Because of its very large c/a ratio, zinc has proven to be a difficult element to model using semi-empirical classical potentials. It has been shown, in particular, that for the modified embedded atom method (MEAM), a potential cannot simultaneously have an hcp ground state and c/a ratio greater than ideal. As an alloying element, however, useful zinc potentials can be generated by relaxing the condition that hcp be the lowest energy structure. In this paper, we present a MEAM zinc potential, which gives accurate material properties for the pure state, as well as a MEAM ternary potential for the Mg–Al–Zn system which will allow the atomistic modeling of a wide class of alloys containing zinc. The effects of zinc in simple Mg–Zn for this potential is demonstrated and these results verify the accuracy for the new potential in these systems.

The increasing demand for materials with well-defined microstructure, accompanied by the advancing miniaturization of devices is the reason for a growing interest in physically motivated, dislocation-based continuum theories of plasticity. In recent years, various advanced continuum theories have been introduced, which are able to described the motion of straight and curved dislocation lines. The focus of this paper is the question of how to include fundamental properties of discrete dislocations during their motion and interaction in a Continuum Dislocation Dynamics (CDD) theory. In our CDD model, we obtain elastic interaction stresses for the bundles of dislocations by a mean-field stress, which represents long range stress components, and a short range corrective stress component, which represents the gradients of the local dislocation density. The attracting and repelling behavior of bundles of straight dislocations of the same and opposite sign are analyzed. Furthermore, considering different dislocation pileup systems, we show that the CDD formulation can solve various fundamental problems of micro plasticity. To obtain a mesh size independent formulation (which is a prerequisite for further application of the theory to more complex situations) we propose a discretization dependent scaling of the short range interaction stress. CDD results are compared to analytical solutions and benchmark data obtained from discrete dislocation simulations.

In this paper, we demonstrate that previously observed β to α transitions for titanium interatomic potentials available in the literature arose from a mechanical instability and thus the potentials underestimated the correct thermodynamic phase transition temperature by hundreds of degrees. Using a relative free energy method for the two phases to calculate the true transition temperature, we present a new modified embedded atom method potential for titanium that shows a transition temperature of 1155 ± 2 K in excellent agreement with the experimentally observed transition. This free energy approach avoids the problems of irreversibility which occur when one relies on direct observation of the phase transition in molecular dynamics simulation. Other transformation mechanisms in addition to the mechanical instability are also considered. Finally, the new potential predicts the proper c-axis plastic twinning for titanium under compression making it the only potential that correctly predicts the phase transition temperature and the plastic behavior of α Ti.

While a Taylor-type yield stress, proportional to the square-root of the dislocation density, may appear at a macroscopic scale, it can be shown with discrete dislocation simulations that it does not accurately describe dislocation motion on the scale of individual dislocations. In this article, we first demonstrate that the Taylor term fails to capture a number of features of dislocation dynamics by comparing the results of a continuum formulation using this yield stress term to discrete dislocation dynamics simulations. We then present an alternate model, based on a mean free path formulation, and demonstrate that this model effectively reproduces the results of the discrete simulation. This mean free path model is proposed as an extension to an existing continuum theory, making use of the key fact that the velocity of dislocations in a realistic system is not single valued, but distributed over several values. The velocity distribution may also change with time. It is demonstrated that this formulation predicts features of both pileups and homogenous distributions which are in agreement with discrete dislocation simulations, but are not reproducible by traditional statistical continuum theories. Finally, possible extensions to this model are discussed, which may enhance the ability to reproduce key features of dislocation yielding

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We propose here a formal foundation for practical calculations of vibrational mode lifetimes in solids. The approach is based on a recursion method analysis of the Liouvillian. From this we derive the lifetime of a vibrational mode in terms of moments of the power spectrum of the Liouvillian as projected onto the relevant subspace of phase space. In practical terms, the moments are evaluated as ensemble averages of well-defined operators, meaning that the entire calculation is to be done with Monte Carlo. These insights should lead to significantly shorter calculations compared to current methods. A companion piece presents numerical results.

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In a two-part publication, we propose and analyze a formal foundation for practical calculations of vibrational mode lifetimes in solids. The approach is based on a recursion method analysis of the Liouvillian. In the first part, we derived the lifetime of vibrational modes in terms of moments of the power spectrum of the Liouvillian as projected onto the relevant subspace of phase space. In practical terms, the moments are evaluated as ensemble averages of well-defined operators, meaning that the entire calculation is to be done with Monte Carlo. In this second part, we present a numerical analysis of a simple anharmonic model of lattice vibrations which exhibits two regimes of behavior, at low temperature and at high temperature. Our results show that, for this simple model, the mode lifetime as a function of temperature and wavevector can be simply approximated as a function of the shift in frequency from the harmonic limit. We next compare these calculations, obtained using both Monte Carlo and computationally intensive molecular dynamics, with those using the lowest order moment formalism from the Part I. We show that, in the high-temperature regime, the lowest order approximation gives a reliable approximation to the calculated lifetimes.The results also show that extension to at least fourth moment is required to obtain reliable results over a full range of temperatures.