The hiphive package for the extraction of high-order force constants by machine learning

The efficient extraction of force constants (FCs) is crucial for the analysis of many thermodynamic materials properties. Approaches based on the systematic enumeration of finite differences scale poorly with system size and can rarely extend beyond third order when input data is obtained from first-principles calculations. Methods based on parameter fitting in the spirit of interatomic potentials, on the other hand, can extract FC parameters from semi-random configurations of high information density and advanced regularized regression methods can recover physical solutions from a limited amount of data. Here, we present the hiPhive Python package, that enables the construction of force constant models up to arbitrary order. hiPhive exploits crystal symmetries to reduce the number of free parameters and then employs advanced machine learning algorithms to extract the force constants. Depending on the problem at hand both over and underdetermined systems are handled efficiently. The FCs can be subsequently analyzed directly and or be used to carry out e.g., molecular dynamics simulations. The utility of this approach is demonstrated via several examples including ideal and defective monolayers of MoS$_2$ as well as bulk nickel

Efficient construction of linear models in materials modeling and applications to force constant expansions

Linear models, such as force constant (FC) and cluster expansions, play a key role in physics and materials science. While they can in principle be parametrized using regression and feature selection approaches, the convergence behavior of these techniques, in particular with respect to thermodynamic properties is not well understood. Here, we therefore analyze the efficacy and efficiency of several state-of-the-art regression and feature selection methods, in particular in the context of FC extraction and the prediction of different thermodynamic properties. Generic feature selection algorithms such as recursive feature elimination with ordinary least-squares (OLS), automatic relevance determination regression, and the adaptive least absolute shrinkage and selection operator can yield physically sound models for systems with a modest number of degrees of freedom. For large unit cells with low symmetry and/or high-order expansions they come, however, with a non-negligible computational cost that can be more than two orders of magnitude higher than that of OLS. In such cases, OLS with cutoff selection provides a viable route as demonstrated here for both second-order FCs in large low-symmetry unit cells and high-order FCs in low-symmetry systems. While regression techniques are thus very powerful, they require well-tuned protocols. Here, the present work establishes guidelines for the design of protocols that are readily usable, e.g., in high-throughput and materials discovery schemes. Since the underlying algorithms are not specific to FC construction, the general conclusions drawn here also have a bearing on the construction of other linear models in physics and materials science.Comment: 15 pages, 12 figure

Atomic-scale investigation of interfacial structures in WC-Co at finite temperatures

WC-Co cemented carbides combine superb hardness with high toughness making them ideal for usage in high-speed machining of steels and in wear resistance tools. These excellent mechanical properties are to a large extent dependent on the microstructure and thus the interfacial properties of the material. Hence, being able to predict and understand interfacial properties in this material can allow for, e.g., optimizing the manufacturing process in order to improve mechanical properties further.Electronic structure calculations allow for accurately predicting interface energies for a given structure and composition. However, finding the ground-state interfacial structure and composition is challenging as the search space is very large when considering all degrees of freedom. Furthermore, direct sampling of interfacial properties at finite temperature using density functional theory (DFT) is usually computationally impractical as hundreds, thousands or even millions of calculations may be required. Therefore, employing atomic-scale models based on DFT calculations is advantageous and allows for investigation of the interface structure, composition and free energy at finite temperatures. In this thesis computational methods for calculating temperature-dependent interfacial free energies are developed and applied to the WC-Co system.The emphasis is on understanding under which conditions cubic interfacial structures (complexions) can form on the WC basal plane in contact with Co.Configurational degrees of freedom are treated with cluster expansions and Monte Carlo simulations.Vibrational properties are mainly treated in the harmonic approximation using a regression approach to extract the harmonic force constants, which significantly reduces the number of DFT calculations.Interfacial phase diagrams are obtained for both the undoped WC-Co system and the Ti-doped system.Detailed information pertaining to structure and composition of the interfacial phases are obtained and show good agreement with experimental observations

Defects from phonons: Atomic transport by concerted motion in simple crystalline metals

Point defects play a crucial role in crystalline materials as they do not only impact the thermodynamic properties but are also central to kinetic processes. While they are necessary in thermodynamic equilibrium spontaneous defect formation in the bulk is normally considered highly improbable except for temperatures close to the melting point. Here, we demonstrate by means of atomistic simulations that processes involving concerted atomic motion that give rise to defect formation are in fact frequent in body-centered cubic metals even down to about 50% of the melting temperature. It is shown that this behavior is intimately related to the anharmonicity of the lattice vibrations and a flat energy landscape along certain crystallographic directions, a feature that is absent in, e.g., face-centered cubic lattice structures. This insight has implications for our general understanding of these materials and furthermore provides a complementary explanation for the so-called anomalous diffusion in group 4 transition metals.Comment: 5 pages; 4 figure

Phase Transitions in Inorganic Halide Perovskites from Machine-Learned Potentials

The atomic scale dynamics of halide perovskites havea direct impactnot only on their thermal stability but also on their optoelectronicproperties. Progress in machine-learned potentials has only recentlyenabled modeling the finite temperature behavior of these materialsusing fully atomistic methods with near first-principles accuracy.Here, we systematically analyze the impact of heating and coolingrate, simulation size, model uncertainty, and the role of the underlyingexchange-correlation functional on the phase behavior of CsPbX3 with X = Cl, Br, and I, including both the perovskite andthe & delta;-phases. We show that rates below approximately 60 K/nsand system sizes of at least a few tens of thousands of atoms shouldbe used to achieve convergence with regard to these parameters. Bycontrolling these factors and constructing models that are specificfor different exchange-correlation functionals, we then assess thebehavior of seven widely used semilocal functionals (LDA, vdW-DF-cx,SCAN, SCAN+rVV10, PBEsol, PBE, and PBE+D3). The models based on LDA,vdW-DF-cx, and SCAN+rVV10 agree well with experimental data for thetetragonal-to-cubic-perovskite transition temperature in CsPbI3 and also achieve reasonable agreement for the perovskite-to-deltaphase transition temperature. They systematically underestimate, however,the orthorhombic-to-tetragonal transition temperature. All other models,including those for CsPbBr3 and CsPbCl3, predicttransition temperatures below the experimentally observed values forall transitions considered here. Among the considered functionals,vdW-DF-cx and SCAN+rVV10 yield the closest agreement with experiment,followed by LDA, SCAN, PBEsol, PBE, and PBE+D3. Our work providesguidelines for the systematic analysis of dynamics and phase transitionsin inorganic halide perovskites and similar systems. It also servesas a benchmark for the further development of machine-learned potentialsas well as exchange-correlation functionals

Computational investigation of interface structure and composition in cemented carbides at finite temperatures

WC-Co cemented carbides combine superb hardness with high toughness making them ideal for usage in high-speed machining of steels and in wear resistance tools. These excellent mechanical properties are to a large extent dependent on the microstructure and thus the interfacial properties of the material. Hence, being able to predict and understand interfacial properties in this material can allow for e.g. optimizing the manufacturing process in order to improve mechanical properties further.Atomic scale ab-initio calculations allow for accurately predicting interface energies for a given structure and composition. However, finding the ground-state interfacial structure and composition becomes a challenge as the search space is very large when considering all degrees of freedom. Furthermore, direct sampling of interfacial properties at finite temperature using density functional theory (DFT) often becomes computationally unfeasible as hundreds, thousands or even millions of calculations may be required. Therefore, employing atomic scale models based on DFT calculations is advantageous and allows for investigation of the interface structure, composition and free energy at finite temperatures. In this thesis the computational methods for calculating temperature dependent interfacial free energies are developed and applied to the WC-Co system.An interfacial phase diagram for cubic thin films in undoped WC-Co is constructed. Here, configurational degrees of freedom are treated using cluster expansion models and Monte Carlo sampling. Vibrations are treated in the harmonic approximation using force constant fitting to significantly reduce the number of DFT calculations.The temperature dependence of interface free energies for surfaces, grain boundaries and phase boundaries is using an analytic bond order potential. Here, multiple different free energy calculation methods are employed such as quasi-harmonic approximation,\ua0λ-integration​​, thermodynamic integration and surface tension calculation

Complexions and grain growth retardation: First-principles modeling of phase boundaries in WC-Co cemented carbides at elevated temperatures

WC-Co cemented carbides combine superb hardness with high toughness making them ideal for usage in metal machining and in wear resistant tools. Controlling the WC grain size is important during sintering as grain size plays a crucial role for the mechanical properties of the material. Experimental studies have observed different growth rates and grain morphologies in W-rich and C-rich materials, but the mechanism behind this has not been clarified. Here, we consider the possibility of an interface-stabilized state, a complexion, at the WC/Co phase boundary in cemented carbides, namely thin WC films with cubic structure. An interfacial phase diagram is derived using ab-initio calculations and first-principles modeling. Cluster expansions are employed to model carbon vacancies and Monte Carlo simulations to sample the configurational entropy. Force-constant fitting is used to extract the harmonic free energy for ground-state structures and the effects from anharmonicity and electronic excitations are effectively incorporated from a companion study on WC bulk phases. We predict the stabilization of thin cubic WC films at liquid phase sintering temperatures but only at W-rich conditions. This is consistent with experimental findings where thin films with cubic stacking have been observed predominantly in W-rich materials. We use this knowledge to suggest an explanation for the observed different growth rates and grain morphologies in W-rich and C-rich cemented carbides

Quantifying Dynamic Tilting in Halide Perovskites: Chemical Trends and Local Correlations

Halide perovskiteshave emerged as one of the most interestingmaterials for optoelectronic applications due to their favorable properties,such as defect tolerance and long charge carrier lifetimes, whichare attributed to their dynamic softness. However, this softness hasled to apparent disagreements between the local instantaneous andglobal average structures of these materials. In this study, we rationalizethis situation through an assessment of the local tilt angles of octahedrain the perovskite structure using large-scale molecular dynamics simulationsbased on machine-learned potentials trained using density functionaltheory calculations. We compare structural properties given by differentdensity functionals [local density approximation, PBE, PBE + D3, PBEsol,strongly constrained and appropriately normed (SCAN), SCAN + rVV10,and van der Waals density functional with consistent exchange] andestablish trends across a family of CsMX3 perovskites withM = Sn or Pb and X = Cl, Br or I. Notably, we demonstrate strong short-rangeordering in the cubic phase of halide perovskites. This ordering isreminiscent of the tetragonal phase and provides the bridge betweenthe disordered local structure and the global cubic arrangement. Ourresults provide a deeper understanding of the structural propertiesof halide perovskites and their local distortions, which is crucialfor further understanding their optoelectronic properties

DYNASOR -- A tool for extracting dynamical structure factors and current correlation functions from molecular dynamics simulations

Perturbative treatments of the lattice dynamics are widely successful for many crystalline materials, their applicability is, however, limited for strongly anharmonic systems, metastable crystal structures and liquids. The full dynamics of these systems can, however, be accessed via molecular dynamics (MD) simulations using correlation functions, which includes dynamical structure factors providing a direct bridge to experiment. To simplify the analysis of correlation functions, here the dynasor package is presented as a flexible and efficient tool that enables the calculation of static and dynamical structure factors, current correlation functions as well as their partial counterparts from MD trajectories. The dynasor code can handle input from several major open source MD packages and thanks to its C/Python structure can be readily extended to support additional codes. The utility of dynasor is demonstrated via examples for both solid and liquid single and multi-component systems. In particular, the possibility to extract the full temperature dependence of phonon frequencies and lifetimes is emphasized