We present an ab initio and atomistic study of the stress-strain response and elastic stability of the ordered Fe 3 Al compound with the D0 3 structure and a disordered Fe-Al solid solution with 18.75 at.% Al as well as of a nanocomposite consisting of an equal molar amount of both phases under uniaxial loading along the [001] direction. The tensile tests were performed under complex conditions including the effect of the lateral stress on the tensile strength and temperature effect. By comparing the behavior of individual phases with that of the nanocomposite we find that the disordered Fe-Al phase represents the weakest point of the studied nanocomposite in terms of tensile loading. The cleavage plane of the whole nanocomposite is identical to that identified when loading is applied solely to the disordered Fe-Al phase. It also turns out that the mechanical stability is strongly affected by softening of elastic constants C ' and/or C 66 and by corresponding elastic instabilities. Interestingly, we found that uniaxial straining of the ordered Fe 3 Al with the D0 3 structure leads almost to hydrostatic loading. Furthermore, increasing lateral stress linearly increases the tensile strength. This was also confirmed by molecular dynamics simulations employing Embedded Atom Method (EAM) potential. The molecular dynamics simulations also revealed that the thermal vibrations significantly decrease the tensile strength.

Central European Institute of Technology CEITEC BUT Brno University of Technology Purkyňova 123 CZ 612 00 Brno Czech Republic

Central European Institute of Technology CEITEC MU Masaryk University Kamenice 5 CZ 625 00 Brno Czech Republic

Department of Chemistry Faculty of Science Masaryk University Kotlářská 2 CZ 611 37 Brno Czech Republic

Department of Physical Metallurgy and Materials Testing Montanuniversität Leoben Franz Josef Strasse 18 A 8700 Leoben Austria

Institute of Physics of Materials Academy of Sciences of the Czech Republic Žižkova 22 CZ 616 62 Brno Czech Republic

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Hotar A., Kejzlar P., Palm M., Minarik J. The effect of Zr on high-temperature oxidation behaviour of Fe3Al-based alloys. Corros. Sci. 2015;100:147–157. doi: 10.1016/j.corsci.2015.07.016. DOI

Brito P., Schuller E., Silva J., Campos T., de Araujo C.R., Carneiro J.R. Electrochemical corrosion behaviour of (100), (110) and (111) Fe3A single crystals in sulphuric acid. Corros. Sci. 2017;126:366–373. doi: 10.1016/j.corsci.2017.05.029. DOI

Sauthoff G. Intermetallics. VCH Verlagsgesellschaft; Weinheim, Germany: 1995.

Liu C.T., Stringer J., Mundy J.N., Horton L.L., Angelini P. Ordered intermetallic alloys: An assessment. Intermetallics. 1997;5:579–596. doi: 10.1016/S0966-9795(97)00045-9. DOI

Stoloff N.S. Iron aluminides: Present status and future prospects. Mater. Sci. Eng. A. 1998;258:1–14. doi: 10.1016/S0921-5093(98)00909-5. DOI

Liu C.T., Lee E.H., McKamey C.G. An environmental-effect as the major cause for room-temperature embrittlement in FeAl. Scr. Metall. 1989;23:875–880. doi: 10.1016/0036-9748(89)90263-9. DOI

Lynch R.J., Heldt L.A., Milligan W.W. Effects of alloy composition on environmental embrittlement of B2 ordered iron aluminides. Scr. Metall. 1991;25:2147–2151. doi: 10.1016/0956-716X(91)90290-H. DOI

Liu C.T., McKamey C.G., Lee E.H. Environmental-effects on room-temperature ductility and fracture in Fe3Al. Scr. Metall. 1990;24:385–389. doi: 10.1016/0956-716X(90)90275-L. DOI

Lynch R.J., Gee K.A., Heldt L.A. Environmental embrittlement of single-crystal and thermomechanically processed B2-ordered iron aluminides. Scr. Metall. 1994;30:945–950. doi: 10.1016/0956-716X(94)90420-0. DOI

Li X., Prokopcakova P., Palm M. Microstructure and mechanical properties of Fe-Al-Ti-B alloys with additions of Mo and W. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. 2014;611:234–241. doi: 10.1016/j.msea.2014.05.077. DOI

Azmi S.A., Michalcova A., Sencekova L., Palm M. Microstructure and mechanical properties of Fe-Al-Nb-B alloys. MRS Adv. 2017;2:1353–1359. doi: 10.1557/adv.2017.138. DOI

Lazinska M., Durejko T., Czujko T., Bojar Z. The Effect of the Traverse Feed Rate on the Microstructure and Mechanical Properties of Laser Deposited Fe3Al (Zr,B) Intermetallic Alloy. Materials. 2018;11:792. doi: 10.3390/ma11050792. PubMed DOI PMC

Kratochvil P., Danis S., Minarik P., Pesicka J., Kral R. Strengthening of Fe3Al Aluminides by One or Two Solute Elements. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 2017;48A:4135–4139. doi: 10.1007/s11661-017-4211-x. DOI

Zamanzade M., Barnoush A., Motz C. A Review on the Properties of Iron Aluminide Intermetallics. Crystals. 2016;6:10. doi: 10.3390/cryst6010010. DOI

Dobeš F., Dymáček P., Friák M. Small punch creep of Fe-Al-Cr alloy with Ce addition and its relation to uniaxial creep tests. Kov. Mater. Metal. Mater. 2018;56:205–212. doi: 10.4149/km_2018_4_205. DOI

Friák M., Oweisová S., Pavlů J., Holec D., Šob M. An ab initio study of thermodynamic and mechanical stability of Heusler-based Fe2AlCo polymorphs. Materials. 2018;11:1543. doi: 10.3390/ma11091543. PubMed DOI PMC

Slávik A., Miháliková I., Friák M., Všianská M., Šob M. Quantum-mechanical study of magnetic properties of superalloy nanocomposite phase Fe2AlTi; Proceedings of the NANOCON 2017 Conference Proceedings (9th International Conference on Nanomaterials—Research & Application; Brno, Czech Republic. 18–20 October 2017; Ostrava, Czech Republic: Tanger Ltd.; 2018. pp. 63–68.

Miháliková I., Friák M., Slávik A., Všianská M., Koutná N., Holec D., Šob M. First-principles study of interface energies in Fe-Al-based superalloy nanocomposites; Proceedings of the NANOCON 2017 Conference Proceedings (9th International Conference on Nanomaterials—Research & Application; Brno, Czech Republic. 18–20 October 2017; Ostrava, Czech Republic: Tanger Ltd.; 2018. pp. 69–74.

Friák M., Slávik A., Miháliková I., Holec D., Všianská M., Šob M., Palm M., Neugebauer J. Origin of the low magnetic moment in Fe2AlTi: An ab initio study. Materials. 2018;11:1732. doi: 10.3390/ma11091732. PubMed DOI PMC

Kratochvil P., Pesicka J., Kral R., Svec M., Palm M. Evaluation of solid-solution hardening of Fe-27 at. pct Al by vanadium and comparison to precipitation strengthening by vanadium carbides. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 2015;46A:5091–5094. doi: 10.1007/s11661-015-3106-y. DOI

Sencekova L., Palm M., Pesicka J., Vesely J. Microstructures, mechanical properties and oxidation behaviour of single-phase Fe3Al (D03) and two-phase α-Fe-Al (A2) + Fe3Al (D03) Fe-Al-V alloys. Intermetallics. 2016;73:58–66. doi: 10.1016/j.intermet.2016.03.004. DOI

Shahid R.N., Scudino S. Strengthening of Al-Fe3Al composites by the generation of harmonic structures. Sci. Rep. 2018;8 doi: 10.1038/s41598-018-24824-y. PubMed DOI PMC

Verona M.N., Setti D., Cortes Paredes R.S. Microstructure and Properties of Fe3Al-Fe3AlC (x) Composite Prepared by Reactive Liquid Processing. Metall. Mater. Trans. B Process Metall. Mater. Process. Sci. 2018;49:529–536. doi: 10.1007/s11663-017-1161-z. DOI

Prakash U. Intermetallic matrix composites based on iron aluminides. In: Mitra R., editor. Intermetallic Matrix Composites: Properties and Applications. Elsevier Science; Amsterdam, The Netherlands: 2018. pp. 21–35. (Woodhead Publishing Series in Composites Science and Engineering).

Sharifitabar M., Khaki J.V., Sabzevar M.H. Formation mechanism of TiC-Al2O3-Fe3Al composites during self-propagating high-temperature synthesis of TiO2-Al-C-Fe system. Ceram. Int. 2016;42:12361–12370. doi: 10.1016/j.ceramint.2016.05.009. DOI

Duan X., Gao S., Dong Q., Zhou Y., Xi M., Xian X., Wang B. Reinforcement mechanism and wear resistance of Al2O3/Fe-Cr-Mo steel composite coating produced by laser cladding. Surf. Coat. Technol. 2016;291:230–238. doi: 10.1016/j.surfcoat.2016.02.045. DOI

Kong J., Wei Y., Li J., Huang J., Wang T. Microwave-assisted combustion synthesis of Fe3Al bulk nanocrystalline intermetallic matrix composites. Adv. Powder Technol. 2015;26:778–782. doi: 10.1016/j.apt.2015.04.002. DOI

Imandoust A., Zarei-Hanzaki A., Ou K.L., Yu C.H. D03 Ordered Phase Strengthening in Dual Phase Twinning-Induced Plasticity Steel. J. Mater. Eng. Perform. 2015;24:2085–2090. doi: 10.1007/s11665-015-1488-z. DOI

Cheng J., Yin B., Qiao Z., Yang J., Liu W. Mechanical and dry-sliding tribological properties of Fe3Al based composites reinforced by novel W0.5Al0.5C0.5 particulates. Mater. Des. 2015;66:67–76. doi: 10.1016/j.matdes.2014.10.035. DOI

Molina A., Torres-Islas A., Serna S., Acosta-Flores M., Rodriguez-Diaz R.A., Colin J. Corrosion, Electrical and Mechanical Performance of Copper Matrix Composites Produced by Mechanical Alloying and Consolidation. Int. J. Electrochem. Sci. 2015;10:1728–1741.

Bai Y., Xing J., Guo Y., Li J., He Y., Ma S. Effect of Cr on Microstructure, Mechanical Properties, and Wear Behavior of In Situ 20 wt.%Al2O3/Fe-25Al Composites. J. Mater. Eng. Perform. 2015;24:936–945. doi: 10.1007/s11665-014-1367-z. DOI

Panda D., Kumar L., Alam S.N. Development of Al-Fe3Al Nanocomposite by Powder Metallurgy Route. Mater. Today Proc. 2015;2:3565–3574. doi: 10.1016/j.matpr.2015.07.070. DOI

Dobes F., Kratochvil P., Kejzlar P. Creep of three-phase alloy Fe-30%Al-5.2%Zr. Kovove Mater. Metal. Mater. 2015;53:127–132. doi: 10.4149/km_2015_3_127. DOI

Jiraskova Y., Pizurova N., Titov A., Janickovic D., Friak M. Phase separation in Fe-Ti-Al alloy - Structural, magnetic, and Mossbauer study. J. Magn. Magn. Mater. 2018;468:91–99. doi: 10.1016/j.jmmm.2018.07.065. DOI

Kattner U., Burton B. Al-Fe (Aluminium-Iron) In: Okamoto H., editor. Phase Diagrams of Binary Iron Alloys. ASM International; Geauga County, OH, USA: 1993. pp. 12–28.

Sundman B., Ohnuma I., Dupin N., Kattner U.R., Fries S.G. An assessment of the entire Al-Fe system including D0(3) ordering. Acta Mater. 2009;57:2896–2908. doi: 10.1016/j.actamat.2009.02.046. DOI

Allen S., Cahn J. Mechanisms of phase-transformations within miscibility gap of Fe-rich Fe-Al alloys. Acta Metall. Mater. 1976;24:425–437. doi: 10.1016/0001-6160(76)90063-8. DOI

Oguma R., Matsumura S., Eguchi T. Kinetics of B2-and D03 type ordering and formation of domain structures in Fe-Al alloys. J. Phys. Condens. Matter. 2008;20:275225. doi: 10.1088/0953-8984/20/27/275225. PubMed DOI

Watson R.E., Weinert M. Transition-metal aluminide formation: Ti, V, Fe, and Ni aluminides. Phys. Rev. B. 1998;58:5981–5988. doi: 10.1103/PhysRevB.58.5981. DOI

Gonzales-Ormeno P., Petrilli H., Schon C. Ab-initio calculations of the formation energies of BCC-based superlattices in the Fe-Al system. Calphad. 2002;26:573–582. doi: 10.1016/S0364-5916(02)80009-8. DOI

Perdew J.P., Burke K., Ernzerhof M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996;77:3865–3868. doi: 10.1103/PhysRevLett.77.3865. PubMed DOI

Lechermann F., Welsch F., Elsässer C., Ederer C., Fähnle M., Sanchez J.M., Meyer B. Density-functional study of Fe3Al: LSDA versus GGA. Phys. Rev. B. 2002;65 doi: 10.1103/PhysRevB.65.132104. DOI

Lechermann F., Fähnle M., Meyer B., Elsässer C. Electronic correlations, magnetism, and structure of Fe-Al subsystems: An LDA+U study. Phys. Rev. B. 2004;69 doi: 10.1103/PhysRevB.69.165116. DOI

Connetable D., Maugis P. First principle calculations of the kappa-Fe3AlC perovskite and iron-aluminium intermetallics. Intermetallics. 2008;16:345–352. doi: 10.1016/j.intermet.2007.09.011. DOI

Amara H., Fu C.C., Soisson F., Maugis P. Aluminum and vacancies in α-iron: Dissolution, diffusion, and clustering. Phys. Rev. B. 2010;81:174101. doi: 10.1103/PhysRevB.81.174101. DOI

Liu S., Duan S., Ma B. First-principles calculation of vibrational entropy for Fe-Al compounds. Phys. Rev. B. 1998;58:9705–9709.

Kulikov N.I., Postnikov A.V., Borstel G., Braun J. Onset of magnetism in B2 transition-metal aluminides. Phys. Rev. B. 1999;59:6824–6833. doi: 10.1103/PhysRevB.59.6824. DOI

Friák M., Neugebauer J. Ab initio study of the anomalous volume-composition dependence in Fe-Al alloys. Intermetallics. 2010;18:1316–1321. doi: 10.1016/j.intermet.2010.03.014. DOI

Fähnle M., Drautz R., Lechermann F., Singer R., Diaz-Ortiz A., Dosch H. Thermodynamic properties from ab-initio calculations: New theoretical developments, and applications to various materials systems. Phys. Status Solidi B-Basic Solid State Phys. 2005;242:1159–1173. doi: 10.1002/pssb.200440010. DOI

Friák M., Deges J., Krein R., Frommeyer G., Neugebauer J. Combined ab initio and experimental study of structural and elastic properties of Fe3Al-based ternaries. Intermetallics. 2010;18:1310. doi: 10.1016/j.intermet.2010.02.025. DOI

Kirklin S., Saal J.E., Hegde V.I., Wolverton C. High-throughput computational search for strengthening precipitates in alloys. Acta Mater. 2016;102:125–135. doi: 10.1016/j.actamat.2015.09.016. DOI

Airiskallio E., Nurmi E., Heinonen M.H., Vayrynen I.J., Kokko K., Ropo M., Punkkinen M.P.J., Pitkanen H., Alatalo M., Kollar J., et al. High temperature oxidation of Fe-Al and Fe-Cr-Al alloys: The role of Cr as a chemically active element. Corros. Sci. 2010;52:3394–3404. doi: 10.1016/j.corsci.2010.06.019. DOI

Medvedeva N.I., Park M.S., Van Aken D.C., Medvedeva J.E. First-principles study of Mn, Al and C distribution and their effect on stacking fault energies in fcc Fe. J. Alloy Compd. 2014;582:475–482. doi: 10.1016/j.jallcom.2013.08.089. DOI

Kresse G., Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B. 1999;59:1758–1775. doi: 10.1103/PhysRevB.59.1758. DOI

Kresse G., Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B. 1996;54:11169–11186. doi: 10.1103/PhysRevB.54.11169. PubMed DOI

Čížek J., Lukáč F., Procházka I., Kužel R., Jirásková Y., Janičkovič D., Anwand W., Brauer G. Characterization of quenched-in vacancies in Fe-Al alloys. Phys. B. 2012;407:2659–2664. doi: 10.1016/j.physb.2011.12.122. DOI

Ipser H., Semenova O., Krachler R. Intermetallic phases with D0(3)-structure: A statistical-thermodynamic model. J. Alloy. Compd. 2002;338:20–25. doi: 10.1016/S0925-8388(02)00177-9. DOI

Kellou A., Grosdidier T., Raulot J.M., Aourag H. Atomistic study of magnetism effect on structural stability in Fe3Al and Fe3AlX (X = H, B, C, N, O) alloys. Phys. Status Solidi B Basic Solid State Phys. 2008;245:750–755. doi: 10.1002/pssb.200743301. DOI

Perdew J.P., Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B. 1992;45:13244–13249. doi: 10.1103/PhysRevB.45.13244. PubMed DOI

Monkhorst H.J., Pack J.D. Special points for Brillouin-zone integrations. Phys. Rev. B. 1976;13:5188–5192. doi: 10.1103/PhysRevB.13.5188. DOI

Zunger A., Wei S., Ferreira L., Bernard J. Special quasirandom structures. Phys. Rev. Lett. 1990;65:353–356. doi: 10.1103/PhysRevLett.65.353. PubMed DOI

Plimpton S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995;117:1–19. doi: 10.1006/jcph.1995.1039. DOI

Mendelev M., Srolovitz D., Ackland G., Han S. Effect of Fe Segregation on the Migration of a Non-Symmetric Σ5 Tilt Grain Boundary in Al. J. Mater. Res. 2005;20:208–218. doi: 10.1557/JMR.2005.0024. DOI

Pokluda J., Černý M., Šob M., Umeno Y. Ab initio calculations of mechanical properties: Methods and applications. Prog. Mater. Sci. 2015;73:127–158. doi: 10.1016/j.pmatsci.2015.04.001. DOI

Černý M., Šesták P., Řehák P., Všianská M., Šob M. Ab initio tensile tests of grain boundaries in the fcc crystals of Ni and Co with segregated sp-impurities. Mater. Sci. Eng. A. 2016;669:218–225. doi: 10.1016/j.msea.2016.05.083. DOI

Černý M., Šesták P., Řehák P., Všianská M., Šob M. Atomistic approaches to cleavage of interfaces. 2018. submitted.

Šob M., Wang L.G., Vitek V. Local stability of higher-energy phases in metallic materials and its relation to the structure of extended defects. Comput. Mater. Sci. 1997;8:100–106. doi: 10.1016/S0927-0256(97)00022-0. DOI

Wang L.G., Šob M., Zhang Z. Instability of higher-energy phases in simple and transition metals. J. Phys. Chem. Solids. 2003;64:863–872. doi: 10.1016/S0022-3697(02)00420-1. DOI

Šob M., Wang L.G., Vitek V. Ab initio calculation of the ideal tensile strength in copper and nickel aluminide. Kov. Mater. Metal. Mater. 1998;36:145–152.

Legut D., Šob M. Ideal Tensile Strength of Ni3Al and Fe3Al with D03 Structure. Volume 567–568. Materials Science Forum; Zurich, Switzerland: 2008. pp. 77–80. (Book Series).

Friák M., Šob M., Vitek V. Ab initio calculation of tensile strength in iron. Philos. Mag. 2003;83:3529–3537. doi: 10.1080/14786430310001605588. DOI

Černý M., Pokluda J. Influence of superimposed biaxial stress on the tensile strength of perfect crystals from first principles. Phys. Rev. B. 2007;76:024115. doi: 10.1103/PhysRevB.76.024115. DOI

Černý M., Pokluda J. Ideal tensile strength of cubic crystals under superimposed transverse biaxial stresses from first principles. Phys. Rev. B. 2010;82:174106. doi: 10.1103/PhysRevB.82.174106. DOI

Friák M., Šob M., Vítek V. Proceedings of the International Conference Juniormat-01. Brno University of Technology; Brno, Czech Republic: 2001. pp. 117–120.

Clatterbuck D.M., Chrzan D.C., Morris J.W., Jr. The inherent tensile strength of iron. Philos. Mag. Lett. 2002;82:141–147. doi: 10.1080/095008302317262642. DOI

Clatterbuck D.M., Chrzan D.C., Morris J.W., Jr. The ideal strength of iron in tension and shear. Acta Mater. 2003;51:2271–2283. doi: 10.1016/S1359-6454(03)00033-8. DOI

Šob M., Friák M., Legut D., Vítek V. In: Complex Inorganic Solids: Structural, Stability, and Magnetic Properties of Alloys. Turchi P.E.A., Gonis A., Rajan K., Meike A., editors. Springer; New York, NY, USA: 2005.

Yue-Lin L., Ying Z., Rong-Jie H., Guang-Hong L. Study of the theoretical tensile strength of Fe by a first-principles computational tensile test. Chin. Phys. B. 2009;18:1923. doi: 10.1088/1674-1056/18/5/033. DOI

Li W., Wang T. Ab initio investigation of the elasticity and stability of aluminium. J. Phys. Condens. Matter. 1998;10:9889–9904. doi: 10.1088/0953-8984/10/43/033. DOI

Clatterbuck D.M., Krenn C.R., Cohen M.L., Morris J.W., Jr. Phonon Instabilities and the Ideal Strength of Aluminum. Phys. Rev. Lett. 2003;91:135501. doi: 10.1103/PhysRevLett.91.135501. PubMed DOI

Řehák P., Černý M., Pokluda J. The [100] Compressive Strength of Perfect Cubic Crystals under Superimposed Biaxial Stresses. Key Eng. Mater. 2011;465:183–186. doi: 10.4028/www.scientific.net/KEM.465.183. DOI

Černý M., Pokluda J. The theoretical tensile strength of fcc crystals predicted from shear strength calculations. J. Phys. Condens. Matter. 2009;21:145406. doi: 10.1088/0953-8984/21/14/145406. PubMed DOI

Yang R., Tang B., Gao T. A comparison of mechanical properties between Al and Al3Mg. Int. J. Mod Phys. B. 2016;30:1550243. doi: 10.1142/S0217979215502434. DOI

Simmons G., Wang H. Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook. MIT Press; Cambridge, MA, USA: 1971.

Moakher M., Norris A.N. The Closest Elastic Tensor of Arbitrary Symmetry to an Elasticity Tensor of Lower Symmetry. J. Elast. 2006;85:215–263. doi: 10.1007/s10659-006-9082-0. DOI

Zhou L., Holec D., Mayrhofer P.H. First-principles study of elastic properties of cubic Cr1-xAlxN alloys. J. Appl. Phys. 2013;113 doi: 10.1063/1.4789378. DOI

Mouhat F., Coudert F.X. Necessary and sufficient elastic stability conditions in various crystal systems. Phys. Rev. B. 2014;90:224104. doi: 10.1103/PhysRevB.90.224104. DOI

Titrian H., Aydin U., Friák M., Ma D., Raabe D., Neugebauer J. Self-consistent Scale-bridging Approach to Compute the Elasticity of Multi-phase Polycrystalline Materials. MRS Proc. 2013;1524 doi: 10.1557/opl.2013.41. DOI

Friák M., Counts W.A., Ma D., Sander B., Holec D., Raabe D., Neugebauer J. Theory-Guided Materials Design of Multi-Phase Ti-Nb Alloys with Bone-Matching Elastic Properties. Materials. 2012;5:1853–1872. doi: 10.3390/ma5101853. DOI

Zhu L.-F., Friák M., Lymperakis L., Titrian H., Aydin U., Janus A.M., Fabritius H.-O., Ziegler A., Nikolov S., Hemzalová P., et al. Ab initio study of single-crystalline and polycrystalline elastic properties of Mg-substituted calcite crystals. J. Mech. Behav. Biomed. Mater. 2013;20:296–304. doi: 10.1016/j.jmbbm.2013.01.030. PubMed DOI

Tasnádi F., Abrikosov I.A., Rogström L., Almer J., Johansson M.P., Oden M. Significant elastic anisotropy in Ti1-xAlxN alloys. Appl. Phys. Lett. 2010;97 doi: 10.1063/1.3524502. DOI

Tasnádi F., Odén M., Abrikosov I.A. Ab initio elastic tensor of cubic Ti0.5Al0.5N alloys: Dependence of elastic constants on size and shape of the supercell model and their convergence. Phys. Rev. B. 2012;85 doi: 10.1103/PhysRevB.85.144112. DOI

von Pezold J., Dick A., Friak M., Neugebauer J. Generation and performance of special quasirandom structures for studying the elastic properties of random alloys: Application to Al-Ti. Phys. Rev. B. 2010;81 doi: 10.1103/PhysRevB.81.094203. DOI

Holec D., Tasnádi F., Wagner P., Friák M., Neugebauer J., Mayrhofer P.H., Keckes J. Macroscopic elastic properties of textured ZrN-AlN polycrystalline aggregates: From ab initio calculations to grainscale interactions. Phys. Rev. B. 2014;90 doi: 10.1103/PhysRevB.90.184106. DOI

Koutná N., Holec D., Friák M., Mayrhofer P.H., Šob M. Stability and elasticity of metastable solid solutions and superlattices in the MoN–TaN system: First-principles calculations. Mater. Des. 2018;144:310–322. doi: 10.1016/j.matdes.2018.02.033. DOI

Park N., Lee S.C., Cha P.R. Effects of alloying elements on the stability and mechanical properties of Fe3Al from first-principles calculations. Comput. Mater. Sci. 2018;146:303–309. doi: 10.1016/j.commatsci.2018.01.042. DOI

Niu X.L., Wang L.J. Effect of transition-metal substitution on electronic and mechanical properties of Fe3Al: First-principles calculations. Comput. Mater. Sci. 2012;53:128–132. doi: 10.1016/j.commatsci.2011.09.015. DOI

Liu Y., Chong X., Jiang Y., Zhou R., Feng J. Mechanical properties and electronic structures of Fe-Al intermetallic. Phys. B Condens. Matter. 2017;506:1–11. doi: 10.1016/j.physb.2016.10.032. DOI

Leamy H., Gibson E., Kayser F. Elastic stiffness coefficients of iron-aluminum alloys. I. experimental results and thermodynamic analysis. Acta Metall. 1967;15:1827. doi: 10.1016/0001-6160(67)90047-8. DOI

Shaojun L., Suqing D., Benkun M. First-principles calculation of vibrational entropy for Fe-Al compounds. Phys. Rev. B. 1998;58:9705–9709. doi: 10.1103/PhysRevB.58.9705. DOI

Voigt W. Lehrbuch der Kristallphysik. Teubner; Stuttgart, Germany: 1928.

Reuss A. Account of the liquid limit of mixed crystals on the basis of the plasticity condition for single crystal. Z. Angew. Math. Mech. 1929;9:49–58. doi: 10.1002/zamm.19290090104. DOI

Hershey A.V. The elasticity of an isotropic aggregate of anisotropic cubic crystals. J. Appl. Mech. 1954;21:236–240.

Friák M., Hickel T., Grabowski B., Lymperakis L., Udyansky A., Dick A., Ma D., Roters F., Zhu L.F., Schlieter A., et al. Methodological challenges in combining quantum-mechanical and continuum approaches for materials science applications. Eur. Phys. J. Plus. 2011;126:101. doi: 10.1140/epjp/i2011-11101-2. DOI

Pugh S. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Philos. Mag. 1954;45:823–843. doi: 10.1080/14786440808520496. DOI

Pettifor D. Theoretical predictions of structure and related properties of intermetallics. Mater. Sci. Technol. 1992;8:345–349. doi: 10.1179/mst.1992.8.4.345. DOI

The Effect of Hydrogen on the Stress-Strain Response in Fe3Al: An ab initio Molecular-Dynamics Study

Impact of Antiphase Boundaries on Structural, Magnetic and Vibrational Properties of Fe3Al

An Ab Initio Study of Magnetism in Disordered Fe-Al Alloys with Thermal Antiphase Boundaries

A Quantum-Mechanical Study of Clean and Cr-Segregated Antiphase Boundaries in Fe3Al

An Ab Initio Study of Vacancies in Disordered Magnetic Systems: A Case Study of Fe-Rich Fe-Al Phases

Impact of Nano-Scale Distribution of Atoms on Electronic and Magnetic Properties of Phases in Fe-Al Nanocomposites: An Ab Initio Study

Quantum-Mechanical Study of Nanocomposites with Low and Ultra-Low Interface Energies

An Ab Initio Study of Connections between Tensorial Elastic Properties and Chemical Bonds in Σ5(210) Grain Boundaries in Ni₃Si