arXiv subjects

Ralf Drautz

Publications and source records attributed to Ralf Drautz.

At least 55 records · Page 3Linked to original sources

arXiv2022

Extending the Variational Quantum Eigensolver to Finite Temperatures

We present a variational quantum thermalizer (VQT), called quantum-VQT (qVQT), which extends the variational quantum eigensolver (VQE) to finite temperatures. The qVQT makes use of an intermediate measurement between two variational circuits to encode a density matrix on a quantum device. A classical optimization provides the thermal state and, simultaneously, all associated excited states of a quantum mechanical system. We demonstrate the capabilities of the qVQT for two different spin systems. First, we analyze the performance of qVQT as a function of the circuit depth and the temperature for a 1-dimensional Heisenberg chain. Second, we use the excited states to map the complete, temperature dependent phase diagram of a 2-dimensional J1-J2 Heisenberg model. The numerical experiments demonstrate the efficiency of our approach, which can be readily applied to study various quantum many-body systems at finite temperatures on currently available NISQ devices.

quant-ph↗

arXiv2022

Effects of thermal, elastic, and surface properties on the stability of SiC polytypes

SiC polytypes have been studied for decades, both experimentally and with atomistic simulations, yet no consensus has been reached on the factors that determine their stability and growth. Proposed governing factors are temperature-dependent differences in the bulk energy, biaxial strain induced through point defects, and surface properties. In this work, we investigate the thermodynamic stability of the 3C, 2H, 4H, and 6H polytypes with density functional theory (DFT) calculations. The small differences of the bulk energies between the polytypes can lead to intricate changes in their energetic ordering depending on the computational method. Therefore, we employ and compare various DFT-codes: VASP, CP2K, and FHI-aims; exchange-correlation functionals: LDA, PBE, PBEsol, PW91, HSE06, SCAN, and RTPSS; and nine different van der Waals (vdW) corrections. At $T=0$~K, 4H-SiC is marginally more stable than 3C-SiC, and the stability further increases with temperature by including entropic effects from lattice vibrations. Neither the most advanced vdW corrections nor strain on the lattice have a significant effect on the relative polytype stability. We further investigate the energies of the (0001) polytype surfaces that are commonly exposed during epitaxial growth. For Si-terminated surfaces, we find 3C-SiC to be significantly more stable than 4H-SiC. We conclude that the difference in surface energy is likely the driving force for 3C-nucleation, whereas the difference in the bulk thermodynamic stability slightly favors the 4H and 6H polytypes. In order to describe the polytype stability during crystal growth correctly, it is thus crucial to take into account both of these effects.

cond-mat.mtrl-sci↗

arXiv2022

Atomic cluster expansion and wave function representations

The atomic cluster expansion (ACE) has been highly successful for the parameterisation of symmetric (invariant or equivariant) properties of many-particle systems. Here, we generalize its derivation to anti-symmetric functions. We show how numerous well-known linear representations of wave functions naturally arise within this framework and we explore how recent successful nonlinear parameterisations can be further enhanced by employing ACE methodology. From this analysis we propose a wide design space of promising wave function representations.

cond-mat.mtrl-sci↗

arXiv2022

Multilayer atomic cluster expansion for semi-local interactions

Traditionally, interatomic potentials assume local bond formation supplemented by long-range electrostatic interactions when necessary. This ignores intermediate range multi-atom interactions that arise from the relaxation of the electronic structure. Here, we present the multilayer atomic cluster expansion (ml-ACE) that includes collective, semi-local multi-atom interactions naturally within its remit. We demonstrate that ml-ACE significantly improves fit accuracy compared to a local expansion on selected examples and provide physical intuition to understand this improvement.

cond-mat.mtrl-sci↗

arXiv2021

Influence of spin fluctuations on structural phase transitions of iron

The effect of spin fluctuations on the $α$ (bcc) - $γ$ (fcc) - $δ$ (bcc) structural phase transitions in iron is investigated with a tight-binding (TB) model. The orthogonal $d$-valent TB model is combined with thermodynamic integration, spin-space averaging and Hamiltonian Monte Carlo to compute the temperature-dependent free-energy difference between bcc and fcc iron. We demonstrate that the TB model captures experimentally observed phonon spectra of bcc iron at elevated temperatures. Our calculations show that spin fluctuations are crucial for both, the $α$ - $γ$ and the $γ$ - $δ$ phase transitions but they enter through different mechanisms. Spin fluctuations impact the $α$ - $γ$ phase transition mainly via the magnetic/electronic free-energy difference between bcc and fcc iron. The $γ$ - $δ$ phase transition, in contrast, is influenced by spin fluctuations only indirectly via the spin-lattice coupling. Combining the two mechanisms, we obtain both, the $α$ - $γ$ and the $γ$ - $δ$ phase transitions with our TB model. The calculated transition temperatures are in very good agreement with experimental values.

cond-mat.stat-mech↗

arXiv2021

Atomic-scale modeling of superalloys

Atomistic theory holds the promise for the ab initio development of superalloys based on the fundamental principles of quantum mechanics. The last years showed a rapid progress in the field. Results from atomistic modeling enter larger-scale simulations of alloy performance and often may be compared directly to experimental characterization. In this chapter we give an overview of atomistic modeling and simulation for Ni-base superalloys. We cover descriptions of the interatomic interaction from quantum-mechanical simulations with a small number of atoms to multi-million-atom simulations with classical interatomic potentials. Methods to determine structural stability for different chemical compositions, thermodynamic and kinetic properties of typical defects in superalloys, and relations to mechanical deformation are discussed. Connections to other modeling techniques are outlined.

cond-mat.mtrl-sci↗

arXiv2021

Automated free energy calculation from atomistic simulations

We devise automated workflows for the calculation of Helmholtz and Gibbs free energies and their temperature and pressure dependence and provide the corresponding computational tools. We employ non-equilibrium thermodynamics for evaluating the free energy of solid and liquid phases at a given temperature and reversible scaling for computing free energies over a wide range of temperatures, including the direct integration of $P$-$T$ coexistence lines. By changing the chemistry and the interatomic potential, alchemical and upscaling free energy calculations are possible. Several examples illustrate the accuracy and efficiency of our implementation.

cond-mat.mtrl-sci↗

arXiv2021

Understanding creep of a single-crystalline Co-Al-W-Ta superalloy by studying the deformation mechanism, segregation tendency and stacking fault energy

A systematic study of the compression creep properties of a single-crystalline Co-base superalloy (Co-9Al-7.5W-2Ta) was conducted at 950 °C, 975 °C and 1000 °C to reveal the influence of temperature and the resulting diffusion velocity of solutes like Al, W and Ta on the deformation mechanisms. Two creep rate minima are observed at all temperatures indicating that the deformation mechanisms causing these minima are quite similar. Atom-probe tomography analysis reveals elemental segregation to stacking faults, which had formed in the $γ\prime$ phase during creep. Density-functional-theory calculations indicate segregation of W and Ta to the stacking fault and an associated considerable reduction of the stacking fault energy. Since solutes diffuse faster at a higher temperature, segregation can take place more quickly. This results in a significantly faster softening of the alloy, since cutting of the $γ\prime$ precipitate phase by partial dislocations is facilitated through segregation already during the early stages of creep. This is confirmed by transmission electron microscopy analysis. Therefore, not only the smaller precipitate fraction at higher temperatures is responsible for the worse creep properties, but also faster diffusion-assisted shearing of the $γ\prime$ phase by partial dislocations. The understanding of these mechanisms will help in future alloy development by offering new design criteria.

cond-mat.mtrl-sci↗

arXiv2021

Atomic Cluster Expansion: Completeness, Efficiency and Stability

The Atomic Cluster Expansion (Drautz, Phys. Rev. B 99, 2019) provides a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling properties of atomistic systems. Our presentation extends the derivation by proposing a precomputation algorithm that yields immediate guarantees that a complete basis is obtained. We provide a fast recursive algorithm for efficient evaluation and illustrate its performance in numerical tests. Finally, we discuss generalisations and open challenges, particularly from a numerical stability perspective, around basis optimisation and parameter estimation, paving the way towards a comprehensive analysis of the convergence to a high-fidelity reference model.

math.NA↗

arXiv2021

Performant implementation of the atomic cluster expansion (PACE): Application to copper and silicon

The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code \verb+PACE+ that is suitable for use in large scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in \verb+PACE+ shifts a previously established Pareto front for machine learning interatomic potentials towards faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the new Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

cond-mat.mtrl-sci↗

arXiv2021

Tight-binding bond parameters for dimers across the periodic table from density-functional theory

We obtain parameters for non-orthogonal and orthogonal TB models from two-atomic molecules for all combinations of elements of period 1 to 6 and group 3 to 18 of the periodic table. The TB bond parameters for 1711 homoatomic and heteroatomic dimers show clear chemical trends. In particular, using our parameters we compare to the rectangular d-band model, the reduced sp TB model as well as canonical TB models for sp- and d-valent systems which have long been used to gain qualitative insight into the interatomic bond. The transferability of our dimer-based TB bond parameters to bulk systems is discussed exemplarily for the bulk ground-state structures of Mo and Si. Our dimer-based TB bond parameters provide a well-defined and promising starting point for developing refined TB parameterizations and for making the insight of TB available for guiding materials design across the periodic table.

cond-mat.mtrl-sci↗

arXiv2020

Identification of a Multi-Dimensional Reaction Coordinate for Crystal Nucleation in $\text{Ni}_3\text{Al}$

Nucleation during solidification in multi-component alloys is a complex process that comprises the competition between different crystalline phases as well as chemical composition and ordering. Here, we combine transition interface sampling with an extensive committor analysis to investigate the atomistic mechanisms during the initial stages of nucleation in $\text{Ni}_3\text{Al}$. The formation and growth of crystalline clusters from the melt are strongly influenced by the interplay between three descriptors: the size, crystallinity, and chemical short-range order of the emerging nuclei. We demonstrate that it is essential to include all three features in a multi-dimensional reaction coordinate to correctly describe the nucleation mechanism, where in particular the chemical short-range order plays a crucial role in the stability of small clusters. The necessity of identifying multi-dimensional reaction coordinates is expected to be of key importance for the atomistic characterization of nucleation processes in complex, multi-component systems.

cond-mat.mtrl-sci↗

arXiv2020

Role of pre-ordered liquid in the selection mechanism of crystal polymorphs during nucleation

We investigate the atomistic mechanism of homogeneous nucleation during solidification in molybdenum employing transition path sampling. The mechanism is characterized by the formation of a pre-structured region of high bond-orientational order in the supercooled liquid followed by the nucleation of the crystalline bulk phase within the center of the growing solid cluster. This precursor plays a crucial role in the process, as it provides a diffusive interface between the liquid and crystalline core, which lowers the interfacial free energy and facilitates the nucleation of the bulk phase. Furthermore, the structural features of the pre-ordered regions are distinct from the liquid and solid phases, and preselect the specific polymorph that nucleates. The similarity in the nucleation mechanism of Mo with that of metals that exhibit different crystalline bulk phases indicates that the formation of a precursor is a general feature observed in these materials. The strong influence of the structural characteristics of the precursors on the final crystalline bulk phase demonstrates that for the investigated system polymorph selection takes place in the very early stages of nucleation.

cond-mat.mtrl-sci↗

arXiv2020

Atomic cluster expansion of scalar, vectorial and tensorial properties and including magnetism and charge transfer

The atomic cluster expansion (Drautz, Phys. Rev. B 99, 014104 (2019)) is extended in two ways, the modelling of vectorial and tensorial atomic properties and the inclusion of atomic degrees of freedom in addition to the positions of the atoms. In particular, atomic species, magnetic moments and charges are attached to the atomic positions and an atomic cluster expansion that includes the different degrees of freedom on equal footing is derived. Expressions for the efficient evaluation of forces and torques are given. Relations to other methods are discussed.

physics.comp-ph↗

arXiv2019

Mastering processing-microstructure complexity through the prediction of thin film structure zone diagrams by generative machine learning models

Thin films are ubiquitous in modern technology and highly useful in materials discovery and design. For achieving optimal extrinsic properties their microstructure needs to be controlled in a multi-parameter space, which usually requires a too-high number of experiments to map. We propose to master thin film processing microstructure complexity and to reduce the cost of microstructure design by joining combinatorial experimentation with generative deep learning models to extract synthesis-composition-microstructure relations. A generative machine learning approach comprising a variational autoencoder and a conditional generative adversarial network predicts structure zone diagrams. We demonstrate that generative models provide a so far unseen level of quality of generated structure zone diagrams comprising chemical and processing complexity for the optimization of chemical composition and processing parameters to achieve a desired microstructure.

physics.app-ph↗

arXiv2019

Discovery of $ω$-free high-temperature Ti-Ta-X shape memory alloys from first principles calculations

The rapid degradation of the functional properties of many Ti-based alloys is due to the precipitation of the $ω$ phase. In the conventional high-temperature shape memory alloy Ti-Ta the formation of this phase compromises completely the shape memory effect and high (>100°C) transformation temperatures cannot be mantained during cycling. A solution to this problem is the addition of other elements to form Ti-Ta-X alloys, which often modifies the transformation temperatures; due to the largely unexplored space of possible compositions, very few elements are known to stabilize the shape memory effect without decreasing the transformation temperatures below 100°C. In this study we use transparent descriptors derived from first principles calculations to search for new ternary Ti-Ta-X alloys that combine stability and high temperatures. We suggest four new alloys with these properties, namely Ti-Ta-Sb, Ti-Ta-Bi, Ti-Ta-In, and Ti-Ta-Sc. Our predictions for the most promising of these alloys, Ti-Ta-Sc, are subsequently fully validated by experimental investigations, the new alloy Ti-Ta-Sc showing no traces of $ω$ phase after cycling. Our computational strategy is immediately transferable to other materials and may contribute to suppress $ω$ phase formation in a large class of alloys.

cond-mat.mtrl-sci↗

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

Phase transitions in titanium with an analytic bond-order potential

Titanium is the base material for a number of technologically important alloys for energy conversion and structural applications. Atomic-scale studies of Ti-based metals employing first-principles methods, such as density functional theory, are limited to ensembles of a few hundred atoms. To perform large-scale and/or finite temperature simulations, computationally more efficient interatomic potentials are required. In this work, we coarse grain the tight-binding (TB) approximation to the electronic structure and develop an analytic bond-order potential (BOP) for Ti by fitting to the energies and forces of elementary deformations of simple structures. The BOP predicts the structural properties of the stable and defective phases of Ti with a quality comparable to previous TB parametrizations at a much lower computational cost. The predictive power of the model is demonstrated for simulations of martensitic transformations.

cond-mat.mtrl-sci↗