Session F47: Computational Design and Discovery of Novel Materials II

Quantifying uncertainty in DFT energy corrections

Density functional theory (DFT) is routinely used to estimate enthalpies of formation, phase stability, and other energy-derived properties. The accuracy of these estimates can be improved by using experimental thermodynamic data to develop energy corrections that remove some of the systematic error in DFT-computed properties. In this work, we demonstrate a method to quantify uncertainty in these energy correction values which captures uncertainty propagated from the underlying experimental data as well as sensitivity to the selection of fit parameters. We then incorporate this method into a new DFT energy correction scheme comprising a mixture of oxidation-state and composition-dependent corrections and show that many chemical systems contain unstable polymorphs that may actually be predicted stable when uncertainty is taken into account.   

Generalized Gibbs' Phase Rule

Gibbs’ Phase Rule describes the nature of phase boundaries on phase diagrams and is a foundational principle in materials thermodynamics. In Gibbs’ original derivation, he stipulates that the Phase Rule applies only to “simple systems”—defined to be homogeneous, isotropic, uncharged, and large enough that surface effects can be neglected; and not acted upon by electric, magnetic or gravitational fields. Modern functional materials—spanning nanomaterials, multiferrorics, materials for energy storage and conversion, colloidal crystals, etc.—are decidedly non-simple, often leveraging additional forms of thermodynamic work to achieve their functionality. Adding thermodynamic variables into a free-energy expression increases the dimensionality of its corresponding thermodynamic space. Here we revisit Gibbs’ original arguments on phase coexistence and show that phase boundaries in high-dimensional Internal Energy space, U(S,X_i,…), are simplicial convex polytopes—which are N-dimensional analogues of triangles and tetrahedra. From this geometric description we derive a generalized form of Gibbs’ Phase Rule; which can be combined with high-throughput DFT calculations of solid-state entropies, strain tensors, surface energies, magnetic structures, and polarization displacements to build entirely new classes of phase diagrams. These generalized phase diagrams can exist in multiple (≥3) thermodynamic dimensions, and exhibit elastic, surface, electromagnetic or electrochemical work on their axes. New phase diagrams are poised to expand the thermodynamic toolkit beyond the common T-P and T-x phase diagrams, enabling materials scientists to fully interrogate the complex thermodynamic environments of modern materials.    

Extracting effective spin-orbit coupling from first principles calculations via the Wannier representation

The construction of Wannier Hamiltonians (WHs) from density-functional calculations can play an important role in theoretical investigations of condensed-matter systems by combining the virtues of an intuitive tight-binding representation with underlying parameter-free first-principles calculations. Such WHs are in widespread use for Wannier interpolation and extraction of topological properties of band structures. Here, instead, we focus on useful local chemical and physical information that can be extracted from the WH. Site energies and interatomic hoppings are easily extracted from the matrix elements of the WH, but more complicated terms such as spin-orbit coupling (SOC) and crystal field splitting require more care. Here we propose a systematic approach for extracting the strength of such complex operators from a WH, and illustrate its power by applying it to several example systems. These include Fe₂S₂, in which the effective SOC was recently reported [1] to exhibit a giant dependence on the Hubbard on-site U. We quantitatively confirm that this is largely an artifact of an instability to the formation of orbital magnetic order at large U values, and that the dependence of the true SOC strength on U is more modest, though still significant.   

Phonon anharmonicity via harmonic ensemble lattice dynamics (HELD)

The vibrations of atoms about their equilibrium positions critically influence the thermal properties of the material, and the vibrations themselves are affected by volume and temperature. The effects of volume (quasiharmonicity) can be handled accurately and efficiently by modern techniques, but the effects of temperature (anharmonicity) are more challenging to compute and much more computationally expensive. We present a method that calculates ‘instantaneous’ phonon dispersion curves in the harmonic approximation from structures with thermal disorder that are then aggregated into intensity maps to produce finite phonon linewidths that approximate anharmonic phonon broadening. The severity of the approximations and the advantages of this technique will be discussed, and the results for several BCC elements and BCC-based alloys will be shared.    

Ab initio structure prediction accelerated with machine learning interatomic potentials

Prescreening candidate structures with inexpensive classical potentials is gaining renewed interest due to recent advances in machine learning (ML) modeling methodology. For effective acceleration of ab initio prediction, ML interatomic potentials must provide accurate description of diverse configurations probed in global structure searches. I will overview an automated framework implemented in our MAISE package that constructs practical neural network interatomic models for multi-element chemical systems. Recent applications of the approach to well-studied crystalline and nanoscale materials have led to the prediction of stable structures overlooked in previous investigations. Our studies highlight evident advantages and remaining limitations of the ML methodology in guiding ab initio structure prediction.   

Useful Machine-Learned Interatomic Potentials

Interatomic Potentials have long been used for atomistic modeling where the interesting questions are out of reach by first-principles approaches. Traditional empirical potentials are typically fitted to experimental data. They typically have poor general accuracy but are physically well-behaved. On the other hand, machine-learned interatomic potentials are far more expressive than physically motivated interatomic potentials like Lennard-Jones, Stillinger-Weber, Embedded Atom Potentials, etc., but they are also more likely to be completely wrong outside of the training domain, are more difficult to train reliably, and are computationally expensive. We have developed MLIPs for the Hf-Ni-Ti shape memory alloy. We share cautionary tales, best practices for generating training sets, and demonstrate how community tools make for "easy entry" to realistic thermodynamic modeling with these potentials.   

Development of neural network interatomic potentials for accelerated prediction of stable compounds

Construction of machine learning interatomic potentials suitable for guiding unconstrained ab initio

structure searches presents a considerable challenge, as they are required to provide an accurate

description of yet unknown configurations probed in global optimizations. We have developed an

open-source wrapper based on our MAISE package that streamlines all stages of the neural network

(NN) model parameterization. An evolutionary sampling scheme for generating reference structures

improves the NNs’ mapping of regions visited in unconstrained searches, while a stratified training

approach enables the creation of standardized NN models for multiple elements. Among first

applications of such NN potentials is the prediction of new Mg-Ca alloys thermodynamically stable

under ambient or high pressures.   

First-principles modeling and machine learning of the Gibbs free energy of the Fe-C system in a magnetic field

Modeling the thermodynamics and kinetics of steels for designing processes in high magnetic fields requires knowledge of the magnetic Gibbs free energy. Monte Carlo and thermodynamic perturbation or integration methods require integrals over configuration space involving millions of accurate potential energy evaluations. Density-functional theory (DFT) calculations provide sufficient accuracy to describe the Fe-C phases. However, the high computational cost of DFT hinders the direct application to thermodynamic and kinetic modeling.

To address this challenge, the ultra-fast force field (UF³) model [1], an ultra-fast machine-learning potential that combines effective two- and three-body potentials in a cubic B-spline basis with regularized linear regression, can be used to approximate the potential energy landscape. In this work, we use the Vienna Ab initio Simulation Package (VASP) to assemble a DFT database of structural configurations of Fe-C systems with various magnetic states. These configurations focus on BCC and FCC phases, and C concentrations up to 20 at. %. We train and validate a UF³ model for the Fe-C energy landscape on the energies and forces. We will discuss the machine learning approach and the resulting accuracy of the UF³ model for predicting thermodynamic properties.

[1] S. R. Xie, M. Rupp, R. G. Hennig, arXiv:2110.00624 (2021).   

ColabFit: Collaborative Development of Data-Driven Interatomic Potentials

Atomic interactions in classical molecular simulations are modeled using a function called an interatomic potential (IP). Traditionally, IPs have used functional forms that explicitly represent aspects of the bonding and/or geometry of the system and are fitted to small datasets of key material properties. Recently, interest has grown in data-driven IPs (DDIPs) which use machine learning methods to interpolate first principles calculations. Due to the lack of explicit physics, DDIPs must be trained on large datasets and frequently retrained when applications fall outside the original dataset. To facilitate this and allow research groups to easily exchange DDIPs and their training datasets, it is important to develop a standard for archiving and retrieving datasets. The ColabFit project (https://colabfit.openkim.org/) aims to address this need by enabling the development, exchange, and deployment of DDIPs and their datasets through the OpenKIM framework (https://openkim.org/). In this work we outline a standard for distributing DDIP training sets and showcase the functionality of the ColabFit tools and data repository for providing open access to a large collection of high quality training data.   

Pressure-dependent layer-by-layer oxidation of ZrS2(001) surface

ZrS₂is an important semiconductor and shows superior chemical catalytic properties among transition metal dichalcogenides family. Recently, ZrS₂has been reported to be easily oxidized under native environment. To understand their long-term stability, oxidation of ZrS₂has been studied experimentally and computationally. In this work, reactive molecular dynamics simulations are performed using a previously developed reactive force field to study the pressure dependence of oxidation of ZrS₂(001) surface. Oxidation rate is found to be tuned under different oxygen partial pressure at a temperature of 300 K. The observed pressure dependence is analyzed in terms of the Deal-Grove model. To quantify the initial oxidation behavior, the binding energy of oxygen is calculated. We also find alayer-by-layer oxidation in the initial oxidation stage. Such atomistic details are indispensable for controlling the oxidation of ZrS₂in actual device processing.  

    

Three-body tight-binding for the periodic table

Over the past two decades, density functional theory calculations (DFT) have become the workhorse method for electronic structure calculations; however, there are always limitations in terms of the number of calculations or sizes of unit-cells. Tight-binding calculations fit to DFT are a way to bridge this gap, but appropriate models are not always available, especially for materials design applications where many materials may be studied.  In this work, we introduce a versatile tight-binding model that builds the Hamiltonian from both the typical two-body interactions between atoms plus three-body interactions. The three-body terms allow the local neighborhood of a pair of atoms to modify their interaction. These terms allow the model to fit a wide range of structures and stoichiometries without loss of accuracy. We fit this model to a database of over 800,000 DFT calculations of elemental and binary systems, allowing users of the model to immediately begin calculations. To ensure the fitting produces accurate predictions out-of-sample, we use the model to relax new structures from random starting structures, and then compare the energies to new DFT calculations. These new calculations are added to the fitting until the performance improves.