758 research outputs found
Automating first-principles phase diagram calculations
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
First-principles computation of the vibrational entropy of ordered and disordered Pd3V
Experimental as well as theoretical work indicates that the relative stability of the ordered and the disordered states of a compound may be significantly affected by their difference in vibrational entropy. The origin of this difference is usually attributed to the fact that disordering reduces the number of stiff bonds between different atomic species in favor of soft bonds between identical atomic species. The results of previous theoretical investigations, however, suggest that this simple mechanism is significantly modified as a result of local atomic relaxations. To gain further insight regarding the importance of relaxations, we employ first-principles calculations to investigate the magnitude of the vibrational entropy difference between the ordered and the disordered state of Pd3V. Our investigation reveals that bond stiffness changes due to relaxation entirely mask the large configurational dependence of vibrational entropy provided by bond stiffness differences. Our analysis also suggests a simple technique to estimate vibrational entropy based on the relationship between bond length and bond stiffness
A critical examination of compound stability predictions from machine-learned formation energies
Machine learning has emerged as a novel tool for the efficient prediction of material properties, and claims have been made that machine-learned models for the formation energy of compounds can approach the accuracy of Density Functional Theory (DFT). The models tested in this work include five recently published compositional models, a baseline model using stoichiometry alone, and a structural model. By testing seven machine learning models for formation energy on stability predictions using the Materials Project database of DFT calculations for 85,014 unique chemical compositions, we show that while formation energies can indeed be predicted well, all compositional models perform poorly on predicting the stability of compounds, making them considerably less useful than DFT for the discovery and design of new solids. Most critically, in sparse chemical spaces where few stoichiometries have stable compounds, only the structural model is capable of efficiently detecting which materials are stable. The nonincremental improvement of structural models compared with compositional models is noteworthy and encourages the use of structural models for materials discovery, with the constraint that for any new composition, the ground-state structure is not known a priori. This work demonstrates that accurate predictions of formation energy do not imply accurate predictions of stability, emphasizing the importance of assessing model performance on stability predictions, for which we provide a set of publicly available tests
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Rationalizing accurate structure prediction in the meta-GGA SCAN functional
The ability of first-principles computational methods to reproduce ground-state crystal structure selection is key to their application in the discovery of new materials, and yet presents a formidable challenge due to the low-energy scale of the problem and lack of systematic error cancellation. The recently developed Strongly Constrained and Appropriately Normed (SCAN) functional is notable for accurately calculating physical properties such as formation energies and in particular, correctly predicting ground-state structures. Here, we attempt to rationalize the improved structure prediction accuracy in SCAN by investigating the relationship between preferred coordination environments, the description of attractive van der Waals (vdW) interactions, and the overall ground-state prediction in bulk main-group solids. We observe a systematic undercoordination error in the traditional Perdew, Burke, and Ernzerhof (PBE) functional which is not present in SCAN results and find that semiempirical dispersion corrections in the form of PBE+D3 fail to correct this error in a consistent or physical manner. We conclude that the medium-range vdW interaction is correctly parametrized in SCAN and yields meaningful relative energies between coordination environments
Phase Separation in LiFePO Induced by Correlation Effects
We report on a significant failure of LDA and GGA to reproduce the phase
stability and thermodynamics of mixed-valence LiFePO compounds.
Experimentally, LiFePO compositions () are known to be
unstable and phase separate into Li FePO and FePO. However,
first-principles calculations with LDA/GGA yield energetically favorable
intermediate compounds an d hence no phase separation. This qualitative failure
of LDA/GGA seems to have its origin in the LDA/GGA self-interaction which de
localizes charge over the mixed-valence Fe ions, and is corrected by explicitly
considering correlation effects in this material. This is demonstrated with
LDA+U calculations which correctly predict phase separation in LiFePO
for eV. T he origin of the destabilization of intermediate
compounds is identified as electron localization and charge ordering at
different iron sites. Introduction of correlation also yields more accurate
electrochemical reaction energies between FePO/LiFePO and
Li/Li electrodes.Comment: 12 pages, 5 figures, Phys. Rev. B 201101R, 200
The Role of hybridization in NaxCoO2 and the Effect of Hydration
Density functional theory (DFT) within the local density approximation (LDA)
is used to understand the electronic properties of Na1/3CoO2 and
Na1/3CoO2(H2O)4/3, which was recently found to be superconducting1. Comparing
the LDA charge density of CoO2 and the Na doped phases indicates that doping
does not simply add electrons to the t2g states. In fact, the electron added in
the t2g state is dressed by hole density in the eg state and electron density
in the oxygen states via rehybridization. In order to fully understand this
phenomenon, a simple extension of the Hubbard Hamiltonian is proposed and
solved using the dynamical mean-field theory (DMFT). This simple model confirms
that the rehybridization is driven by a competition between the on-site coulomb
interaction and the hybridization. In addition, we find that the presence of
eg-oxygen hybridization effectively screens the low energy excitations. To
address the role that water plays in creating the superconducting state, we
compare the LDA band structure of Na1/3CoO2 and its hydrated counterpart. This
demonstrates that hydration does cause the electronic structure to become more
two-dimensional.Comment: 12 pages, 4 figure
Overlap properties of geometric expanders
The {\em overlap number} of a finite -uniform hypergraph is
defined as the largest constant such that no matter how we map
the vertices of into , there is a point covered by at least a
-fraction of the simplices induced by the images of its hyperedges.
In~\cite{Gro2}, motivated by the search for an analogue of the notion of graph
expansion for higher dimensional simplicial complexes, it was asked whether or
not there exists a sequence of arbitrarily large
-uniform hypergraphs with bounded degree, for which . Using both random methods and explicit constructions, we answer this
question positively by constructing infinite families of -uniform
hypergraphs with bounded degree such that their overlap numbers are bounded
from below by a positive constant . We also show that, for every ,
the best value of the constant that can be achieved by such a
construction is asymptotically equal to the limit of the overlap numbers of the
complete -uniform hypergraphs with vertices, as
. For the proof of the latter statement, we establish the
following geometric partitioning result of independent interest. For any
and any , there exists satisfying the
following condition. For any , for any point and
for any finite Borel measure on with respect to which
every hyperplane has measure , there is a partition into measurable parts of equal measure such that all but
at most an -fraction of the -tuples
have the property that either all simplices with
one vertex in each contain or none of these simplices contain
Predicting Crystal Structures with Data Mining of Quantum Calculations
Predicting and characterizing the crystal structure of materials is a key
problem in materials research and development. It is typically addressed with
highly accurate quantum mechanical computations on a small set of candidate
structures, or with empirical rules that have been extracted from a large
amount of experimental information, but have limited predictive power. In this
letter, we transfer the concept of heuristic rule extraction to a large library
of ab-initio calculated information, and demonstrate that this can be developed
into a tool for crystal structure prediction.Comment: 4 pages, 3 pic
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