The core structures of screw and edge dislocations on the basal and prism planes in Mg, and the associated gamma surfaces, were studied using an ab initio method and the embedded-atom-method interatomic potentials developed by Sun et al and Liu et al. The ab initio calculations predict that the basal plane dislocations dissociate into partials split by 16.7 Å (edge) and 6.3 Å (screw), as compared with 14.3 Å and 12.7 Å (Sun and Liu edge), and 6.3 Å and 1.4 Å (Sun and Liu screw), with the Liu screw dislocation being metastable. In the prism plane, the screw and edge cores are compact and the edge core structures are all similar, while ab initio does not predict a stable prismatic screw in stress-free conditions. These results are qualitatively understood through an examination of the gamma surfaces for interplanar sliding on the basal and prism planes. The Peierls stresses at T = 0 K for basal slip are a few megapascals for the Sun potential, in agreement with experiments, but are ten times larger for the Liu potential. The Peierls stresses for prism slip are 10–40 MPa for both potentials. Overall, the dislocation core structures from ab initio are well represented by the Sun potential in all cases while the Liu potential shows some notable differences. These results suggest that the Sun potential is preferable for studying other dislocations in Mg, particularly the ⟨c + a⟩ dislocations, for which the core structures are much larger and not accessible by ab initio methods.

Solid-solution strengthening results from solutes impeding the glide of dislocations. Existing theories of strength rely on solutedislocation interactions, but do not consider dislocation core structures, which need an accurate treatment of chemical bonding. Here, we focus on strengthening of Mg, the lightest of all structural metals and a promising replacement for heavier steel and aluminum alloys. Elasticity theory, which is commonly used to predict the requisite solute-dislocation interaction energetics, is replaced with quantum-mechanical first-principles calculations to construct a predictive mesoscale model for solute strengthening of Mg. Results for 29 different solutes are displayed in a "strengthening design map" as a function of solute misfits that quantify volumetric strain and slip effects. Our strengthening model is validated with available experimental data for several solutes, including Al and Zn, the two most common solutes in Mg. These new results highlight the ability of quantum-mechanical first-principles calculations to predict complex material properties such as strength.

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We develop a first-principles model of thermally-activated cross-slip in magnesium in the presence of a random solute distribution. Electronic structure methods provide data for the interaction of solutes with prismatic dislocation cores and basal dislocation cores. Direct calculations of interaction energies are possible for solutes-K, Na, and Sc-that lower the Mg prismatic stacking fault energy to improve formability. To connect to thermally activated cross-slip, we build a statistical model for the distribution of activation energies for double kink nucleation, barriers for kink migration, and roughness of the energy landscape to be overcome by an athermal stress. These distributions are calculated numerically for a range of concentrations, as well as alternate approximate analytic expressions for the dilute limit. The analytic distributions provide a simplified model for the max-imum cross-slip softening for a solute as a function of temperature. The direct interaction calculations predict lowered forming temperatures for Mg-0.7at.%Sc, Mg-0.4at.%K, and Mg-0.6at.%Na of approximately 250 • C.Increased interest in the light-weight structural metal magnesium[1] to replace aluminum or steels in automotive applications[2] has focused attention on a variety of metallurgical issues, including formability. Current Mg alloys require temperatures near 300 • C for forming to activate the five independent slip systems required by the von Mises criterion [3]; this is in part due to the large anisotropy between basal and prismatic slip [4]. Cross-slip of a-type dislocations from the easy (0001) basal plane onto the hard (0110) prismatic plane requires large stresses or high temperatures. Experimentally, few solutes have been found to lower the stress for cross-slip: Al and Zn lower the stress at low (below room) temperatures[5], while Li can lower the cross-slip stress in both regimes [6,7,8,9]. The difficulty of performing experiments to measure cross-slip stresses for alloys-requiring single-crystal samples oriented for prismatic slip-is compounded by the possibility that, like solid-solution softening in BCC alloys[10], it may occur over a limited concentration and temperature range. Hence, new state-of-the-art first-principles prediction of solute/dislocation interactions coupled with predictive computational modeling of thermally-activated cross-slip in the presence of solutes is necessary to guide the design of new alloys.Couret and Caillard in situ experimental measurements [11,12] found that at

For most organisms with viscous population structure, spatially localized growth drives the invasive advance of a favorable mutation. We model a two-allele competition where recurrent mutation introduces a genotype with a rate of local propagation exceeding the resident's rate. We capture ecologically important properties of the rare invader's stochastic dynamics by assuming discrete individuals and neighborhood interactions. To understand how individuallevel processes may govern population patterns, we invoke the physical theory for nucleation of spatial systems. Nucleation theory discriminates between single-cluster and multi-cluster dynamics. A sufficiently low mutation rate, or a sufficiently small environment, generates singlecluster dynamics, an inherently stochastic process; a favorable mutation advances only if the invader cluster reaches a critical radius. For this mode of invasion we identify the probability distribution of waiting times until the favored allele advances to competitive dominance, and we ask how the critical cluster size varies as propagation or mortality rates vary. Increasing the mutation rate or system size generates multi-cluster invasion, where spatial averaging produces nearly deterministic global dynamics. For this process, an analytical approximation from nucleation theory, called Avrami's Law, describes the time-dependent behavior of the genotype densities with remarkable accuracy.

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Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces, and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic strain. Flexible boundary condition methods embed a defect in infinite harmonic bulk through the lattice Green function. We demonstrate an efficient and accurate calculation of the lattice Green function from the force-constant matrix for general crystals with an arbitrary basis by extending a method for Bravais lattices. New terms appear due to the presence of optical modes and the possible loss of inversion symmetry. By separately treating poles and discontinuities in reciprocal space, numerical accuracy is controlled at all distances. We compute the lattice Green function for a two-dimensional model with broken symmetry to elucidate the role of different coupling terms. The algorithm is generally applicable in two and three dimensions to crystals with arbitrary number of atoms in the unit cell, symmetry, and interactions.

We study a discrete spatial model for invasive allele spread in which two alleles compete preemptively, initially only the "residents" (weaker competitors) being present. We find that the spread of the advantageous mutation is well described by homogeneous nucleation; in particular, in large systems the time-dependent global density of the resident allele is well approximated by Avrami's law.Comment: Computer Simulation Studies in Condensed Matter Physics XVIII, edited by D.P. Landau, S.P. Lewis, and H.-B. Schuttler, (Springer, Heidelberg, Berlin, in press