Jeremy Q. Broughton

Spanning the length scales in dynamic simulation

couple different length and time scales in serial fashion. By this we mean that one set of calculations at a fundamental level, and of high computational complexity, is used to evaluate constants for use in a more approximate or phenomenological computational methodology at longer length or time scales. In pioneering work of this sort in the 1980s, Clementi and coworkers1 used high-quality quantum-mechanical methods to evaluate the interaction of several water molecules. From this database they parameterized an empirical potential for use in molecular-dynamics atomistic simulations. Such a simulation was then used to evaluate the viscosity of water from the atomic autocorrelation function. Finally, the computed viscosity was used in a computational-fluid-dynamics calculation to predict tidal circulation in Buzzards Bay, MA. This tour de force of computational physics is a powerful example of the sequential coupling of length and time scales: one series of calculations is used as input to the next up the length and time hierarchy. There are many other examples in the literature. But what underlies all these schemes is that an appropriate computational methodology is used for a given scale or task, whether it be the accuracy of quantum mechanics at the shortest scales or fluid dynamics at the longest scales. In contrast, there has been comparatively little effort devoted to the parallel coupling of different computational schemes for a simultaneous attack on a given problem; in our case, our interest dictates specific attention toward issues in materials or solid-state physics. We will focus specifically on the coupling of length scales for the three mechanics describing materials phenomena: quantum mechanics, atomistic mechanics, and continuum mechanics.

Molecular dynamics investigation of the crystal–fluid interface. I. Bulk properties

Properties of the crystal and liquid phases have been measured for a system of particles interacting through a modified Lennard‐Jones potential. Through constant pressure molecular dynamics, we have evaluated the density and internal energy of these phases at a pressure that approximates that of the vapor phase. The free energy of the crystal is obtained with the Einstein crystal as a reference state, and the liquid free energy is measured relative to the ideal gas. The triple point temperature is obtained. Compressibilities and Gruneisen parameters are obtained at zero temperature and the triple point. Dynamic properties of the supercooled liquid state are also calculated. These results are applied in forthcoming publications which calculate surface excess quantities and dynamic properties of the fcc (111), (100), and (110) faces.

PATH INTEGRAL GRAND CANONICAL MONTE CARLO

We derive the real-space path integral formulations of Widom’s test particle method and grand canonical Monte Carlo (GCMC). We apply these simulation methods to hydrogen and neon at temperatures ranging from 30 to 120 K. In addition, in order to explore configuration space both efficiently and ergodically, our implementation involves multiple time step hybrid Monte Carlo. Agreement between experiment and simulation for chemical potentials (Widom) and densities (GCMC) is very good over the entire temperature range, even when quantum effects are large.

Neural networks in computational materials science: training algorithms

Neural networks can be used in principle in an unbiased way for a multitude of pattern recognition and interpolation problems within computational material science. Reliably finding the weights of large feed-forward neural networks with both accuracy and speed is crucial to their use. In this paper, the rate of convergence of numerous optimization techniques that can be used to determine the weights is compared for two problems related to the construction of atomistic potentials. Techniques considered were back propagation (steepest descent), conjugate gradient methods, real-string genetic algorithms, simulated annealing and a new swarm search algorithm. For small networks, where only a few optimal solutions exist, we find that conjugate-gradient methods are most successful. However, for larger networks where the parameter space to be searched is more complex, a hybrid scheme is most effective; genetic algorithm or simulated annealing to find a good initial starting set of weights, followed by a conjugate-gradient approach to home in on a final solution. These hybrid approaches are now our method of choice for training large networks.

Ab initio dynamics of rapid fracture

As our title implies, we consider materials failure at the fundamental level of atomic bond breaking and motion. Using computational molecular dynamics, scalable parallel computers and visualization, we are studying the failure of notched solids under tension using in excess of atoms. In rapid brittle fracture, two of the most intriguing features are the roughening of a cracks surface with increasing speed and the terminal crack speed which is much less than the theoretical prediction. Our two-dimensional simulations show conclusively that a dynamic instability of the crack motion occurs as it approaches one-third of the surface sound speed. This discovery provides an explanation for the cracks surface roughening and limiting speed. For three-dimensional slabs, we find that an intrinsically ductile FCC crystal can experience brittle failure for certain crack orientations. A dynamic instability also occurs, but brittle failure is not maintained. The instability is immediately followed by a brittle-to-ductile transition and plasticity. Hyperelasticity, or the elasticity near failure, governs many of the failure processes observed in our simulations and its many roles are elucidated.

Large-scale simulations of brittle and ductile failure in fcc crystals

Abstract We are simulating the failure of three-dimensional notched fcc solids under mode one tension using molecular dynamics, simple interatomic potentials and system of tens of millions of atoms. We have discovered that crystal orientation with respect to the uniaxial loading is important; the solid fails by brittle cleavage for a notch with (1 1 0) faces and by ductile plasticity for a notch with (1 1 1) faces or (1 0 0) faces. We argue that the competition between bond-breaking and interplanar slippage is governed by the nonlinearity and anisotropy of the crystal elasticity near materials failure. If the speed of the (1 1 0) brittle crack velocity reaches approximately one-third of the Rayleigh sound speed, a “brittle-to-ductile” transition occurs and is consistent with the onset of a dynamic instability of brittle fracture. Such an instability was seen in our earlier two-dimensional fracture simulations of rare-gas films and appears to be a general feature of the dynamic brittle fracture process. We close with a simulation showing the consequences of a brittle crack colliding with a void.

Grain-boundary shearing as a test for interface melting

We examine the behaviour of the (310) symmetric tilt boundary with applied shear stress in a face-centred cubic Lennard-Jones crystal. Our purpose is to observe the mechanical properties of grain boundaries resulting from interface melting. The grain boundary is seen to exhibit significant self-diffusion at temperatures above 80% of the bulk melting point . Excess thermodynamic properties and the density of the system change dramatically in this region. However, the system is able to resist shear up to the higher temperature of . Plots of particle trajectories in the interface and estimates of the number of melted layers provide insight into an understanding of this behaviour.

Simulation models of the crystal–vapor interface

The atomic structures of crystal–vapor surfaces have been studied using Monte Carlo simulations of the Ising model and molecular dynamics simulations of a system of Lennard‐Jones particles. The roughening transition and its effects on the kinetics of growth and the crystal structure are discussed together with some implications for the growth of composition modulated crystals. Growth by two‐dimensional nucleation and an impurity mechanism are discussed. Atomic positions at close‐packed crystal–vapor surfaces are obtained from the molecular dynamics model. The atomic mobility in the surface region and the possibility of a surface melting transition are discussed.

Fullerene molecules and tubules polarizabilities, vibrational modes and nanocapillarity

Abstract Recent algorithmic and computational advances for density-functional-based investigations of clusters now allow for the calculation of a multitude of low-energy phenomena in complex clusters and molecules. Here we discuss methods for the first-principles calculation of linear and non-linear electronic polarizabilities and for vibrational modes. Results from recent calculations on the C60 molecule show that the local-density-approximation (LDA) is capable of a very accurate quantitative description of such phenomena. As an example of how the high polarizability of caged carbon compounds might be beneficially exploited for new technological applications, we review recent simulations which predicted that fullerene tubules behave as molecular straws.

Large-scale simulations of crack–void and void–void plasticity in metallic fcc crystals under high strain rates

We have simulated the failure of three-dimensional fcc solids containing voids under mode one tension using molecular dynamics, simple interatomic potentials and a system comprising 15 million atoms. When a linear brittle crack front approaches a void, the void acts to impede the progress of the front by causing dislocation emission, thereby rendering the system ductile. When two voids are alone in the system, failure is via ductility with, first, dislocation loops being emitted from the void surfaces and, then, these loops interacting with one another to form.