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

Unsupervised word embeddings capture latent knowledge from materials science literature.

The overwhelming majority of scientific knowledge is published as text, which is difficult to analyse by either traditional statistical analysis or modern machine learning methods. By contrast, the main source of machine-interpretable data for the materials research community has come from structured property databases1,2, which encompass only a small fraction of the knowledge present in the research literature. Beyond property values, publications contain valuable knowledge regarding the connections and relationships between data items as interpreted by the authors. To improve the identification and use of this knowledge, several studies have focused on the retrieval of information from scientific literature using supervised natural language processing3-10, which requires large hand-labelled datasets for training. Here we show that materials science knowledge present in the published literature can be efficiently encoded as information-dense word embeddings11-13 (vector representations of words) without human labelling or supervision. Without any explicit insertion of chemical knowledge, these embeddings capture complex materials science concepts such as the underlying structure of the periodic table and structure-property relationships in materials. Furthermore, we demonstrate that an unsupervised method can recommend materials for functional applications several years before their discovery. This suggests that latent knowledge regarding future discoveries is to a large extent embedded in past publications. Our findings highlight the possibility of extracting knowledge and relationships from the massive body of scientific literature in a collective manner, and point towards a generalized approach to the mining of scientific literature

Elucidating the Structure of the Magnesium Aluminum Chloride Complex electrolyte for Magnesium-ion batteries

We present a rigorous analysis of the Magnesium Aluminum Chloro Complex (MACC) in tetrahydrofuran (THF), one of the few electrolytes that can reversibly plate and strip Mg. We use \emph{ab initio} calculations and classical molecular dynamics simulations to interrogate the MACC electrolyte composition with the goal of addressing two urgent questions that have puzzled battery researchers: \emph{i}) the functional species of the electrolyte, and \emph{ii}) the complex equilibria regulating the MACC speciation after prolonged electrochemical cycling, a process termed as conditioning, and after prolonged inactivity, a process called aging. A general computational strategy to untangle the complex structure of electrolytes, ionic liquids and other liquid media is presented. The analysis of formation energies and grand-potential phase diagrams of Mg-Al-Cl-THF suggests that the MACC electrolyte bears a simple chemical structure with few simple constituents, namely the electro-active species MgCl$^+$ and AlCl$_4^-$ in equilibrium with MgCl$_2$ and AlCl$_3$. Knowledge of the stable species of the MACC electrolyte allows us to determine the most important equilibria occurring during electrochemical cycling. We observe that Al deposition is always preferred to Mg deposition, explaining why freshly synthesized MACC cannot operate and needs to undergo preparatory conditioning. Similarly, we suggest that aluminum displacement and depletion from the solution upon electrolyte resting (along with continuous MgCl$_2$ regeneration) represents one of the causes of electrolyte aging. Finally, we compute the NMR shifts from shielding tensors of selected molecules and ions providing fingerprints to guide future experimental investigations

Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic

Monte Carlo (MC) simulations of lattice models are a widely used way to compute thermodynamic properties of substitutional alloys. A limitation to their more widespread use is the difficulty of driving a MC simulation in order to obtain the desired quantities. To address this problem, we have devised a variety of high-level algorithms that serve as an interface between the user and a traditional MC code. The user specifies the goals sought in a high-level form that our algorithms convert into elementary tasks to be performed by a standard MC code. For instance, our algorithms permit the determination of the free energy of an alloy phase over its entire region of stability within a specified accuracy, without requiring any user intervention during the calculations. Our algorithms also enable the direct determination of composition-temperature phase boundaries without requiring the calculation of the whole free energy surface of the alloy system

Overlap properties of geometric expanders

The {\em overlap number} of a finite $(d+1)$-uniform hypergraph $H$ is defined as the largest constant $c(H)\in (0,1]$ such that no matter how we map the vertices of $H$ into $\R^d$, there is a point covered by at least a $c(H)$-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 $\{H_n\}_{n=1}^\infty$ of arbitrarily large $(d+1)$-uniform hypergraphs with bounded degree, for which $\inf_{n\ge 1} c(H_n)>0$. Using both random methods and explicit constructions, we answer this question positively by constructing infinite families of $(d+1)$-uniform hypergraphs with bounded degree such that their overlap numbers are bounded from below by a positive constant $c=c(d)$. We also show that, for every $d$, the best value of the constant $c=c(d)$ that can be achieved by such a construction is asymptotically equal to the limit of the overlap numbers of the complete $(d+1)$-uniform hypergraphs with $n$ vertices, as $n\rightarrow\infty$. For the proof of the latter statement, we establish the following geometric partitioning result of independent interest. For any $d$ and any $\epsilon>0$, there exists $K=K(\epsilon,d)\ge d+1$ satisfying the following condition. For any $k\ge K$, for any point $q \in \mathbb{R}^d$ and for any finite Borel measure $\mu$ on $\mathbb{R}^d$ with respect to which every hyperplane has measure $0$, there is a partition $\mathbb{R}^d=A_1 \cup \ldots \cup A_{k}$ into $k$ measurable parts of equal measure such that all but at most an $\epsilon$-fraction of the $(d+1)$-tuples $A_{i_1},\ldots,A_{i_{d+1}}$ have the property that either all simplices with one vertex in each $A_{i_j}$ contain $q$ or none of these simplices contain $q$

Phase Separation in Lix_xFePO4_4 Induced by Correlation Effects

We report on a significant failure of LDA and GGA to reproduce the phase stability and thermodynamics of mixed-valence Li$_x$FePO$_4$ compounds. Experimentally, Li$_x$FePO$_4$ compositions ($0 \leq x \leq 1$) are known to be unstable and phase separate into Li FePO$_4$ and FePO$_4$. 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 Li$_x$FePO$_4$ for $U-J \gtrsim 3.5$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$_4$/Li$_x$FePO$_ 4$ 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