Algorithmic considerations regarding the implementation of various materials science applications of the Monte Carlo technique to single instruction multiple data (SIMD) computer architectures are presented. In particular, implementation of the Ising model with nearest, next nearest. and long range screened Coulomb interactions on the SIMD architecture MasPar MP-1 (DEC mpp-12000) series of massively parallel computers is demonstrated. Methods of code development which optimize processor array use and minimize inter-processor communication are presented including lattice partitioning and the use of processor array spanning tree structures for data reduction. Both geometric and algorithmic parallel approaches are utilized. Benchmarks in terms of Monte Carlo updates per second for the MasPar architecture are presented and compared to values reported in the literature from comparable studies on other architectures.

The fast multipole method (FMM) is implemented in canonical ensemble particle simulations to compute non-bonded interactions efficiently with explicit error control. Multipole and local expansions have been derived to implement the FMM efficiently in Cartesian coordinates for soft-sphere (inverse power law), Lennard- Jones, Morse and Yukawa potential functions. Significant reductions in execution times have been achieved with respect to the direct method. For a given number, N, of particles the execution times of the direct method scale as O(N2). The FMM execution times scale as O(N) on sequential workstations and vector processors and asymptotically 0(logN) on massively parallel computers. Connection Machine CM-2 and WAVETRACER-DTC parallel FMM implementations execute faster than the Cray-YMP vectorized FMM for ensemble sizes larger than 28k and 35k, respectively. For 256k particle ensembles the CM-2 parallel FMM is 12 times faster than the Cray-YMP vectorized direct method and 2.2 times faster than the vectorized FMM. For 256k particle ensembles the WAVETRACER-DTC parallel FMM is 33 times faster than the Cray-YMP vectorized direct method.

We briefly review the numerical transfer-matrix (TM) method and its application to materials science. We report on the conventional use of TM methods to calculate phase diagrams and critical exponents of classical statistical mechanical models in d=2. Examples presented here are spin-1/2 and spin-1 models (two- and three-state lattice-gas models). Discussed are a model for oxygen -ordering in the high temperature superconductor YBa2Cu3O6+x and a model for the electrosorption of an organic substance on a metal. Some results for the spin-1/2 model in d=3 are also presented. Three unconventional applications of the TM method will also be reported. These include a study of the surface tension of spin-1/2 models, a TM formalism for metastability, and a study of a translationally invariant (non-fractal) spin-1/2 model in non-integer dimensions.

The thermodynamics of a fcc hard spheres solid is accurately described by recent density-functional approximations. This state is used as a reference in a thermodynamic perturbation analysis for a density-functional theory of Lennard-Jones solids. The free energy functional incorporates liquid state structural information and a density dependent potential decomposition for the Lennard-Jones interatomic potential. The computed free energies of the solids compare very well with the predictions of atonlistic simulations. Solid-liquid coexistence is predicted consistently to within 15% of results of Monte Carlo simulations, over the temperature range 0.75 ≤ kT/c ε ≤ 10.

A recently developed computational methodology allows the quantitative study of the correlation between the end-to-end distance of a polymer chain and its dipole moment. This paper focuses on the further analysis of this correlation and aims in identifying the structural characteristics of the polymer chain that are responsible for the observed behavior of the correlation. We study chains in the independent rotation approximation with symmetric rotational potentials. We focus on two different orientations of the bond dipole moment vector : 010 and 001 (the bond length vector's orientation is [100]).

The polysiloxanes are known to have unusually high permeabilities, and have therefore been much investigated with regard to their possible use as gasseparation membranes. In particular, their permeabilities are much higher than those of n-alkanes such as polyethylene (PE), a polymer which has already been extensively investigated using molecular dynamics simulations. In order to gain insight into the molecular origin of this high permeability, such simulations have been carried out on hypothetical model systems in which the structure of the polyethylene chain [-CH2-CH2-]x is converted step-wise into that of the most important polysiloxane, poly(dimethylsiloxane) (PDMS) [-Si(CH3)2-O-]x. The structural modifications thus investigated include (i) increase in the C-C bond length, (ii) change of the system's density from the density of PE to the density of PDMS, (iii) change of bond angles of PE to the alternate bond angles of PDMS, (iv) replacement of the torsional potential of PE by the torsional potential of PDMS, (v) change of masses of CH2 units along the chain to alternate masses of Si(CH3)2 and 0 units, (vi) change of Lennard-Jones parameters of CH2 groups for the appropriate parameters of Si and 0 units. At each of the six steps the self-diffusion coefficients of polymer segments and penetrant molecules (CO2) were calculated, allowing for the assessment of the influence of the structure of the polymer on the diffusion of the penetrant.

Atomic oxygen in low Earth orbit (LEO) readily attacks and oxidizes exposed spacecraft polymeric materials such as polyimide Kapton photovoltaic array blankets. The application of thin film silicon dioxide protective coatings can greatly extend the useful life of such materials in LEO. A Monte Carlo computational model has been developed which simulates atomic oxygen interaction with polymeric and protective coating materials for both ground laboratory and in-space experiments, allowing the determination of the geometrical shape of atomic oxygen attack of protected polymeric materials at defect sites in protective coatings. Modeling of attack of unprotected carbon-carbon composite materials predicts textured surfaces suitable for high emittance radiators. Results for fiberglass composites indicate loss of the matrix polymer leading to friable fibers. The computational modeling to project in-space performance based on ground laboratory testing predicts mass loss per fluence in space to be approximately one third that observed in plasma ashers.

Molecular dynamic simulations were used to identify factors which promote char formation during the thermal degradation of polymers. Computer movies based on these simulations, indicate that cross-linked model polymers tend to undergo further cross-linking when burned, eventually forming a high molecular weight, thermally stable char. This prediction was confirmed by char yield measurements made on γ and e - irradiated polyethylene and chemically cross-linked poly(methyl methacrylate).

The conformational dynamics of a model compound for poly(di-n-hexylsilane) (PDHS) has been explored using the new molecular dynamics program MM3-MD. MM3-MD trajectories at variable temperatures reveal two abrupt conformational transitions, one near -182°C and another near -175°C, associated with two energy barriers on the potential-energy surface. The first transition near -182°C allows shifts in the backbone torsion angle from that defined by the global energy minimum designated off-trans to that corresponding to a statistical collection of torsion angles within the range trans ±30°. The second transition near -175°C allows the backbone torsion angle to explore the remainder of its torsional space. The sidechain dynamics follows a similar pattern. We suggest that the abrupt transition calculated here at -182°C for “gas.phase” PDHS corresponds to that observed for PDHS at -28°C in solution and at 42°C in the solid state.

Over the years molecular modeling techniques, such as Molecular Mechanics, Monte Carlo and Molecular Dynamics have been applied to study the equilibrium thermodynamic and mechanical properties of materials. The accuracy of the predictions made by these techniques strongly depend on the force fields employed to represent the interactions in the studied system. Recently developed force field parameters for crystalline polyethylene are shown to reproduce the mechanical properties of polyethylene accurately through molecular mechanics. Here, we will present the statistical fluctuation formulae for the elevated temperature equilibrium thermodynamic and elastic properties in terms of microscopic variables such as energy, enthalpy, pressure, volume, microscopic strain or stress tensors and present preliminary results of our calculations.

Using two simulation techniques, the scanning and the hypothetical scanning methods we study a system of many chains with excluded volume contained in a “box” on a square lattice. With these methods the value of the sampling probability P of a configuration is known and therefore the entropy S can be calculated (S ∼ In P) without the need to resort to thermodynamic integration. Thus, the pressure and the chemical potential can be obtained with high accuracy directly from the entropy using standard thermodynamic relations. Our simulation results are compared to the approximate theories of Flory, Huggins, Miller and Guggenheim and to the recent improved theories of Freed and coworkers.

Fundamental parameters in the Flory-Huggins theory of binary mixture, including the heat of mixing associated with pairwise interactions ( Δw12) and the coordination number, z, are calculated through molecular simulations. The pair energies (w11, w22, w12) are obtained by averaging a large number of configurations generated by a Monte Carlo approach which includes the constraints associated with excluded volume. The temperature dependence of the interaction parameter X is obtained from this study.

The liquid-solid phase transition of cyclohexane in small pores of sol-gel glass is studied by computer simulation. A cavity model is obtained by placing silica clusters at the corners of a cubic box. A molecule inside the cavity is approximated by an assembly of six Lennard-Jones (LJ) potentials. Translational and rotational motions of C6H12 are studied in the temperature range from 190 K to 333 K. Supercooling is observed and the freezing temperature is depressed in comparison to the bulk phase.

The behaviour of two different systems, NiZr2 and Cu3Au, submitted to a chemical disordering process under various thermodynamical conditions has been investigated by Molecular Dynamics simulations. The role played by volume expansion and elastic softening in the onset of the transition has been discussed in the framework of the percolation model (C.Massobrio and V.Pontikis, Phys.Rev.B 45 (1992) 2484), correlating the elastic instability with the percolation of the distorted regions which establishes in the lattice as a consequence of the external perturbations (introduction of defects, volume expansion, chemical disorder etc.).

In this work, the benefits of a modern personal computer are used to get a deeper insight into the processes occurring in a ceramic material just before and during a dielectric breakdown. Especially, a model to simulate the thermal breakdown behavior in a two-phase material is presented, which is based on a random resistor network. To study the influence of different parameters on the thermal breakdown, simulations were done changing the values of a set of six variables, e.g. external voltage, resistivity, etc. The resulting plots time vs. maximum temperature are shown.

The relationship between oxygen structure, charge transfer (hole count), and oxygen content in the YBa2Cu3Oz superconductor is studied by combining Monte-Carlo simulation with existing electronic structure calculations. The present model proposes an expansion of the hole count in terms of oxygen configuration variables for states of an arbitrary degree of order. Calculations of hole count as a function of oxygen content suggest that oxygen ordering is, at least in part, responsible for the observed plateau structure of Tc vs. oxygen content z.

We have implemented a modified diffusion limited aggregation model to simulate the porous silicon structure obtained by electro-chemical dissolution. The fractal structures thus obtained have been used as starting configurations from which a fully equilibrated structure was determined by the method of molecular dynamics.

A systematic analysis based on atomistic simulations is presented for the calculation of energies and equilibrium concentrations of intrinsic point defects in silicon. Calculation of Gibbs free energies is based on the quasi-harmonic approximation for the reference state and the cumulant analysis of the enthalpy distribution function from Monte Carlo simulations in the reference state. Results are presented for the temperature dependence of enthalpies, volumes, and free energies of formation and thermal equilibrium concentrations of vacancies and self-interstitials.

A parameter-free technique already proposed by the authors to estimate the binding energy of elementary crystals is here extended to more complex crystal structures. Test calculations are presented here for several families of semiconductors of technological interest, such as XAs (X = Al, Ga, In), InX (X = P, As, Sb) and MgX (X = 0, S, Se). The accuracy of our predictions turns out to be comparable with that of previous results obtained within the local density approximation. The computational advantages of the method will be also discussed.

We describe a computer program which solves the complete set Of transport equations for device-quality amorphous silicon in two spatial dimensions and time. When modeling amorphous silicon devices, it is extremely important to account for the high concentration of time-dependent trapped charge present due to the continuous distribution of localized states in the semiconductor's bandgap. Our model is based on a realistic density-of-states distribution and includes a detailed description of the trap occupation functions for electrons and holes. These occupation functions are calculated self-consistently with respect to the electrostatic potential and free-carrier concentrations within the semiconductor.