Richard Alan Lesar

Scale-Free Intermittent Flow in Crystal Plasticity

Under stress, crystals irreversibly deform through complex dislocation processes that intermittently change the microscopic material shape through isolated slip events. These underlying processes can be revealed in the statistics of the discrete changes. Through ultraprecise nanoscale measurements on nickel microcrystals, we directly determined the size of discrete slip events. The sizes ranged over nearly three orders of magnitude and exhibited a shock-and-aftershock, earthquake-like behavior over time. Analysis of the events reveals power-law scaling between the number of events and their magnitude, or scale-free flow. We show that dislocated crystals are a model system for studying scale-free behavior as observed in many macroscopic systems. In analogy to plate tectonics, smooth macroscopic-scale crystalline glide arises from the spatial and time averages of disruptive earthquake-like events at the nanometer scale.

A parallel algorithm for 3D dislocation dynamics

Dislocation dynamics (DD), a discrete dynamic simulation method in which dislocations are the fundamental entities, is a powerful tool for investigation of plasticity, deformation and fracture of materials at the micron length scale. However, severe computational difficulties arising from complex, long-range interactions between these curvilinear line defects limit the application of DD in the study of large-scale plastic deformation. We present here the development of a parallel algorithm for accelerated computer simulations of DD. By representing dislocations as a 3D set of dislocation particles, we show here that the problem of an interacting ensemble of dislocations can be converted to a problem of a particle ensemble, interacting with a long-range force field. A grid using binary space partitioning is constructed to keep track of node connectivity across domains. We demonstrate the computational efficiency of the parallel micro-plasticity code and discuss how O(N) methods map naturally onto the parallel data structure. Finally, we present results from applications of the parallel code to deformation in single crystal fcc metals.

O(N) algorithm for dislocation dynamics

Abstract We present an extension of the fast-multipole method of Greengard and Rokhlin to the case of the long-range interactions between parallel edge (in arbitrary orientations) and screw dislocations. By finding complex potentials from which the stress terms can be calculated, and expanding those potentials in multipole series, we convert a computationally difficult O(N 2) problem into a much faster O(N) approach. To reach sufficient numerical accuracy, only a few terms are needed in the multipole expansions (four screws and six for edges) so that the interactions between millions of dislocations can be calculated in a few minutes on a workstation. We present results of a study of the relaxed configurations of 16384 edge dislocations of arbitrary orientations.

Location of melting point at 300 K of nitrogen by Monte Carlo simulation

We present an accurate new method to compute absolute free energies of molecular solids by computer simulations. As a first application, we computed the thermodynamic phase transition between the fluid phase and the orientational disordered solid β phase of nitrogen at 300 K, using a well tested pair potential. The computed coexistence pressure and the volume change coincides within the error margins with the experimental values. The coexistence volume differed by 2% from the experimental value. To our knowledge these results constitutes the first numerical calculation of the thermodynamic stability for a model of a realistic molecular solid.

Calculated thermodynamic properties and phase transitions of solid N2 at temperatures 0≤T≤300 K and pressures 0≤P≤100 GPa

Thermodynamic properties of solid nitrogen are calculated over a variety of isotherms and isobars using a constant pressure Monte Carlo method with deformable, periodic boundary conditions. Vibron frequencies are calculated using a simple perturbation theory. In addition, pressure–volume relations, thermal expansion coefficients, structures, and phase transition pressures and temperatures are determined. In particular, the nature of the orientational disorder in the plastic crystal phases is examined by calculating a variety of orientational order parameters.

Dislocation motion in the presence of diffusing solutes: a computer simulation study

A discrete lattice, kinetic Monte Carlo model is developed to simulate the motion of an edge dislocation in the presence of interacting, diffusing solute atoms that have a misfit with respect to the matrix. The simulation self-consistently determines the solute concentration profile (in two spatial dimensions), as well as the associated dislocation velocity. The solute segregation profile around the moving dislocation is characterized at low velocity by a condensed solute cloud near and on one side of the dislocation core, a region depleted of solute on the opposite side and a diffuse solute (Cottrell) atmosphere further from the core. At high velocity, no condensed solute cloud forms. The relation between the dislocation velocity and the applied stress shows a low-velocity, solute drag branch and a high-velocity branch, typified by no solute cloud but with occasional solute trapping. At intermediate velocities, the dislocation stochastically jumps between these two branches.

Thermodynamic properties and equation of state of dense fluid nitrogen

Results of constant‐pressure Monte Carlo calculations on dense fluid nitrogen over a pressure range of 2 to 300 kbar and a temperature range of 300–3000 K are presented. From analytic fits to the calculated volumes, enthalpies and vibrational frequency shifts, a comprehensive set of thermodynamic quantities is derived, including: thermal expansivity, compressibility, specific heat, Gruneisen parameter, and speed of sound. Comparison of the theoretical results to experiment at room temperature shows very good agreement (within 0.3% in volume and 1% in speed of sound, for instance). Good agreement is also obtained with earlier simulation data. In agreement with experimental studies of fluid metals, we find that the speed of sound varies linearly with density; along isotherms as well as along the Hugoniot. We find that ργG, the density times the Gruneisen parameter, which is assumed to be a constant in an often‐used phenomenological equation of state, varies considerably with density and temperature. Compari...

Density‐functional theory for solid nitrogen and carbon dioxide at high pressure

Structural properties of solid N2 and CO2 under pressure have been studied with a recently reported theory. The model allows for calculation of the structure and dissociation energy of molecular crystals, using no empirical parameters where dispersion energy is included as a sum of the pair interactions. Comparison with available low temperature experimental results shows good agreement with average errors in lattice constants of about 1% and in lattice energies of about 6%. Calculations were performed on nitrogen in a number of structures, including the experimentally observed Pa3 (α), P42/mnm (γ), P63/mmc (β), and Pm3n structures, as well as a recently proposed structure with space group R3m. The R3m structure was found to be more stable than the Pa3 structure at about 10 kbar. Calculations were carried out on carbon dioxide in the Pa3 structure. Comparison of the calculated pressure‐volume curves with room temperature experimental curves to 100 kbar shows very close agreement for both N2 and CO2.

Thermodynamics of solid and liquid embedded‐atom‐method metals: A variational study

We present results of variational calculations of the Helmholtz free energy and the thermodynamic properties of a series of metallic liquids and solids (Ag, Au, Cu, Ni, Pd, Pt) described by embedded‐atom‐method potentials. For the solids, we use a variational procedure based on an Einstein‐model reference state. The free energies of liquids are calculated with an approximate variational method proposed by Ross. At the respective melting points, the present results for the Helmholtz free energy are within about 1% of the results of accurate Monte Carlo (MC) calculations with the same interaction potentials, both for the fluid and the solid. The average error in the melting points calculated with the present procedure relative to Monte Carlo results is about 7.5%. The internal energies and entropies are compared to MC results, and show, in general, good agreement.

A new method for the simulation of alloys: Application to interfacial segregation

Abstract We present a new, accurate method for determining the properties of defects in alloys at finite temperature, including equilibrium segregation. This method is based upon a point approximation for the configurational entropy, an Einstein model for vibrational contributions to the free energy and may be employed with any type of description of atomic interactions. The atomic structure, segregation and thermodynamics of a defect in an alloy is determined by minimizing the free energy with respect to atomic coordinates and composition of each site at constant chemical potential. In order to test the accuracy of this approach, we compare our results with accurate Monte Carlo determinations. Overall, very good agreement for segregation to free surfaces and grain boundaries in CuNi alloys is obtained. One of the main advantages this new method enjoys over other methods such as Monte Carlo, is the efficiency with which the atomic structure of a defect, segregation and thermodynamic properties can be determined. This efficiency is obtained in the framework of a very straightforward method and with little loss in accuracy.