arXiv subjects

Gus L. W. Hart

Publications and source records attributed to Gus L. W. Hart.

At least 37 records · Page 2Linked to original sources

arXiv2019

Generalized Regular k-point Grid Generation On The Fly

In the DFT community, it is common practice to use regular k-point grids (Monkhorst-Pack, MP) for Brillioun zone integration. Recently Wisesa et. al.\cite{wisesa2016efficient} and Morgan et. al.\cite{MORGAN2018424} demonstrated that generalized regular (GR) grids offer advantages over traditional MP grids. GR grids have not been widely adopted because one must search through a large number of candidate grids. This work describes an algorithm that can quickly search over GR grids for those that have the most uniform distribution of points and the best symmetry reduction. The grids are ~60% more efficient, on average, than MP grids and can now be generated on the fly in seconds.

cond-mat.mtrl-sci↗

arXiv2018

Structural Characterization of Grain Boundaries and Machine Learning of Grain Boundary Energy and Mobility

Recent advances in the numerical representation of materials opened the way for successful machine learning of grain boundary (GB) energies and the classification of GB mobility and shear coupling. Two representations were needed for these machine learning applications: 1) the ASR representation, based on averaged local environment descriptors; and 2) the LER descriptor, based on fractions of globally unique local environments within the entire GB system. We present a detailed tutorial on how to construct these two representations to learn energy, mobility and shear coupling. Additionally, we catalog some of the null results encountered along the way.

cond-mat.mtrl-sci↗

arXiv2018

Accelerating high-throughput searches for new alloys with active learning of interatomic potentials

We propose an approach to materials prediction that uses a machine-learning interatomic potential to approximate quantum-mechanical energies and an active learning algorithm for the automatic selection of an optimal training dataset. Our approach significantly reduces the amount of DFT calculations needed, resorting to DFT only to produce the training data, while structural optimization is performed using the interatomic potentials. Our approach is not limited to one (or a small number of) lattice types (as is the case for cluster expansion, for example) and can predict structures with lattice types not present in the training dataset. We demonstrate the effectiveness of our algorithm by predicting the convex hull for the following three systems: Cu-Pd, Co-Nb-V, and Al-Ni-Ti. Our method is three to four orders of magnitude faster than conventional high-throughput DFT calculations and explores a wider range of materials space. In all three systems, we found unreported stable structures compared to the AFLOW database. Because our method is much cheaper and explores much more of materials space than high-throughput methods or cluster expansion, and because our interatomic potentials have a systematically improvable accuracy compared to empirical potentials such as EAM, etc., it will have a significant impact in the discovery of new alloy phases, particularly those with three or more components.

cond-mat.mtrl-sci↗

arXiv2018

Efficiency of Generalized Regular k-point Grids

Most DFT practitioners use regular grids (Monkhorst-Pack, MP) for integrations in the Brillioun zone. Although regular grids are the natural choice and easy to generate, more general grids whose generating vectors are not merely integer divisions of the reciprocal lattice vectors, are usually more efficient.\cite{wisesa2016efficient} We demonstrate the efficiency of \emph{generalized regular} (GR) grids compared to Monkhorst-Pack (MP) and \emph{simultaneously commensurate} (SC) grids. In the case of metals, for total energy accuracies of one meV/atom, GR grids are 60\% faster on average than MP grids and 20\% faster than SC grids. GR grids also have greater freedom in choosing the \kb-point density, enabling the practitioner to achieve a target accuracy with the minimum computational cost.

cond-mat.mtrl-sci↗

arXiv2017

Discovering the Building Blocks of Atomic Systems using Machine Learning

Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset in the first place. Here we present a description of atomic systems that generates machine learning representations with a direct path to physical interpretation. As an example, we demonstrate its usefulness as a universal descriptor of grain boundary systems. Grain boundaries in crystalline materials are a quintessential example of a complex, high-dimensional system with broad impact on many physical properties including strength, ductility, corrosion resistance, crack resistance, and conductivity. In addition to modeling such properties, the method also provides insight into the physical "building blocks" that influence them. This opens the way to discover the underlying physics behind behaviors by understanding which building blocks map to particular properties. Once the structures are understood, they can then be optimized for desirable behaviors.

cond-mat.mtrl-sci↗

arXiv2017

The Robustness of Cluster Expansion: Assessing the Roles of Relaxation and Numerical Error

Cluster expansion (CE) is effective in modeling the stability of metallic alloys, but sometimes cluster expansions fail. Failures are often attributed to atomic relaxation in the DFT-calculated data, but there is no metric for quantifying the degree of relaxation. Additionally, numerical errors can also be responsible for slow CE convergence. We studied over one hundred different Hamiltonians and identified a heuristic, based on a normalized mean-squared displacement of atomic positions in a crystal, to determine if the effects of relaxation in CE data are too severe to build a reliable CE model. Using this heuristic, CE practitioners can determine a priori whether or not an alloy system can be reliably expanded in the cluster basis. We also examined the error distributions of the fitting data. We find no clear relationship between the type of error distribution and CE prediction ability, but there are clear correlations between CE formalism reliability, model complexity, and the number of significant terms in the model. Our results show that the \emph{size} of the errors is much more important than their distribution.

cond-mat.mtrl-sci↗

arXiv2017

Generating derivative superstructures for systems with high configurational freedom

Modeling potential alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways of displacing the atoms. One solution to finding all symmetrically unique configurations and displacements is to generate the complete list of possible configurations and remove those that are symmetrically equivalent. This approach, however, suffers from the combinatorial explosion that happens when the supercell size is large, when there are more than two atom types, or when there are multiple displaced atoms. This problem persists even when there are only a relatively small number of unique arrangements that survive the elimination process. Here, we extend an existing algorithm\cite{enum1,enum2,enum3} to include the extra configurational degree of freedom from the inclusion of displacement directions. The algorithm uses group theory to eliminate large classes of configurations, avoiding the combinatoric explosion. With this approach we can now enumerate previously inaccessible systems, including atomic displacements.

cond-mat.mtrl-sci↗

arXiv2016

A computational high-throughput search for new ternary superalloys

In 2006, a novel cobalt-based superalloy was discovered [1] with mechanical properties better than some conventional nickel-based superalloys. As with conventional superalloys, its high performance arises from the precipitate-hardening effect of a coherent L1$_2$ phase, which is in two-phase equilibrium with the fcc matrix. Inspired by this unexpected discovery of an L1$_2$ ternary phase, we performed a first-principles search through 2224 ternary metallic systems for analogous precipitate-hardening phases of the form $X_{3}$[$A_{0.5}, B_{0.5}$], where $X$ = Ni, Co, or Fe, and [$A,B$] = Li, Be, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn Ga, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, or Tl. We found 102 systems that have a smaller decomposition energy and a lower formation enthalpy than the Co$_{3}$(Al, W) superalloy. They have a stable two-phase equilibrium with the host matrix within the concentration range $0<x<1$ ($X_{3}$[$A_{x}, B_{1-x}$]) and have a relative lattice mismatch with the host matrix of less than or equal to 5%. These new candidates, narrowed from 2224 systems, suggest possible experimental exploration for identifying new superalloys. Of these 102 systems, 37 are new; they have no reported phase diagrams in standard databases. Based on cost, experimental difficulty, and toxicity, we limit these 37 to a shorter list of six promising candidates of immediate interest. Our calculations are consistent with current experimental literature where data exists.

cond-mat.mtrl-sci↗

arXiv2015

First principles thermodynamical modeling of the binodal and spinodal curves in lead chalcogenides

High-throughput ab-initio calculations, cluster expansion techniques and thermodynamic modeling have been synergistically combined to characterize the binodal and the spinodal decompositions features in the pseudo-binary lead chalcogenides PbSe-PbTe, PbS-PbTe, and PbS-PbSe. While our results agree with the available experimental data, our consolute temperatures substantially improve with respect to previous computational modeling. The computed phase diagrams corroborate that the formation of spinodal nanostructures causes low thermal conductivities in these alloys. The presented approach, making a rational use of online quantum repositories, can be extended to study thermodynamical and kinetic properties of materials of technological interest.

cond-mat.mtrl-sci↗

arXiv2014

Numerical Algorithm for Pólya Enumeration Theorem

Although the Pólya enumeration theorem has been used extensively for decades, an optimized, purely numerical algorithm for calculating its coefficients is not readily available. We present such an algorithm for finding the number of unique colorings of a finite set under the action of a finite group.

math.CO↗

arXiv2014

Finding the stable structures of W$_x$N$_1$$_-$$_x$ with an $ab$$-$$initio$ high-throughput approach

Using density functional theory calculations, many researchers have predicted that various tungsten-nitride compounds WN$_x$ ($x$ > 1) will be "ultra-compressible" or "superhard", $i.e.$ as hard as or harder than diamond. These compounds are predicted to have large bulk and shear moduli (> 200 GPa) and to be elastically and vibrationally stable. Compounds with such desirable properties must be energetically stable against decomposition into other compounds. This stability can only be found after the determination of the convex hull for W$_x$N$_1$$_-$$_x$ lines which connect the lowest enthalpy structures as a function of composition. The phase diagram of the W-N structure is uncertain, both experimentally and computationally. Complex van der Waals forces play a significant role in determining the structure of solid N$_2$. Here we use high-throughput calculations to map out the convex hull and other low energy structures for the W-N system. We find that the ground state of the system is the NbO structure, and that the WN$_2$ structures found by Wang $et$ $al$. are also stable when the van der Waals forces are neglected. Other proposed structures are above the convex hull of the W-N system. We show how the choice of density functional influences the shape of the curve and the structures that form the hull. In nitrogen-rich compounds, the choice of functional can dramatically change the structural parameters and mechanical behavior. Using any of the functionals, the bulk and shear moduli of the NbO phase are comparable to the WN$_x$ compounds that have been claimed to be ultra-compressible for superhard.

cond-mat.mtrl-sci↗

arXiv2014

A high-throughput ab initio review of platinum-group alloy systems

We report a comprehensive study of the binary systems of the platinum group metals with the transition metals, using high-throughput first-principles calculations. These computations predict stability of new compounds in 38 binary systems where no compounds have been reported in the literature experimentally, and a few dozen of as yet unreported compounds in additional systems. Our calculations also identify stable structures at compound compositions that have been previously reported without detailed structural data and indicate that some experimentally reported compounds may actually be unstable at low temperatures. With these results we construct enhanced structure maps for the binary alloys of platinum group metals. These are much more complete, systematic and predictive than those based on empirical results alone.

cond-mat.mtrl-sci↗

arXiv2013

AFLOW: An automatic framework for high-throughput materials discovery

Recent advances in computational materials science present novel opportunities for structure discovery and optimization, including uncovering of unsuspected compounds and metastable structures, electronic structure, surface, and nano-particle properties. The practical realization of these opportunities requires systematic generation and classification of the relevant computational data by high-throughput methods. In this paper we present Aflow (Automatic Flow), a software framework for high-throughput calculation of crystal structure properties of alloys, intermetallics and inorganic compounds. The Aflow software is available for the scientific community on the website of the materials research consortium, aflowlib.org. Its geometric and electronic structure analysis and manipulation tools are additionally available for online operation at the same website. The combination of automatic methods and user online interfaces provide a powerful tool for efficient quantum computational materials discovery and characterization.

cond-mat.mtrl-sci↗

arXiv2013

Stable ordered structures of binary technetium alloys from first principles

Technetium, element 43, is the only radioactive transition metal. It occurs naturally on earth in only trace amounts. Experimental investigation of its possible compounds is thus inherently difficult and limited. Half of the Tc-transition-metal systems (14 out of 28) are reported to be phase separating or lack experimental data. Using high-throughput first-principles calculations, we present a comprehensive investigation of the binary alloys of technetium with the transition metals. The calculations predict stable, ordered structures in nine of these 14 binary systems. They also predict additional compounds in all nine known compound-forming systems and in two of the five systems reported with disordered \c{hi} or σ phases. These results accentuate the incompleteness of the current knowledge of technetium alloys and should guide experimental studies to obtain accurate structural information on potential compounds, obviating some of the difficulties associated with such work.

cond-mat.mtrl-sci↗

arXiv2013

Cluster expansion made easy with Bayesian compressive sensing

Long-standing challenges in cluster expansion (CE) construction include choosing how to truncate the expansion and which crystal structures to use for training. Compressive sensing (CS), which is emerging as a powerful tool for model construction in physics, provides a mathematically rigorous framework for addressing these challenges. A recently-developed Bayesian implementation of CS (BCS) provides a parameterless framework, a vast speed up over current CE construction techniques, and error estimates on model coefficients. Here, we demonstrate the use of BCS to build cluster expansion models for several binary alloy systems. The speed of the method and the accuracy of the resulting fits are shown to be far superior than state-of-the-art evolutionary methods for all alloy systems shown. When combined with high throughput first-principles frameworks, the implications of BCS are that hundreds of lattice models can be automatically constructed, paving the way to high throughput thermodynamic modeling of alloys.

cond-mat.mtrl-sci↗

arXiv2012

Compressive sensing as a new paradigm for model building

The widely-accepted intuition that the important properties of solids are determined by a few key variables underpins many methods in physics. Though this reductionist paradigm is applicable in many physical problems, its utility can be limited because the intuition for identifying the key variables often does not exist or is difficult to develop. Machine learning algorithms (genetic programming, neural networks, Bayesian methods, etc.) attempt to eliminate the a priori need for such intuition but often do so with increased computational burden and human time. A recently-developed technique in the field of signal processing, compressive sensing (CS), provides a simple, general, and efficient way of finding the key descriptive variables. CS is a new paradigm for model building-we show that its models are just as robust as those built by current state-of-the-art approaches, but can be constructed at a fraction of the computational cost and user effort.

cond-mat.mtrl-sci↗

arXiv2010

Density Functional Study of the L1_0 - alpha-IrV Transition in IrV and RhV

Both IrV and RhV crystallize in the alpha-IrV structure, with a transition to the higher symmetry L1_0 structure at high temperature, or with the addition of excess Ir or Rh. Here we present evidence that this transition is driven by the lowering of the electronic density of states at the Fermi level of the alpha-IrV structure. The transition has long been thought to be second order, with a simple doubling of the L1_0 unit cell due to an unstable phonon at the R point (0 1/2 1/2). We use first-principles calculations to show that all phonons at the R point are, in fact, stable, but do find a region of reciprocal space where the L1_0 structure has unstable (imaginary frequency) phonons. We use the frozen phonon method to examine two of these modes, relaxing the structures associated with the unstable phonon modes to obtain new structures which are lower in energy than L1_0 but still above alpha-IrV. We examine the phonon spectra of these structures as well, looking for instabilities, and find further instabilities, and more relaxed structures, all of which have energies above the alpha-IrV phase. In addition, we find that all of the relaxed structures, stable and unstable, have a density comparable to the L1_0 phase (and less than the alpha-IrV phase), so that any transition from one of these structures to the ground state will have a volume change as well as an energy discontinuity. We conclude that the transition from L1_0 to alpha-IrV is probably weakly first order.

cond-mat.mtrl-sci↗

arXiv2009

Hafnium binary alloys from experiments and first principles

Despite the increasing importance of hafnium in numerous technological applications, experimental and computational data on its binary alloys is sparse. In particular, data is scant on those binary systems believed to be phase separating. We performed a comprehensive study of 44 hafnium binary systems with alkali metals, alkaline earths, transition metals and metals, using high-throughput first principles calculations. These computations predict novel unsuspected compounds in six binary systems previously believed to be phase separating They also predict a few unreported compounds in additional systems and indicate that some reported compounds may actually be unstable at low temperatures. We report the results for the following systems: AgHf, AlHf, AuHf, BaHf*, BeHf, BiHf, CaHf*, CdHf, CoHf, CrHf, CuHf, FeHf, GaHf, HfHg, HfIn, HfIr, HfK*, HfLa*, HfLi*, HfMg, HfMn, HfMo, HfNa*, HfNb*, HfNi, HfOs, HfPb, HfPd, HfPt, HfRe, HfRh, HfRu, HfSc, HfSn, HfSr*, HfTa*, HfTc, HfTi, HfTl, HfV*, HfW, HfY*, HfZn, and HfZr. (* = systems in which the ab initio method predicts that no compounds are stable).

cond-mat.mtrl-sci↗