arXiv subjects

Thomas Hammerschmidt

Publications and source records attributed to Thomas Hammerschmidt.

26 records · Page 2Linked to original sources

arXiv2019

BOPcat software package for the construction and testing of tight-binding models and bond-order potentials

Atomistic models like tight-binding (TB), bond-order potentials (BOP) and classical potentials describe the interatomic interaction in terms of mathematical functions with parameters that need to be adjusted for a particular material. The procedures for constructing TB/BOP models differ from the ones for classical potentials. We developed the BOPcat software package as a modular python code for the construction and testing of TB/BOP parameterizations. It makes use of atomic energies, forces and stresses obtained by TB/BOP calculations with the BOPfox software package. It provides a graphical user interface and flexible control of raw reference data, of derived reference data like defect energies, of automated construction and testing protocols, and of parallel execution in queuing systems. We outline the concepts and usage of the BOPcat software and illustrate its key capabilities by exemplary constructing and testing of an analytic BOP for Fe. The parameterization protocol with a successively increasing set of reference data leads to a magnetic BOP that is transferable to a variety of properties of the ferromagnetic bcc groundstate and to crystal structures that were not part of the training set.

physics.comp-ph↗

arXiv2019

Imaging individual solute atoms at crystalline imperfections in metals

Directly imaging all atoms constituting a material and, maybe more importantly, crystalline defects that dictate materials' properties, remains a formidable challenge. Here, we propose a new approach to chemistry-sensitive field-ion microscopy (FIM) combining contrast interpretation from density-functional theory (DFT) and elemental identification enabled by time-of-flight mass-spectrometry and data mining. Analytical-FIM has true atomic resolution and we demonstrate how the technique can reveal the presence of individual solute atoms at specific positions in the microstructure. The performance of this new technique is showcased in revealing individual Re atoms at crystalline defects formed in Ni during creep deformation. The atomistic details offered by A-FIM allowed us to directly compare our results with simulations, and to tackle a long-standing question of how Re extends lifetime of Ni-based superalloys in service at high-temperature.

cond-mat.mtrl-sci↗

arXiv2019

Accelerating spin-space sampling by auxiliary spin-dynamics and temperature-dependent spin-cluster expansion

Atomistic simulations of thermodynamic properties of magnetic materials rely on an accurate modelling of magnetic interactions and an efficient sampling of the high-dimensional spin space. Recent years have seen significant progress with a clear trend from model systems to material specific simulations that are usually based on electronic-structure methods. Here we develop a Hamiltonian Monte Carlo framework that makes use of auxiliary spin-dynamics and an auxiliary effective model, the temperature-dependent spin-cluster expansion, in order to efficiently sample the spin space. Our method does not require a specific form of the model and is suitable for simulations based on electronic-structure methods. We demonstrate fast warm-up and a reasonably small dynamical critical exponent of our sampler for the classical Heisenberg model. We further present an application of our method to the magnetic phase transition in bcc iron using magnetic bond-order potentials.

cond-mat.stat-mech↗

arXiv2018

NOMAD 2018 Kaggle Competition: Solving Materials Science Challenges Through Crowd Sourcing

Machine learning (ML) is increasingly used in the field of materials science, where statistical estimates of computed properties are employed to rapidly examine the chemical space for new compounds. However, a systematic comparison of several ML models for this domain has been hindered by the scarcity of appropriate datasets of materials properties, as well as the lack of thorough benchmarking studies. To address this, a public data-analytics competition was organized by the Novel Materials Discovery (NOMAD) Centre of Excellence and hosted by the on-line platform Kaggle using a dataset of $3\,000$ (Al$_x$ Ga$_y$ In$_z$)$_2$ O$_3$ compounds (with $x+y+z = 1$). The aim of this challenge was to identify the best ML model for the prediction of two key physical properties that are relevant for optoelectronic applications: the electronic band gap energy and the crystalline formation energy. In this contribution, we present a summary of the top three ML approaches of the competition including the 1st place solution based on a crystal graph representation that is new for ML of the properties of materials. The 2nd place model combined many candidate descriptors from a set of compositional, atomic environment-based, and average structural properties with the light gradient-boosting machine regression model. The 3rd place model employed the smooth overlap of atomic positions representation with a neural network. To gain insight into whether the representation or the regression model determines the overall model performance, nine ML models obtained by combining the representations and regression models of the top three approaches were compared by looking at the correlations among prediction errors. At fixed representation, the largest correlation is observed in predictions made with kernel ridge regression and neural network, reflecting a similar performance on the same test set samples.

cond-mat.mtrl-sci↗

arXiv2018

Electronic structure based descriptor for characterizing local atomic environments

A quantitative descriptor of local atomic environments is often required for the analysis of atomistic data. Descriptors of the local atomic environment ideally provide physically and chemically intuitive insight. This requires descriptors that are low-dimensional representations of the interplay between atomic geometry and electronic bond formation. The moments of the local density of states (DOS) relate the atomic structure to the electronic structure and bond chemistry. This makes it possible to construct electronic structure based descriptors of the local atomic environment that have an immediate relation to the binding energy. We show that a low-dimensional moments-descriptor is sufficient as the lowest moments, calculated from the closest atomic neighborhood, carry the largest contributions to the local bond energy. Here, we construct moments-descriptors that project the space of local atomic environments on a 2-D map. We discuss in detail the separation of various atomic environments and their connections in the map. The distances in the map may be related to energy differences between local atomic environments as we show by analytic considerations based on analytic bond-order potentials (BOP) and by numerical assessment using TB and density-functional theory calculations. Possible applications of the proposed moments-descriptors include the classification of local atomic environments in molecular-dynamic simulations, the selection of structure sets for developing and testing interatomic potentials, as well as the construction of descriptors for machine-learning applications.

cond-mat.mtrl-sci↗

arXiv2018

{110} planar faults in strained bcc metals: Origins and implications of a commonly observed artifact of classical potentials

Large-scale atomistic simulations with classical potentials can provide valuable insights into microscopic deformation mechanisms and defect-defect interactions in materials. Unfortunately, these assets often come with the uncertainty of whether the observed mechanisms are based on realistic physical phenomena or whether they are artifacts of the employed material models. One such example is the often reported occurrence of stable planar faults (PFs) in body-centered cubic (bcc) metals subjected to high strains, e.g., at crack tips or in strained nano-objects. In this paper, we study the strain dependence of the generalized stacking fault energy (GSFE) of {110} planes in various bcc metals with material models of increasing sophistication, i.e., (modified) embedded atom method, angular-dependent, Tersoff, and bond-order potentials as well as density functional theory. We show that under applied tensile strains the GSFE curves of many classical potentials exhibit a local minimum which gives rise to the formation of stable PFs. These PFs do not appear when more sophisticated material models are used and have thus to be regarded as artifacts of the potentials. We demonstrate that the local GSFE minimum is not formed for reasons of symmetry and we recommend including the determination of the strain-dependent (110) GSFE as a benchmark for newly developed potentials.

cond-mat.mtrl-sci↗

arXiv2016

Comparison of analytic and numerical bond-order potentials for W and Mo

Bond-order potentials (BOPs) are derived from the tight-binding (TB) approximation and provide a linearly-scaling computation of the energy and forces for a system of interacting atoms. While the numerical BOPs involve the numerical integration of the response (Green's) function, the expressions for the energy and interatomic forces are analytical within the formalism of the analytic BOPs. In this paper we present a detailed comparison of numerical and analytic BOPs. We use established parametrisations for the bcc refractory metals W and Mo and test structural energy differences; tetragonal, trigonal, hexagonal and orthorhombic deformation paths; formation energies of point defects as well as phonon dispersion relations. We find that the numerical and analytic BOPs generally are in very good agreement for the calculation of energies. Different from the numerical BOPs, the forces in the analytic BOPs correspond exactly to the negative gradients of the energy. This makes it possible to use the analytic BOPs in dynamical simulations and leads to improved predictions of defect energies and phonons as compared to the numerical BOPs.

cond-mat.mtrl-sci↗

arXiv2016

Topologically close-packed phases in binary transition-metal compounds: matching high-throughput ab initio calculations to an empirical structure map

In steels and single-crystal superalloys the control of the formation of topologically close-packed (TCP) phases is critical for the performance of the material. The structural stability of TCP phases in multi-component transition-metal alloys may be rationalised in terms of the average valence-electron count $\bar{N}$ and the composition-dependent relative volume-difference $\overline{ΔV/V}$. We elucidate the interplay of these factors by comparing density-functional theory calculations to an empirical structure map based on experimental data. In particular, we calculate the heat of formation for the TCP phases A15, C14, C15, C36, $χ$, $μ$, and $σ$ for all possible binary occupations of the Wyckoff positions. We discuss the isovalent systems V/Nb-Ta to highlight the role of atomic-size difference and observe the expected stabilisation of C14/C15/C36/$μ$ by $\overline{ΔV/V}$ at $ΔN=0$ in V-Ta. In the systems V/Nb-Re, we focus on the well-known trend of A15$- σ- χ$ stability with increasing $\bar{N}$ and show that the influence of $\overline{ΔV/V}$ is too weak to stabilise C14/C15/C36/$μ$ in Nb-Re. As an example for a significant influence of both $\bar{N}$ and $\overline{ΔV/V}$, we also consider the systems Cr/Mo-Co. Here the sequence A15$- σ- χ$ is observed in both systems but in Mo-Co the large size-mismatch stabilises C14/C15/C36/$μ$. We also include V/Nb-Co that cover the entire valence range of TCP stability and also show the stabilisation of C14/C15/C36/$μ$. Moreover, the combination of a large volume difference with a large mismatch in valence-electron count reduces the stability of the A15/$σ$/$χ$ phases in Nb-Co as compared to V-Co. By comparison to non-magnetic calculations we also find that magnetism is of minor importance for the structural stability of TCP phases in Cr/Mo-Co and in V/Nb-Co.

cond-mat.mtrl-sci↗