Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

We propose an elastic-anisotropy measure. Zener’s familiar anisotropy index A=2C44∕(C11−C12) applies only to cubic symmetry [Elasticity and Anelasticity of Metals (University of Chicago Press, Chicago, 1948), p. 16]. Its extension to hexagonal symmetry creates ambiguities. Extension to orthorhombic (or lower) symmetries becomes meaningless because C11−C12 loses physical meaning. We define elastic anisotropy as the squared ratio of the maximum/minimum shear-wave velocity. We compute the extrema velocities from the Christoffel equations [M. Musgrave, Crystal Acoustics (Holden-Day, San Francisco, 1970), p. 84]. The measure is unambiguous, applies to all crystal symmetries (cubic-triclinic), and reduces to Zener’s definition in the cubic-symmetry limit. The measure permits comparisons between and among different crystal symmetries, say, in allotropic transformations or in a homologous series. It gives meaning to previously unanswerable questions such as the following: is zinc (hexagonal) more or less anisotropic than copper (cubic)? is alpha-uranium (orthorhombic) more or less anisotropic than delta-plutonium (cubic)? The most interesting finding is that close-packed-hexagonal elements show an anisotropy near 1.3, about half that of their close-packed-cubic counterparts. A central-force near-neighbor model supports this finding.

A general elastic-anisotropy measure

Quantum Dot Heterostructures

This paper reports the experimental results on macroscopic deformation instability and domain morphology evolution during stress-induced austenite → martensite (A→M) phase transformation in superelastic NiTi polycrystalline shape memory alloy microtubes. High-speed data and image acquisition techniques were used to investigate the dynamic and quasi-static events which took place in a displacement-controlled quasi-static tensile loading/unloading process of the tube. These events include dynamic formation, self-merging, topology transition, convoluted front motion and front instability of a macroscopic deformation domain. The reported phenomena brought up several fundamental issues regarding the roles of macroscopic domain wall energy and kinetics as well as their interplay with the bulk strain energy of the tube in the observed morphology instability and pattern evolution under a mechanical force. These issues are believed to be essential elements in the theoretical modeling of macroscopic deformation patterns in polycrystals and need systematic examination in the future.

http://repository.ust.hk/ir/bitstream/1783.1-2653/1/JMPS_Feng_Sunfinalsubmitted.pdf

Experimental investigation on macroscopic domain formation and evolution in polycrystalline NiTi microtubing under mechanical force

Anti-phase boundary energy of β series precipitates in Mg-Y-Nd system

Orthorhombic martensitic phase in Ti–Nb alloys: A first principles study

Tuning planar fault energies of Ni3Al with substitutional alloying: First-principles description for guiding rational alloy design

Crystal-melt kinetic coefficients of Ni3Al

In this study we attempt to improve the strength of titanium alloys by utilizing the precipitation hardening technique, a route that is relatively unexplored in titanium alloy development. It was found that copper satisfies the conditions necessary for precipitation hardening in titanium alloys and hence the following alloy, Ti–6Al–1.5V–2.5Cu (TAVC), was chosen for our studies. It was decided to ascertain the performance of this alloy in comparison to a standard titanium alloy, Ti–6Al–4V (TAV). Both the alloys were melted using a double Vacuum Arc Melting technique followed by forging and rolling in α–β regime. Subsequently, the alloys were β heat treated at 1010 °C and water quenched. Following this the alloys were aged at 500 °C. The aging characteristics were studied systematically through hardness and tensile testing techniques. While TAVC exhibited typical aging characteristics (hardening followed by softening), TAV displayed monotonic increase in strength following heat treatment. The yield strength of TAVC following peak aging is 1059 MPa which is 70 MPa higher than TAV heat treated under similar conditions. The higher, albeit limited strengthening, of TAVC vis-a-vis TAV was attributed to the formation of metastable precipitates of Ti–Cu which were revealed by TEM studies. The Mott–Nabarro model was able to rationalize the strengthening provided by the precipitates.

Microstructure and mechanical properties of a copper containing three phase titanium alloy

We present a general approach for determining the equilibrium shape of isolated, coherent, misfitting particles by minimizing the sum of elastic and interfacial energies using a synthesis of finite element and optimization techniques. The generality derives from the fact that there is no restriction on the initial or final shape, or on the elastic moduli of the particle and matrix, or on the nature of misfit. The particle shape is parametrized using a set of design variables which are the magnitudes of vectors from a reference point inside the particle to points on the particle/matrix interface. We use a sequential quadratic programming approach to carry out the optimization. Although this approach can be used to find equilibrium shapes of three-dimensional (3D) particles, we have presented the details of our formulation for two-dimensional systems under plane strain conditions. For systems with cubic elastic anisotropy, the equilibrium shapes and their size dependence are analyzed within the framework of symmetry-breaking shape transitions. For systems with dilatational misfit, our results on shape transitions are in agreement with those in the literature. For systems with non-dilatational misfit, we obtain a symmetry-breaking shape transition that involves a loss of mirror symmetry normal to the x- and y-axes; small particles have this symmetry, while those beyond a critical size do not. With these results, we now have a comprehensive picture of symmetry-breaking transitions in two-dimensional systems driven by anisotropy in misfit and elastic modul.

R. Sankarasubramanian

Papers

Orthorhombic martensitic phase in Ti–Nb alloys: A first principles study

Tuning planar fault energies of Ni3Al with substitutional alloying: First-principles description for guiding rational alloy design

Crystal-melt kinetic coefficients of Ni3Al

Microstructure and mechanical properties of a copper containing three phase titanium alloy

Symmetry-breaking transitions in equilibrium shapes of coherent precipitates