arXiv subjects

Anton Van der Ven

Publications and source records attributed to Anton Van der Ven.

25 records · Page 2Linked to original sources

arXiv2019

Machine learning the DFT potential energy surface for inorganic halide perovskite CsPbBr$_3$

Structural phase transitions as a function of temperature dictate the structure--functionality relationships in many technologically important materials. Harmonic Hamiltonians have proven successful in predicting the vibrational properties of many materials. However, they are inadequate for modeling structural phase transitions in crystals with potential energy surfaces that are either strongly anharmonic or no\ n-convex with respect to collective atomic displacements or homogeneous strains. In this paper we develop a framework to express highly anharmonic first-principles potential energy surfaces as polynomials of collective cluster deformati\ ons. We further adapt the approach to a nonlinear extension of the cluster expansion formalism through the use of an artificial neural net model. The machine learning models are trained on a large database of first-principles calculations and are shown to reproduce the potential energy surface with l\ ow error.

cond-mat.mtrl-sci↗

arXiv2017

First-principles investigation of competing magnetic interactions in (Mn,Fe)Ru$_2$Sn Heusler solid solutions

Many Heusler compounds possess magnetic properties well-suited for applications as spintronic materials. The pseudo-binary Mn$_{0.5}$Fe$_{0.5}$Ru$_2$Sn, formed as a solid solution of two full Heuslers, has recently been shown to exhibit exchange hardening suggestive of two magnetic phases, despite existing as a \textit{single} chemical phase. We have performed a first-principles study of the chemical and magnetic degrees of freedom in the Mn$_{1-x}$Fe$_{x}$Ru$_2$Sn pseudo-binary to determine the origin of the unique magnetic behavior responsible for exchange hardening within a single phase. We find a transition from antiferromagnetic (AFM) to ferromagnetic (FM) behavior upon replacement of Mn with Fe, consistent with experimental results. The lowest energy orderings in Mn$_{1-x}$Fe$_{x}$Ru$_2$Sn consist of chemically- and magnetically-uniform (111) planes, with Fe-rich regions preferring FM ordering and Mn-rich regions preferring AFM ordering, independent of the overall composition. Analysis of the electronic structure suggests that the magnetic behavior of this alloy arises from a competition between AFM-favoring Sn-mediated superexchange and FM-favoring RKKY exchange mediated by spin-polarized conduction electrons. Changes in valency upon replacement of Mn with Fe shifts the balance from superexchange-dominated interactions to RKKY-dominated interactions.

cond-mat.mtrl-sci↗

arXiv2016

A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations

Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. Continuum partial differential equations (PDEs) of atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability, accuracy and robustness of numerical methods to solve these PDEs are sensitive to the particular functional representations of the free energy. In this communication we investigate the influence of different representations of thermodynamic data on phase field computations of diffusion and two-phase reactions in the solid state. First-principles statistical mechanics methods were used to generate realistic free energy data for HCP titanium with interstitially dissolved oxygen. While Redlich-Kister polynomials have formed the mainstay of thermodynamic descriptions of multi-component solids, they require high order terms to fit oscillations in chemical potentials around phase transitions. Here we demonstrate that high fidelity fits to rapidly fluctuating free energy functions are obtained with spline functions. Spline functions that are many degrees lower than Redlich-Kister polynomials provide equal or superior fits to chemical potential data and, when used in phase field computations, result in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials.

cond-mat.mtrl-sci↗

arXiv2016

Multi-physics simulations of lithiation-induced stress in Li$_{\rm 1+x}$Ti$_2$O$_4$ electrode particles

Cubic spinel Li$_{\rm 1+x}$Ti$_2$O$_4$ is a promising electrode material as it exhibits a high lithium diffusivity and undergoes minimal changes in lattice parameters during lithiation and delithiation, thereby ensuring favorable cycleability. The present work is a multi-physics and multi-scale study of Li$_{\rm 1+x}$Ti$_2$O$_4$ that combines first principles computations of thermodynamic and kinetic properties with continuum scale modeling of lithiation-delithiation kinetics. Density functional theory calculations and statistical mechanics methods are used to calculate lattice parameters, elastic coefficients, thermodynamic potentials, migration barriers and Li diffusion coefficients. These quantities then inform a phase field framework to model the coupled chemo-mechanical evolution of electrode particles. Several case studies accounting for either homogeneous or heterogeneous nucleation are considered to explore the temporal evolution of maximum principle stress values, which serve to indicate stress localization and the potential for crack initiation, during lithiation and delithiation.

cond-mat.mtrl-sci↗

arXiv2016

Mechano-chemical spinodal decomposition: A phenomenological theory of phase transformations in multi-component, crystalline solids

We present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes diffusional phase transformations that are accompanied by symmetry breaking structural changes of the crystal unit cell and reveals the importance of a mechano-chemical spinodal, defined as the region in strain-composition space where the free energy density function is non-convex. The approach is relevant to phase transformations wherein the structural order parameters can be expressed as linear combinations of strains relative to a high-symmetry reference crystal. The governing equations describing mechano-chemical spinodal decomposition are variationally derived from a free energy density function that accounts for interfacial energy via gradients of the rapidly varying strain and composition fields. A robust computational framework for treating the coupled, higher order diffusion and nonlinear strain gradient elasticity problems is presented. Because the local strains in an inhomogeneous, transforming microstructure can be finite, the elasticity problem must account for geometric nonlinearity. An evaluation of available experimental phase diagrams and first-principles free energies suggests mechano-chemical spinodal decomposition should occur in metal hydrides such as ZrH$_{2-2c}$. The rich physics that ensues is explored in several numerical examples in two and three dimensions and the relevance of the mechanism is discussed in the context of important electrode materials for Li-ion batteries and high temperature ceramics.

physics.chem-ph↗

arXiv2016

Recovering 0 Kelvin Effective Hamiltonian Parameters from High-Temperature Disordered Phases

Effective Hamiltonians, when used in tandem with statistical mechanics techniques, offer a rigorous connection between 0 Kelvin ab-initio predictions and finite temperature experimental observations. For alloys, cluster expansion Hamiltonians can coarse-grain out the complex, many-body electron problem of density functional theory, yielding a series of simple site-wise basis functions (e.g., products of site occupancy variables) on an atomic scale. The resulting energy polynomial is computationally inexpensive, and hence suitable for the (tens of) thousands of calculations of large systems required by stochastic methods. We present a new method to run the statical mechanics problem "in reverse", using high-temperature observations and thermodynamic connections to construct an effective Hamiltonian and thereby predict the 0 Kelvin energy spectrum and associated ground states. By re-examining the cluster expansion formalism through the lens of entropy-maximization approaches, we develop an algorithm to select clusters and determine cluster interactions using only a few, high-temperature experiments on disordered phases. We demonstrate that our approach can recover not only the stable ground states at 0 Kelvin, but also the full phase behavior for three realistic two-dimensional and three-dimensional alloy test-cases.

cond-mat.mtrl-sci↗

arXiv2015

Testing Predictions from Density Functional Theory at Finite Temperatures: $β_2$-Like Ground States in Co-Pt

We perform a critical assessment of the accuracy of DFT-based methods in predicting stable phases within the Co-Pt binary alloy. Statistical mechanical analysis applied to zero kelvin DFT predictions yields finite-temperature results that can be directly compared with experimental measurements. The predicted temperature-composition phase diagram is qualitatively incompatible with experimental observations, indicating that the predicted stability of long-period superstructures as ground states in the Co-Pt binary is incorrect. We also show that recently suggested methods to better align DFT and experiment via the hybrid functional HSE06 are unable to resolve the discrepancies in this system. Our results indicate a need for better verification of DFT based phase stability predictions, and highlight fundamental flaws in the ability of DFT to treat late 3$d$-5$d$ binary alloys.

cond-mat.mtrl-sci↗