#### Dr. Matous Mrovec

Atomistic Modelling and Simulation at ICAMS

Ruhr-Universität Bochum

##### Contact

- matous.mrovec@icams.rub.de
- +49 234 32 29313
- personal website

##### Hub

**Atomistic description of self-diffusion in molybdenum: A comparative theoretical study of non-Arrhenius behavior**

Smirnova, D. and Starikov, S. and Leines, G.D. and Liang, Y. and Wang, N. and Popov, M.N. and Abrikosov, I.A. and Sangiovanni, D.G. and Drautz, R. and Mrovec, M.*Physical Review Materials*4 (2020)According to experimental observations, the temperature dependence of self-diffusion coefficient in most body-centered cubic metals (bcc) exhibits non-Arrhenius behavior. The origin of this behavior is likely related to anharmonic vibrational effects at elevated temperatures. However, it is still debated whether anharmonicity affects more the formation or migration of monovacancies, which are known to govern the self-diffusion. In this extensive atomistic simulation study we investigated thermodynamic properties of monovacancies in bcc molybdenum, here taken as a representative model system, from zero temperature to the melting point. We combined first-principles calculations and classical simulations based on three widely used interatomic potentials for Mo. In our analysis we employ static and dynamic atomistic calculations as well as statistical sampling techniques and thermodynamic integration to achieve thorough information about temperature variations of vacancy formation and migration free energies and diffusivities. In addition, we carry out large-scale molecular dynamics simulations that enable direct observation of high-temperature self-diffusion at the atomic scale. By scrutinizing the results obtained by different models and methods, we conclude that the peculiar self-diffusion behavior is likely caused by strong temperature dependence of the vacancy formation energy. © 2020 American Physical Society.view abstract 10.1103/PhysRevMaterials.4.013605 **Fast diffusion mechanism in Li4P2S6: Via a concerted process of interstitial Li ions**

Stamminger, A.R. and Ziebarth, B. and Mrovec, M. and Hammerschmidt, T. and Drautz, R.*RSC Advances*10 (2020)The synthesis of Li superionic conductor Li7P3S11 may be accompanied by the formation of a detrimental Li4P2S6 phase due to a high mixing sensitivity of precursor materials. This phase exhibits a poor ionic conductivity whose origins are not fully understood. Recently Dietrich et al. investigated the energetics of Li ion migration in Li4P2S6 with nudged elastic band (NEB) calculations. The observed large migration barrier of 0.51 eV for purely interstitial diffusion leads to an interpretation of the low ionic conductivity by kinetic limitations. Based on ab initio molecular dynamics simulations (AIMD) we propose a new and energetically much more favorable diffusion path available to interstitial Li ion charge carriers that has not been considered so far. It consists of a concerted process in which a second lithium atom is pushed out from its equilibrium lattice position by the diffusing lithium ion. A detailed analysis with NEB calculations shows that the energy barrier for this concerted diffusion is only 0.08 eV, i.e. an order of magnitude lower than the previously reported value for purely interstitial diffusion. Therefore, the observed low ionic conductivity of Li4P2S6 is likely not originating from kinetic limitations due to high diffusion barriers but rather from thermodynamic reasons associated with a low concentration of free charge carriers. We therefore expect that increasing the charge carrier concentration by doping is a viable design route to optimize the ionic conductivity of this material. © 2020 The Royal Society of Chemistry.view abstract 10.1039/d0ra00932f **Study of grain boundary self-diffusion in iron with different atomistic models**

Starikov, S. and Mrovec, M. and Drautz, R.*Acta Materialia*188 (2020)We studied grain boundary (GB) self-diffusion in body-centered cubic iron using ab initio calculations and molecular dynamics simulations with various interatomic potentials. A combination of different models allowed us to determine the principal characteristics of self-diffusion along different types of GBs. In particular, we found that atomic self-diffusion in symmetric tilt GBs is mostly driven by self-interstitial atoms. In contrast, in general GBs atoms diffuse predominantly via an exchange mechanism that does not involve a particular defect but is similar to diffusion in a liquid. Most observed mechanisms lead to a significant enhancement of self-diffusion along GBs as compared to diffusion in the bulk. The results of simulations are verified by comparison with available experimental data. © 2020 Acta Materialia Inc.view abstract 10.1016/j.actamat.2020.02.027 **BOPfox program for tight-binding and analytic bond-order potential calculations**

Hammerschmidt, T. and Seiser, B. and Ford, M.E. and Ladines, A.N. and Schreiber, S. and Wang, N. and Jenke, J. and Lysogorskiy, Y. and Teijeiro, C. and Mrovec, M. and Cak, M. and Margine, E.R. and Pettifor, D.G. and Drautz, R.*Computer Physics Communications*235 (2019)Bond-order potentials (BOPs) provide a local and physically transparent description of the interatomic interaction. Here we describe the efficient implementation of analytic BOPs in the BOPfox program and library. We discuss the integration of the underlying non-magnetic, collinear-magnetic and noncollinear-magnetic tight-binding models that are evaluated by the analytic BOPs. We summarise the flow of an analytic BOP calculation including the determination of self-returning paths for computing the moments, the self-consistency cycle, the estimation of the band-width from the recursion coefficients, and the termination of the BOP expansion. We discuss the implementation of the calculations of forces, stresses and magnetic torques with analytic BOPs. We show the scaling of analytic BOP calculations with the number of atoms and moments, present options for speeding up the calculations and outline different concepts of parallelisation. In the appendix we compile the implemented equations of the analytic BOP methodology and comments on the implementation. This description should be relevant for other implementations and further developments of analytic bond-order potentials. © 2018 Elsevier B.V.view abstract 10.1016/j.cpc.2018.08.013 **Density functional theory calculations of iron - vanadium carbide interfaces and the effect of hydrogen**

Echeverri Restrepo, S. and Di Stefano, D. and Mrovec, M. and Paxton, A.T.*International Journal of Hydrogen Energy*(2019)According to recent experimental research, vanadium-carbide precipitates can improve hydrogen resistance and hardness in steels. In the present article, density functional theory calculations are performed to study the structure and energetics of iron–vanadium carbide interfaces and how hydrogen interacts with them. A comparison of the solubility of hydrogen in different sites shows that hydrogen will tend to segregate towards the iron–vanadium carbide interface and that carbon vacancies within a vanadium carbide precipitate behave as strong hydrogen traps. Additionally, it is shown that the presence of hydrogen at an iron–vanadium carbide interface does not cause a significant embrittlement of the material. © 2019 Hydrogen Energy Publications LLCview abstract 10.1016/j.ijhydene.2019.11.102 **Ionic Conductivity and Its Dependence on Structural Disorder in Halogenated Argyrodites Li6PS5X (X = Br, Cl, I)**

Stamminger, A.R. and Ziebarth, B. and Mrovec, M. and Hammerschmidt, T. and Drautz, R.*Chemistry of Materials*(2019)Halogenated argyrodites Li6PS5Br, Li6PS5Cl, and Li6PS5I exhibit large differences in the measured Li ionic conductivities. Crystallographic analysis has shown that these differences may be related to occupations of specific Wyckoff sites in different argyrodite types, but detailed understanding of the relationship between the atomic structure and operating diffusion mechanisms is still lacking. In this work, we employed ab initio molecular dynamics simulations to calculate the Li diffusivity for different argyrodite structure types. Our calculations show that the Li diffusivity does not depend implicitly on the type of halogen but is rather governed by the degree of structural disorder. Assuming disordered structures to arise naturally from the ordered structure type by thermally activated antisite defects, we are able to explain the degree of disorder found for the different types of halogens from the calculated defect formation energies. Comparing the calculated formation energies to the ionic radii of the halogen atoms, we find a strong correlation between the radii and energies required for introducing the antisite defects. © 2019 American Chemical Society.view abstract 10.1021/acs.chemmater.9b02047 **Phase transitions in titanium with an analytic bond-order potential**

Ferrari, A. and Schröder, M. and Lysogorskiy, Y. and Rogal, J. and Mrovec, M. and Drautz, R.*Modelling and Simulation in Materials Science and Engineering*27 (2019)Titanium is the base material for a number of technologically important alloys for energy conversion and structural applications. Atomic-scale studies of Ti-based metals employing first-principles methods, such as density functional theory, are limited to ensembles of a few hundred atoms. To perform large-scale and/or finite temperature simulations, computationally more efficient interatomic potentials are required. In this work, we coarse grain the tight-binding (TB) approximation to the electronic structure and develop an analytic bond-order potential (BOP) for Ti by fitting to the energies and forces of elementary deformations of simple structures. The BOP predicts the structural properties of the stable and defective phases of Ti with a quality comparable to previous TB parameterizations at a much lower computational cost. The predictive power of the model is demonstrated for simulations of martensitic transformations. © 2019 IOP Publishing Ltd.view abstract 10.1088/1361-651X/ab471d **Predicting grain boundary structure and energy in BCC metals by integrated atomistic and phase-field modeling**

Qiu, D. and Zhao, P. and Shen, C. and Lu, W. and Zhang, D. and Mrovec, M. and Wang, Y.*Acta Materialia*164 (2019)We predict structure and energy of low-angle (11¯0) pure twist grain boundaries (GBs) in five BCC transition metals (β-titanium, molybdenum, niobium, tungsten, and tantalum) using a combination of atomistic and microscopic phase-field (MPF) modeling. The MPF model takes as inputs solely the generalized stacking fault energy surfaces (i.e., the γ-surface) and elastic constants obtained from the atomistic simulations. Being an energy-based method, the MPF model lifts the degeneracy of the geometric models in predicting GB structures. For example, the multiple indefinite solutions offered by the Frank-Bilby equation are shown to converge to exactly the same equilibrium structure. It predicts a transition of the equilibrium GB structure from a pure screw hexagonal network (Mo and W) to mixed hexagonal networks (Nb and Ta) to a rhombus network (β-Ti) of dislocations. Parametric simulation studies and detailed analyses of the underlying dislocation reactions that are responsible for the formation of the rhombus and hexagonal structures reveal a close correlation between material properties (including the elastic anisotropic ratio and the local curvature on the γ-surface) and the GB structure and energy in BCC metals. This integrated approach allows one to explore, through high throughput calculations, the potential to tailor the structure and energy of special GBs in BCC metals by alloying. © 2018 Acta Materialia Inc.view abstract 10.1016/j.actamat.2018.11.023 **Superioniclike diffusion in an elemental crystal: Bcc Titanium**

Sangiovanni, D.G. and Klarbring, J. and Smirnova, D. and Skripnyak, N.V. and Gambino, D. and Mrovec, M. and Simak, S.I. and Abrikosov, I.A.*Physical Review Letters*123 (2019)Recent theoretical investigations [A. B. Belonoshko et al. Nat. Geosci. 10, 312 (2017)1752-089410.1038/ngeo2892] revealed the occurrence of the concerted migration of several atoms in bcc Fe at inner-core temperatures and pressures. Here, we combine first-principles and semiempirical atomistic simulations to show that a diffusion mechanism analogous to the one predicted for bcc iron at extreme conditions is also operative and of relevance for the high-temperature bcc phase of pure Ti at ambient pressure. The mechanism entails a rapid collective movement of numerous (from two to dozens) neighbors along tangled closed-loop paths in defect-free crystal regions. We argue that this phenomenon closely resembles the diffusion behavior of superionics and liquid metals. Furthermore, we suggest that concerted migration is the atomistic manifestation of vanishingly small ω-mode phonon frequencies previously detected via neutron scattering and the mechanism underlying anomalously large and markedly non-Arrhenius self-diffusivities characteristic of bcc Ti. © 2019 American Physical Society.view abstract 10.1103/PhysRevLett.123.105501 **{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 abstract 10.1103/PhysRevMaterials.2.093606 **Development of bond-order potentials for BCC transition metals**

Vitek, V. and Lin, Y.-S. and Mrovec, M.*Solid State Phenomena*258 SSP (2017)In this paper we present bond-order potentials (BOPs) based on the tight-binding method. The potentials have been developed for bcc non-magnetic metals of group V.B (V, Nb, Ta) and group VI.B (Cr, Mo, W) as well as for the ferromagnetic bcc iron. The testing of the transferability of BOPs involves energies of alternate structures, formation energies of vacancies and selfinterstitials, transformation paths between different structures and phonon dispersion relations. An example of the application of these potentials is modeling of the structure and glide of ½<111> screw dislocations under the effect of applied shear and tensile/compressive stresses. © 2017 Trans Tech Publications, Switzerland.view abstract 10.4028/www.scientific.net/SSP.258.3 **Bond-order potential for magnetic body-centered-cubic iron and its transferability**

Lin, Y.-S. and Mrovec, M. and Vitek, V.*Physical Review B - Condensed Matter and Materials Physics*93 (2016)We derived and thoroughly tested a bond-order potential (BOP) for body-centered-cubic (bcc) magnetic iron that can be employed in atomistic calculations of a broad variety of crystal defects that control structural, mechanical, and thermodynamic properties of this technologically important metal. The constructed BOP reflects correctly the mixed nearly free electron and covalent bonding arising from the partially filled d band as well as the ferromagnetism that is actually responsible for the stability of the bcc structure of iron at low temperatures. The covalent part of the cohesive energy is determined within the tight-binding bond model with the Green's function of the Schrödinger equation determined using the method of continued fractions terminated at a sufficient level of the moments of the density of states. This makes the BOP an O(N) method usable for very large numbers of particles. Only dd bonds are included explicitly, but the effect of s electrons on the covalent energy is included via their screening of the corresponding dd bonds. The magnetic part of the cohesive energy is included using the Stoner model of itinerant magnetism. The repulsive part of the cohesive energy is represented, as in any tight-binding scheme, by an empirical formula. Its functional form is physically justified by studies of the repulsion in face-centered-cubic (fcc) solid argon under very high pressure where the repulsion originates from overlapping s and p closed-shell electrons just as it does from closed-shell s electrons in transition metals squeezed into the ion core under the influence of the large covalent d bonding. Testing of the transferability of the developed BOP to environments significantly different from those of the ideal bcc lattice was carried out by studying crystal structures and magnetic states alternative to the ferromagnetic bcc lattice, vacancies, divacancies, self-interstitial atoms (SIAs), paths continuously transforming the bcc structure to different less symmetric structures and phonons. The results of these calculations are compared with either experiments or calculations based on the density functional theory (DFT), and they all show very good agreement. Importantly, the lowest energy configuration of SIAs agrees with DFT calculations that show that it is an exception within bcc transition metals controlled by magnetism. Moreover, the migration energy of interstitials is significantly lower than that of vacancies, which is essential for correct analysis of the effects of irradiation. Finally, the core structure and glide of 1/2(111) screw dislocations that control the plastic flow in single crystals of bcc metals was explored. The results fully agree with available DFT based studies and with experimental observations of the slip geometry of bcc iron at low temperatures. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.93.214107 **First principles characterisation of brittle transgranular fracture of titanium hydrides**

Olsson, P.A.T. and Mrovec, M. and Kroon, M.*Acta Materialia*118 (2016)In this work we have studied transgranular cleavage and the fracture toughness of titanium hydrides by means of quantum mechanical calculations based on density functional theory. The calculations show that the surface energy decreases and the unstable stacking fault energy increases with increasing hydrogen content. This is consistent with experimental findings of brittle behaviour of titanium hydrides at low temperatures. Based on Griffith-Irwin theory we estimate the fracture toughness of the hydrides to be of the order of 1 MPa⋅m1/2, which concurs well with experimental data. To investigate the cleavage energetics, we analyse the decohesion at various crystallographic planes and determine the traction-separation laws based on the Rose's extended universal binding energy relation. The calculations predict that the peak stresses do not depend on the hydrogen content of the phases, but it is rather dependent on the crystallographic cleavage direction. However, it is found that the work of fracture decreases with increasing hydrogen content, which is an indication of hydrogen induced bond weakening in the material. © 2016 Acta Materialia Inc.view abstract 10.1016/j.actamat.2016.07.037 **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 abstract 10.1103/PhysRevB.93.184108 **Hydrogen diffusion and trapping in Ti-modified advanced high strength steels**

Winzer, N. and Rott, O. and Thiessen, R. and Thomas, I. and Mraczek, K. and Höche, T. and Wright, L. and Mrovec, M.*Materials and Design*92 (2016)The influence of Ti on hydrogen diffusion and trapping in various advanced high strength steels was investigated. Electrochemical hydrogen permeation tests were performed on various model steels, with and without Ti, with benchmark tests performed using a commercial steel variant. The hydrogen trapping parameters for each steel were determined by fitting the permeation curves with a finite element model based on the McNabb and Foster equations using least squares minimisation. The influence of Ti on the hydrogen trapping parameters was greatly dependent on microstructure, with ferrite-containing grades being most affected. The results are inconsistent with hydrogen trapping by TiC particles, but consistent with trapping by boundaries between neighbouring ferrite and martensite grains. © 2015 Elsevier Ltd.view abstract 10.1016/j.matdes.2015.12.060 **Importance of inclusion of the effect of s electrons into bond-order potentials for transition bcc metals with d-band mediated bonding**

Lin, Y.-S. and Mrovec, M. and Vitek, V.*Modelling and Simulation in Materials Science and Engineering*24 (2016)In bond-order potentials (BOPs) for transition metals only the bonding mediated by the d electrons is included explicitly and the covalent part of the cohesive energy is evaluated using Slater-Koster dd bond integrals. However, the effect of s electrons with orbitals centered on atoms neighboring the corresponding dd bond is not necessarily negligible. As shown in Nguyen-Manh et al (2000 Phys. Rev. Lett. 85 4136) this can be taken into account via screening of the dd bond integrals. In a recent paper (Lin et al 2014 Model. Simul. Mater. Sci. Eng. 22 034002) the dd bond integrals were determined using a projection scheme utilizing atomic orbitals that give the best representation of the electronic wave functions in the calculations based on the density functional theory (DFT) (Madsen et al 2011 Phys. Rev. B 83 4119) and it was inferred that in this case the effect of s electrons was already included. In this paper we analyze this hypothesis by comparing studies employing BOPs with both unscreened and screened dd bond integrals. In all cases results are compared with calculations based on DFT and/or experiments. Studies of structures alternate to the bcc lattice, transformation paths that connect the bcc structure with fcc, simple cubic (sc), body centered tetragonal (bct) and hcp structures via continuously distorted configurations and calculations of γ-surfaces were all found to be insensitive to the screening of bond integrals. On the other hand, when the bond integrals are screened, formation energies of vacancies are improved and calculated phonon dispersion spectra reproduce the experimentally observed ones much better. Most importantly, dislocation core structure and dislocation glide are significantly different without and with screening of dd bond integrals. The latter lead to a much better agreement with available experiments. These findings suggest that the effect of s electrons on dd bonds, emulated by the screening of corresponding bond integrals, is the least significant when the lattice is distorted away from the ideal bcc structure homogeneously even if such distortion is large. On the other hand, when the distortion is local and inhomogeneous the impact of screening of the dd bond integrals is significant. In the studies presented in this paper such local inhomogeneities occur when phonons propagate through the lattice, at point defects and in the cores of dislocations. © 2016 IOP Publishing Ltd.view abstract 10.1088/0965-0393/24/8/085001 **Atomistically enabled nonsingular anisotropic elastic representation of near-core dislocation stress fields in α -iron**

Seif, D. and Po, G. and Mrovec, M. and Lazar, M. and Elsässer, C. and Gumbsch, P.*Physical Review B - Condensed Matter and Materials Physics*91 (2015)The stress fields of dislocations predicted by classical elasticity are known to be unrealistically large approaching the dislocation core, due to the singular nature of the theory. While in many cases this is remedied with the approximation of an effective core radius, inside which ad hoc regularizations are implemented, such approximations lead to a compromise in the accuracy of the calculations. In this work an anisotropic nonsingular elastic representation of dislocation fields is developed to accurately represent the near-core stresses of dislocations in α-iron. The regularized stress field is enabled through the use of a nonsingular Green's tensor function of Helmholtz-type gradient anisotropic elasticity, which requires only a single characteristic length parameter in addition to the material's elastic constants. Using a magnetic bond-order potential to model atomic interactions in iron, molecular statics calculations are performed, and an optimization procedure is developed to extract the required length parameter. Results show the method can accurately replicate the magnitude and decay of the near-core dislocation stresses even for atoms belonging to the core itself. Comparisons with the singular isotropic and anisotropic theories show the nonsingular anisotropic theory leads to a substantially more accurate representation of the stresses of both screw and edge dislocations near the core, in some cases showing improvements in accuracy of up to an order of magnitude. The spatial extent of the region in which the singular and nonsingular stress differ substantially is also discussed. The general procedure we describe may in principle be applied to accurately model the near-core dislocation stresses of any arbitrarily shaped dislocation in anisotropic cubic media. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.91.184102 **First-principles investigation of hydrogen trapping and diffusion at grain boundaries in nickel**

Di Stefano, D. and Mrovec, M. and Elsässer, C.*Acta Materialia*98 (2015)Abstract In this work, the interaction of hydrogen with high-angle GBs in nickel has been investigated by means of density functional theory simulations. Two distinct types of GBs have been considered: the Σ3(111)[1¯10] with a close-packed interface structure and the Σ5(210)[001] with a less dense interface structure consisting of open structural units. Our calculations reveal that these two GBs have a markedly different interaction behavior with atomic hydrogen. The close-packed Σ3 GB neither traps H nor enhances its diffusion, but instead acts as a two-dimensional diffusion barrier. In contrast, the Σ5 GB provides numerous trapping sites for H within the open structural units as well as easy migration pathways for H diffusion along the GB plane that can enhance the H diffusivity by about two orders of magnitude compared to bulk Ni. The obtained results are analysed in detail and compared with available experimental and other theoretical data. © 2015 Acta Materialia Inc.view abstract 10.1016/j.actamat.2015.07.031 **First-principles investigation of quantum mechanical effects on the diffusion of hydrogen in iron and nickel**

Di Stefano, D. and Mrovec, M. and Elsässer, C.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)The diffusion coefficients of interstitial hydrogen in bulk Fe and Ni crystals have been calculated over a wide range of temperatures employing first-principles methods based on density functional theory. Quantum mechanical effects have been included by means of the semiclassical transition state theory and the small-polaron model of Flynn and Stoneham. Our results show that to include such effects is crucial for a quantitative simulation of H diffusion in bcc Fe even at room temperature, while in the case of fcc Ni this is less important. The comparison with other theoretical approaches as well as with experimental studies emphasizes the main advantages of the present approach: it is quantitatively accurate and computationally efficient. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.92.224301 **Influence of dislocation strain fields on the diffusion of interstitial iron impurities in silicon**

Ziebarth, B. and Mrovec, M. and Elsässer, C. and Gumbsch, P.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)The efficiency of silicon (Si)-based solar cells is strongly affected by crystal defects and impurities. Metallic impurities, in particular interstitial iron (Fe) atoms, cause large electric losses because they act as recombination centers for photogenerated charge carriers. Here, we present a systematic first-principles density functional theory (DFT) study focusing on the influence of hydrostatic, uniaxial, and shear strains on the thermodynamic stability and the diffusivity of Fe impurities in crystalline Si. Our calculations show that the formation energy of neutral Fe interstitials in tetrahedral interstitial sites is almost unaffected by uniform deformations of the Si crystal up to strains of 5%. In contrast, the migration barrier varies significantly with strain, especially for hydrostatic deformation. In order to determine effective diffusion coefficients for different strain states, a kinetic Monte Carlo (kMC) model was set up based on the activation energy barriers and frequency factors obtained from the DFT simulations. By using the strain dependence of the migration barrier, we examined the migration of Fe interstitials in the vicinity of perfect 1/2(110) screw and 60 mixed dislocations, and 1/6(112)90 and 30 partial dislocations. While the strain field of the perfect screw dislocation always enhances the local Fe diffusion, the existence of tensile and compressive regions around the 60 mixed dislocation results in a strong anisotropic diffusion profile with significantly faster and slower diffusivities on its tensile and compressive sides. The influences of the partial dislocations are qualitatively similar to that of the 60 mixed dislocation. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.92.115309 **Interstitial iron impurities at cores of dissociated dislocations in silicon**

Ziebarth, B. and Mrovec, M. and Elsässer, C. and Gumbsch, P.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)Dislocations play an important role in semiconductor devices made of crystalline silicon (Si). They are known to be strongly performance-limiting defects in solar cell applications, since they act as preferred segregation sites for metallic impurities. In this work we investigate the segregation of iron (Fe) to the cores of the 30°C and 90°C partial dislocations in Si using atomistic calculations based on first-principles density functional theory. Our simulations show that interstitial Fe impurities segregate readily to all investigated cores and the driving force for the segregation increases with impurity concentration. Moreover, our analysis of the electronic structure reveals the existence of deep defect levels within the band gap that can be related to experimental observations by deep-level transient spectroscopy. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.92.195308 **Interstitial iron impurities at grain boundaries in silicon: A first-principles study**

Ziebarth, B. and Mrovec, M. and Elsässer, C. and Gumbsch, P.*Physical Review B - Condensed Matter and Materials Physics*91 (2015)Iron impurities have a negative effect on the efficiency of silicon-based solar cells because they act as trapping centers for charge carriers. Various processing techniques have been applied to improve the efficiency by passivating the Fe contaminants. For instance, internal gettering exploits the attractive interaction between interfaces and the diffusing Fe atoms. Therefore, it is interesting and important to develop a fundamental understanding of mechanisms for this interaction. In this work, we employ density functional theory to study the electronic structure and the segregation behavior of impurity atoms at grain boundaries (GBs). The investigated set of symmetrical tilt or twist GBs in Si provides a variety of interface orientations and structures at the atomic scale. Our results suggest that segregation of interstitial Fe occurs only at specific sites at some of these GBs, e.g., the Σ3 (112) GBs and Σ3 (110) GBs. However, there seems to be no obvious relation between the computed segregation energies and the local coordination and electronic structure at the segregation sites. Hence, the thermodynamics of interstitial Fe at GBs in Si is determined by rather subtle features of structure and bonding. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.91.035309 **Multiferroic grain boundaries in oxygen-deficient ferroelectric lead titanate**

Shimada, T. and Wang, J. and Ueda, T. and Uratani, Y. and Arisue, K. and Mrovec, M. and Elsä Sser, C. and Kitamura, T.*Nano Letters*15 (2015)Ultimately thin multiferroics arouse remarkable interest, motivated by the diverse utility of coexisting ferroelectric and (anti)ferromagnetic order parameters for novel functional device paradigms. However, the ferroic order is inevitably destroyed below a critical size of several nanometers. Here, we demonstrate a new path toward realization of atomically thin multiferroic monolayers while resolving a controversial origin for unexpected "-dilute ferromagnetism" emerged in nanocrystals of nonmagnetic ferroelectrics PbTiO3. The state-of-the-art hybrid functional of Hartree-Fock and density functional theories successfully identifies the origin and underlying physics; oxygen vacancies interacting with grain boundaries (GBs) bring about (anti)ferromagnetism with localized spin moments at the neighboring Ti atoms. This is due to spin-polarized defect states with broken orbital symmetries at GBs. In addition, the energetics of oxygen vacancies indicates their self-assembling nature at GBs resulting in considerably high concentration, which convert the oxygen-deficient GBs into multiferroic monolayers due to their atomically thin interfacial structure. This synthetic concept that realizes multiferroic and multifunctional oxides in a monolayered geometry through the self-assembly of atomic defects and grain boundary engineering opens a new avenue for promising paradigms of novel functional devices. © 2014 American Chemical Society.view abstract 10.1021/nl502471a **Multiferroic Vacancies at Ferroelectric PbTiO3 Surfaces**

Shimada, T. and Wang, J. and Araki, Y. and Mrovec, M. and Elsässer, C. and Kitamura, T.*Physical Review Letters*115 (2015)Multiferroics in nanoscale dimensions are promising for novel functional device paradigms, such as magnetoelectric memories, due to an intriguing cross-coupling between coexisting ferroelectric and (anti)ferromagnetic order parameters. However, the ferroic order is inevitably destroyed below the critical dimension of several nanometers. Here, we demonstrate a new path towards atomic-size multiferroics while resolving the controversial origin of dilute ferromagnetism that unexpectedly emerges in nanoparticles of nonmagnetic ferroelectric PbTiO3. Systematic exploration using predictive quantum-mechanical calculations demonstrates that oxygen vacancies formed at surfaces induce ferromagnetism due to local nonstoichiometry and orbital symmetry breaking. The localized character of the emerged magnetization allows an individual oxygen vacancy to act as an atomic-scale multiferroic element with a nonlinear magnetoelectric effect that involves rich ferromagnetic-antiferromagnetic-nonmagnetic phase transitions in response to switching of the spontaneous polarization. © 2015 American Physical Society.view abstract 10.1103/PhysRevLett.115.107202 **Multiscale Simulation of Plasticity in bcc Metals**

Weygand, D. and Mrovec, M. and Hochrainer, T. and Gumbsch, P.*Annual Review of Materials Research*45 (2015)Significant progress in our understanding of plasticity in body-centered cubic (bcc) metals during the last decade has enabled rigorous multiscale modeling based on quantitative physical principles. Significant advances have been made at the atomistic level in the understanding of dislocation core structures and energetics associated with dislocation glide by using high-fidelity models originating from quantum mechanical principles. These simulations revealed important details about the influence of non-Schmid (nonglide) stresses on the mobility of screw dislocations in bcc metals that could be implemented to mesoscopic discrete dislocation simulations with atomistically informed dislocation mobility laws. First applications of dislocation dynamics simulations to studies of plasticity in small-scale bcc single crystals have been performed. Dislocation dynamics simulations inspired the development of continuum models based on advanced 3D dislocation density measures with evolution equations that naturally track dislocation motion. These advances open new opportunities and perspectives for future quantitative and materials-specific multiscale simulation methods to describe plastic deformation in bcc metals and their alloys. Copyright © 2015 by Annual Reviews. All rights reserved.view abstract 10.1146/annurev-matsci-070214-020852 **Reduced tight-binding models for elemental Si and N, and ordered binary Si-N systems**

Gehrmann, J. and Pettifor, D.G. and Kolmogorov, A.N. and Reese, M. and Mrovec, M. and Elsässer, C. and Drautz, R.*Physical Review B - Condensed Matter and Materials Physics*91 (2015)Silicon nitride is a bulk and a coating material exhibiting excellent mechanical properties. We present a transferable reduced tight-binding (TB) model for the silicon nitride system, developed within the framework of coarse graining the electronic structure from density-functional theory (DFT) to tight binding (TB) to bond-order potentials (BOPs). The TB bond integrals are obtained directly from mixed-basis DFT projections of wave functions onto a minimal basis of atom-centered orbitals. This approach reduces the number of overall parameters to be fitted. Furthermore, applying the reduced TB approximation automatically leads to a single σ bond order that contributes to the bond energy. DFT binding energies of ground state and metastable crystal structures are used as the benchmark to which the TB repulsive parameters are fitted. The quality of the TB models is demonstrated by comparing their predictions for the binding energies, heats of formation, elastic constants, and defect energies with DFT and experimental values. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.91.054109 **Theoretical and experimental study of the core structure and mobility of dislocations and their influence on the ferroelectric polarization in perovskite KNbO3**

Hirel, P. and Mark, A.F. and Castillo-Rodriguez, M. and Sigle, W. and Mrovec, M. and Elsässer, C.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)Potassium niobate KNbO3 is a lead-free perovskite and a promising candidate to replace lead-containing ferroelectrics related to PbTiO3. In this study, we use atomistic computer simulation and transmission electron microscopy to investigate dislocations in KNbO3, first to establish the relationship between their atomic-scale properties and the macroscopic mechanical behavior, and second to study their influence on the ferroelectric properties of the material. The easiest dislocation glide system is found to be (110){11¯0} at all temperatures, independent from structural phase transformations. The mobility of dislocations and the evolution of the microstructure are measured from room temperature up to 1173 K. A sharp transition in the yield stress is found around 800 K, attributed to the additional activation of the (100){010} glide system at high temperature. Atomistic simulations quantify the effect of dislocations on the ferroelectric polarization, and TEM observations give indication of the nucleation of domain walls at dislocation cores. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.92.214101 **A new method for development of bond-order potentials for transition bcc metals**

Lin, Y.-S. and Mrovec, M. and Vitek, V.*Modelling and Simulation in Materials Science and Engineering*22 (2014)A new development of numerical bond-order potentials (BOPs) for the non-magnetic transition metals V, Nb, Ta, Cr, Mo and W is presented. The principles on which the BOPs have been set up are the same as in earlier developments (Aoki et al 2007 Prog. Mater. Sci. 52 154). However, the bond integrals are based on the recently advanced method of parametrization of tight-binding from DFT calculations (Madsen et al 2011 Phys. Rev. B 83 4119, Urban et al 2011 Phys. Rev. B 84 155119) and do not require any screening. At the same time, the functional form of the environmentally dependent repulsion is identified with the functional form of the repulsion arising from the overlap of s and p electrons in argon as proposed in Aoki and Kurokawa (2007 J. Phys.: Condens. Matter 19 136228). This is justified by the same physical origin of the environment dependent repulsion, which in transition metals arises from the overlap of s electrons that are being squeezed into the ion core regions under the influence of the strong covalent d bonds. The testing of the developed BOPs involves investigation of alternative higher energy structures, transformation paths connecting the bcc structure with other structures via continuously distorted configurations, evaluation of the vacancy formation energy and calculation of phonon spectra. In all cases, the BOP calculations are in more than satisfactory agreement with either DFT calculations and/or available experimental data. The calculated γ-surfaces for {1 0 1} planes all suggest that the core of 1/21 1 1 screw dislocations is non-degenerate in the transition metals. This is also in full agreement with available calculations that account fully for the quantum-mechanical nature of the d electrons that provide the bulk of the bonding in transition metals. The testing of developed BOPs clearly demonstrates that they are transferable to structures well outside the regime of the ideal bcc lattice and are suitable for investigating the atomic structure and behaviour of extended crystal defects. © 2014 IOP Publishing Ltd.view abstract 10.1088/0965-0393/22/3/034002 **Coarse graining and localized plasticity between sliding nanocrystalline metals**

Romero, P.A. and Järvi, T.T. and Beckmann, N. and Mrovec, M. and Moseler, M.*Physical Review Letters*113 (2014)Tribological shearing of polycrystalline metals typically leads to grain refinement at the sliding interface. This study, however, shows that nanocrystalline metals exhibit qualitatively different behavior. Using large-scale atomistic simulations, we demonstrate that during sliding, contact interface nanocrystalline grains self-organize through extensive grain coarsening and lattice rotation until the optimal plastic slip orientation is established. Subsequently, plastic deformation is frequently confined to localized nanoshear bands aligned with the shearing direction and emanating from voids and other defects in the vicinity of the sliding interface. © 2014 American Physical Society.view abstract 10.1103/PhysRevLett.113.036101 **Multiscale Approaches to Hydrogen-Assisted Degradation of Metals**

Winzer, N. and Mrovec, M.*JOM*66 (2014)view abstract 10.1007/s11837-014-1082-0 **Potential-induced degradation in solar cells: Electronic structure and diffusion mechanism of sodium in stacking faults of silicon**

Ziebarth, B. and Mrovec, M. and Elsässer, C. and Gumbsch, P.*Journal of Applied Physics*116 (2014)Sodium decorated stacking faults (SFs) were recently identified as the primary cause of potential-induced degradation in silicon (Si) solar-cells due to local electrical short-circuiting of the p-n junctions. In the present study, we investigate these defects by first principles calculations based on density functional theory in order to elucidate their structural, thermodynamic, and electronic properties. Our calculations show that the presence of sodium (Na) atoms leads to a substantial elongation of the Si-Si bonds across the SF, and the coverage and continuity of the Na layer strongly affect the diffusion behavior of Na within the SF. An analysis of the electronic structure reveals that the presence of Na in the SF gives rise to partially occupied defect levels within the Si band gap that participate in electrical conduction along the SF. © 2014 AIP Publishing LLC.view abstract 10.1063/1.4894007 **Atomistic aspects of 〈1 1 1〉 screw dislocation behavior in α-iron and the derivation of microscopic yield criterion**

Chen, Z.M. and Mrovec, M. and Gumbsch, P.*Modelling and Simulation in Materials Science and Engineering*21 (2013)The plastic deformation of body-centered cubic iron at low temperatures is governed by slip behavior of 1 2 〈1 1 1〉 screw dislocations. Their non-planar core structure gives rise to a strong temperature dependence of the yield stress and overall plastic behavior that does not follow the Schmid law common to most close-packed metals. In this work,we carry out a systematic study of the screw dislocation behavior in α-Fe by means of atomistic simulations using a state-of-the-art magnetic bond-order potential. Based on the atomistic simulations of the screw dislocations under various external loadings, we formulate an analytical yield criterion that correctly captures the non-Schmid plastic response of iron single crystals under general loading conditions. The theoretical predictions of operative slip systems for uniaxial loadings agree well with available experimental observations, and demonstrate the robustness and reliability of such atomistically based yield criterion. In addition, this bottom-up approach can be directly utilized to formulate dislocation mobility rules in mesoscopic discrete dislocation dynamics simulations. © 2013 IOP Publishing Ltd.view abstract 10.1088/0965-0393/21/5/055023 **Atomistic simulation study of 〈1 1 0〉 dislocations in strontium titanate**

Hirel, P. and Mrovec, M. and Elsässer, C.*Acta Materialia*60 (2012)The core structures of glide-dissociated screw and edge 〈110〉{11̄0} dislocations in strontium titanate are investigated by means of atomistic simulations. It is shown that for both dislocations the Sr, Ti and O sublattices follow different patterns of elastic displacements and that the partial dislocations have extended core structures. Dissociation distances in the range of experimental results are obtained, and a long-standing discrepancy between theoretical and experimental predictions of the anti-phase boundary energy is resolved. Studies of dislocations under applied load reveal marked difference in mobilities of the screw and edge dislocations that are consistent with experimental observations. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.view abstract 10.1016/j.actamat.2011.09.049 **Bond order potentials for fracture, wear, and plasticity**

Pastewka, L. and Mrovec, M. and Moseler, M. and Gumbsch, P.*MRS Bulletin*37 (2012)Coulson's bond order is a chemically intuitive quantity that measures the difference in the occupation of bonding and anti-bonding orbitals. Both empirical and rigorously derived bond order expressions have evolved in the course of time and proven very useful for atomistic modeling of materials. The latest generation of empirical formulations has recently been augmented by screening-function approaches. Using friction and wear of diamond and diamond-like carbon as examples, we demonstrate that such a screened bond order scheme allows for a faithful description of dynamical bond-breaking processes in materials far from equilibrium. The rigorous bond order expansions are obtained by systematic coarse-graining of the tight binding approximation and form a bridge between the electronic structure and the atomistic modeling hierarchies. They have enabled bottom-up derivations of bond order potentials for covalently bonded semiconductors, transition metals, and multicomponent intermetallics. The recently developed magnetic bond order potential gives a correct description of both directional covalent bonds and magnetic interactions in iron and is able to correctly predict the stability of bulk Fe polymorphs as well as the intricate properties of dislocation cores. The bond order schemes hence represent a family of reliable and powerful models that can be applied in large-scale simulations of complex processes involving fracture, wear, and plasticity. © 2012 Materials Research Society.view abstract 10.1557/mrs.2012.94 **Development of orthogonal tight-binding models for Ti-C and Ti-N systems**

Margine, E.R. and Kolmogorov, A.N. and Reese, M. and Mrovec, M. and Elsässer, C. and Meyer, B. and Drautz, R. and Pettifor, D.G.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)We develop p-d orthogonal tight-binding (OTB) models for the description of TiCx and TiNx compounds in the 1.0>x>0.5 composition range. For the parametrization of bond integrals we use a recently developed method allowing projection of the one-electron wave functions obtained within the density functional theory onto optimized atom-centered orbitals. The performance of the OTB models is investigated for a wide range of properties: binding energy of elements and compounds, density of states, formation energy of vacancy-ordered defects, elastic constants, and phonon dispersions. The models provide a good description of the ground state properties at 1:1 composition and show a fair transferability for various atomic environments in elemental and binary phases. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.155120 **Dislocation-vacancy interactions in tungsten**

Chen, Z.M. and Mrovec, M. and Gumbsch, P.*Modelling and Simulation in Materials Science and Engineering*19 (2011)We systematically investigate the interaction between a monovacancy and various lattice dislocations in body-centered cubic (bcc) metal tungsten by means of atomistic simulations. Two models with a different level of sophistication have been employed for the description of interatomic interactions - the empirical Finnis-Sinclair potential, which is a central-force scheme, and the bond-order potential, which is able to describe correctly unsaturated directional covalent bonds that are crucial for the cohesion and structure of bcc transition metals. Our simulation results show that the vacancy-dislocation interaction depends sensitively on the separation distance and orientation of the two defects. A comparison of the simulation results with the predictions of elasticity theory shows excellent agreement between the two approaches when the separation between the vacancy and the dislocation core is above 0.5 nm. Large deviations from the elastic limit are found at close distances, when the vacancy enters the dislocation core. © 2011 IOP Publishing Ltd.view abstract 10.1088/0965-0393/19/7/074002 **Magnetic bond-order potential for iron**

Mrovec, M. and Nguyen-Manh, D. and Elsässer, C. and Gumbsch, P.*Physical Review Letters*106 (2011)We present a magnetic bond-order potential (BOP) that is able to provide a correct description of both directional covalent bonds and magnetic interactions in iron. This potential, based on the tight binding approximation and the Stoner model of itinerant magnetism, forms a direct bridge between the electronic-structure and the atomistic modeling hierarchies. Even though BOP calculations are computationally more demanding than those using common empirical potentials, the formalism can be used for studies of complex defect configurations in large atomic ensembles exceeding 105 atoms. Our studies of dislocations in α-Fe demonstrate that correct descriptions of directional covalent bonds and magnetism are crucial for a reliable modeling of these defects. © 2011 American Physical Society.view abstract 10.1103/PhysRevLett.106.246402 **Parameterization of tight-binding models from density functional theory calculations**

Urban, A. and Reese, M. and Mrovec, M. and Elsässer, C. and Meyer, B.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)We present a rigorous bottom-up approach for the derivation of the electronic structure part of tight-binding (TB) models from density functional theory (DFT) calculations. The approach is based on a simultaneous optimization and projection of atomic-like orbitals on self-consistent DFT wave functions and is universally applicable to elements and compounds in arbitrary structural arrangements. The quality and transferability of the derived TB bond and overlap integrals are demonstrated for the examples of a covalent semiconductor (carbon), a transition metal (titanium), and a binary compound with mixed metallic-covalent bonding (TiC). The method can serve as a transparent and physically justified coarse-graining scheme for the construction of nonorthogonal and orthogonal TB total-energy models as well as the closely related bond-order potentials. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.155119 **Atomistic simulations of lattice defects in tungsten**

Mrovec, M. and Elsässer, C. and Gumbsch, P.*International Journal of Refractory Metals and Hard Materials*28 (2010)The mechanical behavior of materials is ultimately determined by events occurring at the atomic scale. The onset of plastic yield corresponds to triggering of dislocation motion. Subsequent hardening is mainly controlled by interaction of gliding dislocations with other lattice defects such as forest dislocations, grain boundaries, interfaces and surfaces. Finally, material failure is influenced by processes at the tip of a crack propagating in a crystal lattice. In this work we review atomistic simulations of lattice defects in tungsten. We show that these studies are able to provide not only a detailed understanding of defect properties but also reveal how the fundamental processes at the atomic scale are linked to macroscopic material behavior. © 2010 Elsevier Ltd. All rights reserved.view abstract 10.1016/j.ijrmhm.2010.05.007 **Theoretical investigation of {110} generalized stacking faults and their relation to dislocation behavior in perovskite oxides**

Hirel, P. and Marton, P. and Mrovec, M. and Elsässer, C.*Acta Materialia*58 (2010)Studies of generalized stacking fault energy surfaces, or γ-surfaces, provide a convenient and efficient source of information on possible dislocation dissociation mechanisms and favorable glide systems. We carried out an extensive theoretical investigation of the {110}c-surface for three technologically important perovskite oxides SrTiO3, BaTiO 3, and PbTiO3. The calculations were performed using both a highly accurate first-principles density functional theory approach and simple empirical interatomic potentials. The main characteristic features common to all {110} γ-surfaces are the low energy path along the 〈110〉 direction and the existence of a single local energy minimum along this path. This minimum corresponds to an antiphase boundary that has been observed experimentally in dissociated dislocation cores in various perovskites. The energy profiles obtained using the empirical potentials agree qualitatively well with the first-principles results but there are significant quantitative discrepancies. This comparison provides a valuable insight into the quality and limitations of empirical potentials for atomistic simulations of dislocations and other extended defects in these materials. © 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.view abstract 10.1016/j.actamat.2010.07.025

#### alloys

#### atomistic simulations

#### bond-order potential

#### defects

#### dislocations

#### fracture

#### hydrogen embrittlement

#### mechanical properties

#### modelling and simulation