the assumed long-range, pairwise interactions between the atoms. In previous studies, these two factors have been treated separately in an “ad hoc” manner and the strain energy due to the odd-size solute atom in the solvent lattice has been estimated using various continuum elasticity models. We demonstrate the short-comings of the conventional approach, in particular the failure of the simple continuum elasticity theory to accurately estimate the elastic driving force. We invent the ϵ∗−σ∗ representation which greatly facilitates a comparison of the various theories with one another and with experiments, the usefulness of this representation residing in the important finding that the theoretical boundary separating segregation and non-segregation regions depends only on ϵ∗ and σ∗. Comparison of our theory with experiment in 31 cases yields 28 correct predictions.

The phases of two-dimensional matter, their transitions, and solid-state stability: A perspective via computer simulation of simple atomic systems

Abstract An extensive computer simulation investigation of the structure, thermodynamics and phase stability of the two-dimensional Lennard-Jones system is presented, with special emphasis on the low-pressure melting regime of the phase diagram. This investigation includes isobaric-isothermal Monte Carlo simulations of the various phases of the two-dimensional Lennard-Jones system and of the melting and vaporization processes in configuration space, the isodensity-isothermal Monte Carlo simulations of two-phase coexistence between crystal and liquid and between liquid and vapor, the determination of the phase diagram, the establishment of the thermodynamic melting temperature, and the determination of the physical significance of the Kosterlitz-Thouless-Feynman dislocation model for melting in relation to the stability of the crystalline phase. I conclude that th phase diagram of the Lennard-Jones system in two dimensions is qualitatively similar to that in three dimensions. Finally, I present a new simulation method for doing molecular dynamics at constant pressure and/or constant temperature, and employ this method to study the temporal-spatial evolution of two-dimensional melting and vaporization.

The structure and thermodynamics of binary microclusters: A Monte Carlo simulation

Abstract The Monte Carlo computer simulation technique of classical statistical mechanics is employed to determine the structure and thermodynamics of binary microclusters of Lennard-Jones atoms as a function of cluster size, composition and temperature. Further, amorphous microclusters are prepared by a Monte Carlo quench, and their structural properties are examined. The properties of interest include the internal energy, instantaneous “snapshot” pictures of the microclusters atomic configuration, and the single-particle and pair distribution functions. The Lennard-Jones potential parameters are chosen to model Ar 13 , Ar 7 Kr 6 , Ar 36 Kr 19 and Ar 19 Kr 36 , as well as to crudely model the bimetallic clusters of Cu 19 Ni 36 , Cu 19 Ru 36 and Cu 19 Os 36 . A large variety of interesting features associated with these systems are described.

Comparison of the potential energies for various packings of microcrystallites

Abstract We compare the nature of different geometrical packings by presenting the dependence of the surface potential energy for microcrystallites of spherical atoms as a function of the cluster size, cluster packing and interaction range. Five polyhedron packings and the “approximately spherical” packing are studied. In general, the cubo-octahedron packings possess the minimum surface potential energy configuration.

The entropy of small clusters of atoms using an Einstein model

Abstract We present a generalized Einstein model for calculating thermodynamic properties of small clusters of atoms and demonstrate its validity by comparing its predictions with Burtons exact calculations. The simplicity of the method enables one to easily compute thermodynamic quantities for many systems beyond those previously considered.

A computer simulation of an amorphous thin film on a crystalline substrate

Abstract We employ the Monte Carlo simulation method of classical statistical mechanics to study the structure and energetics of the crystal/amorphous interface. The interface is found to be approximately four atomic layers thick and provides good bonding between the amorphous and crystalline phases.

On the fluctuation theory for the liquid—vapor interface

Abstract Using the statistical mechanical formulation of Triezenberg and Zwanzig, we argue that the “intrinsic” or “bare” width of the liquid—vapor interface in the Buff—Lovett—Stillinger capillary model may be identified as the interfacial width described by the “van der Waals-like” theories.

On the dynamics of spinodal decomposition: A numerical solution of a generalized diffusion equation

Abstract A numerical solution of a recently proposed diffusion equation governing spinodal decomposition of a fluid is presented. The results are compared with those of Cahns theory. For times beyond the linear regime, the two theories differ significantly in detail for the coarsening process and for the equilibrium structure of the liquid-vapor interface.

On the theory of critical opalescence for a classical fluid

Using a recent theory for the thermodyanmics of nonuniform fluids, the structure factor of a fluid near the critical point is calculated and found to deviate significantly from the predictions of the Ornstein-Zernike/Landau-Lifshitz theories when the square of the wave vector k2 ⪆ 10−2 A−2.