No Arabic abstract
The generalized stacking fault energy is a key ingredient to mesoscale models of dislocations. Here we develop an approach to quantify the dependence of generalized stacking fault energies on the degree of chemical disorder in multicomponent alloys. We introduce the notion of a configurationally-resolved planar fault (CRPF) energy and extend the cluster expansion method from alloy theory to express the CRPF as a function of chemical occupation variables of sites surrounding the fault. We apply the approach to explore the composition and temperature dependence of the unstable stacking fault energy (USF) in binary Mo-Nb alloys. First-principles calculations are used to parameterize a formation energy and CRPF cluster expansion. Monte Carlo simulations show that the distribution of USF energies is significantly affected by chemical composition and temperature. The formalism can be applied to any multicomponent alloy and will enable the development of rigorous models for deformation mechanisms in high-entropy alloys.
A density-functional-theory based approach to efficiently compute numerically exact vibrational free energies - including anharmonicity - for chemically complex multicomponent alloys is developed. It is based on a combination of thermodynamic integration and a machine-learning potential. We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy.
Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.
We propose a simple scheme to construct composition-dependent interatomic potentials for multicomponent systems that when superposed onto the potentials for the pure elements can reproduce not only the heat of mixing of the solid solution in the entire concentration range but also the energetics of a wider range of configurations including intermetallic phases. We show that an expansion in cluster interactions provides a way to systematically increase the accuracy of the model, and that it is straightforward to generalise this procedure to multicomponent systems. Concentration-dependent interatomic potentials can be built upon almost any type of potential for the pure elements including embedded atom method (EAM), modified EAM, bond-order, and Stillinger-Weber type potentials. In general, composition-dependent N-body terms in the total energy lead to explicit (N+1)-body forces, which potentially renders them computationally expensive. We present an algorithm that overcomes this problem and that can speed up the calculation of the forces for composition-dependent pair potentials in such a way as to make them computationally comparable in efficiency and scaling behaviour to standard EAM potentials. We also discuss the implementation in Monte-Carlo simulations. Finally, we exemplarily review the composition-dependent EAM model for the Fe-Cr system [PRL 95, 075702 (2005)].
The generalized stacking fault (SFE) energy curves of pure gold (Au) and its binary alloys with transition metals are determined from density functional theory (DFT). Alloy elements Ag, Al, Cu, Ni, Ti, Zr, Zn, In, Ga, Sn, Mn, Cd, Sn, Ta and Cr are substituted into Au at concentrations up to 4%. A comparison of various proposed methodologies to calculate SFEs is given. The intrinsic SFE decreases for all alloying elements from its value for pure Au, but SFE energies (both stable and unstable) vary strongly with the distance of the alloying element from the stacking fault region, and with alloy concentration. The compositional dependence of the SFE on the volume change associated with alloying element is determined. This work demonstrates that the SFE is strongly influenced by misfit strain caused by the alloying elements. Moreover, the computed generalized SFE curves provide information valuable to developing an understanding of the deformation behavior of Au and Au-alloys.
A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.