Dr. Tilmann Hickel

Computational Materials Design
Max-Planck-Institut für Eisenforschung


  • Ab initio based models for temperature-dependent magnetochemical interplay in bcc Fe-Mn alloys
    Schneider, A. and Fu, C.-C. and Waseda, O. and Barreteau, C. and Hickel, T.
    Physical Review B 103 (2021)
    Body-centered cubic (bcc) Fe-Mn systems are known to exhibit a complex and atypical magnetic behavior from both experiments and 0 K electronic-structure calculations, which is due to the half-filled 3d band of Mn. We propose effective interaction models for these alloys, which contain both atomic-spin and chemical variables. They were parameterized on a set of key density functional theory (DFT) data, with the inclusion of noncollinear magnetic configurations being indispensable. Two distinct approaches, namely a knowledge-driven and a machine-learning approach have been employed for the fitting. Employing these models in atomic Monte Carlo simulations enables the prediction of magnetic and thermodynamic properties of the Fe-Mn alloys, and their coupling, as functions of temperature. This includes the decrease of Curie temperature with increasing Mn concentration, the temperature evolution of the mixing enthalpy, and its correlation with the alloy magnetization. Also, going beyond the defect-free systems, we determined the binding free energy between a vacancy and a Mn atom, which is a key parameter controlling the atomic transport in Fe-Mn alloys. © 2021 American Physical Society.
    view abstract10.1103/PhysRevB.103.024421
  • Atomic relaxation around defects in magnetically disordered materials computed by atomic spin constraints within an efficient Lagrange formalism
    Hegde, O. and Grabowski, M. and Zhang, X. and Waseda, O. and Hickel, T. and Freysoldt, C. and Neugebauer, J.
    Physical Review B 102 (2020)
    Lattice and magnetic degrees of freedom are strongly coupled in magnetic materials. We propose a consistent first-principles framework to explore the joint configurational space. For this, we define atomic spin moments from the projector augmented-wave formalism of density-functional theory and control them via Lagrangian constraints. We demonstrate our approach for vacancy formation and migration in collinear paramagnetic bcc iron by implementing a relaxation scheme based on spin-space averaged forces (SSA relaxation). Based on these results we discuss the impact of the magnetic state on vacancy formation energies, migration barriers, and relaxations. © 2020 authors. Published by the American Physical Society.
    view abstract10.1103/PhysRevB.102.144101
  • Atomic scale configuration of planar defects in the Nb-rich C14 Laves phase NbFe2
    Šlapáková, M. and Zendegani, A. and Liebscher, C.H. and Hickel, T. and Neugebauer, J. and Hammerschmidt, T. and Ormeci, A. and Grin, J. and Dehm, G. and Kumar, K.S. and Stein, F.
    Acta Materialia 183 (2020)
    Laves phases belong to the group of tetrahedrally close-packed intermetallic phases, and their crystal structure can be described by discrete layer arrangements. They often possess extended homogeneity ranges and the general notion is that deviations from stoichiometry are accommodated by anti-site atoms or vacancies. The present work shows that excess Nb atoms in a Nb-rich NbFe2 C14 Laves phase can also be incorporated in various types of planar defects. Aberration-corrected scanning transmission electron microscopy and density functional theory calculations are employed to characterize the atomic configuration of these defects and to establish stability criteria for them. The planar defects can be categorized as extended or confined ones. The extended defects lie parallel to the basal plane of the surrounding C14 Laves phase and are fully coherent. They contain the characteristic Zr4Al3-type (O) units found in the neighboring Nb6Fe7 µ phase. An analysis of the chemical bonding reveals that the local reduction of the charge transfer is a possible reason for the preference of this atomic arrangement. However, the overall layer stacking deviates from that of the perfect µ phase. The ab initio calculations establish why these exceptionally layered defects can be more stable configurations than coherent nano-precipitates of the perfect µ phase. The confined defects are observed with pyramidal and basal habit planes. The pyramidal defect is only ~1 nm thick and resembles the perfect µ phase. In contrast, the confined basal defect can be regarded as only one single O unit and it appears as if the stacking sequence is disrupted. This configuration is confirmed by ab initio calculations to be metastable. © 2019
    view abstract10.1016/j.actamat.2019.11.004
  • Diffusion, defects and understanding the growth of a multicomponent interdiffusion zone between Pt-modified B2 NiAl bond coat and single crystal superalloy
    Esakkiraja, N. and Gupta, A. and Jayaram, V. and Hickel, T. and Divinski, S.V. and Paul, A.
    Acta Materialia 195 (2020)
    Composition-dependent diffusion coefficients are determined in B2-Ni(CoPt)Al system following the pseudo-binary and pseudo-ternary diffusion couple methods, which would not be possible otherwise in a quaternary inhomogeneous material fulfilling the conditions to solve the equations developed based on the Onsager formalism. The end-member compositions to produce ideal/near-ideal diffusion profiles are chosen based on thermodynamic details. The pseudo-binary interdiffusion coefficients of Ni and Al decrease in the presence of Co but increase in the presence of Pt. The pseudo-ternary interdiffusion coefficients indicate that the main interdiffusion coefficients increase significantly in the presence of Pt. Marginal changes of the cross interdiffusion coefficients substantiate a minor change of the diffusional interactions between the components. The thermodynamic driving forces show opposite trends with respect to composition as compared to the changes of the interdiffusion coefficients advocating a dominating role of the Pt(Co)-induced modifications of point defect concentrations. DFT-based calculations revealed that Pt alloying increases the Ni vacancy concentration and decreases the activation energy for the triple defect diffusion mechanism. These findings explain the increase in the thickness of the interdiffusion zone between the B2-Ni(Pt)Al bond coat and the single crystal superalloy René N5 because of Pt addition. Furthermore, the EPMA and TEM analyses reveal the growth of refractory elements-enriched precipitates. © 2020 Acta Materialia Inc.
    view abstract10.1016/j.actamat.2020.04.016
  • Impact of magnetism on the phase stability of rare-earth based hard magnetic materials
    Sözen, H.İ. and Hickel, T. and Neugebauer, J.
    Calphad: Computer Coupling of Phase Diagrams and Thermochemistry 68 (2020)
    In recent years, quantum-mechanically guided materials design has been used to identify candidate hard magnetic materials with a reduced content of rare earth elements. The focus of these studies was on optimal magnetic properties. In the present work we address the issue of thermodynamic stability of such materials. As prototype system we consider CeFe11Ti and focus on the impact of magnetism on the free energy. To this end, we use the magnetic model suggested by Gerhard Inden as a reference. The performance of this model is compared to Monte Carlo simulations for the magnetic entropy contribution. We conclude that despite the empirical nature of the Inden model, it provides a surprisingly accurate description of the magnetic contribution. Based on this approach we are able to faithfully predict the critical temperature for the decomposition of CeFe11Ti into competing Laves phases. We further show that the Inden model can be improved if the reduction of the magnetic moment at finite temperatures is taken into account. This is demonstrated for the hard magnetic phase Nd2Fe14B. In addition, the impact of magnetism on the lattice vibrations of relevant phases in the Ce–Fe–Ti system is analyzed. © 2019 Elsevier Ltd
    view abstract10.1016/j.calphad.2019.101731
  • Mechanism of collective interstitial ordering in Fe–C alloys
    Zhang, X. and Wang, H. and Hickel, T. and Rogal, J. and Li, Y. and Neugebauer, J.
    Nature Materials 19 (2020)
    Collective interstitial ordering is at the core of martensite formation in Fe–C-based alloys, laying the foundation for high-strength steels. Even though this ordering has been studied extensively for more than a century, some fundamental mechanisms remain elusive. Here, we show the unexpected effects of two correlated phenomena on the ordering mechanism: anharmonicity and segregation. The local anharmonicity in the strain fields induced by interstitials substantially reduces the critical concentration for interstitial ordering, up to a factor of three. Further, the competition between interstitial ordering and segregation results in an effective decrease of interstitial segregation into extended defects for high interstitial concentrations. The mechanism and corresponding impact on interstitial ordering identified here enrich the theory of phase transitions in materials and constitute a crucial step in the design of ultra-high-performance alloys. © 2020, The Author(s), under exclusive licence to Springer Nature Limited.
    view abstract10.1038/s41563-020-0677-9
  • Phonons in magnetically disordered materials: Magnetic versus phononic time scales
    Dutta, B. and Körmann, F. and Ghosh, S. and Sanyal, B. and Neugebauer, J. and Hickel, T.
    Physical Review B 101 (2020)
    The lattice dynamics in magnetic materials, such as Fe depends on the degree of disorder of the atomic magnetic moments and the time scale of spin fluctuations. Using first-principles methods, we have studied this effect by determining the force constant matrix in two limits: (i) When spin fluctuations are much faster than the atom vibrations, their combined impact is captured by a spin-space averaged force constant matrix, (ii) when individual spin fluctuations are sufficiently slow to scatter the phonon modes, the itinerant coherent potential approximation with spin-pair resolved force constants (i.e., φ↑↑,φ↓↓, and φ↑↓) is employed in this paper. The physical consequences for the vibrational spectral functions are analyzed by systematically modifying the input parameters (magnetization and ratio of force constants betweens atoms with equal and opposite spin directions) and by deriving them for the prototype material system bcc Fe from first-principles calculations. In the paramagnetic regime, the two limits yield identical phonon spectra. Below the Curie temperature, however, there are regions in the parametric study that show qualitative differences, including a broadening of the phonon peaks. For bcc Fe, however, the quantitative modifications of phonon frequencies turn out to be small. © 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
    view abstract10.1103/PhysRevB.101.094201
  • Unfolding the complexity of phonon quasi-particle physics in disordered materials
    Mu, S. and Olsen, R.J. and Dutta, B. and Lindsay, L. and Samolyuk, G.D. and Berlijn, T. and Specht, E.D. and Jin, K. and Bei, H. and Hickel, T. and Larson, B.C. and Stocks, G.M.
    npj Computational Materials 6 (2020)
    The concept of quasi-particles forms the theoretical basis of our microscopic understanding of emergent phenomena associated with quantum-mechanical many-body interactions. However, the quasi-particle theory in disordered materials has proven difficult, resulting in the predominance of mean-field solutions. Here, we report first-principles phonon calculations and inelastic X-ray and neutron-scattering measurements on equiatomic alloys (NiCo, NiFe, AgPd, and NiFeCo) with force-constant dominant disorder—confronting a key 50-year-old assumption in the Hamiltonian of all mean-field quasi-particle solutions for off-diagonal disorder. Our results have revealed the presence of a large, and heretofore unrecognized, impact of local chemical environments on the distribution of the species-pair-resolved force-constant disorder that can dominate phonon scattering. This discovery not only identifies a critical analysis issue that has broad implications for other elementary excitations, such as magnons and skyrmions in magnetic alloys, but also provides an important tool for the design of materials with ultralow thermal conductivities. © 2020, The Author(s).
    view abstract10.1038/s41524-020-0271-3
  • Ab initio phase stabilities of Ce-based hard magnetic materials and comparison with experimental phase diagrams
    Sözen, H.Ä. and Ener, S. and MacCari, F. and Skokov, K.P. and Gutfleisch, O. and Körmann, F. and Neugebauer, J. and Hickel, T.
    Physical Review Materials 3 (2019)
    Recent developments in electrical transportation and renewable energies have significantly increased the demand of hard magnetic materials with a reduced critical rare-earth content, but with properties comparable to (Nd,Dy)-Fe-B permanent magnets. Though promising alternative compositions have been identified in high-throughput screenings, the thermodynamic stability of these phases against decomposition into structures with much less favorable magnetic properties is often unclear. In the case of Ce-Fe-Ti alloys, we have used finite temperature ab initio methods to provide this missing information. Employing state-of-the-art approaches for vibrational, electronic, and magnetic entropy contributions, the Helmholtz free energy, F(T,V), is calculated for the desired hard magnetic CeFe11Ti phase and all relevant competing phases. The latter have been confirmed experimentally by employing reactive crucible melting (RCM) and energy-dispersive x-ray spectroscopy (EDS). Our ab initio based free energy calculations reveal that the presence of the CeFe2 Laves phase suppresses the formation of CeFe11Ti up to 700 K. The result is in agreement with RCM, in which CeFe11Ti is only observed above 1000 K, while the CeFe2 and Ce2Fe17 phases are stable at lower temperatures. © 2019 American Physical Society.
    view abstract10.1103/PhysRevMaterials.3.084407
  • An insight into using DFT data for Calphad modeling of solid phases in the third generation of Calphad databases, a case study for Al
    Bigdeli, S. and Zhu, L.-F. and Glensk, A. and Grabowski, B. and Lindahl, B. and Hickel, T. and Selleby, M.
    Calphad: Computer Coupling of Phase Diagrams and Thermochemistry 65 (2019)
    In developing the next generation of Calphad databases, new models are used in which each term contributing to the Gibbs energy has a physical meaning. To continue the development, finite temperature density-functional-theory (DFT) results are used in the present work to discuss and suggest the most applicable and physically based model for Calphad assessments of solid phases above the melting point (the breakpoint for modeling the solid phase in previous assessments). These results are applied to investigate the properties of a solid in the superheated temperature region and to replace the melting temperature as the breakpoint with a more physically based temperature, i.e., where the superheated solid collapses into the liquid. The advantages and limitations of such an approach are presented in terms of a new assessment for unary aluminum. © 2019 Elsevier Ltd
    view abstract10.1016/j.calphad.2019.02.008
  • Phonon Lifetimes throughout the Brillouin Zone at Elevated Temperatures from Experiment and Ab Initio
    Glensk, A. and Grabowski, B. and Hickel, T. and Neugebauer, J. and Neuhaus, J. and Hradil, K. and Petry, W. and Leitner, M.
    Physical review letters 123 (2019)
    We obtain phonon lifetimes in aluminium by inelastic neutron scattering experiments, by ab initio molecular dynamics, and by perturbation theory. At elevated temperatures significant discrepancies are found between experiment and perturbation theory, which disappear when using molecular dynamics due to the inclusion of full anharmonicity and the correct treatment of the multiphonon background. We show that multiple-site interactions are small and that local pairwise anharmonicity dominates phonon-phonon interactions, which permits an efficient computation of phonon lifetimes.
    view abstract10.1103/PhysRevLett.123.235501
  • pyiron: An integrated development environment for computational materials science
    Janssen, J. and Surendralal, S. and Lysogorskiy, Y. and Todorova, M. and Hickel, T. and Drautz, R. and Neugebauer, J.
    Computational Materials Science 163 (2019)
    To support and accelerate the development of simulation protocols in atomistic modelling, we introduce an integrated development environment (IDE) for computational materials science called pyiron (http://pyiron.org). The pyiron IDE combines a web based source code editor, a job management system for build automation, and a hierarchical data management solution. The core components of the pyiron IDE are pyiron objects based on an abstract class, which links application structures such as atomistic structures, projects, jobs, simulation protocols and computing resources with persistent storage and an interactive user environment. The simulation protocols within the pyiron IDE are constructed using the Python programming language. To highlight key concepts of this tool as well as to demonstrate its ability to simplify the implementation and testing of simulation protocols we discuss two applications. In these examples we show how pyiron supports the whole life cycle of a typical simulation, seamlessly combines ab initio with empirical potential calculations, and how complex feedback loops can be implemented. While originally developed with focus on ab initio thermodynamics simulations, the concepts and implementation of pyiron are general thus allowing to employ it for a wide range of simulation topics. © 2019 The Authors
    view abstract10.1016/j.commatsci.2018.07.043
  • Ab initio simulation of hydrogen-induced decohesion in cementite-containing microstructures
    McEniry, E.J. and Hickel, T. and Neugebauer, J.
    Acta Materialia 150 (2018)
    In high-strength carbon steels suitable for use in the automotive industry, hydrogen embrittlement (HE) is a potential barrier to the widespread application of these materials. The behaviour of hydrogen within the most prevalent carbide, namely cementite, has been investigated via ab initio simulation. In order to examine possible decohesion effects of hydrogen on carbon steels, the binding and diffusion of hydrogen at the interface between ferrite and cementite has been examined. In order to understand the effect of hydrogen on the mechanical properties of carbon steels, simulated ab initio tensile tests have been performed on the ferrite-cementite bicrystal. The results of the tensile tests can be combined with thermodynamic considerations in order to obtain the expected hydrogen concentrations at such ferrite-cementite phase boundaries. We find that the effect of hydrogen on the cohesion of the phase boundary may be significant, even when the bulk hydrogen concentration is low. © 2018 Acta Materialia Inc.
    view abstract10.1016/j.actamat.2018.03.005
  • Anomalous Phonon Lifetime Shortening in Paramagnetic CrN Caused by Spin-Lattice Coupling: A Combined Spin and Ab Initio Molecular Dynamics Study
    Stockem, I. and Bergman, A. and Glensk, A. and Hickel, T. and Körmann, F. and Grabowski, B. and Neugebauer, J. and Alling, B.
    Physical Review Letters 121 (2018)
    We study the mutual coupling of spin fluctuations and lattice vibrations in paramagnetic CrN by combining atomistic spin dynamics and ab initio molecular dynamics. The two degrees of freedom are dynamically coupled, leading to nonadiabatic effects. Those effects suppress the phonon lifetimes at low temperature compared to an adiabatic approach. The dynamic coupling identified here provides an explanation for the experimentally observed unexpected temperature dependence of the thermal conductivity of magnetic semiconductors above the magnetic ordering temperature. © 2018 American Physical Society.
    view abstract10.1103/PhysRevLett.121.125902
  • Calculating free energies of point defects from ab initio
    Zhang, X. and Grabowski, B. and Hickel, T. and Neugebauer, J.
    Computational Materials Science 148 (2018)
    The formation and lifetime of point defects is governed by an interplay of kinetics and thermodynamic stability. To evaluate the stability under process conditions, empirical potentials and ab initio calculations at T=0K are often not sufficient. Therefore, various concepts to determine the full temperature dependence of the free energy of point defects with ab initio accuracy are reviewed. Examples for the importance of accurately describing defect properties include the stabilization of vacancies by impurities and the non-Arrhenius behaviour of vacancy formation energies due to anharmonic lattice vibrations. © 2018
    view abstract10.1016/j.commatsci.2018.02.042
  • Coupling Phenomena in Magnetocaloric Materials
    Waske, A. and Dutta, B. and Teichert, N. and Weise, B. and Shayanfar, N. and Becker, A. and Hütten, A. and Hickel, T.
    Energy Technology 6 (2018)
    Strong coupling effects in magnetocaloric materials are the key factor to achieve a large magnetic entropy change. Combining insights from experiments and ab initio calculations, we review relevant coupling phenomena, including atomic coupling, stress coupling, and magnetostatic coupling. For the investigations on atomic coupling, we have used Heusler compounds as a flexible model system. Stress coupling occurs in first-order magnetocaloric materials, which exhibit a structural transformation or volume change together with the magnetic transition. Magnetostatic coupling has been experimentally demonstrated in magnetocaloric particles and fragment ensembles. Based on the achieved insights, we have demonstrated that the materials properties can be tailored to achieve optimized magnetocaloric performance for cooling applications. © 2018 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.
    view abstract10.1002/ente.201800163
  • Impact of Co and Fe Doping on the Martensitic Transformation and the Magnetic Properties in Ni-Mn-Based Heusler Alloys
    Dutta, B. and Körmann, F. and Hickel, T. and Neugebauer, J.
    Physica Status Solidi (B) Basic Research 255 (2018)
    Doping with Co and Fe is a promising strategy to enhance the performance of Ni-Mn-based magnetocaloric materials. We investigate here the impact of these two elements on the magnetic properties and the martensitic transformations in Mn-rich Ni-Mn-Al Heusler alloy. Based on ab initio ground-state energies, we explain the martensitic transformation temperatures in these alloys. The magnetic ground states of the austenite and the martensite phases are discussed on the basis of magnetic exchange parameters. A thorough comparison of the transition temperatures and the change in saturation moments during martensitic transformation brings into light the relative potential of the two substitutional elements for future applications. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    view abstract10.1002/pssb.201700455
  • Multiscale modelling of hydrogen transport and segregation in polycrystalline steels
    Hüter, C. and Shanthraj, P. and McEniry, E. and Spatschek, R. and Hickel, T. and Tehranchi, A. and Guo, X. and Roters, F.
    Metals 8 (2018)
    A key issue in understanding and effectively managing hydrogen embrittlement in complex alloys is identifying and exploiting the critical role of the various defects involved. A chemo-mechanical model for hydrogen diffusion is developed taking into account stress gradients in the material, as well as microstructural trapping sites such as grain boundaries and dislocations. In particular, the energetic parameters used in this coupled approach are determined from ab initio calculations. Complementary experimental investigations that are presented show that a numerical approach capable of massive scale-bridging up to the macroscale is required. Due to the wide range of length scales accounted for, we apply homogenisation schemes for the hydrogen concentration to reach simulation dimensions comparable to metallurgical process scales. Via a representative volume element approach, an ab initio based scale bridging description of dislocation-induced hydrogen aggregation is easily accessible. When we extend the representative volume approach to also include an analytical approximation for the ab initio based description of grain boundaries, we find conceptual limitations that hinder a quantitative comparison to experimental data in the current stage. Based on this understanding, the development of improved strategies for further efficient scale bridging approaches is foreseen. © 2018 by the authors. Licensee MDPI, Basel, Switzerland.
    view abstract10.3390/met8060430
  • Precipitate-induced nonlinearities of diffusion along grain boundaries in Al-based alloys
    Gupta, A. and Kulitcki, V. and Kavakbasi, B.T. and Buranova, Y. and Neugebauer, J. and Wilde, G. and Hickel, T. and Divinski, S.V.
    Physical Review Materials 2 (2018)
    The formation of precipitates in metallic alloys is determined by a two-way chemomechanical coupling. While the dependence on solute diffusion is apparent, the opposite effect, namely the impact of nanoprecipitates on the diffusion, is highlighted in the present paper. Using severe plastic deformation and post-deformation annealing of an Al-based alloy, different microstructures and sizes of Al3Sc-based nanoprecipitates are produced. The enhanced diffusion along grain boundaries in the so-called C-type kinetic regime is used as a probe to ensure a well-defined distance of the diffusion path from the precipitates and to prohibit their evolution during measurements. Tracer measurements with the radioisotope Co57 reveal a remarkable nonmonotonic dependence of the diffusion rates on the annealing temperature. It has been fully explained by an ab initio informed phenomenological model that considers the elastic stress around the coherent and noncoherent precipitates. © 2018 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
    view abstract10.1103/PhysRevMaterials.2.073801
  • Role of disorder when upscaling magnetocaloric Ni-Co-Mn-Al Heusler alloys from thin films to ribbons
    Weise, B. and Dutta, B. and Teichert, N. and Hütten, A. and Hickel, T. and Waske, A.
    Scientific Reports 8 (2018)
    Research in functional magnetic materials often employs thin films as model systems for finding new chemical compositions with promising properties. However, the scale-up of thin films towards bulk-like structures is challenging, since the material synthesis conditions are entirely different for thin films and e.g. rapid quenching methods. As one of the consequences, the type and degree of order in thin films and melt-spun ribbons are usually different, leading to different magnetic properties. In this work, using the example of magnetocaloric Ni-Co-Mn-Al melt-spun ribbons and thin films, we show that the excellent functional properties of the films can be reproduced also in ribbons, if an appropriate heat treatment is applied, that installs the right degree of order in the ribbons. We show that some chemical disorder is needed to get a pronounced and sharp martensitic transition. Increasing the order with annealing improves the magnetic properties only up to a point where selected types of disorder survive, which in turn compromise the magnetic properties. These findings allow us to understand the impact of the type and degree of disorder on the functional properties, paving the way for a faster transfer of combinatorial thin film research towards bulk-like materials for magnetic Heusler alloys. © 2018 The Author(s).
    view abstract10.1038/s41598-018-27428-8
  • Temperature dependence of the stacking-fault Gibbs energy for Al, Cu, and Ni
    Zhang, X. and Grabowski, B. and Körmann, F. and Ruban, A.V. and Gong, Y. and Reed, R.C. and Hickel, T. and Neugebauer, J.
    Physical Review B 98 (2018)
    The temperature-dependent intrinsic stacking fault Gibbs energy is computed based on highly converged density-functional-theory (DFT) calculations for the three prototype face-centered cubic metals Al, Cu, and Ni. All relevant temperature-dependent contributions are considered including electronic, vibrational, magnetic, and explicit anharmonic Gibbs energy contributions as well as coupling terms employing state-of-the-art statistical sampling techniques. Particular emphasis is put on a careful comparison of different theoretical concepts to derive the stacking fault energy such as the axial-next-nearest-neighbor-Ising (ANNNI) model or the vacuum-slab approach. Our theoretical results are compared with an extensive set of previous theoretical and experimental data. Large uncertainties in the experimental data highlight the necessity of complementary parameter-free calculations. Specifically, the temperature dependence is experimentally unknown and poorly described by thermodynamic databases. Whereas calphad derived data shows an increase of the stacking fault energy with temperature for two of the systems (Cu and Ni), our results predict a decrease for all studied systems. For Ni, the temperature induced change is in fact so strong that in the temperature interval relevant for super-alloy applications the stacking fault energy falls below one third of the low temperature value. Such large changes clearly call for a revision of the stacking fault energy when modeling or designing alloys based on such elements. © 2018 authors.
    view abstract10.1103/PhysRevB.98.224106
  • Tetragonal fcc-Fe induced by κ -carbide precipitates: Atomic scale insights from correlative electron microscopy, atom probe tomography, and density functional theory
    Liebscher, C.H. and Yao, M. and Dey, P. and Lipińska-Chwalek, M. and Berkels, B. and Gault, B. and Hickel, T. and Herbig, M. and Mayer, J. and Neugebauer, J. and Raabe, D. and Dehm, G. and Scheu, C.
    Physical Review Materials 2 (2018)
    Correlative scanning transmission electron microscopy, atom probe tomography, and density functional theory calculations resolve the correlation between elastic strain fields and local impurity concentrations on the atomic scale. The correlative approach is applied to coherent interfaces in a κ-carbide strengthened low-density steel and establishes a tetragonal distortion of fcc-Fe. An interfacial roughness of ∼1nm and a localized carbon concentration gradient extending over ∼2-3nm is revealed, which originates from the mechano-chemical coupling between local strain and composition. © 2018 American Physical Society.
    view abstract10.1103/PhysRevMaterials.2.023804
  • {110} planar faults in strained bcc metals: Origins and implications of a commonly observed artifact of classical potentials
    Möller, J.J. and Mrovec, M. and Bleskov, I. and Neugebauer, J. and Hammerschmidt, T. and Drautz, R. and Elsässer, C. and Hickel, T. and Bitzek, E.
    Physical Review Materials 2 (2018)
    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. © 2018 American Physical Society.
    view abstract10.1103/PhysRevMaterials.2.093606
  • Ab initio explanation of disorder and off-stoichiometry in Fe-Mn-Al-C κ carbides
    Dey, P. and Nazarov, R. and Dutta, B. and Yao, M. and Herbig, M. and Friák, M. and Hickel, T. and Raabe, D. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 95 (2017)
    Carbides play a central role for the strength and ductility in many materials. Simulating the impact of these precipitates on the mechanical performance requires knowledge about their atomic configuration. In particular, the C content is often observed to substantially deviate from the ideal stoichiometric composition. In this work, we focus on Fe-Mn-Al-C steels, for which we determined the composition of the nanosized κ carbides (Fe,Mn)3AlC by atom probe tomography in comparison to larger precipitates located in grain boundaries. Combining density functional theory with thermodynamic concepts, we first determine the critical temperatures for the presence of chemical and magnetic disorder in these carbides. Second, the experimentally observed reduction of the C content is explained as a compromise between the gain in chemical energy during partitioning and the elastic strains emerging in coherent microstructures. © 2017 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
    view abstract10.1103/PhysRevB.95.104108
  • Atomic structures of twin boundaries in hexagonal close-packed metallic crystals with particular focus on Mg
    Pei, Z. and Zhang, X. and Hickel, T. and Friák, M. and Sandlöbes, S. and Dutta, B. and Neugebauer, J.
    npj Computational Materials 3 (2017)
    We have investigated twin boundaries in double-lattice hexagonal close-packed metallic materials, focusing on their atomic geometry. Combining accurate ab-initio methods and large-scale atomistic simulations we address the following two fundamental questions: (i) What are the possible intrinsic twin boundary structures in hcp crystals? (ii) Are these structures stable against small distortions? In order to help end a decade-long controversy over the experimental observations of the atomic structures of twin boundaries, we have determined the energetics, spectra, and transition mechanisms of the twin boundaries. Our results confirm that the mechanical stability controls structures which are observed. © 2017 The Author(s).
    view abstract10.1038/s41524-017-0010-6
  • Crystal structures of Fe4C vs. Fe4N analysed by DFT calculations: Fcc-based interstitial superstructures explored
    Leineweber, A. and Hickel, T. and Azimi-Manavi, B. and Maisel, S.B.
    Acta Materialia 140 (2017)
    Knowledge of the thermodynamic and structural properties of iron carbide and nitride phases is crucial for understanding phase transformations and related microstructure formation in steels. While the existence and crystal structure of the primitive cubic fcc-based γ′-Fe4N1-z phase is experimentally well-established, there is no consensus in contemporary literature about an analogous γ′-Fe4C compound. Here, we present DFT calculations for all fcc-like Fe4C and Fe4N superstructures with up to two formula units per primitive unit cell, providing energy values and the relaxed atomic structures, which were analysed mathematically and by visual inspection of the atomic arrangement. Notably, all considered Fe4C and Fe4N superstructures are metastable with respect to α-Fe and cementite-Fe3C/ε-Fe3N. Unsurprisingly, we find the well-known γ′ compound's crystal structure to be most favourable among these metastable Fe4N superstructures. However, we find the equivalent superstructure to be quite unfavourable in Fe4C. The most favourable among these metastable Fe4C structures are stabilised by a partial Bain-like distortion into the direction of a body-centred cubic arrangement of Fe atoms. This makes the particular C-ordering interesting for comparison with the short-range order in Fe-C martensites. However, even the lowest-energy Fe4C structure releases about 0.056 eV/atom upon decomposition into α + Fe3C, much more than it is the case for Fe4N (0.019 eV/atom). That energy difference is difficult to overcome even at T > 0 K, in agreement with the lack of clear experimental evidence for existence of a Fe4C phase. © 2017 Acta Materialia Inc.
    view abstract10.1016/j.actamat.2017.08.059
  • Effect of Pt substitution on the magnetocrystalline anisotropy of Ni2MnGa: A competition between chemistry and elasticity
    Caron, L. and Dutta, B. and Devi, P. and Ghorbani Zavareh, M. and Hickel, T. and Cabassi, R. and Bolzoni, F. and Fabbrici, S. and Albertini, F. and Felser, C. and Singh, S.
    Physical Review B 96 (2017)
    The magnetocrystalline anisotropy (MAE) of Ni2-xPtxMnGa(0≤x≤0.25) alloys are investigated using the singular point detection technique and density functional theory. A slight reduction in MAE as compared to that of Ni2MnGa is observed due to Pt substitution. The calculated MAE varies almost linearly with the orbital moment anisotropy. A competition between the elastic and the chemical contributions explains the observed trend of the MAE with increasing Pt content. The large MAE in combination with the previously reported increase of the martensitic transition temperature makes these alloys promising candidates for ferromagnetic shape memory applications near room temperature. © 2017 American Physical Society.
    view abstract10.1103/PhysRevB.96.054105
  • Electronic properties, low-energy Hamiltonian, and superconducting instabilities in CaKFe4As4
    Lochner, F. and Ahn, F. and Hickel, T. and Eremin, I.
    Physical Review B 96 (2017)
    We analyze the electronic properties of the recently discovered stoichiometric superconductor CaKFe4As4 by combining an ab initio approach and a projection of the band structure to a low-energy tight-binding Hamiltonian, based on the maximally localized Wannier orbitals of the 3d Fe states. We identify the key symmetries as well as differences and similarities in the electronic structure between CaKFe4As4 and the parent systems CaFe2As2 and KFe2As2. In particular, we find CaKFe4As4 to have a significantly more quasi-two-dimensional electronic structure than the latter systems. Finally, we study the superconducting instabilities in CaKFe4As4 by employing the leading angular harmonics approximation and find two potential A1g-symmetry representations of the superconducting gap to be the dominant instabilities in this system. © 2017 American Physical Society.
    view abstract10.1103/PhysRevB.96.094521
  • Hydrogen behaviour at twist {110} grain boundaries in α-Fe
    McEniry, E.J. and Hickel, T. and Neugebauer, J.
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375 (2017)
    The behaviour of hydrogen at structural defects such as grain boundaries plays a critical role in the phenomenon of hydrogen embrittlement. However, characterization of the energetics and diffusion of hydrogen in the vicinity of such extended defects using conventional ab initio techniques is challenging due to the relatively large system sizes required when dealing with realistic grain boundary geometries. In order to be able to access the required system sizes, as well as high-Throughput testing of a large number of configurations, while remaining within a quantum-mechanical framework, an environmental tight-binding model for the iron-hydrogen system has been developed. The resulting model is applied to study the behaviour of hydrogen at a class of low-energy {110}-Terminated twist grain boundaries in α-Fe. We find that, for particular Σ values within the coincidence site lattice description, the atomic geometry at the interface plane provides extremely favourable trap sites for H, which also possess high escape barriers for diffusion. By contrast, via simulated tensile testing, weakly trapped hydrogen at the interface plane of the bulk-like Σ3 boundary acts as a 'glue' for the boundary, increasing both the energetic barrier and the elongation to rupture. © 2017 The Author(s) Published by the Royal Society. All rights reserved.
    view abstract10.1098/rsta.2016.0402
  • Low-temperature features in the heat capacity of unary metals and intermetallics for the example of bulk aluminum and Al3 Sc
    Gupta, A. and Kavakbasi, B.T. and Dutta, B. and Grabowski, B. and Peterlechner, M. and Hickel, T. and Divinski, S.V. and Wilde, G. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 95 (2017)
    We explore the competition and coupling of vibrational and electronic contributions to the heat capacity of Al and Al3Sc at temperatures below 50 K, combining experimental calorimetry with highly converged finite-temperature density functional theory calculations. We find that semilocal exchange-correlation functionals accurately describe the rich feature set observed for these temperatures, including electron-phonon coupling. Using different representations of the heat capacity, we are therefore able to identify and explain deviations from the Debye behavior in the low-temperature limit and in the temperature regime 30-50 K as well as the reduction of these features due to the addition of Sc. © 2017 authors. Published by the American Physical Society.
    view abstract10.1103/PhysRevB.95.094307
  • Operando Phonon Studies of the Protonation Mechanism in Highly Active Hydrogen Evolution Reaction Pentlandite Catalysts
    Zegkinoglou, I. and Zendegani, A. and Sinev, I. and Kunze, S. and Mistry, H. and Jeon, H.S. and Zhao, J. and Hu, M.Y. and Alp, E.E. and Piontek, S. and Smialkowski, M. and Apfel, U.-P. and Körmann, F. and Neugebauer, J. and Hickel, T. and Roldan Cuenya, B.
    Journal of the American Chemical Society 139 (2017)
    Synthetic pentlandite (Fe4.5Ni4.5S8) is a promising electrocatalyst for hydrogen evolution, demonstrating high current densities, low overpotential, and remarkable stability in bulk form. The depletion of sulfur from the surface of this catalyst during the electrochemical reaction has been proposed to be beneficial for its catalytic performance, but the role of sulfur vacancies and the mechanism determining the reaction kinetics are still unknown. We have performed electrochemical operando studies of the vibrational dynamics of pentlandite under hydrogen evolution reaction conditions using 57Fe nuclear resonant inelastic X-ray scattering. Comparing the measured Fe partial vibrational density of states with density functional theory calculations, we have demonstrated that hydrogen atoms preferentially occupy substitutional positions replacing pre-existing sulfur vacancies. Once all vacancies are filled, the protonation proceeds interstitially, which slows down the reaction. Our results highlight the beneficial role of sulfur vacancies in the electrocatalytic performance of pentlandite and give insights into the hydrogen adsorption mechanism during the reaction. © 2017 American Chemical Society.
    view abstract10.1021/jacs.7b07902
  • Origin of Structural Modulations in Ultrathin Fe Films on Cu(001)
    Zhang, X. and Hickel, T. and Rogal, J. and Neugebauer, J.
    Physical Review Letters 118 (2017)
    Employing ab initio calculations we demonstrate that the complex structural modulations experimentally observed in ultrathin Fe films on Cu(001) originate from Fe bulk phases that arise under extreme deformations. Specifically, we show that the structural modulations correspond to the motifs observed when transforming fcc Fe to bcc Fe in the Pitsch orientation relationship [(001)fcc||(110)bcc]. The observed structural equivalence between surface and unstable bulk structures naturally explains the experimentally reported magnetic and structural transitions when going from low (two to four MLs) to intermediate (four to ten MLs) film coverages. © 2017 American Physical Society.
    view abstract10.1103/PhysRevLett.118.236101
  • Phase-field study of ripening and rearrangement of precipitates under chemomechanical coupling
    Schwarze, C. and Gupta, A. and Hickel, T. and Darvishi Kamachali, R.
    Physical Review B 95 (2017)
    We investigate the evolution of large number of δ′ coherent precipitates from a supersaturated Al-8 at.% Li alloy using large-scale phase-field simulations. A chemomechanical cross-coupling between mechanical relaxation and diffusion is taken into account by considering the dependence of elastic constants of the matrix phase onto the local concentration of solute atoms. The elastic constants as a function of solute concentration have been obtained using density functional theory calculations. As a result of the coupling, inverse ripening has been observed where the smaller precipitates grow at the expense of the larger ones. This is due to size-dependent concentration gradients existing around the precipitates. At the same time, precipitates rearrange themselves as a consequence of minimization of the total elastic energy of the system. It is found that the anisotropy of the chemomechanical coupling leads to the formation of new patterns of elasticity in the matrix thereby resulting in new alignments of the precipitates. © 2017 American Physical Society.
    view abstract10.1103/PhysRevB.95.174101
  • Robust Bain distortion in the premartensite phase of a platinum-substituted Ni2MnGa magnetic shape memory alloy
    Singh, S. and Dutta, B. and D'Souza, S.W. and Zavareh, M.G. and Devi, P. and Gibbs, A.S. and Hickel, T. and Chadov, S. and Felser, C. and Pandey, D.
    Nature Communications 8 (2017)
    The premartensite phase of shape memory and magnetic shape memory alloys (MSMAs) is believed to be a precursor state of the martensite phase with preserved austenite phase symmetry. The thermodynamic stability of the premartensite phase and its relation to the martensitic phase is still an unresolved issue, even though it is critical to the understanding of the functional properties of MSMAs. We present here unambiguous evidence for macroscopic symmetry breaking leading to robust Bain distortion in the premartensite phase of 10% Pt-substituted Ni2MnGa. We show that the robust Bain-distorted premartensite (T2) phase results from another premartensite (T1) phase with preserved cubic-like symmetry through an isostructural phase transition. The T2 phase finally transforms to the martensite phase with additional Bain distortion on further cooling. Our results demonstrate that the premartensite phase should not be considered as a precursor state with the preserved symmetry of the cubic austenite phase. © 2017 The Author(s).
    view abstract10.1038/s41467-017-00883-z
  • Strengthening and strain hardening mechanisms in a precipitation-hardened high-Mn lightweight steel
    Yao, M.J. and Welsch, E. and Ponge, D. and Haghighat, S.M.H. and Sandlöbes, S. and Choi, P. and Herbig, M. and Bleskov, I. and Hickel, T. and Lipinska-Chwalek, M. and Shanthraj, P. and Scheu, C. and Zaefferer, S. and Gault, B. and Raabe, D.
    Acta Materialia 140 (2017)
    We report on the strengthening and strain hardening mechanisms in an aged high-Mn lightweight steel (Fe-30.4Mn-8Al-1.2C, wt.%) studied by electron channeling contrast imaging (ECCI), transmission electron microscopy (TEM), atom probe tomography (APT) and correlative TEM/APT. Upon isothermal annealing at 600 °C, nano-sized κ-carbides form, as characterized by TEM and APT. The resultant alloy exhibits high strength and excellent ductility accompanied by a high constant strain hardening rate. In comparison to the as-quenched κ-free state, the precipitation of κ-carbides leads to a significant increase in yield strength (∼480 MPa) without sacrificing much tensile elongation. To study the strengthening and strain hardening behavior of the precipitation-hardened material, deformation microstructures were analyzed at different strain levels. TEM and correlative TEM/APT results show that the κ-carbides are primarily sheared by lattice dislocations, gliding on the typical face-centered-cubic (fcc) slip system {111}<110>, leading to particle dissolution and solute segregation. Ordering strengthening is the predominant strengthening mechanism. As the deformation substructure is characterized by planar slip bands, we quantitatively studied the evolution of the slip band spacing during straining to understand the strain hardening behavior. A good agreement between the calculated flow stresses and the experimental data suggests that dynamic slip band refinement is the main strain hardening mechanism. The influence of κ-carbides on mechanical properties is discussed by comparing the results with that of the same alloy in the as-quenched, κ-free state. © 2017 Acta Materialia Inc.
    view abstract10.1016/j.actamat.2017.08.049
  • The role of κ-carbides as hydrogen traps in high-Mn steels
    Timmerscheidt, T.A. and Dey, P. and Bogdanovski, D. and von Appen, J. and Hickel, T. and Neugebauer, J. and Dronskowski, R.
    Metals 7 (2017)
    Since the addition of Al to high-Mn steels is known to reduce their sensitivity to hydrogen-induced delayed fracture, we investigate possible trapping effects connected to the presence of Al in the grain interior employing density-functional theory (DFT). The role of Al-based precipitates is also investigated to understand the relevance of short-range ordering effects. So-called E21-Fe3AlC κ-carbides are frequently observed in Fe-Mn-Al-C alloys. Since H tends to occupy the same positions as C in these precipitates, the interaction and competition between both interstitials is also investigated via DFT-based simulations. While the individual H–H/C–H chemical interactions are generally repulsive, the tendency of interstitials to increase the lattice parameter can yield a net increase of the trapping capability. An increased Mn content is shown to enhance H trapping due to attractive short-range interactions. Favorable short-range ordering is expected to occur at the interface between an Fe matrix and the E21-Fe3AlC κ-carbides, which is identified as a particularly attractive trapping site for H. At the same time, accumulation of H at sites of this type is observed to yield decohesion of this interface, thereby promoting fracture formation. The interplay of these effects, evident in the trapping energies at various locations and dependent on the H concentration, can be expressed mathematically, resulting in a term that describes the hydrogen embrittlement. © 2017 by the authors. Licensee MDPI, Basel, Switzerland.
    view abstract10.3390/met7070264
  • Ab initio Prediction of Martensitic and Intermartensitic Phase Boundaries in Ni-Mn-Ga
    Dutta, B. and Çaklr, A. and Giacobbe, C. and Al-Zubi, A. and Hickel, T. and Acet, M. and Neugebauer, J.
    Physical Review Letters 116 (2016)
    Despite the importance of martensitic transformations of Ni-Mn-Ga Heusler alloys for their magnetocaloric and shape-memory properties, the martensitic part of their phase diagrams is not well determined. Using an ab initio approach that includes the interplay of lattice and vibrational degrees of freedom we identify an intermartensitic transformation between a modulated and a nonmodulated phase as a function of excess Ni and Mn content. Based on an evaluation of the theoretical findings and experimental x-ray diffraction data for Mn-rich alloys, we are able to predict the phase diagram for Ni-rich alloys. In contrast to other mechanisms discussed for various material systems in the literature, we herewith show that the intermartensitic transformation can be understood solely using thermodynamic concepts. © 2016 American Physical Society.
    view abstract10.1103/PhysRevLett.116.025503
  • Ab initio-guided design of twinning-induced plasticity steels
    Raabe, D. and Roters, F. and Neugebauer, J. and Gutierrez-Urrutia, I. and Hickel, T. and Bleck, W. and Schneider, J.M. and Wittig, J.E. and Mayer, J.
    MRS Bulletin 41 (2016)
    The twinning-induced plasticity effect enables designing austenitic Fe-Mn-C-based steels with >70% elongation with an ultimate tensile strength >1 GPa. These steels are characterized by high strain hardening due to the formation of twins and complex dislocation substructures that dynamically reduce the dislocation mean free path. Both mechanisms are governed by the stacking-fault energy (SFE) that depends on composition. This connection between composition and substructure renders these steels ideal model materials for theory-based alloy design: Ab initio-guided composition adjustment is used to tune the SFE, and thus, the strain-hardening behavior for promoting the onset of twinning at intermediate deformation levels where the strain-hardening capacity provided by the dislocation substructure is exhausted. We present thermodynamic simulations and their use in constitutive models, as well as electron microscopy and combinatorial methods that enable validation of the strain-hardening mechanisms. Copyright © 2016 Materials Research Society.
    view abstract10.1557/mrs.2016.63
  • Combined atom probe tomography and density functional theory investigation of the Al off-stoichiometry of κ-carbides in an austenitic Fe-Mn-Al-C low density steel
    Yao, M.J. and Dey, P. and Seol, J.-B. and Choi, P. and Herbig, M. and Marceau, R.K.W. and Hickel, T. and Neugebauer, J. and Raabe, D.
    Acta Materialia 106 (2016)
    We report on the investigation of the off-stoichiometry and site-occupancy of κ-carbide precipitates within an austenitic (γ), Fe-29.8Mn-7.7Al-1.3C (wt.%) alloy using a combination of atom probe tomography and density functional theory. The chemical composition of the κ-carbides as measured by atom probe tomography indicates depletion of both interstitial C and substitutional Al, in comparison to the ideal stoichiometric L′12 bulk perovskite. In this work we demonstrate that both these effects are coupled. The off-stoichiometric concentration of Al can, to a certain extent, be explained by strain caused by the κ/γ mismatch, which facilitates occupation of Al sites in κ-carbide by Mn atoms (Mnγ Al anti-site defects). The large anti-site concentrations observed by our experiments, however, can only be stabilized if there are C vacancies in the vicinity of the anti-site. © 2016 Acta Materialia Inc.
    view abstract10.1016/j.actamat.2016.01.007
  • First-principles investigation of hydrogen interaction with TiC precipitates in α -Fe
    Di Stefano, D. and Nazarov, R. and Hickel, T. and Neugebauer, J. and Mrovec, M. and Elsässer, C.
    Physical Review B - Condensed Matter and Materials Physics 93 (2016)
    A correct description of hydrogen diffusion and trapping is the prerequisite for an understanding of the phenomenon of hydrogen embrittlement. In this study, we carried out extensive first-principles calculations based on density functional theory to investigate the interaction of H with TiC precipitates that are assumed to be efficient trapping agents mitigating HE in advanced high-strength steels. We found that there exists a large variety of possible trapping sites for H associated with different types of interfaces between the TiC particle and the Fe matrix, with misfit dislocations and other defects at these interfaces, and with carbon vacancies in TiC. The most efficient trapping by more than 1 eV occurs at carbon vacancies in the interior of TiC particles. However, these traps are difficult to populate at ambient temperatures since the energy barrier for H entering the particles is high. H trapping at the semicoherent interfaces between the TiC particles and the Fe matrix is moderate, ranging from 0.3 to 0.5 eV. However, a sufficiently large concentration of the carbide particles can significantly reduce the amount of H segregated at dislocation cores in the Fe matrix. A systematic comparison of the obtained theoretical results with available experimental observations reveals a consistent picture of hydrogen trapping at the TiC particles that is expected to be qualitatively valid also for other carbide precipitates with the rock-salt crystal structure. © 2016 American Physical Society.
    view abstract10.1103/PhysRevB.93.184108
  • Impact of local magnetism on stacking fault energies: A first-principles investigation for fcc iron
    Bleskov, I. and Hickel, T. and Neugebauer, J. and Ruban, A.
    Physical Review B - Condensed Matter and Materials Physics 93 (2016)
    A systematic ab initio study of the influence of local magnetism on the generalized stacking fault energy (GSFE) surface in pure fcc iron at 0 K has been performed. In the calculations we considered ferro- and antiferro- (single- and double-layer) magnetic order of local moments as well as their complete disorder, corresponding to paramagnetic (PM) state. We have shown that local magnetism is one of the most important factors stabilizing austenitic structure in iron (with respect to more stable at 0 K hcp) and that the perturbation of magnetic structure by the formation of stacking fault is a short-range effect. Local magnetism also strongly influences the GSFE surface topology and, therefore, the material's plasticity by reducing the energetic barriers that need to be overcome to form the intrinsic stacking fault (ISF) or return from the ISF structure to fcc. The influence of atomic relaxations on such barriers is moderate and does not exceed 15%. In addition, a methodology to evaluate the PM ISF energy using a superposition of the ISF energies obtained for ordered magnetic structures is proposed to overcome computational impediments arising when dealing with disorder in the PM state. The complications of the proposed methodology together with the ways to overcome them are also discussed. © 2016 American Physical Society.
    view abstract10.1103/PhysRevB.93.214115
  • Influence of magnetic excitations on the phase stability of metals and steels
    Körmann, F. and Hickel, T. and Neugebauer, J.
    Current Opinion in Solid State and Materials Science 20 (2016)
    Within this article we highlight recent advances in the modeling of magnetic contributions to the finite temperature phase stability of structural materials. A key quantity in this context is the specific heat capacity Cp, since it provides a sensitive link to thermophysical and calorimetric experiments and to established thermodynamic databases. For iron-based materials, the Heisenberg model and its extensions are used as an elegant way for coupling ground-state ab initio calculations with concepts of many-body theory to simulate the temperature dependence. Besides analytical concepts to derive the free energy of the Heisenberg model, our work is mainly devoted to numerical approaches such as Monte-Carlo methods. In particular, we highlight the need to go beyond a classical to a fully quantum-mechanical description of magnetic excitations. In order to achieve a quantitative description of Cp, also lattice and electronic degrees of freedom as well as their dependence on magnetism are addressed. Due to the large variety of experimental data, pure iron is best suited to discuss the method developments and to perform evaluations. Nevertheless, the application to other magnetic elements (e.g. Co, Ni) and Fe-based materials (e.g. Fe3C) will also be addressed. © 2015 Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.cossms.2015.06.001
  • Interface effects on the magnetic properties of layered Ni2MnGa/Ni2MnSn alloys: A first-principles investigation
    Dutta, B. and Opahle, I. and Hickel, T.
    Functional Materials Letters 9 (2016)
    The effect of interfaces on the magnetic properties of multilayers is analyzed forNi2MnGa/Ni2MnSn system using density functional theory. The Ni spin moments at the interface change by about 30% compared to the bulk value, whereas the effect on the Mn spin moments is much less pronounced. A similar strong effect is also observed for the Ni orbital moments at the interface. The magneto-crystalline anisotropy of the multilayer systems can be understood by the additive contribution of the respective values of strained bulk materials. © 2016 World Scientific Publishing Company.
    view abstract10.1142/S1793604716420108
  • Interplay between interstitial displacement and displacive lattice transformations
    Zhang, X. and Hickel, T. and Rogal, J. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 94 (2016)
    Diffusionless displacive lattice rearrangements, which include martensitic transformations, are in real materials often accompanied by a displacive drag of interstitials. The interplay of both processes leads to a particular atomistic arrangement of the interstitials in the product phase, which is decisive for its performance. An archetype example is the martensitic transformation in Fe-C alloys. One of the puzzles for this system is that the deviation from the cubic symmetry (i.e., the tetragonality) in the martensite resulting from this interplay is lower than what thermodynamics dictates. In our ab initio approach, the relative motion of C in the transforming lattice is studied with the nudged elastic band method. We prove that an atomic shearlike shuffle mechanism of adjacent (112) Fe layers along the ±[111]bcc directions is essential to achieve a redistribution of C atoms during the fcc → bcc transition, which fully explains the abnormal behavior. Furthermore, the good agreement with experiment validates our method to treat a diffusionless redistribution of interstitials and a displacive rearrangement of the host lattice simultaneously. © 2016 American Physical Society.
    view abstract10.1103/PhysRevB.94.104109
  • Partitioning of Cr and Si between cementite and ferrite derived from first-principles thermodynamics
    Sawada, H. and Kawakami, K. and Körmann, F. and Grabowski, B. and Hickel, T. and Neugebauer, J.
    Acta Materialia 102 (2016)
    Partitioning of Cr and Si between cementite and ferrite was investigated by first-principles thermodynamics taking into account vibrational, electronic, and magnetic Gibbs energy contributions. At finite temperatures, these contributions lower the partitioning Gibbs energy and compete with the configurational entropy, which favors impurity segregation to ferrite due to its larger volume fraction compared to cementite. Due to the large positive partitioning enthalpy contribution of Si at T = 0 K, partitioning of Si to cementite is virtually absent in agreement with experiment. The situation is drastically different for Cr impurities. Incorporation of finite-temperature effects resolves the discrepancy between experimental observations and previous T = 0 K first-principles calculations. Cr strongly segregates to cementite due to the enhanced magnetic entropy of cementite above 400 K, i.e., near the Curie temperature of cementite. The increasing magnetic fluctuations in ferrite cause a strong reduction of the partitioning coefficient in the temperature range from 773 to 973 K in qualitative agreement with experiment. Quantitative agreement with calphad data and experimental data for equilibrium Cr concentrations in a wide range of alloy compositions is achieved by renormalizing the theoretical magnetic partitioning Gibbs energy by a constant scaling factor. © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2015.09.010
  • Quaternary Al-Cu-Mg-Si Q Phase: Sample Preparation, Heat Capacity Measurement and First-Principles Calculations
    Löffler, A. and Zendegani, A. and Gröbner, J. and Hampl, M. and Schmid-Fetzer, R. and Engelhardt, H. and Rettenmayr, M. and Körmann, F. and Hickel, T. and Neugebauer, J.
    Journal of Phase Equilibria and Diffusion 37 (2016)
    The quaternary Q phase is an important precipitate phase in the Al-Cu-Mg-Si alloy system and its accurate thermodynamic description is crucial for further tailoring this material class for light-weight structural applications. In order to achieve an improved thermochemical parameter set of this phase, we used a combination of experimental measurements and first-principles calculations, which was focussed on the heat capacity. Its accurate experimental determination required the preparation of pure samples of Q phase and sophisticated calorimetric measurements. On the theoretical side, a simultaneous treatment of lattice vibrations within the quasiharmonic approximation, electronic excitations, and configuration entropy within the compound energy formalism were required to achieve a complete description of the heat capacity. The evaluation demonstrates the high predictive power of the first-principles as well as the Calphad modeling. © 2015, ASM International.
    view abstract10.1007/s11669-015-0426-y
  • The impact of carbon and oxygen in alpha-titanium: Ab initio study of solution enthalpies and grain boundary segregation
    Aksyonov, D.A. and Hickel, T. and Neugebauer, J. and Lipnitskii, A.G.
    Journal of Physics Condensed Matter 28 (2016)
    The solution, grain boundary (GB) segregation, and co-segregation of carbon and oxygen atoms in α-titanium are studied using density functional theory. For five titanium tilt boundaries, including T1, T2, and C1 twin systems, we determine the GB structure, as well as GB energy and excess volume. The segregation energies and volumes of carbon and oxygen are calculated for 23 inequivalent interstitial voids, while for co-segregation 75 configurations are considered. It is obtained that depending on the type of the segregation void both a positive and a negative segregation process is possible. The physical reasons of segregation are explained in terms of the analysis of the void atomic geometry, excess volume and features of the electronic structure at the Fermi level. Although carbon and oxygen show qualitatively similar properties in α-Ti, several distinctions are observed for their segregation behavior and mutual interactions. © 2016 IOP Publishing Ltd.
    view abstract10.1088/0953-8984/28/38/385001
  • ICME for Crashworthiness of TWIP Steels: From Ab Initio to the Crash Performance
    Güvenç, O. and Roters, F. and Hickel, T. and Bambach, M.
    JOM 67 (2015)
    During the last decade, integrated computational materials engineering (ICME) emerged as a field which aims to promote synergetic usage of formerly isolated simulation models, data and knowledge in materials science and engineering, in order to solve complex engineering problems. In our work, we applied the ICME approach to a crash box, a common automobile component crucial to passenger safety. A newly developed high manganese steel was selected as the material of the component and its crashworthiness was assessed by simulated and real drop tower tests. The crashworthiness of twinning-induced plasticity (TWIP) steel is intrinsically related to the strain hardening behavior caused by the combination of dislocation glide and deformation twinning. The relative contributions of those to the overall hardening behavior depend on the stacking fault energy (SFE) of the selected material. Both the deformation twinning mechanism and the stacking fault energy are individually well-researched topics, but especially for high-manganese steels, the determination of the stacking-fault energy and the occurrence of deformation twinning as a function of the SFE are crucial to understand the strain hardening behavior. We applied ab initio methods to calculate the stacking fault energy of the selected steel composition as an input to a recently developed strain hardening model which models deformation twinning based on the SFE-dependent dislocation mechanisms. This physically based material model is then applied to simulate a drop tower test in order to calculate the energy absorption capacity of the designed component. The results are in good agreement with experiments. The model chain links the crash performance to the SFE and hence to the chemical composition, which paves the way for computational materials design for crashworthiness. © 2014, The Minerals, Metals & Materials Society.
    view abstract10.1007/s11837-014-1192-8
  • Interplay of strain and interdiffusion in Heusler alloy bilayers
    Dutta, B. and Hickel, T. and Neugebauer, J. and Behler, C. and Fähler, S. and Behler, A. and Waske, A. and Teichert, N. and Schmalhorst, J.-M. and Hütten, A.
    Physica Status Solidi - Rapid Research Letters 9 (2015)
    Combining conventional and inverse magnetocaloric materials promises to enhance solid state refrigeration. As a first step here we present epitaxial Ni-Mn-Ga/Ni-Mn-Sn bilayer films. We examine the dependence of the lateral and normal lattice constants on the deposition sequence by combining experimental and ab initio techniques. Structural properties are determined with X-ray diffraction as well as highresolution transmission electron microscopy, while ab initio calculations explain the interplay of strain, local relaxations and the interdiffusion of atoms. The latter is confirmed by Auger electron spectroscopy and is expected to have a noticeable impact on the functional properties of the Heusler materials. ( © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstract10.1002/pssr.201510070
  • Random phase approximation up to the melting point: Impact of anharmonicity and nonlocal many-body effects on the thermodynamics of Au
    Grabowski, B. and Wippermann, S. and Glensk, A. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 91 (2015)
    Application of the generalized gradient corrected functional within standard density-functional theory results in a dramatic failure for Au, leading to divergent thermodynamic properties well below the melting point. By combining the upsampled thermodynamic integration using Langevin dynamics technique with the random phase approximation, we show that inclusion of nonlocal many-body effects leads to a stabilization and to an excellent agreement with experiment. © Published by the American Physical Society.
    view abstract10.1103/PhysRevB.91.201103
  • Structural transformations among austenite, ferrite and cementite in Fe-C alloys: A unified theory based on ab initio simulations
    Zhang, X. and Hickel, T. and Rogal, J. and Fähler, S. and Drautz, R. and Neugebauer, J.
    Acta Materialia 99 (2015)
    Structural transformations in Fe-C alloys are decisive for the mechanical properties of steels, but their modeling remains a challenge due to the simultaneous changes in Fe lattice and redistribution of C. With a combination of the orientation relationships between austenite, ferrite and cementite, we identify a metastable intermediate structure (MIS), which can serve as a link between the three phases. Based on this framework, different mechanisms depending on the local conditions (C concentration, strain, magnetism) are revealed from ab initio nudged elastic band simulations, which allow us to construct a unified theory for the structural transformations among austenite, ferrite and cementite. © 2015 Acta Materialia Inc. All rights reserved.
    view abstract10.1016/j.actamat.2015.07.075
  • Understanding anharmonicity in fcc materials: From its origin to ab initio strategies beyond the quasiharmonic approximation
    Glensk, A. and Grabowski, B. and Hickel, T. and Neugebauer, J.
    Physical Review Letters 114 (2015)
    We derive the Gibbs energy including the anharmonic contribution due to phonon-phonon interactions for an extensive set of unary fcc metals (Al, Ag, Au, Cu, Ir, Ni, Pb, Pd, Pt, Rh) by combining density-functional-theory (DFT) calculations with efficient statistical sampling approaches. We show that the anharmonicity of the macroscopic system can be traced back to the anharmonicity in local pairwise interactions. Using this insight, we derive and benchmark a highly efficient approach which allows the computation of anharmonic contributions using a few T=0K DFT calculations only. © Published by the American Physical Society 2015.
    view abstract10.1103/PhysRevLett.114.195901
  • A generalized plane-wave formulation of k · p formalism and continuum-elasticity approach to elastic and electronic properties of semiconductor nanostructures
    Marquardt, O. and Boeck, S. and Freysoldt, C. and Hickel, T. and Schulz, S. and Neugebauer, J. and O'Reilly, E.P.
    Computational Materials Science 95 (2014)
    We present a generalized and flexible plane-wave based implementation of the multiband k·p formalism to study the electronic properties of semiconductor nanostructures. All ingredients of the modeling process, namely the Hamiltonian, the nanostructure's geometry and the required material parameters, are defined in human-readable input files that can be easily generated and modified. The generalized k·p model can contain an arbitrary number of directly treated bands as well as strain, piezoelectric, and external potentials. All calculations can be performed for arbitrary crystal structures. The nanostructure is described in terms of a real-space composition map that may contain an arbitrary number of base compounds and alloys. We demonstrate the applicability and flexibility of our implementation for the example of (111)-oriented, site-controlled InGaAs quantum dots, where a rotated eight-band k·p Hamiltonian is employed. As a second example, a 14-band k·p model that captures the bulk inversion asymmetry of the zinc-blende lattice is applied for the case of a pyramidal (0 0 1)-oriented InAs/GaAs quantum dot. Here we show that the explicit treatment of 14 bands removes the well known shortcoming of eight-band k·p models for (0 0 1)-oriented zinc-blende quantum dots which leads to artificially degenerate p-like electron states. © 2014 Elsevier B.V. All rights reserved.
    view abstract10.1016/j.commatsci.2014.06.047
  • Ab initio based understanding of the segregation and diffusion mechanisms of hydrogen in steels
    Hickel, T. and Nazarov, R. and McEniry, E.J. and Leyson, G. and Grabowski, B. and Neugebauer, J.
    JOM 66 (2014)
    A microscopic understanding of the processes that lead to hydrogen embrittlement is of critical importance for developing new generations of high-strength steels. With this article, we provide an overview of insights that can be gained from ab initio based methods when investigating the segregation and diffusion mechanisms of hydrogen in steels. We first discuss the solubility and diffusion behavior of hydrogen in the ferrite, austenite, and martensite phases. We consider not only defect-free bulk phases but also the influence of alloying elements and geometric defects such as vacancies and grain boundaries. In the second part, the behavior of hydrogen in the presence of precipitates, the solubility, the surface absorption, and the influence of hydrogen on the interface cohesion are studied. Finally, we provide simulation results for the interaction of hydrogen with dislocations. For all these applications, we will comment on advantages and shortcomings of ab initio methods and will demonstrate how the obtained data and insights can complement experimental approaches to extract general trends and to identify causes of hydrogen embrittlement. © 2014 The Minerals, Metals & Materials Society.
    view abstract10.1007/s11837-014-1055-3
  • Ab Initio Predicted Impact of Pt on Phase Stabilities in Ni-Mn-Ga Heusler Alloys
    Dutta, B. and Hickel, T. and Entel, P. and Neugebauer, J.
    Journal of Phase Equilibria and Diffusion 35 (2014)
    The paper discusses the stabilization of the martensite in Ni2MnGa at finite temperatures that is caused by the substitution of Ni by Pt. For this purpose a recently developed ab initio based formalism employing density functional theory is applied. The free energies of the relevant austenite and martensite phases of Ni1.75Pt0.25MnGa are determined incorporating quasiharmonic phonons and fixed-spin magnons. In addition the dependence of the transition temperatures on the Pt concentration is investigated. Though our results are in qualitative agreement with estimates based on ground-state energies, they clearly demonstrate that a proper treatment of finite temperature contributions is important to predict the martensitic transition quantitatively. © 2014, ASM International.
    view abstract10.1007/s11669-014-0342-6
  • Ab initio study of H-vacancy interactions in fcc metals: Implications for the formation of superabundant vacancies
    Nazarov, R. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 89 (2014)
    Hydrogen solubility and interaction with vacancies and divacancies are investigated in 12 fcc metals by density functional theory. We show that in all studied fcc metals, vacancies trap H very efficiently and multiple H trapping is possible. H is stronger trapped by divacancies and even stronger by surfaces. We derive a condition for the maximum number of trapped H atoms as a function of the H chemical potential. Based on this criterion, the possibility of a dramatic increase of vacancy concentration (superabundant vacancy formation) in the studied metals is discussed. © 2014 American Physical Society.
    view abstract10.1103/PhysRevB.89.144108
  • Breakdown of the arrhenius law in describing vacancy formation energies: The importance of local anharmonicity revealed by Ab initio thermodynamics
    Glensk, A. and Grabowski, B. and Hickel, T. and Neugebauer, J.
    Physical Review X 4 (2014)
    We study the temperature dependence of the Gibbs energy of vacancy formation in Al and Cu from T = 0 K up to the melting temperature, fully taking into account anharmonic contributions. Our results show that the formation entropy of vacancies is not constant as often assumed but increases almost linearly with temperature. The resulting highly nonlinear temperature dependence in the Gibbs formation energy naturally explains the differences between positron annihilation spectroscopy and differential dilatometry data and shows that nonlinear thermal corrections are crucial to extrapolate high-temperature experimental data to T = 0 K. Employing these corrections-rather than the linear Arrhenius extrapolation that is commonly assumed in analyzing experimental data-revised formation enthalpies are obtained that differ up to 20% from the previously accepted ones. Using the revised experimental formation enthalpies, we show that a large part of the discrepancies between DFT-GGA and unrevised experimental vacancy formation energies disappears. The substantial shift between previously accepted and the newly revised T = 0 K formation enthalpies also has severe consequences in benchmarking ab initio methods against experiments, e.g., in deriving corrections that go beyond commonly used LDA and GGA exchangecorrelation functionals such as the AM05 functional.
    view abstract10.1103/PhysRevX.4.011018
  • Computational Thermodynamics: Recent developments and future potential and prospects
    Hickel, T. and Kattner, U.R. and Fries, S.G.
    Physica Status Solidi (B) Basic Research 251 (2014)
    view abstract10.1002/pssb.201470107
  • Designing Heusler nanoprecipitates by elastic misfit stabilization in Fe-Mn maraging steels
    Millán, J. and Sandlöbes, S. and Al-Zubi, A. and Hickel, T. and Choi, P. and Neugebauer, J. and Ponge, D. and Raabe, D.
    Acta Materialia 76 (2014)
    B2 NiMn and Ni2MnAl Heusler nanoprecipitates are designed via elastic misfit stabilization in Fe-Mn maraging steels by combining transmission electron microscopy (TEM) correlated atom probe tomography (APT) with ab initio simulations. Guided by these predictions, the Al content of the alloys is systematically varied, and the influence of the Al concentration on structure stability, size and distribution of precipitates formed during ageing at 450 °C is studied using scanning electron microscopy-electron backscatter diffraction, TEM and APT. Specifically, the Ni2MnAl Heusler nanoprecipitates exhibit the finest sizes and highest dispersion and hence lead to significant strengthening. The formation of the different types of precipitates and their structure, size, dispersion and effect on the mechanical properties of the alloys are discussed. © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2014.05.016
  • First-principles calculations for point defects in solids
    Freysoldt, C. and Grabowski, B. and Hickel, T. and Neugebauer, J. and Kresse, G. and Janotti, A. and Van De Walle, C.G.
    Reviews of Modern Physics 86 (2014)
    Point defects and impurities strongly affect the physical properties of materials and have a decisive impact on their performance in applications. First-principles calculations have emerged as a powerful approach that complements experiments and can serve as a predictive tool in the identification and characterization of defects. The theoretical modeling of point defects in crystalline materials by means of electronic-structure calculations, with an emphasis on approaches based on density functional theory (DFT), is reviewed. A general thermodynamic formalism is laid down to investigate the physical properties of point defects independent of the materials class (semiconductors, insulators, and metals), indicating how the relevant thermodynamic quantities, such as formation energy, entropy, and excess volume, can be obtained from electronic structure calculations. Practical aspects such as the supercell approach and efficient strategies to extrapolate to the isolated-defect or dilute limit are discussed. Recent advances in tractable approximations to the exchange-correlation functional (DFT+U, hybrid functionals) and approaches beyond DFT are highlighted. These advances have largely removed the long-standing uncertainty of defect formation energies in semiconductors and insulators due to the failure of standard DFT to reproduce band gaps. Two case studies illustrate how such calculations provide new insight into the physics and role of point defects in real materials. © 2014 American Physical Society.
    view abstract10.1103/RevModPhys.86.253
  • Impact of Mn on the solution enthalpy of hydrogen in austenitic Fe-Mn alloys: A first-principles study
    Von Appen, J. and Dronskowski, R. and Chakrabarty, A. and Hickel, T. and Spatschek, R. and Neugebauer, J.
    Journal of Computational Chemistry 35 (2014)
    Hydrogen interstitials in austenitic Fe-Mn alloys were studied using density-functional theory to gain insights into the mechanisms of hydrogen embrittlement in high-strength Mn steels. The investigations reveal that H atoms at octahedral interstitial sites prefer a local environment containing Mn atoms rather than Fe atoms. This phenomenon is closely examined combining total energy calculations and crystal orbital Hamilton population analysis. Contributions from various electronic phenomena such as elastic, chemical, and magnetic effects are characterized. The primary reason for the environmental preference is a volumetric effect, which causes a linear dependence on the number of nearest-neighbour Mn atoms. A secondary electronic/magnetic effect explains the deviations from this linearity. © 2014 Wiley Periodicals, Inc.
    view abstract10.1002/jcc.23742
  • Impact of nanodiffusion on the stacking fault energy in high-strength steels
    Hickel, T. and Sandlöbes, S. and Marceau, R.K.W. and Dick, A. and Bleskov, I. and Neugebauer, J. and Raabe, D.
    Acta Materialia 75 (2014)
    A key requirement of modern steels - the combination of high strength and high deformability - can best be achieved by enabling a local adaptation of the microstructure during deformation. A local hardening is most efficiently obtained by a modification of the stacking sequence of atomic layers, resulting in the formation of twins or martensite. Combining ab initio calculations with in situ transmission electron microscopy, we show that the ability of a material to incorporate such stacking faults depends on its overall chemical composition and, importantly, the local composition near the defect, which is controlled by nanodiffusion. Specifically, the role of carbon for the stacking fault energy in high-Mn steels is investigated. Consequences for the long-term mechanical properties and the characterisation of these materials are discussed. © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2014.04.062
  • Lambda transitions in materials science: Recent advances in CALPHAD and first-principles modelling
    Körmann, F. and Breidi, A.A.H. and Dudarev, S.L. and Dupin, N. and Ghosh, G. and Hickel, T. and Korzhavyi, P. and Muñoz, J.A. and Ohnuma, I.
    Physica Status Solidi (B) Basic Research 251 (2014)
    This paper provides a comprehensive overview of state-of-the-art computational techniques to thermodynamically model magnetic and chemical order-disorder transitions. Recent advances as well as limitations of various approaches to these so-called lambda transitions are examined in detail, focussing on calphad models and first-principles methods based on density functional theory (DFT). On the one hand empirical implementations -based on the Inden-Hillert-Jarl formalism -are investigated, including a detailed interpretation of the relevant parameters, physical limiting cases and potential extensions. In addition, Bragg-Williams-based approaches as well as cluster-variation methods of chemical order-disorder transitions are discussed. On the other hand, it is shown how magnetic contributions can be introduced based on various microscopic model Hamiltonians (Hubbard model, Heisenberg model and beyond) in combination with DFT-computed parameters. As a result of the investigation we were able to indicate similarities between the treatment of chemical and magnetic degrees of freedom as well as the treatment within the calphad and DFT approaches. Potential synergy effects resulting from this overlap have been derived and alternative approaches have been suggested, in order to improve future thermodynamic modelling of lambda transitions. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstract10.1002/pssb.201350136
  • Reliability evaluation of thermophysical properties from first-principles calculations
    Palumbo, M. and Fries, S.G. and Corso, A.D. and Körmann, F. and Hickel, T. and Neugebauer, J.
    Journal of Physics Condensed Matter 26 (2014)
    Thermophysical properties, such as heat capacity, bulk modulus and thermal expansion, are of great importance for many technological applications and are traditionally determined experimentally. With the rapid development of computational methods, however, first-principles computed temperature-dependent data are nowadays accessible. We evaluate various computational realizations of such data in comparison to the experimental scatter. The work is focussed on the impact of different first-principles codes (quantum espresso and vasp), pseudopotentials (ultrasoft and projector augmented wave) as well as phonon determination methods (linear response and direct force constant method) on these properties. Based on the analysis of data for two pure elements, Cr and Ni, consequences for the reliability of temperature-dependent first-principles data in computational thermodynamics are discussed. © 2014 IOP Publishing Ltd.
    view abstract10.1088/0953-8984/26/33/335401
  • Temperature dependent magnon-phonon coupling in bcc Fe from theory and experiment
    Körmann, F. and Grabowski, B. and Dutta, B. and Hickel, T. and Mauger, L. and Fultz, B. and Neugebauer, J.
    Physical Review Letters 113 (2014)
    An ab initio based framework for quantitatively assessing the phonon contribution due to magnon-phonon interactions and lattice expansion is developed. The theoretical results for bcc Fe are in very good agreement with high-quality phonon frequency measurements. For some phonon branches, the magnon-phonon interaction is an order of magnitude larger than the phonon shift due to lattice expansion, demonstrating the strong impact of magnetic short-range order even significantly above the Curie temperature. The framework closes the previous simulation gap between the ferro- and paramagnetic limits. © 2014 American Physical Society.
    view abstract10.1103/PhysRevLett.113.165503
  • Density functional theory in materials science
    Neugebauer, J. and Hickel, T.
    Wiley Interdisciplinary Reviews: Computational Molecular Science 3 (2013)
    Materials science is a highly interdisciplinary field. It is devoted to the understanding of the relationship between (a) fundamental physical and chemical properties governing processes at the atomistic scale with (b) typically macroscopic properties required of materials in engineering applications. For many materials, this relationship is not only determined by chemical composition, but strongly governed by microstructure. The latter is a consequence of carefully selected process conditions (e.g., mechanical forming and annealing in metallurgy or epitaxial growth in semiconductor technology). A key task of computational materials science is to unravel the often hidden composition-structure-property relationships using computational techniques. The present paper does not aim to give a complete review of all aspects of materials science. Rather, we will present the key concepts underlying the computation of selected material properties and discuss the major classes of materials to which they are applied. Specifically, our focus will be on methods used to describe single or polycrystalline bulk materials of semiconductor, metal or ceramic form. © 2013 John Wiley & Sons, Ltd.
    view abstract10.1002/wcms.1125
  • Interplay between Coulomb interaction and quantum-confined Stark-effect in polar and nonpolar wurtzite InN/GaN quantum dots
    Barthel, S. and Schuh, K. and Marquardt, O. and Hickel, T. and Neugebauer, J. and Jahnke, F. and Czycholl, G.
    European Physical Journal B 86 (2013)
    In this paper we systematically analyze the electronic structures of polar and nonpolar wurtzite-InN/GaN quantum dots and their modification due to the quantum-confined Stark effect caused by intrinsic fields. This is achieved by combining continuum elasticity theory with an effective-bond orbital model to describe the elastic and single-particle electronic properties in these nitride systems. Based on these results, a many-body treatment is used to determine optical absorption spectra. The efficiency of optical transitions depends on the interplay between the Coulomb interaction and the quantum-confined Stark effect. We introduce an effective confinement potential which represents the electronic structure under the influence of the intrinsic polarization fields and calculate the needed strength of Coulomb interaction to diminish the separation of electrons and holes. © 2013 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
    view abstract10.1140/epjb/e2013-40542-0
  • Polarization effects due to thickness fluctuations in nonpolar InGaN/GaN quantum wells
    Marquardt, O. and Hickel, T. and Neugebauer, J. and Van De Walle, C.G.
    Applied Physics Letters 103 (2013)
    We have employed continuum elasticity theory and an eight band k·p model to study the influence of thickness fluctuations in In 0.2Ga0.8N quantum wells grown along the [11 2 ̄ 0] direction in GaN. Such fluctuations are the origin of polarization potentials that may spatially separate electrons and holes in the vicinity of a thickness fluctuation and therefore reduce the efficiency of light emitters. Our calculations reveal that even shallow fluctuations of one or two monolayers can induce a significant spatial separation of electrons and holes, in particular, if the lateral extent of such a fluctuation is large. © 2013 AIP Publishing LLC.
    view abstract10.1063/1.4818752
  • Revealing the strain-hardening behavior of twinning-induced plasticity steels: Theory, simulations, experiments
    Steinmetz, D.R. and Jäpel, T. and Wietbrock, B. and Eisenlohr, P. and Gutierrez-Urrutia, I. and Saeed-Akbari, A. and Hickel, T. and Roters, F. and Raabe, D.
    Acta Materialia 61 (2013)
    We present a multiscale dislocation density-based constitutive model for the strain-hardening behavior in twinning-induced plasticity (TWIP) steels. The approach is a physics-based strain rate- and temperature-sensitive model which reflects microstructural investigations of twins and dislocation structures in TWIP steels. One distinct advantage of the approach is that the model parameters, some of which are derived by ab initio predictions, are physics-based and known within an order of magnitude. This allows more complex microstructural information to be included in the model without losing the ability to identify reasonable initial values and bounds for all parameters. Dislocation cells, grain size and twin volume fraction evolution are included. Particular attention is placed on the mechanism by which new deformation twins are nucleated, and a new formulation for the critical twinning stress is presented. Various temperatures were included in the parameter optimization process. Dissipative heating is also considered. The use of physically justified parameters enables the identification of a universal parameter set for the example of an Fe-22Mn-0.6C TWIP steel. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2012.09.064
  • Thermodynamic modeling of chromium: Strong and weak magnetic coupling
    Körmann, F. and Grabowski, B. and Söderlind, P. and Palumbo, M. and Fries, S.G. and Hickel, T. and Neugebauer, J.
    Journal of Physics Condensed Matter 25 (2013)
    As chromium is a decisive ingredient for stainless steels, a reliable understanding of its thermodynamic properties is indispensable. Parameter-free first-principles methods have nowadays evolved to a state allowing such thermodynamic predictions. For materials such as Cr, however, the inclusion of magnetic entropy and higher order contributions such as anharmonic entropy is still a formidable task. Employing state-of-the-art ab initio molecular dynamics simulations and statistical concepts, we compute a set of thermodynamic properties based on quasiharmonic, anharmonic, electronic and magnetic free energy contributions from first principles. The magnetic contribution is modeled by an effective nearest-neighbor Heisenberg model, which itself is solved numerically exactly by means of a quantum Monte Carlo method. We investigate two different scenarios: a weak magnetic coupling scenario for Cr, as usually presumed in empirical thermodynamic models, turns out to be in clear disagreement with experimental observations. We show that instead a mixed Hamiltonian including weak and strong magnetic coupling provides a consistent picture with good agreement to experimental thermodynamic data. © 2013 IOP Publishing Ltd.
    view abstract10.1088/0953-8984/25/42/425401
  • Thickness dependent exchange bias in martensitic epitaxial Ni-Mn-Sn thin films
    Behler, A. and Teichert, N. and Dutta, B. and Waske, A. and Hickel, T. and Auge, A. and Hütten, A. and Eckert, J.
    AIP Advances 3 (2013)
    A thickness dependent exchange bias in the low temperature martensitic state of epitaxial Ni-Mn-Sn thin films is found. The effect can be retained down to very small thicknesses. For a Ni50Mn32Sn18 thin film, which does not undergo a martensitic transformation, no exchange bias is observed. Our results suggest that a significant interplay between ferromagnetic and antiferromagnetic regions, which is the origin for exchange bias, is only present in the martensite. The finding is supported by ab initio calculations showing that the antiferromagnetic order is stabilized in the phase. © 2013 Author(s).
    view abstract10.1063/1.4849795
  • A flexible, plane-wave based multiband k ·p model
    Marquardt, O. and Schulz, S. and Freysoldt, C. and Boeck, S. and Hickel, T. and O'Reilly, E.P. and Neugebauer, J.
    Optical and Quantum Electronics 44 (2012)
    In this work, we present a highly generalized implementation of multiband k · p models. We have achieved a high efficiency of our approach by incorporating it in a planewave framework within the Density Functional Theory package S/PHI/nX. To demonstrate the flexibility and applicability of our code, we have chosen two example studies that are directly accessible with the standard eight-band k · p model. By employing a 14-band k · p model for the description of pyramidal InAs/GaAs quantum dots (QDs), we show that this model is able to accomodate for the correct symmetry of the underlying zincblende lattice, which is not reflected in the standard eight-band model. Our second example provides a description of site-controlled (111)-oriented InGaAs/GaAs QDs. The extremely small aspect ratio of these QDs makes a description using conventional k · p Hamiltonians computationally highly expensive.We have therefore rotated the standard eight-band Hamiltonian, to suit the description of these systems. The studies of electronic properties of the above mentioned model systems demonstrate the efficiency and flexibility of our approach. © Springer Science+Business Media, LLC. 2011.
    view abstract10.1007/s11082-011-9506-3
  • Ab initio-based prediction of phase diagrams: Application to magnetic shape memory alloys
    Hickel, T. and Uijttewaal, M. and Al-Zubi, A. and Dutta, B. and Grabowski, B. and Neugebauer, J.
    Advanced Engineering Materials 14 (2012)
    An ultimate goal of material scientists is the prediction of the thermodynamics of tailored materials solely based on first principles methods. The present work reviews recent methodological developments and advancements providing thereby an up-to-date basis for such an approach. Key ideas and the performance of these methods are discussed with respect to the Heusler alloy Ni-Mn-Ga - a prototype magnetic shape-memory alloy of great technological interest for various applications. Ni-Mn-Ga shows an interesting and complex sequence of phase transitions, rendering it a significant theoretical challenge for any first principles approach. The primary goal of this investigation is to determine the composition dependence of the martensitic transition temperature in these alloys. Quasiharmonic phonons and the magnetic exchange interactions as well as the delicate interplay of vibrational and magnetic excitations are taken into account employing density functional theory. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstract10.1002/adem.201200092
  • Advancing density functional theory to finite temperatures: Methods and applications in steel design
    Hickel, T. and Grabowski, B. and Körmann, F. and Neugebauer, J.
    Journal of Physics Condensed Matter 24 (2012)
    The performance of materials such as steels, their high strength and formability, is based on an impressive variety of competing mechanisms on the microscopic/atomic scale (e.g. dislocation gliding, solid solution hardening, mechanical twinning or structural phase transformations). Whereas many of the currently available concepts to describe these mechanisms are based on empirical and experimental data, it becomes more and more apparent that further improvement of materials needs to be based on a more fundamental level. Recent progress for methods based on density functional theory (DFT) now makes the exploration of chemical trends, the determination of parameters for phenomenological models and the identification of new routes for the optimization of steel properties feasible. A major challenge in applying these methods to a true materials design is, however, the inclusion of temperature-driven effects on the desired properties. Therefore, a large range of computational tools has been developed in order to improve the capability and accuracy of first-principles methods in determining free energies. These combine electronic, vibrational and magnetic effects as well as structural defects in an integrated approach. Based on these simulation tools, one is now able to successfully predict mechanical and thermodynamic properties of metals with a hitherto not achievable accuracy. © 2012 IOP Publishing Ltd.
    view abstract10.1088/0953-8984/24/5/053202
  • Atomic forces at finite magnetic temperatures: Phonons in paramagnetic iron
    Körmann, F. and Dick, A. and Grabowski, B. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 85 (2012)
    A density-functional theory (DFT) based scheme to calculate effective forces for magnetic materials at finite temperatures is proposed. The approach is based on a coarse graining procedure in the magnetic configuration space. As application we calculate phonon spectra of paramagnetic bcc and fcc iron and show good agreement with experimental data. © 2012 American Physical Society.
    view abstract10.1103/PhysRevB.85.125104
  • Combined ab initio, experimental, and CALPHAD approach for an improved thermodynamic evaluation of the Mg-Si system
    Schick, M. and Hallstedt, B. and Glensk, A. and Grabowski, B. and Hickel, T. and Hampl, M. and Gröbner, J. and Neugebauer, J. and Schmid-Fetzer, R.
    Calphad: Computer Coupling of Phase Diagrams and Thermochemistry 37 (2012)
    A new thermodynamic evaluation of the well-known Mg-Si system is presented with the aim to resolve persistent uncertainties in the Gibbs energy of its only compound, Mg 2Si. For this purpose the heat capacity and enthalpy of melting of Mg 2Si were measured by differential scanning calorimetry. Using finite temperature density functional theory and the quasiharmonic approximation, thermodynamic properties of Mg 2Si were additionally calculated up to and above its melting temperature. Using these new data, in particular the heat capacity, the Mg-Si system was evaluated thermodynamically with the CALPHAD method leading to a thermodynamic description of the system within narrow bounds. In contrast to several previous evaluations there is no problem with an inverted miscibility gap in the liquid. Although present enthalpy of melting data turned out to be inconsistent with other data in this system, the new evaluation accurately describes all other available data in this system. In particular the Gibbs energy of Mg 2Si can now be considered reliably described.© 2012 Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.calphad.2012.02.001
  • First-principles study of the thermodynamic and elastic properties of eutectic Fe-Ti alloys
    Zhu, L.-F. and Friák, M. and Dick, A. and Grabowski, B. and Hickel, T. and Liot, F. and Holec, D. and Schlieter, A. and Kühn, U. and Eckert, J. and Ebrahimi, Z. and Emmerich, H. and Neugebauer, J.
    Acta Materialia 60 (2012)
    Ti-Fe alloys covering a broad range of Ti concentrations are studied using quantum-mechanical calculations. Employing density functional theory, we correctly reproduce selected key features of the experimental Fe-Ti phase diagram. Analyzing the electronic structure of the stable phases in detail provides an explanation for the thermodynamic stability in terms of the strong correlation between the composition and density of states at the Fermi energy (DOS(EF)). Based on this insight, we extend our study on both single-crystalline and polycrystalline elasticity of various Fe-Ti alloys by computing the compositional dependence of homogenized elastic constants. These quantities and their compositional dependence provide a direct explanation for the origin of the ductility and softness of the β-Ti(Fe) phase. Specifically, we find that this phase has an Fe concentration close to a threshold value connected with the onset of mechanical instability. By interlinking thermodynamic and mechanical stabilities we explain the softness and ductility of the β-Ti(Fe) in terms of a reduced mechanical stability that is connected with an increased DOS(EF) in the β-Ti(Fe). © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2011.11.046
  • Solution enthalpy of hydrogen in fourth row elements: Systematic trends derived from first principles
    Aydin, U. and Ismer, L. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 85 (2012)
    Based on first-principles calculations, we identify a master curve for the solution enthalpy of H in fourth row elements including all 3d transition metals. Assuming nonmagnetic fcc crystal structures, we find two different classes of materials with either the octahedral or the tetrahedral interstitial site being preferred by hydrogen. An interaction radius for H in octahedral site of ≈0.7 Å (≈0.4Å for H in tetrahedral site) turns out to be a characteristic value for which the chemical interaction energy has an optimum for all studied elements. © 2012 American Physical Society.
    view abstract10.1103/PhysRevB.85.155144
  • Strong dipole coupling in nonpolar nitride quantum dots due to Coulomb effects
    Schuh, K. and Barthel, S. and Marquardt, O. and Hickel, T. and Neugebauer, J. and Czycholl, G. and Jahnke, F.
    Applied Physics Letters 100 (2012)
    Optical properties of polar and nonpolar nitride quantum dots (QDs) are determined on the basis of a microscopic theory which combines a continuum elasticity approach to the polarization potential, a tight-binding model for the electronic energies and wavefunctions, and a many-body theory for the optical properties. For nonpolar nitride quantum dots, we find that optical absorption and emission spectra exhibit a weak ground-state oscillator strength in a single-particle calculation whereas the Coulomb configuration interaction strongly enhances the ground-state transitions. This finding sheds new light on existing discrepancies between previous theoretical and experimental results for these systems, as a weak ground state transition was predicted because of the spatial separation of the corresponding electron and hole state due to intrinsic fields whereas experimentally fast optical transitions have been observed. © 2012 American Institute of Physics.
    view abstract10.1063/1.3688900
  • Thermodynamic and physical properties of FeAl and Fe 3Al: An atomistic study by EAM simulation
    Ouyang, Y. and Tong, X. and Li, C. and Chen, H. and Tao, X. and Hickel, T. and Du, Y.
    Physica B: Condensed Matter 407 (2012)
    With this work we present a newly developed potential for the Fe-Al system, which is based on the analytical embedded atom method (EAM) with long range atomic interactions. The potential yields for the two most relevant phases B2-FeAl and D0 3-Fe 3Al lattice constants, elastic constants, as well as bulk and point defect formation enthalpies, which are in good agreement with experimental and other theoretical data. In addition, the phonon dispersions for B2-FeAl and D0 3-Fe 3Al show a good agreement with available experiments. The calculated lattice constants and formation enthalpy for disordered Fe-Al alloys are in good agreement with experimental data or other theoretical calculations. This indicates that the present EAM potentials of Fe-Al system is suitable for atomistic simulations of structural and kinetic properties for the Fe-Al system. © 2012 Elsevier B.V.
    view abstract10.1016/j.physb.2012.08.025
  • Vacancy formation energies in fcc metals: Influence of exchange-correlation functionals and correction schemes
    Nazarov, R. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 85 (2012)
    The performance of various exchange-correlation functionals (LDA, PBE, PW91, and AM05) in predicting vacancy formation energies has been evaluated for 12 fcc metals. A careful analysis of the results shows that differences between the theoretical result and experiment are mainly related to the way the various exchange-correlation functionals describe the internal surface of the vacancy. Based on this insight we propose a modified version of the correction scheme of Mattsson, Wixom, and Armiento. Applying this approach to our results yields a perfect alignment of vacancy formation energies for all exchange-correlation functionals. These corrected values are also in very good agreement with the vacancy formation energies obtained in experiment. © 2012 American Physical Society.
    view abstract10.1103/PhysRevB.85.144118
  • A flexible, plane-wave-based formulation of continuum elasticity and multiband k·p models
    Marquardt, O. and Schulz, S. and O'Reilly, E.P. and Freysoldt, C. and Boeck, S. and Hickel, T. and Neugebauer, J.
    Proceedings of the International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD (2011)
    We present a highly flexible, plane-wave based formulation of continuum elasticity and multiband k·p-formalism to study the elastic and electronic properties of semiconductor nanostructures. This approach has been implemented in the framework of the density functional theory (DFT) software library S/Phi/nX [1] and allows the investigation of arbitrary-shaped nanostructures such as quantum wells, wires and dots consisting of various materials. Moreover, our approach grants the flexibility to employ user-generated k·p Hamiltonians suited to the requirements of the study regarding accuracy and computational costs. © 2011 IEEE.
    view abstract10.1109/NUSOD.2011.6041165
  • Ab initio based determination of thermodynamic properties of cementite including vibronic, magnetic, and electronic excitations
    Dick, A. and Körmann, F. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 84 (2011)
    The thermodynamic properties of cementite have been evaluated with a hybrid approach, which describes the vibrational and electronic excitations based on density functional theory calculations, while the magnetic free energy is evaluated using the spin quantum Monte Carlo scheme. Our ansatz allows us to calculate the heat capacity and free energy of cementite with a high accuracy resulting in a free-energy difference of less than 10 meV/atom at 1500 K when compared with experiment. For the formation energy of cementite we observe, however, that the accuracy of density functional theory within the Perdew-Burke-Ernzerhof exchange-correlation functional is not sufficient to provide quantitative agreement with experiment. We show that the main limit in the accuracy of this exchange-correlation functional is the T=0 K potential energy surface. © 2011 American Physical Society.
    view abstract10.1103/PhysRevB.84.125101
  • Designing shape-memory Heusler alloys from first-principles
    Siewert, M. and Gruner, M.E. and Dannenberg, A. and Chakrabarti, A. and Herper, H.C. and Wuttig, M. and Barman, S.R. and Singh, S. and Al-Zubi, A. and Hickel, T. and Neugebauer, J. and Gillessen, M. and Dronskowski, R. and Entel, P.
    Applied Physics Letters 99 (2011)
    The phase diagrams of magnetic shape-memory Heusler alloys, in particular, ternary Ni-Mn-Z and quarternary (Pt, Ni)-Mn-Z alloys with Z = Ga, Sn, have been addressed by density functional theory and Monte Carlo simulations. Finite temperature free energy calculations show that the phonon contribution stabilizes the high-temperature austenite structure while at low temperatures magnetism and the band Jahn-Teller effect favor the modulated monoclinic 14M or the nonmodulated tetragonal structure. The substitution of Ni by Pt leads to a series of magnetic shape-memory alloys with very similar properties to Ni-Mn-Ga but with a maximal eigenstrain of 14. © 2011 American Institute of Physics.
    view abstract10.1063/1.3655905
  • Determining the elasticity of materials employing quantum-mechanical approaches from the electronic ground state to the limits of materials stability
    Friák, M. and Hickel, T. and Körmann, F. and Udyansky, A. and Dick, A. and Von Pezold, J. and Ma, D. and Kim, O. and Counts, W.A. and Šob, M. and Gebhardt, T. and Music, D. and Schneider, J. and Raabe, D. and Neugebauer, J.
    Steel Research International 82 (2011)
    Quantum-mechanical (so-called ab initio) calculations have achieved considerable reliability in predicting physical and chemical properties and phenomena. Due to their reliability they are becoming increasingly useful when designing new alloys or revealing the origin of phenomena in existing materials, also because these calculations are able to accurately predict basic material properties without experimental input. Due to the universal validity of fundamental quantum mechanics, not only ground-state properties, but also materials responses to external parameters can reliably be determined. The focus of the present paper is on ab initio approaches to the elasticity of materials. First, the methodology to determine single-crystalline elastic constants and polycrystalline moduli of ordered compounds as well as disordered alloys is introduced. In a second part, the methodology is applied on α-Fe, with a main focus on (i) investigating the influence of magnetism on its elasticity and phase stability and (ii) simulating extreme loading conditions that go up to the theoretical tensile strength limits and beyond. Copyright © 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstract10.1002/srin.201000264
  • First-principles investigation of the effect of carbon on the stacking fault energy of Fe-C alloys
    Abbasi, A. and Dick, A. and Hickel, T. and Neugebauer, J.
    Acta Materialia 59 (2011)
    The intrinsic stacking fault energy (SFE) is a critical parameter that defines the type of plasticity mechanisms in austenitic high-Mn steels. We have performed ab initio investigations to study the effect of interstitial carbon atoms on the SFE of face-centred cubic (fcc) Fe-C alloys. Simulating the stacking fault explicitly, we observe a strong dependence of the SFE on the position of carbon atoms with respect to the stacking-fault layer and the carbon concentration. To determine the SFE for realistic carbon distributions we consider two scenarios, assuming (i) an equilibration of the carbon atoms in response to the stacking fault formation and (ii) a homogeneous distribution of the C atoms when creating the stacking fault (i.e. diffusion is suppressed). This distinction allows us to interpret two sets of apparently contradicting experimental data sets, where some find an almost negligible dependence on the carbon concentration while others report a large carbon dependence. In particular, our results for the second scenario show a significant increase in the SFE as a function of carbon concentration. These trends are consistently found for the explicit calculations as well as for the computationally much more efficient axial next-nearest-neighbour Ising approach. They will be decisive for the selection of specific plasticity mechanisms in steels (such as twin formation, martensitic transformations and dislocation gliding). © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2011.01.044
  • First-principles study on the interaction of H interstitials with grain boundaries in α- and γ-Fe
    Du, Y.A. and Ismer, L. and Rogal, J. and Hickel, T. and Neugebauer, J. and Drautz, R.
    Physical Review B - Condensed Matter and Materials Physics 84 (2011)
    The presence of hydrogen may weaken the bonding of iron atoms at grain boundaries, leading to intergranular embrittlement and thus failure of the bulk material. In this paper, we study the interaction of hydrogen interstitials with close-packed and open grain boundary structures in α- and γ-Fe using density-functional theory. We find that hydrogen accommodation within the grain boundaries strongly depends on the local coordination of the available interstitial sites. Within the open grain boundary structures larger interstitial sites are available, enhancing the solubility as compared to that in the respective bulk phases. The mobility of hydrogen within the investigated grain boundaries is low compared to diffusion in perfect single-crystalline bulk. The grain boundaries do not provide fast diffusion channels for hydrogen, but act as hydrogen traps. Hydrogen that is accumulated within the grain boundaries can lead to a lowering of the critical strain required to fracture the material. © 2011 American Physical Society.
    view abstract10.1103/PhysRevB.84.144121
  • Formation Energies of Point Defects at Finite Temperatures
    Grabowski, B. and Hickel, T. and Neugebauer, J.
    Advanced Calculations for Defects in Materials: Electronic Structure Methods (2011)
    view abstract10.1002/9783527638529.ch15
  • Formation energies of point defects at finite temperatures
    Grabowski, B. and Hickel, T. and Neugebauer, J.
    Physica Status Solidi (B) Basic Research 248 (2011)
    The dominant entropy contribution affecting defect concentrations is configurational entropy. Other contributions such as harmonic and anharmonic lattice vibrations are second order effects and computationally expensive to calculate. Therefore, such contributions have been rarely considered in defect investigations. However, to achieve the next accuracy level in defect calculations and thus significantly improve the agreement with experiment, the inclusion of these contributions is critical. In this paper, we present the methods needed to compute highly accurate free energies of point defects from first principles. We demonstrate how to include all relevant free energy contributions up to the melting point. The focus will be on nonmagnetic metals and point defects in the dilute limit. We consider all relevant excitation mechanisms: electronic excitations and ionic vibrations both in the quasiharmonic approximation and explicitly including anharmonicity (i.e., phonon-phonon interaction). Since computing such interactions requires to sample large parts of the phase space, straightforward ab initio based simulations (such as molecular dynamics) are in most cases out of reach even on supercomputers. To overcome this difficulty, a recently developed hierarchical scheme will be presented which allows to coarse grain the configuration space and thus to efficiently calculate anharmonic contributions to defect formation. We discuss the performance and accuracy of the developed methodology for the example of vacancies in aluminum. An important insight is that the entropy of vacancy formation is significantly affected by anharmonicity. We further show that the inclusion of all the aforementioned excitation mechanisms is critical to guarantee an accurate description of thermodynamic properties up to the melting point. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstract10.1002/pssb.201046302
  • Growth process, characterization, and modeling of electronic properties of coupled InAsSbP nanostructures
    Marquardt, O. and Hickel, T. and Neugebauer, J. and Gambaryan, K.M. and Aroutiounian, V.M.
    Journal of Applied Physics 110 (2011)
    Quaternary III-V InAsSbP quantum dots (QDs) have been grown in the form of cooperative InAsSb/InAsP structures using a modified version of the liquid phase epitaxy. High resolution scanning electron microscopy, atomic force microscopy, and Fourier-transform infrared spectrometry were used to investigate these so-called nano-camomiles, mainly consisting of a central InAsSb QD surrounded by six InAsP-QDs, that shall be referred to as leaves in the following. The observed QDs average density ranges from 0.8 to 2 × 109 cm -2, with heights and widths dimensions from 2 to 20 nm and 5 to 45 nm, respectively. The average density of the leaves is equal to (6-10) × 109 cm-2 with dimensions of approx. 5 to 40 nm in width and depth. To achieve a first basic understanding of the electronic properties, we have modeled these novel nanostructures using second-order continuum elasticity theory and an eight-band k p model to calculate the electronic structure. Our calculations found a clear localization of hole states in the central InAsSb dot. The localization of electron states, however, was found to be weak and might thus be easily influenced by external electric fields or strain. © 2011 American Institute of Physics.
    view abstract10.1063/1.3624621
  • Methodological challenges in combining quantum-mechanical and continuum approaches for materials science applications
    Friák, M. and Hickel, T. and Grabowski, B. and Lymperakis, L. and Udyansky, A. and Dick, A. and Ma, D. and Roters, F. and Zhu, L.-F. and Schlieter, A. and Kühn, U. and Ebrahimi, Z. and Lebensohn, R.A. and Holec, D. and Eckert, J. and Emmerich, H. and Raabe, D. and Neugebauer, J.
    European Physical Journal Plus 126 (2011)
    Multi-methodological approaches combining quantum-mechanical and/or atomistic simulations with continuum methods have become increasingly important when addressing multi-scale phenomena in computational materials science. A crucial aspect when applying these strategies is to carefully check, and if possible to control, a variety of intrinsic errors and their propagation through a particular multimethodological scheme. The first part of our paper critically reviews a few selected sources of errors frequently occurring in quantum-mechanical approaches to materials science and their multi-scale propagation when describing properties of multi-component and multi-phase polycrystalline metallic alloys. Our analysis is illustrated in particular on the determination of i) thermodynamic materials properties at finite temperatures and ii) integral elastic responses. The second part addresses methodological challenges emerging at interfaces between electronic structure and/or atomistic modeling on the one side and selected continuum methods, such as crystal elasticity and crystal plasticity finite element method (CEFEM and CPFEM), new fast Fourier transforms (FFT) approach, and phase-field modeling, on the other side. © Società Italiana di Fisica / Springer-Verlag 2011.
    view abstract10.1140/epjp/i2011-11101-2
  • Role of spin quantization in determining the thermodynamic properties of magnetic transition metals
    Körmann, F. and Dick, A. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 83 (2011)
    We propose a combined ab initio-spin quantum Monte Carlo (QMC) approach to compute thermodynamic properties of magnetic materials by first principles. The key to the proposed approach is a mapping of the magnetic long-range system onto an effective, nearest-neighbor quantum Heisenberg model, for which the QMC approach provides a numerically exact solution. The performance of the proposed method is demonstrated for the transition metals Fe, Co, and Ni by computing magnetization shapes, specific heat capacities, and free energies. Spin-quantization effects are found to be critical, even close to T C.© 2011 American Physical Society.
    view abstract10.1103/PhysRevB.83.165114
  • Temperature-driven phase transitions from first principles including all relevant excitations: The fcc-to-bcc transition in Ca
    Grabowski, B. and Söderlind, P. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 84 (2011)
    The temperature-driven fcc-to-bcc phase transition in calcium is examined by a fully ab initio-based integrated technique including all relevant finite-temperature excitation mechanisms. The approach is based on density-functional-theory calculations with a controlled numerical stability of below 0.5 meV/atom for the electronic, quasiharmonic, and structural excitations and better than 1 meV/atom for the explicitly anharmonic contribution. The latter is achieved by successfully utilizing the recently developed hierarchical upsampled thermodynamic integration using Langevin dynamics method. This approach gives direct access to a numerically highly precise volume- and temperature-dependent free-energy surface and derived properties. It enables us to assign the remaining deviations from experiment to inherent errors of the presently available exchange-correlation functionals. Performing the full analysis with both of the conventional functionals, local density approximation and generalized gradient approximation, we demonstrate that-when considered on an absolute scale-thermodynamic properties are dictated by a strikingly similar free energy vs volume curve. Further, we show that, despite an error in the T=0 K energy difference between the two phases (∼6 meV in the present case), an excellent agreement of the temperature dependence of the Gibbs energy difference with experimentally derived data is feasible. This makes it possible, for instance, to unveil unreliable and possibly erroneous experimental input used in popular thermodynamic databases as we explicitly demonstrate for the isobaric heat capacity of calcium. © 2011 American Physical Society.
    view abstract10.1103/PhysRevB.84.214107
  • The influence of additions of Al and Si on the lattice stability of fcc and hcp Fe-Mn random alloys
    Gebhardt, T. and Music, D. and Ekholm, M. and Abrikosov, I.A. and Vitos, L. and Dick, A. and Hickel, T. and Neugebauer, J. and Schneider, J.M.
    Journal of Physics Condensed Matter 23 (2011)
    We have studied the influence of additions of Al and Si on the lattice stability of face-centred-cubic (fcc) versus hexagonal-closed-packed (hcp) Fe-Mn random alloys, considering the influence of magnetism below and above the fcc Néel temperature. Employing two different ab initio approaches with respect to basis sets and treatment of magnetic and chemical disorder, we are able to quantify the predictive power of the ab initio methods. We find that the addition of Al strongly stabilizes the fcc lattice independent of the regarded magnetic states. For Si a much stronger dependence on magnetism is observed. Compared to Al, almost no volume change is observed as Si is added to Fe-Mn, indicating that the electronic contributions are responsible for stabilization/destabilization of the fcc phase. © 2010 IOP Publishing Ltd.
    view abstract10.1088/0953-8984/23/24/246003
  • Theoretical modeling of growth processes, extended defects, and electronic properties of III-nitride semiconductor nanostructures
    Lymperakis, L. and Abu-Farsakh, H. and Marquardt, O. and Hickel, T. and Neugebauer, J.
    Physica Status Solidi (B) Basic Research 248 (2011)
    Ab initio based simulations have been proven in the past to be and still are a valuable and indispensable tool in the field of III-nitride semiconductors. They have been successfully used to explain, describe and guide growth and characterization experiments and to address a large variety of material problems at different length scales. In the present report we review on five selected topics which span different length scales, various method developments, and diverse material properties that have been theoretically addressed within the research group "Physics of nitride-based, nanostructured, light emitting devices." Schematic representation of theoretical modeling in synergy with experiment. Left: Ab initio calculated potential energy surface for adatom diffusion on the side facets of a GaN nanowire [theory from L. Lymperakis et al., Phys. Rev. B 79, 241308 (2009), SEM image from T. Aschenbrenner et al., Nanotechnology 20, 075604 (2009)]. Right: Electrostatic potential in a QD calculated by Poisson solver [theory from O. Marquardt et al., J. Appl. Phys. 106, 083707 (2009), HRTEM image from A. Pretorius et al., J. Cryst. Growth 310, 748 (2008)]. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstract10.1002/pssb.201046511
  • Ab initio study of the solubility and kinetics of hydrogen in austenitic high Mn steels
    Ismer, L. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 81 (2010)
    Chemical trends for the solubility and diffusivity of hydrogen in austenitic high Mn steels have been studied employing density-functional theory. Considering the dilute limit of hydrogen, we observe strong volumetric effects of substitutional Mn and interstitial carbon on the energetics of a hydrogen atom within the lattice. This volume dependence yields a significant increase both in the solubility and the mobility of the H impurity when comparing Fe1-x Mnx Cy with pure Fe. By means of kinetic Monte Carlo calculations, we also show that H impurities can use Mn percolation chains as efficient diffusion channels. These trends may explain why Mn-rich steels are often observed to be more prone to hydrogen embrittlement than conventional austenitic steels. © 2010 The American Physical Society.
    view abstract10.1103/PhysRevB.81.094111
  • Ab initio study of thermodynamic, structural, and elastic properties of Mg-substituted crystalline calcite
    Elstnerová, P. and Friák, M. and Fabritius, H.O. and Lymperakis, L. and Hickel, T. and Petrov, M. and Nikolov, S. and Raabe, D. and Ziegler, A. and Hild, S. and Neugebauer, J.
    Acta Biomaterialia 6 (2010)
    Arthropoda, which represent nearly 80% of all known animal species, are protected by an exoskeleton formed by their cuticle. The cuticle represents a hierarchically structured multifunctional biocomposite based on chitin and proteins. Some groups, such as Crustacea, reinforce the load-bearing parts of their cuticle with calcite. As the calcite sometimes contains Mg it was speculated that Mg may have a stiffening impact on the mechanical properties of the cuticle (Becker et al., Dalton Trans. (2005) 1814). Motivated by these facts, we present a theoretical parameter-free quantum-mechanical study of the phase stability and structural and elastic properties of Mg-substituted calcite crystals. The Mg-substitutions were chosen as examples of states that occur in complex chemical environments typical for biological systems in which calcite crystals contain impurities, the role of which is still the topic of debate. Density functional theory calculations of bulk (Ca,Mg)CO3 were performed employing 30-atom supercells within the generalized gradient approximation as implemented in the Vienna Ab-initio Simulation Package. Based on the calculated thermodynamic results, low concentrations of Mg atoms are predicted to be stable in calcite crystals in agreement with experimental findings. Examining the structural characteristics, Mg additions nearly linearly reduce the volume of substituted crystals. The predicted elastic bulk modulus results reveal that the Mg substitution nearly linearly stiffens the calcite crystals. Due to the quite large size-mismatch of Mg and Ca atoms, Mg substitution results in local distortions such as off-planar tilting of the CO32- group. © 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actbio.2010.07.015
  • First-principles study of the thermodynamics of hydrogen-vacancy interaction in fcc iron
    Nazarov, R. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 82 (2010)
    The interaction of vacancies and hydrogen in an fcc iron bulk crystal was studied combining thermodynamic concepts with ab initio calculations and considering various magnetic structures. We show that up to six H atoms can be trapped by a monovacancy. All of the studied point defects (single vacancy, H in interstitial positions, and H-vacancy complexes) cause an anisotropic elastic field in antiferromagnetic fcc iron and significantly change the local and total magnetization of the system. The proposed thermodynamical model allows the determination of the equilibrium vacancy concentration and the concentration of dissolved hydrogen for a given temperature and H chemical potential in the reservoir. For H-rich conditions a dramatic increase in the vacancy concentration in the crystal is found. © 2010 The American Physical Society.
    view abstract10.1103/PhysRevB.82.224104
  • Plane-wave implementation of the real-space k ṡ p formalism and continuum elasticity theory
    Marquardt, O. and Boeck, S. and Freysoldt, C. and Hickel, T. and Neugebauer, J.
    Computer Physics Communications 181 (2010)
    In this work we demonstrate how second-order continuum elasticity theory and an eight-band k ṡ p model can be implemented in an existing density functional theory (DFT) plane-wave code. The plane-wave formulation of these two formalisms allows for an accurate and efficient description of elastic and electronic properties of semiconductor nanostructures such as quantum dots, wires, and films. Gradient operators that are computationally expensive in a real-space formulation can be calculated much more efficiently in reciprocal space. The accuracy can be directly controlled by the plane-wave cutoff. Furthermore, minimization schemes typically available in plane-wave DFT codes can be applied straightforwardly with only a few modifications to a plane-wave formulation of these continuum models. As an example, the elastic and electronic properties of a III-nitride quantum dot system are calculated. © 2009 Elsevier B.V. All rights reserved.
    view abstract10.1016/j.cpc.2009.12.009
  • Rescaled Monte Carlo approach for magnetic systems: Ab initio thermodynamics of bcc iron
    Körmann, F. and Dick, A. and Hickel, T. and Neugebauer, J.
    Physical Review B - Condensed Matter and Materials Physics 81 (2010)
    A combined ab initio approach to calculate the thermodynamic properties of bcc iron including vibrational, electronic, and magnetic free-energy contributions is derived. Special emphasis is placed on the magnetic contribution that is obtained using the frozen-magnon approach combined with Monte Carlo (MC) calculations. The importance of spin quantum-mechanical effects has been studied for magnetically nonfrustrated model systems by comparing classical and quantum MC. Based on this analysis, we propose a rescaling scheme which allows an approximate ad hoc inclusion of the quantum effects into the classical MC simulations. The rescaled MC scheme is found to be robust with respect to the specific magnetic configuration and the lattice type and is therefore expected to yield an approximate yet reliable description of the magnetic contribution for cases where quantum MC calculations are not practical. Applying the method to bcc iron and combining the magnetic, vibronic and electronic contributions, we find an excellent agreement with experimental data for the heat capacity and free energy, both, below and above the Curie temperature. © 2010 The American Physical Society.
    view abstract10.1103/PhysRevB.81.134425
  • Thermodynamic properties of cementite (Fe3 C)
    Hallstedt, B. and Djurovic, D. and von Appen, J. and Dronskowski, R. and Dick, A. and Körmann, F. and Hickel, T. and Neugebauer, J.
    Calphad: Computer Coupling of Phase Diagrams and Thermochemistry 34 (2010)
    Cementite (Fe3 C) is one of the most common phases in steel. In spite of its importance, thermodynamic investigations, either experimental or theoretical, of cementite are infrequent. In the present work, the thermodynamic properties of cementite are reevaluated and Gibbs energy functions valid from 0 K upwards presented. At high temperature (1000 K and above), the Gibbs energy is practically unchanged compared to previous evaluations. The energy of formation at 0 K was also calculated using density functional theory. This energy of formation (+8 kJ/mol at 0 K) is in reasonable agreement with the present thermodynamic evaluation (+23.5 kJ/mol at 0 K and +27.0 kJ/mol at 298.15 K) and with a solution calorimetric measurement of the enthalpy of formation (+18.8 kJ/mol at 298.15 K). In addition, the heat capacity was calculated theoretically using ab initio data combined with statistical concepts such as the quasiharmonic approximation. The theoretical calculation agrees equally well as the present evaluation with experimental data, but suggests a different weighting of the experimental data. In order to use it directly in the thermodynamic evaluation further modifications in the Fe-C system, primarily of the fcc phase, would be required in order to reproduce phase equilibrium data with sufficient accuracy. © 2010 Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.calphad.2010.01.004
  • ab initio calculations

  • alloys

  • electronic properties

  • magnetism

  • modelling and simulation

  • phase diagrams

  • shape-memory alloys

  • thermodynamics

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