# Atomistic Modelling

The group for Atomistic Modeling is dealing with the simulation of materials on the atomic level. Ab-initio calculations on high-performance computers are a modern tool for alloy design, since they are able to reveal the behavior of materials from the atomic structure and predict the properties of novel materials.

The focus at MCL is at the determination of basic thermodynamic quantities (thermal expansion, phase stability), mechanical properties and interface design. In terms of materials, our focus is on steels, refractory metals, Ni and Al base alloys as well as materials for microelectronics ( (oxides, nitrides). In addition, the MCL is also active in creating computational tools for deriving materials properties from ab-initio data and improving ab-initio methods for the calculation of alloy properties

## Basic thermodynamic quantities

Ab-initio methods based on density functional theory (DFT) allow to predict materials properties based on the chemical composition and crystal structure. For example, DFT calculations give access to the thermal expansion coefficients in alloys [Razumovskiy2014, Bochkarev2016, Dengg2016] which opens the way to design alloys with specially tuned temperature behavior for reducing the thermo-mechanical load and improving the reliability of components.

Moreover, ab-initio calculations can be used to predict defects formation energies (vacancies, impurities) as a function of the external conditions like pressure and temperature [Razumovskiy2014, Razumovskiy2015, Ruban2016], which impacts a series of material quantities like mechanical properties, thermal transport, electric conductivity or diffusion.

Using state-of-the-art methods it is also possible to predict diffusion coefficients for a material with specific chemical compositions [Ding2014, Muehlbacher2015, Bochkarev2016]. Finally, ab-initio calculations allow one to determine the phase stability in a system as a function of the crystal structure, the chemical composition and the magnetic state.To do so, ab-initio calculations are linked to methods on larger lengths scales, such as the cluster expansion technique [Chakraborty2010, Sax2015], Monte-Carlo simulations [Ruban2012, Gorbatov2013, He2016] or the CALPHAD method [Yeddu2012, Razumovskiy2014, Povoden-Karadeniz2015].

## Mechanical Properties

The mechanical properties of a material are determined by the elastic behavior, lattice defects such as stacking faults or dislocations as well as the microstructure. Using ab-initio-calculations one can determine the atomistic origin of mechanical properties and explore them for new materials, including alloys, which opens up new possibilities for computational alloy design.

The MCL focuses on several topics in the area of atomistic origins of mechanical properties. The first focus lies on accurate prediction of elastic properties using ab-initio methods [Golesorkhtabar2012, Razumovskiy2011a], where MCL has developed a computational tool [ElaStic]. Recently, we have also extended this approach to to calculate the temperature dependence of the elastic tensor or of macroscopic elastic moduli using ab-initio methods [Dengg2016a].

A second focus lies on the prediction of the properties of lattice defects that play a key role for the mechanical properties of materials. With the aid of methods developed at MCL it ispossible to calculate the stacking fault energies of alloys with complex magnetic phases [SFE-Tool, Reyes-Huamantinco2012, Razumovskiy2016]. Furthermore the symmetry and Peierls stress of screw dislocations as a function of chemical composition can be predicted [Romaner2010, Li2012, Romaner2014, Li2016].

## Interface design

Atomistic modeling gives direct insight into the atomic structure and composition of grain boundaries [Scheiber2016], allows one to determine segregation profiles and strength of grain boundaries in metals [Scheiber2015], and to investigate the mechanical and electronic properties of phase boundaries and grain boundaries in materials for microelectronics [Popov2012].

The MCL has a special focus on the analysis of grain boundary strength under the influence of segregation. Using high-throughput calculations it is identified, which solute elements segregate to the grain boundary and how the grain boundary cohesion is affected. This information obtained by means of DFT calculations can be used for designing alloys with grain boundaries that are less prone to fracture [Butrim2015, Li2015, Razumovskiy2015a, Scheiber2016, Scheiber2016a, Scheiber2016b]. The activities of the MCL in this area have resulted in the development of a software tool for describing grain boundary segregation in alloys [SEGROcalc].

Apart from interfaces between solid phases the MCL is also dealing with surfaces of gas sensing materials. In this context, ab-initio techniques are used to investigate the adsorption of molecules on oxide surfaces and its impact on the electronic properties and the conductivity.

## Code Development

The development of new programs for calculating materials’ properties from ab-initio results is another focus of our group. Among others, the programs ElaStic, SFEtool and SEGROcalc have been developed in the frame of MCL-Projects. Moreover, MCL is active in the development of DFT methods based on Green’s functions which are especially suitable for treating chemically and magnetically disordered alloys.

Read more under "Software".

## Publications

#### Basic thermodynamic quantities

- [Bochkarev2016] A. S. Bochkarev, M. N. Popov, V. I. Razumovskiy, J. Spitaler and P. Puschnig, "Ab initio study of Cu impurity diffusion in bulk TiN", Phys. Rev. B 94 (2016), p. 104303
- [Chakraborty2010] M. Chakraborty, J. Spitaler, P. Puschnig and C. Ambrosch-Draxl, "ATAT@WIEN2k: An interface for cluster expansion based on the linearized augmented planewave method", Comp. Phys. Comm. 181 (2010), p. 913-920
- [Dengg2016] T. Dengg, L. Romaner, V. Razumovskiy, P. Puschnig and J. Spitaler, “Thermal expansion coeffcient of WRe alloys from first principles”,
*to be submitted* - [Ding2014] H. Ding, V. I. Razumovskiy and M. Asta, "Self diffusion anomaly in ferromagnetic metals: A density-functional-theory investigation of magnetically ordered and disordered Fe and Co", Acta Materialia 70 (2014), p. 130 – 136
- [Gorbatov2013] O. I. Gorbatov, I. K. Razumov, Y. N. Gornostyrev, V. I. Razumovskiy, P. A. Korzhavyi and A. V. Ruban, "Role of magnetism in Cu precipitation in alpha-Fe", Phys. Rev. B 88 (2013), p. 174113
- [He2016] S. He, P. Peng, O. I. Gorbatov and A. V. Ruban, "Effective interactions and atomic ordering in Ni-rich Ni-Re alloys", Phys. Rev. B 94 (2016), p. 024111
- [Muehlbacher2015] M. Mühlbacher, A. S. Bochkarev, F. Mendez-Martin, B. Sartory, L. Chitu, M. N. Popov, P. Puschnig, J. Spitaler, H. Ding, N. Schalk, J. Lu, L. Hultman and C. Mitterer, "Cu diffusion in single-crystal and polycrystalline TiN barrier layers: A high-resolution experimental study supported by first-principles calculations", Journal of Applied Physics 118 (2015), p. 085307
- [Povoden-Karadeniz2015] E. Povoden-Karadeniz, P. Lang, F. Moszner, S. Pogatscher, A. Ruban, P. Uggowitzer and E. Kozeschnik, "Thermodynamics of Pd-Mn phases and extension to the Fe-Mn-Pd system", Calphad 51 (2015), p. 314 - 333
- [Razumovskiy2011] V. I. Razumovskiy, A. V. Ruban and P. A. Korzhavyi, "Effect of Temperature on the Elastic Anisotropy of Pure Fe and Fe
_{0.9}Cr_{0.1}Random Alloy", Phys. Rev. Lett. 107 (2011), p. 205504 - [Razumovskiy2014] V. Razumovskiy, A. Ruban, J. Odqvist, D. Dilner and P. Korzhavyi, "Effect of carbon vacancies on thermodynamic properties of TiC-ZrC mixed carbides", Calphad 46 (2014), p. 87 – 91
- [Razumovskiy2015] V. Razumovskiy, M. Popov, H. Ding and J. Odqvist, "Formation and interaction of point defects in group IVb transition metal carbides and nitrides", Computational Materials Science 104 (2015), p. 147 – 154
- [Ruban2012] A. V. Ruban and V. I. Razumovskiy, "First-principles based thermodynamic model of phase equilibria in bcc Fe-Cr alloys", Phys. Rev. B 86 (2012), p. 174111
- [Ruban2016] A. V. Ruban, "Thermal vacancies in random alloys in the single-site mean-field approximation", Phys. Rev. B 93 (2016)
- [Sax2015] C. R. Sax, B. Schönfeld and A. V. Ruban, "Effect of magnetism and atomic order on static atomic displacements in the Invar alloy Fe-27 at.% Pt", Phys. Rev. B 92 (2015), p. 054205
- [Yeddu2012] H. K. Yeddu, V. I. Razumovskiy, A. Borgenstam, P. A. Korzhavyi, A. V. Ruban and J. Agren, "Multi-length scale modeling of martensitic transformations in stainless steels", ACTA MATERIALIA 60 (2012), p. 6508-6517

#### Mechanische Eigenschaften

- [ElaStic]
- [Golesorkhtabar2013] R. Golesorkhtabar, P. Pavone, J. Spitaler, P. Puschnig and C. Draxl, "ElaStic: A tool for calculating second-order elastic constants from first principles", Computer Physics Communications 184 (2013), p. 1861 – 1873
- [Gorbatov2013a] O. I. Gorbatov, I. K. Razumov, Y. N. Gornostyrev, V. I. Razumovskiy, P. A. Korzhavyi and A. V. Ruban, "Role of magnetism in Cu precipitation in alpha-Fe", Phys. Rev. B 88 (2013), p. 174113
- [Li2012] H. Li, S. Wurster, C. Motz, L. Romaner, C. Ambrosch-Draxl and R. Pippan, "Dislocation-core symmetry and slip planes in tungsten alloys: Ab initio calculations and microcantilever bending experiments", Acta Materialia 60 (2012), p. 748
- [Li2016] H.Li, C. Draxl, S. Wurster, R. Pippan and L. Romaner, “Impact of d-band filling on the brittleness of bcc transition metals: The case of tantalum-tungsten alloys investigated by density-functional theory”,
*accepted by Modelling Simul. Mater. Sci. Eng* - [Razumovskiy2011a] V. I. Razumovskiy, A. V. Ruban and P. A. Korzhavyi, "Effect of Temperature on the Elastic Anisotropy of Pure Fe and Fe
_{0.9}Cr_{0.1}Random Alloy", Phys. Rev. Lett. 107 (2011), p. 205504 - [Razumovskiy2014] V. Razumovskiy, A. Ruban, J. Odqvist, D. Dilner and P. Korzhavyi, "Effect of carbon vacancies on thermodynamic properties of TiC-ZrC mixed carbides", Calphad 46 (2014), p. 87 - 91
- [Razumovskiy2015] V. Razumovskiy, M. Popov, H. Ding and J. Odqvist, "Formation and interaction of point defects in group IVb transition metal carbides and nitrides", Computational Materials Science 104 (2015), p. 147 - 154
- [Razumovskiy2015b] V. Razumovskiy and G. Ghosh, "A first-principles study of cementite (Fe3C) and its alloyed counterparts: Structural properties, stability, and electronic structure", Computational Materials Science 110 (2015), p. 169 - 181
- [Razumovskiy2016] V. I. Razumovskiy, A. Reyes-Huamantinco, P. Puschnig and A. V. Ruban, "Effect of thermal lattice expansion on the stacking fault energies of fcc Fe and Fe75Mn25 alloy", Phys. Rev. B 93 (2016), p. 054111
- [Reyes-Huamantinco2012] A. Reyes-Huamantinco, P. Puschnig, C. Ambrosch-Draxl, O. E. Peil and A. V. Ruban, "Stacking-fault energy and anti-Invar effect in Fe-Mn alloy from first principles", Phys. Rev. B 86 (2012), p. 060201
- [Romaner2010] L. Romaner, C. Ambrosch-Draxl and R. Pippan, "Effect of Rhenium on the Dislocation Core Structure in Tungsten", Phys. Rev. Lett. 104 (2010), p. 195503
- [Romaner2014] L. Romaner, V. Razumovskiy and R. Pippan, "Core polarity of screw dislocations in Fe-Co alloys", Philosophical Magazine Letters 0 (2014), p. 1-8
- [SFE-Tool]

#### Grenzflächendesign

- [Butrim 2015] V. Butrim, I. M. Razumovskii, A. Beresnev, A. Kartsev, V. I. Razumovskiy and A. Trushnikova, "Effect of alloying elements and impurity (N) on bulk and grain boundary cohesion in Cr-base alloys", Advanced Materials Research, 1119 (2015), p. 569-574
- [Li 2015] J. Li, F. Hage, M. Wiessner, L. Romaner, D. Scheiber, B. Sartory, Q. Ramasse and P. Schumacher, "The roles of Eu during the growth of eutectic Si in Al-Si alloys", Scientific Reports 5 (2015), p. 13802
- [Popov 2012] M. N. Popov, J. Spitaler, M. Mühlbacher, C. Walter, J. Keckes, C. Mitterer and C. Draxl, "TiO2(100)/Al2O3(0001) interface: A first-principles study supported by experiment", Phys. Rev. B 86 (2012), p. 205309
- [Razumovskiy 2015a] V. Razumovskiy, A. Lozovoi and I. Razumovskiy, "First-principles-aided design of a new Ni-base superalloy: Influence of transition metal alloying elements on grain boundary and bulk cohesion", Acta Materialia 82 (2015), p. 369 - 377
- [Scheiber 2015] D. Scheiber, V. I. Razumovskiy, P. Puschnig, R. Pippan and L. Romaner, "Ab initio description of segregation and cohesion of grain boundaries in W-25at.% Re alloys", Acta Materialia 88 (2015), p. 180-189
- [Scheiber 2016] D. Scheiber, R. Pippan, P. Puschnig and L. Romaner, "Ab initio calculations of grain boundaries in bcc metals", Modelling Simul. Mater. Sci. Eng. 24 (2016), p. 35013-31
- [Scheiber 2016a] D. Scheiber, R. Pippan, P. Puschnig, A. Ruban and L. Romaner, "Ab-initio search for cohesion-enhancing solute elements at grain boundaries in molybdenum and tungsten ", International Journal of Refractory Metals and Hard Materials 60 (2016), p. 75 - 81
- [SEGROcalc]