Efficient stochastic generation of special quasirandom structures
01 Sep 2013-Calphad-computer Coupling of Phase Diagrams and Thermochemistry (Pergamon)-Vol. 42, Iss: 42, pp 13-18
TL;DR: The proposed method optimizes the shape of the supercell jointly with the occupation of the atomic sites, thus ensuring that the configurational space searched is exhaustive and not biased by a pre-specified supercell shape.
Abstract: We present a new algorithm to generate Special Quasirandom Structures (SQS), i.e., best periodic supercell approximations to the true disordered state for a given number of atoms per supercell. The method is based on a Monte Carlo simulated annealing loop with an objective function that seeks to perfectly match the maximum number of correlation functions (as opposed to merely minimizing the distance between the SQS correlation and the disordered state correlations for a pre-specified set of correlations). The proposed method optimizes the shape of the supercell jointly with the occupation of the atomic sites, thus ensuring that the configurational space searched is exhaustive and not biased by a pre-specified supercell shape. The method has been implemented in the “mcsqs” code of the Alloy Theoretic Automated Toolkit (ATAT) in the most general framework of multicomponent multisublattice systems and in a way that minimizes the amount of input information the user needs to specify and that allows for efficient parallelization.
Citations
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TL;DR: It is demonstrated that the approach of preventing Na+/vacancy ordering by breaking charge ordering in the transition metal layer opens a simple way to design disordered electrode materials with high power density and long cycle life.
Abstract: Most P2-type layered oxides exhibit Na(+)/vacancy-ordered superstructures because of strong Na(+)-Na(+) interaction in the alkali metal layer and charge ordering in the transition metal layer. These superstructures evidenced by voltage plateaus in the electrochemical curves limit the Na(+) ion transport kinetics and cycle performance in rechargeable batteries. Here we show that such Na(+)/vacancy ordering can be avoided by choosing the transition metal ions with similar ionic radii and different redox potentials, for example, Cr(3+) and Ti(4+). The designed P2-Na(0.6)[Cr(0.6)Ti(0.4)]O2 is completely Na(+)/vacancy-disordered at any sodium content and displays excellent rate capability and long cycle life. A symmetric sodium-ion battery using the same P2-Na(0.6)[Cr(0.6)Ti(0.4)]O2 electrode delivers 75% of the initial capacity at 12C rate. Our contribution demonstrates that the approach of preventing Na(+)/vacancy ordering by breaking charge ordering in the transition metal layer opens a simple way to design disordered electrode materials with high power density and long cycle life.
382 citations
TL;DR: In this paper, the authors investigated the origin of the exceptional properties of NiCoCr alloy, which are related to the evolution of the deformation substructure with strain, interrupted tensile testing was conducted on the equiatomic NiCo-Cr single-phase solid solution alloy at both cryogenic and room temperatures at five different plastic strain levels of 1.5, 6.5%, 29, 50% and 70%.
330 citations
TL;DR: The all-in-one approach to process point disordered structures, powerful command line interface, excellent performance, flexibility and GNU GPL license make the supercell program a versatile set of tools for disordered structure manipulations.
Abstract: Disordered compounds are crucially important for fundamental science and industrial applications. Yet most available methods to explore solid-state material properties require ideal periodicity, which, strictly speaking, does not exist in this type of materials. The supercell approximation is a way to imply periodicity to disordered systems while preserving “disordered” properties at the local level. Although this approach is very common, most of the reported research still uses supercells that are constructed “by hand” and ad-hoc. This paper describes a software named supercell, which has been designed to facilitate the construction of structural models for the description of vacancy or substitution defects in otherwise periodically-ordered (crystalline) materials. The presented software allows to apply the supercell approximation systematically with an all-in-one implementation of algorithms for structure manipulation, supercell generation, permutations of atoms and vacancies, charge balancing, detecting symmetry-equivalent structures, Coulomb energy calculations and sampling output configurations. The mathematical and physical backgrounds of the program are presented, along with an explanation of the main algorithms and relevant technical details of their implementation. Practical applications of the program to different types of solid-state materials are given to illustrate some of its potential fields of application. Comparisons of the various algorithms implemented within supercell with similar solutions are presented where possible. The all-in-one approach to process point disordered structures, powerful command line interface, excellent performance, flexibility and GNU GPL license make the supercell program a versatile set of tools for disordered structures manipulations.
304 citations
TL;DR: In this paper, a NbTaTiV refractory HEA with a single body-centered-cubic (BCC) structure using an integrated experimental and theoretical approach was developed.
276 citations
Cites methods from "Efficient stochastic generation of ..."
...The BCC NbTaTiV HEAs were modeled through the special quasi-random-structure (SQS) [76] method....
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...Furthermore, we investigated the lattice distortion and the local atomic environment of the BCC NbTaTiV alloy system through the ab initio method, based on Special Quasirandom Structures (SQS) [40] that approximate random distributions of atomic species in a medium-sized supercell....
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...Considering both the range of the interatomic distances and the mean value of a pair, a large number of atoms in the SQS shift strongly away from their ideal lattice sites, indicating a severe local lattice distortion in the NbTaTiV system....
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...A supercell containing 16 atoms is employed to construct the binary systems through SQS, and the lattice vectors of the supercell are defined as a ¼ 1 1 1; b ¼ 1 1 1; and c ¼ 2 2 0....
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...The lattice distortions can be defined as the change of the bond length with respect to the reference bond length: Lattice distortion ¼ jdi drj dr 100 (12) where di is the interatomic distance of a pair in the relaxed SQS, and dr is the interatomic distance obtained for a pair with a BCC or B2 structure....
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TL;DR: It is shown that a nanostructured phase at lattice defects in CoCrNi causes its extraordinary properties, while it is magnetically frustrated and suppressed in CrMnFeCoNi.
Abstract: CrCoNi alloy exhibits a remarkable combination of strength and plastic deformation, even superior to the CrMnFeCoNi high-entropy alloy. We connect the magnetic and mechanical properties of CrCoNi, via a magnetically tunable phase transformation. While both alloys crystallize as single-phase face-centered-cubic (fcc) solid solutions, we find a distinctly lower-energy phase in CrCoNi alloy with a hexagonal close-packed (hcp) structure. Comparing the magnetic configurations of CrCoNi with those of other equiatomic ternary derivatives of CrMnFeCoNi confirms that magnetically frustrated Mn eliminates the fcc-hcp energy difference. This highlights the unique combination of chemistry and magnetic properties in CrCoNi, leading to a fcc-hcp phase transformation that occurs only in this alloy, and is triggered by dislocation slip and interaction with internal boundaries. This phase transformation sets CrCoNi apart from the parent quinary, and its other equiatomic ternary derivatives, and provides a new way for increasing strength without compromising plastic deformation.
259 citations
References
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TL;DR: It is shown that it is possible to design special quasirandom structures'' (SQS) that mimic for small {ital N} the first few, physically most relevant radial correlation functions of a perfectly random structure far better than the standard technique does.
Abstract: Structural models used in calculations of properties of substitutionally random ${\mathit{A}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathit{B}}_{\mathit{x}}$ alloys are usually constructed by randomly occupying each of the N sites of a periodic cell by A or B. We show that it is possible to design ``special quasirandom structures'' (SQS's) that mimic for small N (even N=8) the first few, physically most relevant radial correlation functions of a perfectly random structure far better than the standard technique does. We demonstrate the usefulness of these SQS's by calculating optical and thermodynamic properties of a number of semiconductor alloys in the local-density formalism.
2,545 citations
"Efficient stochastic generation of ..." refers methods or result in this paper
...Different properties have difference dependences on the correlations and this dependence is itself system-dependent, as previously noted in [1,10,15]....
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...The concept of Special Quasirandom Structures (SQS) [1] provides a systematic improvement over this method....
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TL;DR: In this paper, the physical decay properties of the density matrix were studied for both metals and insulators, and several strategies for constructing O(N) algorithms were presented and critically examined.
Abstract: Methods exhibiting linear scaling with respect to the size of the system, the so-called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms that take advantage of the decay properties of the density matrix. In this article the physical decay properties of the density matrix will first be studied for both metals and insulators. Several strategies for constructing O(N) algorithms will then be presented and critically examined. Some issues that are relevant only for self-consistent O(N) methods, such as the calculation of the Hartree potential and mixing issues, will also be discussed. Finally some typical applications of O(N) methods are briefly described.
1,313 citations
"Efficient stochastic generation of ..." refers background in this paper
...As is well-known in the field of so-called “order N”methods, numerous physical arguments lead to localized expansions of the total energy [16]....
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TL;DR: A concise user guide is presented outlining the steps required to obtain thermodynamic information from ab initio calculations of alloy thermodynamic properties from first-principles.
Abstract: Although the formalism that allows the calculation of alloy thermodynamic properties from
first-principles has been known for decades, its practical implementation has so far remained a tedious
process. The Alloy Theoretic Automated Toolkit (ATAT) drastically simplifies this procedure by implementing
decision rules based on formal statistical analysis that frees the researchers from a constant
monitoring during the calculation process and automatically “glues” together the input and the output of
various codes, in order to provide a high-level interface to the calculation of alloy thermodynamic properties
from first-principles. ATAT implements the Structure Inversion Method (SIM), also known as the
Connolly-Williams method, in combination with semi-grand-canonical Monte Carlo simulations. In order
to make this powerful toolkit available to the wide community of researchers who could benefit from it,
this article present a concise user guide outlining the steps required to obtain thermodynamic information
from ab initio calculations.
1,001 citations
"Efficient stochastic generation of ..." refers methods in this paper
...Finally, we describe the implementation of this scheme in the Alloy Theoretic Automated Toolkit (ATAT) [12–14], which is designed to minimize the amount of input information the user needs to specify and exploits natural avenues for efficient parallelization....
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TL;DR: In this article, the authors present a statistical basis for the selection of both the interaction parameters to include in the cluster expansion and the structures to use to determine them, which is based on the concepts of cross-validation and variance minimization.
Abstract: Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a “virtual laboratory,” where materials could be designed from first principles without relying on experimental input. Although the formalism that allows the calculation of solid-state phase diagrams from first principles is well established, its practical implementation remains a tedious process. The development of a fully automated algorithm to perform such calculations serves two purposes. First, it will make this powerful tool available to a large number of researchers. Second, it frees the calculation process from arbitrary parameters, guaranteeing that the results obtained are truly derived from the underlying first-principles calculations. The proposed algorithm formalizes the most difficult step of phase diagram calculations, namely the determination of the “cluster expanison,” which is a compact representation of the configurational dependence of the alloy’s energy. This is traditionally achieved by a fit of the unknown interaction parameters of the cluster expansion to a set of structural energies calculated from first principles. We present a formal statistical basis for the selection of both the interaction parameters to include in the cluster expansion and the structures to use to determine them. The proposed method relies on the concepts of cross-validation and variance minimization. An application to the calculation of the phase diagram of the Si-Ge, CaO-MgO, Ti-Al, and Cu-Au systems is presented.
716 citations
TL;DR: The Alloy Theoretic Automated Toolkit (ATATAT) as mentioned in this paper can handle multisublattice alloy systems, nonconfigurational sources of entropy (e.g. vibrational and electronic entropy), Special Quasirandom Structures (SQS) generation, tensorial cluster expansion construction and interfaces for multiple atomistic or ab initio codes.
Abstract: A number of new functionalities have been added to the Alloy Theoretic Automated Toolkit (ATAT) since it was last reviewed in this journal in 2002. ATAT can now handle multicomponent multisublattice alloy systems, nonconfigurational sources of entropy (e.g. vibrational and electronic entropy), Special Quasirandom Structures (SQS) generation, tensorial cluster expansion construction and includes interfaces for multiple atomistic or ab initio codes. This paper presents an overview of these features geared towards the practical use of the code. The extensions to the cluster expansion formalism needed to cover multicomponent multisublattice alloys are also formally demonstrated.
605 citations
"Efficient stochastic generation of ..." refers background or methods in this paper
...Let us first briefly recall the cluster expansion formalism generalized for multicomponent multisublattice systems [12]....
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...Second, we implement the method in the most general framework of multicomponent multisublattice systems [12] in order to encompass large classes of technologically relevant alloys (many of which exhibit disorder on different sublattices [8])....
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...Finally, we describe the implementation of this scheme in the Alloy Theoretic Automated Toolkit (ATAT) [12–14], which is designed to minimize the amount of input information the user needs to specify and exploits natural avenues for efficient parallelization....
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...) The convention used in ATAT for multicomponent systems is described in [12]....
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...-crf1⁄4[string] Select correlation functions (default: trigo, a convention described in [12])....
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