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Computer Simulation of Materials Using Parallel Architectures

  • Priya Vashishta
  • Rajiv K. Kalia
  • Aiichiro Nakano
  • Wei Jin
  • Jin Yu

Abstract

Algorithms are designed to implement molecular dynamics (MD) and quantum molecular dynamics (QMD) simulations on emerging concurrent architectures. A highly efficient multiresolution algorithm is designed to carry out large-scale MD simulations for systems with long-range Coulomb and three-body covalent interactions on distributed-memory MIMD (multiple instruction multiple data) machines. The performances of these algorithms are tested on the Intel Touchstone Delta and IBM SP-1 systems. The computational complexities of these algorithms are O(N) and parallel efficiencies close to 0.9. The core computational kernel of the QMD approach consists of solutions of parabolic partial differential equations (PDE) such as the time-dependent Schrödinger equation or time-dependent Kohn-Sham equation. This problem is coupled with another computationally intensive problem, i.e., solution of elliptic PDEs (the Poisson equation) for the long-range electron-electron interaction. We have designed parallel algorithms for both problems on SIMD (single instruction multiple data) machines.

In the past three years, we have used the parallel computer architectures in our Concurrent Computing Laboratory for Materials Simulations (CCLMS) to carry out MD and QMD simulations on network glasses, ceramic composites, nanophase materials, solid C60 and graphitic tubules, and quantum transport in nanoscale devices.

Structural transformation, intermediate-range order and dynamical behavior of SiO2 glass at high pressures are investigated with molecular dynamics. At high densities, the height of the first sharp diffraction peak is considerably diminished, its position changes from 1.6 to 2.2 Å−1, and a new peak appears at 2.85 Å−1. At twice the normal density, Si-O bond length increases, Si-O coordination changes from 4 to 6, and O-Si-O bond-angle changes from 109° to 90°. This is a tetrahedral to octahedral transformation, which was reported recently by Meade, Hemley, and Mao.

Molecular dynamics simulations of porous silica, in the density range 2.2 − 0.1 g/cm3, are carried out on a 41,472-particle systems using a MIMD computer. The internal surface area, pore surface-to-volume ratio, pore-size distribution, fractal dimension, correlation length, and mean-particle size are determined as a function of the density. Structural transition between a condensed amorphous phase and a low-density porous phase is characterized by these quantities. Various dissimilar porous structures with different fractal dimensions are obtained by controlling the preparation schedule and temperature.

Pore interface growth and the roughness of fracture surfaces in silica glasses are investigated by MD simulations with 1.12-million particles. During uniform dilation, the pores coalesce and grow in size. When the mass density is reduced to 1.4 g/cm3, the pores grow catastrophically to cause fracture. The roughness exponent for fracture surfaces, α = 0.87 ± 0.02, supports experimental claims about the universality of α.

Lattice dynamics of solid C60 is studied using a unified interaction model which consists of a tight-binding potential for the intra-molecular interaction and a Lennard-Jones and bond charge model for the inter-molecular interaction. Phonon dispersion and density of states of solid C60 are calculated in the energy range from 0 to 210 meV. The inter-molecular phonon density of states shows peaks around 2.3 meV and 3.7 meV, and extends to 7.6 meV. The calculated phonon spectrum agrees well with inelastic neutron scattering experiments. The effects of orientational disordering and pressure on the inter- and intra-molecular phonons of solid C60 are investigated.

Recently a new form of carbon — graphitic tubule — has been discovered. It is the fourth member of the carbon family with dimension of one (diamond in 3D, graphite in 2D, and fullerene in 0D). Using the tight binding molecular dynamics method (TBMD), the structural and dynamical properties of graphitic tubules are studied. The phonon dispersion and density of states of graphitic tubules with various helicities and diameters are calculated. Compared with graphite, phonon modes in tubules are softened by the curvature. Unique features of the graphitic tubule, with special emphasis on low-frequency modes, are discussed. The symmetry of phonon modes is analyzed, and infrared and Raman active modes are identified. Sound velocities in graphitic tubules are also calculated as functions of tubule helicity and diameter.

Keywords

Phonon Dispersion Single Instruction Multiple Data Multi Grid Method Raman Active Mode Fast Multipole Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Priya Vashishta
    • 1
  • Rajiv K. Kalia
    • 1
  • Aiichiro Nakano
    • 1
  • Wei Jin
    • 1
  • Jin Yu
    • 1
  1. 1.Concurrent Computing Laboratory for Materials Simulations, Department of Physics & Astronomy and Department of Computer ScienceLouisiana State UniversityBaton RougeUSA

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