arXiv subjects

Karsten Albe

Publications and source records attributed to Karsten Albe.

At least 19 recordsLinked to original sources

arXiv2026

Electron Polaron at Neutral 180$^\circ$ Domain Wall in PbTiO$_3$: Stability, Trapping Energies, and Transverse Polarization

We use density-functional theory with a Hubbard correction to investigate Ti-centered electron polarons at neutral PbO-centered $180^\circ$ domain walls in tetragonal PbTiO$_{3}$. The Hubbard parameter for Ti $3d$ states is determined using the finite-size-corrected polaronic energy-level alignment procedure, yielding stable electron-polaron formation in bulk PbTiO$_3$ with a trapping energy of $-$0.06 eV. In the domain-wall supercell, the excess electron localizes on Ti and forms a Ti$^{3+}$ center with an occupied $d_{xy}$ orbital in-gap state. Comparison of bulk-like and near-wall Ti sites shows that their trapping energies differ by only about 0.01 eV, indicating that this neutral domain wall does not provide a significant thermodynamic driving force for electron-polaron segregation. While the Ising-like reversal of the out-of-plane polarization is preserved, the localized electron induces a finite transverse polarization component normal to the wall, enhancing a local N\'eel-like distortion that is strongest when the polaron is located at the wall. These results show that neutral $180^\circ$ domain walls in PbTiO$_3$ do not substantially alter the stability of Ti-centered electron polarons, but they can couple to the polaron-induced lattice distortion through a localized transverse polarization response.

cond-mat.mtrl-sci↗

arXiv2026

Atomistic-Continuum Coupling by Homogenization

Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for micrometer-scale structural analyses. We develop a two-scale atomistic-continuum framework that couples a nonlinear finite-element boundary-value problem at the microscale to periodic molecular-statics cell problems at quadrature points. The scale transition is formulated by computational homogenization in the sense of Hill-Mandel energy equivalence. Instead of prescribing a continuum constitutive law on the lower scale, the atomistic cell is driven directly by the continuum deformation and returns volume-averaged stresses in work-conjugate form together with effective tangent moduli. Numerical examples for single-crystalline copper show pronounced tension-compression asymmetry, abrupt instability-driven defect nucleation, rapid stabilization under reversed cyclic loading, and localized elastic-plastic transition in cantilever bending. In all these strongly nonlinear scenarios, the coarse-scale Newton solver remains robust and recovers near-quadratic convergence in its final iterations. The two-scale framework thus extends potential-based atomistic modeling to structural length scales that are inaccessible to direct atomistic simulation in the present quasi-static, athermal setting.

math.NA↗

arXiv2026

Chemo-mechanical coupling stabilizes mixed $\mathrm{Ag}_{x}\mathrm{Cu}_{1-x}\mathrm{GaSe}_{2}$ solar-cell absorbers: Insights from Monte-Carlo simulations assisted by ab initio informed machine-learning potentials

Alloying Ag into Cu(In,Ga)Se$_2$ has enabled record solar-cell efficiencies ($\sim23.6\%$), yet their long-term stability remains in question because initio calculations predict a Ag-Cu miscibility gap near ambient temperature. By off-lattice Monte-Carlo simulations using a newly developed machine learning (ML) interatomic potential we show that the presence of coherency strain is resolving the controversy between experimental observations and the predicted phase stability. Incorporating elastic energy contributions present in a coherent setup results in complete Ag-Cu miscibility, whereas the expected phase separation occurs in the absence of coherency strains with respect to the end boundary phases, which are mimicked by an incoherent interface with misfit dislocations. The developed ML-MC framework provides a novel approach for resolving discrepancies in thermodynamic stability for systems where mechanical and chemical effects compete.

cond-mat.mtrl-sci↗

arXiv2026

First-principles investigation of small polarons in rhombohedral NaNbO$_{3}$

Sodium niobate (NaNbO$_{3}$) is a perovskite oxide and a key component of emerging lead-free antiferroelectric capacitors for high-energy-density applications. However, its performance can be hindered by irreversible phase transitions and leakage currents associated with low electrical resistivity. Defect and doping engineering offers a potential way to overcome these problems, but its use requires a detailed understanding of electronic, ionic, and polaron charge-compensation mechanisms, where the role of polarons remains largely unexplored. Here, we investigate the stability of small hole and electron polarons in rhombohedral NaNbO$_{3}$, which is a structurally well-defined model system that avoids lattice-dynamical instabilities. Trapping energies are calculated using density-functional theory corrected by a Hubbard $U$, using the enforced-piecewise-linearity approach including finite-size scaling. For the small hole-polaron centered on O-2$p$ orbital, we find a trapping energy of $-$0.65 (eV) and an adiabatic migration barrier of 0.32 (eV) determined by nudged-elastic-band calculations. In contrast, we show that excess electrons do not self-trap on Nb-4$d$ orbitals, reflecting weak electron-phonon coupling in the conduction band manifold. These results identify oxygen as an intrinsic hole trap in NaNbO$_{3}$ and highlight the importance of including hole polarons in defect models of NaNbO$_{3}$-based electroceramics.

cond-mat.mtrl-sci↗

arXiv2026

Why hole polaron formation on oxygen is limiting the Fermi level in Fe acceptor doped BaTiO$_{3}$ under oxidizing conditions

Oxidizing Fe-doped BaTiO$_3$ is commonly expected to convert substitutional Fe$^{3+}$ acceptors into formal Fe$^{4+}$ centers. Yet, the experimentally accessible picture based on electron-paramagnetic resonance (EPR) is dominated by Fe$^{3+}$-related signatures, while Fe$^{4+}$ is not a straightforward observable. Here we show that this apparent discrepancy reflects the preferred location of the oxidizing hole: not on Fe, but on oxygen. Using density-functional theory with with occupation-matrix control and a piecewise-linearity-based Hubbard correction (DFT+$U$) for O-2$p$ states, we find that an oxygen-centered hole polaron is forming a Fe$^{3+}$-O$^{-}$ complex that is lower in energy than the formal Fe$^{4+}$ configuration. Our results identify ligand-hole formation as a favorable charge-compensation mechanism in oxidized Fe-doped BaTiO$_3$ and provide an explanation for the predominance of Fe$^{3+}$-based centers in spectroscopy. More broadly, they show how oxygen polarons can limit Fermi-level shifts and control the electronic response of acceptor-doped ferroelectric perovskites.

cond-mat.mtrl-sci↗

arXiv2026

Accurate Nanoscale Mapping of Electric Fields across Random Grain Boundaries in Polycrystalline Oxides Using Precession-Assisted 4D-STEM

Space charge layers (SCLs) at grain boundaries play a crucial role in modulating local electric fields and influencing the functional properties of materials, such as oxygen vacancy migration and ionic conductivity in oxide ceramics. However, the direct experimental analysis of such localized electric fields and the corresponding charge distribution remains challenging. Conventional center-of-mass (CoM) analysis in scanning transmission electron microscopy differential phase contrast (STEM-DPC) is strongly affected by orientation-dependent contrast and dynamical scattering. Here, we demonstrate that combining electron beam precession with advanced post-processing, employing iterative edge detection via a Sobel filter and singular value decomposition (SVD), enables reliable and accurate, unbiased diffraction shift measurements with minimal crystallographic artefacts. The new method accurately refines the central disk position in nanobeam electron diffraction (NBED) patterns and thus significantly improves the extraction of the local electric field and corresponding charge distribution. Comparative analysis with conventional CoM methods shows superior accuracy and robustness for random grain boundaries in BaTiO3 and SrTiO3 as exemplary case studies. The experimental work is complemented by atomistic simulations to separate the electric field of the SCL from the mean inner potential difference of the grain boundary and the elemental segregation around the grain boundary. The in-depth analysis shows that our approach enables high-fidelity mapping of electromagnetic fields and their charge distribution in complex polycrystalline specimens, laying the groundwork for improved quantitative analysis using STEM-DPC.

cond-mat.mtrl-sci↗

arXiv2026

Impact of charge transition levels on grain boundary properties in acceptor doped oxide ceramics: A phase-field study

Advanced doping strategies enable oxide ceramic functionalities by tailoring bulk defect chemistry and space-charge-layer (SCL) behavior at interfaces. Charge transition levels (CTLs), defined as the Fermi level at which a defect changes its stable charge state, play a central role. Their alignment governs bulk defect chemistry, while their bending within SCLs induces additional charge-state transitions. Incorporating CTLs is therefore essential for a consistent description of defect equilibria and SCL formation. In this work, we propose a defect-chemistry-consistent phase-field model explicitly coupled with CTLs to investigate their role in SCL evolution. The model includes multivalent oxygen vacancies, multivalent acceptor dopants, electrons, and holes. It is applied to Fe-doped SrTiO3 over wide ranges of oxygen partial pressure and temperature, capturing both symmetric SCLs at stationary grain boundaries and asymmetric SCLs during migration. Two distinct grain boundary types, slow and fast boundaries, emerge during migration, consistent with experimental observations. Simulations reveal that CTL-governed bulk defect chemistry, together with CTL-induced charge-state transitions within SCLs, critically determine SCL characteristics. Moreover, CTL-mediated hole transport is significantly faster than acceptor dopant diffusion, modulating solute drag and grain boundary kinetics. Finally, the model predicts grain boundary properties dependent on both thermal history and boundary type, with slow and fast boundaries exhibiting distinct behaviors. This framework links defect chemistry, Fermi level, CTLs, and grain boundary kinetics, providing new insights for designing oxide ceramics with tailored properties.

cond-mat.mtrl-sci↗

arXiv2026

How semiconducting are ferroelectrics: The fundamental, optical and transport gaps of Na$_{0.5}$Bi$_{0.5}$TiO$_3$-BaTiO$_3$ and NaNbO$_{3}$

The energy gap is a fundamental property of materials, directly related to their optical and electronic properties. The energy gap of ferroelectric compounds and its adjustment by compositional variation has particularly attracted attention in recent years due to potential application in energy conversion and/or catalytic devices. It is demonstrated that it is necessary to distinguish between the fundamental gap, $E_{\rm g}^{0}$, the optical gap, $E_{\rm g}^{\rm opt}$, and the transport gap, $E_{\rm g}^{\rm tr}$, of ferroelectrics, which can differ significantly. The situation is comparable to those in organic semiconductors and emerges from the presence of localized charges. The fundamental gap is a ground state property, i.e.\ the energy difference between the maximum of the fully occupied valence band and the minimum of the completely empty conduction band. In contrast, the optical and transport gaps are excited state properties involving localized (polaronic) electrons and/or holes at energies considerably different from the band edges. This work illustrates how the different energy gaps of ferroelectrics can be determined by combining optical measurements, X-ray photoelectron spectroscopy and temperature and oxygen partial pressure dependent electrical conductivity measurements. We determine fundamental gaps of $\approx 4.5\,$eV for both materials, optical gaps of $3.25-3.45\,$eV/$3.5\,$eV and electrical gaps of $\approx 1.4\,$eV/$3.3\,$eV for Na$_{0.5}$Bi$_{0.5}$TiO$_3$-BaTiO$_3$/NaNbO$_{3}$, respectively.

cond-mat.mtrl-sci↗

arXiv2025

Defect thermodynamics of orthorhombic Ba$_2$In$_2$O$_5$: First-principles calculations on the role of oxygen dumbbell interstitials

The brownmillerite-type barium indate (Ba$_2$In$_2$O$_5$) is a potential electrolyte for mixed ionic-electronic conduction in solid oxide fuel cells. Revealing the defect chemistry of this material is key to understanding its ionic and electronic conductivity. In this contribution, we report the existence of oxygen interstitials in a dumbbell configuration, which are also observed in In$_2$O$_3$. Using Density Functional Theory within the generalized gradient approximation, complemented by selected hybrid-functional calculations, we investigate vacancies, various oxygen interstitials, and Frenkel pairs. In doing so, we evaluate the formation energies, charge transition levels, and concentrations as a function of oxygen partial pressure. Our results show that oxygen vacancies and interstitials dominate the intrinsic defect landscape. Among the interstitials, we identify stable dumbbell configurations that remain neutral across the entire band gap. Other interstitial configurations exhibit charged states and become the prevailing compensating defects at high oxygen partial pressures, alongside oxygen vacancies. Our results provide a consistent picture of the thermodynamics of intrinsic defects in barium indate, setting the stage for future investigations of the diffusion dynamics of oxygen vacancies and interstitials.

cond-mat.mtrl-sci↗

arXiv2025

Machine-learning interatomic potentials from a users perspective: A comparison of accuracy, speed and data efficiency

Machine learning interatomic potentials (MLIPs) have massively changed the field of atomistic modeling. They enable the accuracy of density functional theory in large-scale simulations while being nearly as fast as classical interatomic potentials. Over the last few years, a wide range of different types of MLIPs have been developed, but it is often difficult to judge which approach is the best for a given problem setting. For the case of structurally and chemically complex solids, namely Al-Cu-Zr and Si-O, we benchmark a range of machine learning interatomic potential approaches, in particular, the Gaussian approximation potential (GAP), high-dimensional neural network potentials (HDNNP), moment tensor potentials (MTP), the atomic cluster expansion (ACE) in its linear and nonlinear version, neural equivariant interatomic potentials (NequIP), Allegro, and MACE. We find that nonlinear ACE and the equivariant, message-passing graph neural networks NequIP and MACE form the Pareto front in the accuracy vs. computational cost trade-off. In case of the Al-Cu-Zr system we find that MACE and Allegro offer the highest accuracy, while NequIP outperforms them for Si-O. Furthermore, GPUs can massively accelerate the MLIPs, bringing them on par with and even ahead of non-accelerated classical interatomic potentials (IPs) with regards to accessible timescales. Finally, we explore the extrapolation behavior of the corresponding potentials, probe the smoothness of the potential energy surfaces, and finally estimate the user friendliness of the corresponding fitting codes and molecular dynamics interfaces.

cond-mat.mtrl-sci↗

arXiv2024

A defect-chemistry-informed phase-field model of grain growth in oxide ceramics: application to Fe-doped SrTiO3

Dopants can significantly affect the properties of oxide ceramics through their impact on the property-determined microstructure characteristics such as grain boundary (GB) segregation, space charge layer formation in the GB vicinity, and the grain growth deviating from normal patterns. To support the rational design of oxide ceramics, we propose a defect-chemistry-informed phase-field grain growth model to simulate the microstructure evolution of oxide ceramics. It fully respects the defect-chemistry theory by accounting for the distinct segregation energies and available site densities of charged point defects (oxygen vacancies and acceptor dopants) in both the grain interior and boundaries, and it considers the competing kinetics of defect diffusion and GB movement. The proposed phase-field model is benchmarked against well-known bicrystal models, including the Mott-Schottky and Gouy-Chapman models. Various simulation results are presented to reveal the effect of different defect-chemistry parameters on the space charge layer formation and key microstructural aspects. In particular, simulation results confirm that the solute drag effect alone can lead to skewed grain size distribution that do not follow the log-normal distribution, without any contribution from grain misorientation and other anisotropy. Interestingly, simulations also demonstrate that grain boundary potentials can vary substantially: GBs of larger grains tend to have lower potentials than those of smaller grains. Such heterogeneous GB potential distribution may inspire a new material optimization strategy through microstructure design. This study provides a comprehensive framework for defect-chemistry-consistent investigations of microstructure evolution in polycrystalline oxide ceramics, offering fundamental insights into microscopic processes during critical manufacturing stages.

cond-mat.mtrl-sci↗

arXiv2024

Understanding phase transitions of $\alpha$-quartz under dynamic compression conditions by machine-learning driven atomistic simulations

Characteristic shock effects in silica serve as a key indicator of historical impacts at geological sites. Despite this geological significance, atomistic details of structural transformations under high pressure and shock compression remain poorly understood. This ambiguity is evidenced by conflicting experimental observations of both amorphization and crystallization transitions. Utilizing a newly developed machine-learning interatomic potential, we examine the response of $\alpha$-quartz to shock compression with a peak pressure of 60 GPa over nano-second timescales. We initially observe amorphization before recrystallization into a d-NiAs-structured silica with disorder on the silicon sublattice, accompanied by the formation of domains with partial order of silicon. Investigating a variety of strain conditions enables us to identify the non-hydrostatic stress and strain states that allow the direct diffusionless formation of rosiaite-structured silica.

cond-mat.mtrl-sci↗

arXiv2024

Crystal structure identification with 3D convolutional neural networks with application to high-pressure phase transitions in SiO$_2$

Efficient, reliable and easy-to-use structure recognition of atomic environments is essential for the analysis of atomic scale computer simulations. In this work, we train two neuronal network (NN) architectures, namely PointNet and dynamic graph convolutional NN (DG-CNN) using different hyperparameters and training regimes to assess their performance in structure identification tasks of atomistic structure data. We show benchmarks on simple crystal structures, where we can compare against established methods. The approach is subsequently extended to structurally more complex SiO$_2$ phases. By making use of this structure recognition tool, we are able to achieve a deeper understanding of the crystallization process in amorphous SiO$_2$ under shock compression. Lastly, we show how the NN based structure identification workflows can be integrated into OVITO using its python interface.

cond-mat.mtrl-sci↗

arXiv2024

Structure-property relations of silicon oxycarbides studied using a machine learning interatomic potential

Silicon oxycarbides show outstanding versatility due to their highly tunable composition and microstructure. Consequently, a key challenge is a thorough knowledge of structure-property relations in the system. In this work, we fit an atomic cluster expansion potential to a set of actively learned DFT training data spanning a wide configurational space. We demonstrate the ability of the potential to produce realistic amorphous structures and rationalize the formation of different morphologies of the turbostratic free carbon phase. Finally, we relate the materials stiffness to its composition and microstructure, finding a delicate dependence on Si-C bonds that contradicts commonly assumed relations to the free carbon phase.

cond-mat.mtrl-sci↗

arXiv2024

From electrons to phase diagrams with classical and machine learning potentials: automated workflows for materials science with pyiron

We present a comprehensive and user-friendly framework built upon the pyiron integrated development environment (IDE), enabling researchers to perform the entire Machine Learning Potential (MLP) development cycle consisting of (i) creating systematic DFT databases, (ii) fitting the Density Functional Theory (DFT) data to empirical potentials or MLPs, and (iii) validating the potentials in a largely automatic approach. The power and performance of this framework are demonstrated for three conceptually very different classes of interatomic potentials: an empirical potential (embedded atom method - EAM), neural networks (high-dimensional neural network potentials - HDNNP) and expansions in basis sets (atomic cluster expansion - ACE). As an advanced example for validation and application, we show the computation of a binary composition-temperature phase diagram for Al-Li, a technologically important lightweight alloy system with applications in the aerospace industry.

cond-mat.mtrl-sci↗

arXiv2023

Modelling atomic and nanoscale structure in the silicon-oxygen system through active machine learning

Silicon-oxygen compounds are among the most important ones in the natural sciences, occurring as building blocks in minerals and being used in semiconductors and catalysis. Beyond the well known silicon dioxide, there are phases with different stoichiometric composition and nanostructured composites. One of the key challenges in understanding the Si-O system is therefore to accurately account for its nanoscale heterogeneity beyond the length scale of individual atoms. Here we show that a unified computational description of the full Si-O system is indeed possible, based on atomistic machine learning coupled to an active-learning workflow. We showcase applications to very-high-pressure silica, to surfaces and aerogels, and to the structure of amorphous silicon monoxide. In a wider context, our work illustrates how structural complexity in functional materials beyond the atomic and few-nanometre length scales can be captured with active machine learning.

cond-mat.mtrl-sci↗

arXiv2023

Tailoring magnetic hysteresis of Fe-Ni permalloy by additive manufacturing: Multiphysics-multiscale simulations of process-property relationships

Designing the microstructure of Fe-Ni permalloy by additive manufacturing (AM) opens new avenues to tailor the materials' magnetic properties. Yet, AM-produced parts suffer from spatially inhomogeneous thermal-mechanical and magnetic responses, which are less investigated in terms of process simulation and modeling schemes. Here we present a powder-resolved multiphysics-multiscale simulation scheme for describing magnetic hysteresis in materials produced via AM. The underlying physical processes are explicitly considered, including the coupled thermal-structural evolution, chemical order-disorder transitions, and associated thermo-elasto-plastic behaviors. The residual stress is identified as the key thread in connecting the physical processes and in-process phenomena across scales. By employing this scheme, we investigate the dependence of the fusion zone size, the residual stress and plastic strain, and the magnetic hysteresis of AM-produced Fe21.5Ni78.5 permalloy on beam power and scan speed. Simulation results also suggest a phenomenological relation between magnetic coercivity and average residual stress, which can guide the magnetic hysteresis design of soft magnetic materials by choosing appropriate AM-process parameters.

cond-mat.mtrl-sci↗

arXiv2022

Mechanical Characterization of Superelastic NiTi Nanofoams by Molecular Dynamics Simulations

Nanoporous metals or nanofoams are a promising material class that is considered for sensing, actuation, and catalysis. To date, they mostly based on simple noble metals such as nanoporous gold, which exhibit peculiar stress-strain response different from the bulk material. At the same time bulk alloys such as NiTi feature a reversible martensitic phase transition giving rise to interesting shape memory and superelastic effects. Combining the rich mechanics of NiTi with the geometrical features of a nanofoam is expected to improve the mechanical performance of this material. In this atomistic study we explore the behavior of a NiTi nanofoam at varying temperature and its reaction to (cyclic) compression. Using molecular dynamics simulations we track the microscopic processes enabling reversible deformation as well as the mechanical failure mechanisms of the NiTi nanofoam.

cond-mat.mtrl-sci↗