Skip to main content
Log in

DFT Study of the Structural Stability, Electronic, Magnetic, and Elastic Properties of the Binary Intermetallic Compounds AB2 (A = Ti, Zr; B = Cr, Mn and Fe)

  • Original Research
  • Published:
Journal of Electronic Materials Aims and scope Submit manuscript

Abstract

Laves phase binary intermetallics AB2 (A = Ti, Zr; B = Cr, Mn, and Fe) are investigated through hybrid density functional theory (HF-DFT). The calculated structural properties are found consistent with experiments. Cohesive energy (Ecoh), formation enthalpy (ΔH), and elastic properties demonstrated that these compounds are stable in C15 Laves phase. The electronic band profiles and electrical resistivity (ρ) confirmed the metallic nature of these intermetallics and showed that ZrMn2 is a good conductor among the series. The ground state optimized energies (Eo) and magnetic susceptibility (χ) by post-DFT treatment revealed that TiFe2, ZrMn2 and ZrFe2 are ferromagnetic (FM), ZrCr2 is antiferromagnetic (AFM), whereas TiCr2 and TiMn2 are paramagnetic (PM). The elastic parameters show that all these intermetallics are ductile, incompressible, and elastically anisotropic.

Graphical Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data Availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to legal or ethical reasons.

References

  1. T. Takasugi, S. Hanada, and M. Yoshida, High temperature mechanical properties of C15 Laves phase Cr2Nb intermetallics. Mater. Sci. Eng. 192, 805 (1995). https://doi.org/10.1016/0921-5093(94)03319-6.

    Article  Google Scholar 

  2. X.Q. Chen, W. Wolf, R. Podloucky, P. Rogl, and M. Marsman, Ab initio study of ground-state properties of the laves-phase compound ZrMn2. Phys. Rev. B. 72(5), 054440 (2005). https://doi.org/10.1103/PhysRevB.72.054440.

    Article  CAS  Google Scholar 

  3. S. Hong and C. Fu, Hydrogen in Laves phase ZrX2 (X= V, Cr, Mn, Fe Co, Ni) compounds, binding energies and electronic and magnetic structure. Phys. Rev B. 66(9), 094109 (2002). https://doi.org/10.1103/PhysRevB.66.094109.

    Article  CAS  Google Scholar 

  4. A. Von Keitz, and G. Sauthoff, Laves phases for high temperatures—Part II, stability and mechanical properties. Intermetallics 10(5), 497 (2002). https://doi.org/10.1016/S0966-9795(02)00025-0.

    Article  Google Scholar 

  5. B. Matthias, V.B. Compton, and E. Corenzwit, J. Phys. Chem. Solids. 19, 130 (1961). https://doi.org/10.1016/0022-3697(61)90066-X.

    Article  CAS  Google Scholar 

  6. J. Livingston, Laves-phase superalloys. Phys. Status Solidi A. 131(2), 415 (1992). https://doi.org/10.1016/j.msea.2019.05.092.

    Article  CAS  Google Scholar 

  7. B. Mayer, H. Anton, E. Bott, M. Methfessel, J. Sticht, J. Harris et al., Ab-initio calculation of the elastic constants and thermal expansion coefficients of Laves phases. Intermetallics 11(1), 23 (2003). https://doi.org/10.1016/S0966-9795(02)00127-9.

    Article  CAS  Google Scholar 

  8. K.C. Chen, S.M. Allen, and J.D. Livingston, Factors affecting the room-temperature mechanical properties of TiCr2-base Laves phase alloys. Mater. Sci. Eng. A. 242(1–2), 162 (1998). https://doi.org/10.1016/S0921-5093(97)00526-1.

    Article  Google Scholar 

  9. F. Li, J. Zhao, D. Tian, H. Zhang, X. Ke, and B. Johansson, Hydrogen storage behavior in C15 Laves phase compound TiCr2 by first principles. J. Appl. Phys. 105(4), 043707 (2009). https://doi.org/10.1063/1.3081636.

    Article  CAS  Google Scholar 

  10. X. Chen, V. Witusiewicz, R. Podloucky, P. Rogl, and F. Sommer, Computational and experimental study of phase stability, cohesive properties, magnetism and electronic structure of TiMn2. Acta Mater. 51(5), 1239 (2003). https://doi.org/10.1016/S1359-6454(02)00497-4.

    Article  CAS  Google Scholar 

  11. W. Brückner, R. Perthel, K. Kleinstück, and G. Schulze, Magnetic properties of ZrFe2 and TiFe2 within their homogeneity range. Phys. Status Solidi. (b). 29(1), 211 (1968). https://doi.org/10.1002/pssb.19680290124.

    Article  Google Scholar 

  12. C. Kocher and P. Brown, The atomic moments and hyperfine fields in Fe2Ti and Fe2Zr. J. Appl. Phys. 33(3), 1091 (1962). https://doi.org/10.1063/1.1728613.

    Article  CAS  Google Scholar 

  13. S. Asano and S. Ishida, Hyperfine fields of Laves phase compounds. J. Magn. Magn. Mater. 70(1–3), 187 (1987). https://doi.org/10.1016/0304-8853(87)90400-8.

    Article  CAS  Google Scholar 

  14. Z.-S. Nong, Y.-N. Lei, and J.-C. Zhu, First principles study of ground-state properties of Laves phase ZrMn2 and its hydride. EPJ Appl. Phys. 84(1), 10901 (2018). https://doi.org/10.1051/epjap/2018180045.

    Article  CAS  Google Scholar 

  15. Z.C. Wen, Z. Zhong, W. Shao-Qing, L. Hua, D. Jian-Min, and X. Nai-Sheng, First-principles study of electronic structure of the laves phase ZrFe2. Chin. Phys. Lett. 24(2), 524 (2007). https://doi.org/10.1088/0256-307X/24/2/061.

    Article  Google Scholar 

  16. H. Yamada, and M. Shimizu, Electronic structure and magnetic properties of the cubic Laves phase compounds AFe2 (A= Zr, Lu and Hf). J. Phys. F Met. Phys. 16(8), 1039 (1986). https://doi.org/10.1088/0305-4608/16/8/017.

    Article  CAS  Google Scholar 

  17. A. Abel, and R. Craig, Magnetic and structural characteristics of TiCr2, ZrCr2, HfCr2 and the TiCo2/ ZrCo2 and YFe2/YCo2 alloy systems. J. Less-Common Met. 16(2), 77 (1968). https://doi.org/10.1016/0022-5088(68)90064-7.

    Article  CAS  Google Scholar 

  18. J. Heyd, and G.E. Scuseria, Efficient hybrid density functional calculations in solids, assessment of the Heyd–Scuseria–Ernzerhof screened coulomb hybrid functional. J. Chem. Phys. 121(3), 1187 (2004). https://doi.org/10.1063/1.1760074.

    Article  CAS  Google Scholar 

  19. I. Vlasdimir, I. Solovyev, M. Korotin, M. Czyżyk, and G. Sawatzky, Density-functional theory and NiO photoemission spectra. Phys. Rev. B. 48(23), 16929 (1993). https://doi.org/10.1103/PhysRevB.48.16929.

    Article  Google Scholar 

  20. M. Shah, F. Yasmeen, S.R. Ejaz, R.Y. Khosa, M. Imran, M.A. Assiri, and H.M.T. Farid, Structure, electronic, magnetic, and thermoelectric properties of highly Mg-rich intermetallic NdNiMg15 by hybrid density functional theory. J. Electron. Mater. 50, 3976 (2021). https://doi.org/10.1007/s11664-021-08923-7.

    Article  CAS  Google Scholar 

  21. S. Khan, K. Yazdani, S. Jalali-Asadabadi, M.B. Farooq, and I. Ahmad, Electronic and magnetic structures, magnetic hyperfine fields and electric field gradients in UX3 (X= In, Tl, Pb) intermetallic compounds. J. Electron. Mater. 47, 1045 (2018). https://doi.org/10.1007/s11664-017-5811-3.

    Article  CAS  Google Scholar 

  22. G.K. Madsen, J. Carrete, and M.J. Verstraete, BoltzTraP2 a program for interpolating band structures and calculating semi-classical transport coefficients. Comput. Phys. Commun. 231, 140 (2018). https://doi.org/10.1016/j.cpc.2018.05.010.

    Article  CAS  Google Scholar 

  23. P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G.K. Madsen, and L.D. Marks, WIEN2k, An APW+ lo program for calculating the properties of solids. J. Chem. Phys. 152(7), 074101 (2020). https://doi.org/10.1063/1.5143061.

    Article  CAS  Google Scholar 

  24. V. Tyuterev, and N. Vast, Murnaghan’s equation of state for the electronic ground state energy. Comput. Mater. Sci. 38(2), 350 (2006). https://doi.org/10.1016/j.commatsci.2005.08.012.

    Article  CAS  Google Scholar 

  25. Y. Nakamura, M. Shiga, and S. Kawano, Antiferromagnetism of YMn2 intermetallic compound. Physica B+ C 120, 212 (1983). https://doi.org/10.1016/0378-4363(83)90376-5.

    Article  CAS  Google Scholar 

  26. P. Warren, J. Forsyth, G. McIntyre, and N. Bernhoeft, A single-crystal neutron diffraction study of the magnetization density in Fe2Zr. J. Condens. Matter Phys. 4(26), 5795 (1992). https://doi.org/10.1016/j.jallcom.2018.03.312.

    Article  CAS  Google Scholar 

  27. J. Bodega, J. Fernández, F. Leardini, J. Ares, and C. Sanchez, Synthesis of hexagonal C14/C36 and cubic C15 ZrCr2 Laves phases and thermodynamic stability of their hydrides. J. Phys. Chem. Solids 72(11), 1334 (2011). https://doi.org/10.1016/j.jpcs.2011.08.004.

    Article  CAS  Google Scholar 

  28. M. Murad, Z. Ali, and M. Idrees, Hybrid DFT study of structural, electronic, magnetic and elastic properties of laves phase binary intermetallics RFe2 (R= La Ce, Pr and Nd). J. Rare Earths (2022). https://doi.org/10.1016/j.jre.2022.06.002.

    Article  Google Scholar 

  29. F.R De Boer, W. Matterns, A. Miedema, A. Niessen, Cohesion in metals. Amsterdam. North-Holland (1998). https://inis.iaea.org/search/search.aspx?orig_q=RN:20078890

  30. J. Gachon, and J. Hertz, Enthalpies of formation of binary phases in the systems FeTi, FeZr, CoTi, CoZr, NiTi, and NiZr, by direct reaction calorimetry. Calphad 7(1), 1 (1983). https://doi.org/10.1016/0364-5916(83)90024-X.

    Article  CAS  Google Scholar 

  31. K. Ikeda, and T. Nakamichi, Electrical resistivity of laves phase compounds containing transition elements I Fe2A (A = Sc, Y, Ti, Zr, Hf, Nb, and Ta). J. Phys. Soc. Jpn. 39(4), 963 (1975). https://doi.org/10.1143/JPSJ.39.963.

    Article  CAS  Google Scholar 

  32. A.Y. Takeuchi, and S. Cunha, Electrical resistivity of CeFe2. J. Phys. F: Met. Phys. 11, L241 (1981). https://doi.org/10.1088/0305-4608/11/10/002.

    Article  CAS  Google Scholar 

  33. X.Q. Chen, X.W. Wolf, R. Podloucky, and P. Rogl, Density functional study of structural and phase stabilities for RMn2 Laves phases (R= Sc, Y, Lu, Ti, Zr Hf). J Alloys Compd. 383, 228 (2004). https://doi.org/10.1016/j.jallcom.2004.04.066.

    Article  CAS  Google Scholar 

  34. I. Waller, Dynamical theory of crystal lattices by M. Born and K. Huang. Acta Crystallogr. 9(10), 837 (1956). https://doi.org/10.1107/S0365110X56002370.

    Article  Google Scholar 

  35. P.H. Mott, J.R. Dorgan, and C. Roland, The bulk modulus and Poisson’s ratio of incompressible materials. J. Sound Vib. 312(4–5), 572 (2008). https://doi.org/10.1016/j.jsv.2008.01.026.

    Article  Google Scholar 

  36. S.F. Pugh, XCII Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Lond. Edinb. Dublin Philos. Mag. J. Sci. 45(367), 823 (1954). https://doi.org/10.1080/14786440808520496.

    Article  CAS  Google Scholar 

  37. L.Z. He, J. Zhu, and L. Zhang, First-principles study of structural phase transition, electronic, elastic and thermodynamic properties of C15-type Laves phase TiCr2 under pressure. Phys. B. Condens. Matter. 531, 79 (2018). https://doi.org/10.1016/j.physb.2017.11.051.

    Article  CAS  Google Scholar 

  38. L. Ma, Y. Duan, and R. Li, Phase stability, anisotropic elastic properties and electronic structures of C15-type Laves phases ZrM2 (M= Cr, Mo and W) from first-principles calculations. Philos. Mag. 97(27), 2406 (2017). https://doi.org/10.1080/14786435.2017.1334135.

    Article  CAS  Google Scholar 

  39. K. Benayed, A. Settouf, N. Benkhettou, D. Rached, and B. Abidri, Electronic and magnetic properties of AFe2 (A= Zr, Hf, Lu) compounds in the cubic Laves phase. Phys. B. Condens. Matter. 551, 152 (2018). https://doi.org/10.1016/j.physb.2018.03.024.

    Article  CAS  Google Scholar 

  40. M. Shafiq, I. Ahmad, and S. Jalali Asadabadi, Theoretical studies of strongly correlated rare-earth intermetallics RIn3 and RSn3 (R= Sm, Eu, and Gd). J. Appl. Phys. 116(10), 103905 (2014). https://doi.org/10.1063/1.4894833.

    Article  CAS  Google Scholar 

  41. P. Mohn, and K. Schwarz, Binding mechanism and itinerant magnetism of ZrFe2 and YFe2. Phys. B+ C 130, 26 (1985). https://doi.org/10.1016/0378-4363(85)90173-1.

    Article  CAS  Google Scholar 

  42. V. Pokatilov, Hyperfine fields and magnetic moments in Laves phase compounds RFe2 (R= Sc, Y, Zr, Gd, Ce, Lu). J. Magn. Magn. Mater. 189(2), 189 (1998). https://doi.org/10.1016/S0304-8853(98)00146-2.

    Article  CAS  Google Scholar 

  43. A. Sari, G. Merad, and H.S. Abdelkader, Ab initio calculations of structural, elastic and thermal properties of TiCr2 and (Ti, Mg)(Mg, Cr)2 Laves phases. Comput. Mater. Sci. 96, 348 (2015). https://doi.org/10.1016/j.commatsci.2014.09.040.

    Article  CAS  Google Scholar 

  44. J. Sun, and B. Jiang, Ab initio calculation of the phase stability, mechanical properties and electronic structure of ZrCr2 Laves phase compounds. Philos. Mag. 84(29), 3133 (2004). https://doi.org/10.1080/14786430410001720345.

    Article  CAS  Google Scholar 

  45. W. Zhang, and W. Zhang, Prediction of magnetic moment collapse in ZrFe2 under hydrostatic pressure. J. Appl. Phys. 117(16), 163917 (2015). https://doi.org/10.1063/1.4919424.

    Article  CAS  Google Scholar 

  46. M. Krcmar, and C. Fu, First-principles study of point-defect structures in C15 ZrCo2 and ZrCr2 and B2ZrCo. Phys. Rev. B. 68(13), 134110 (2003). https://doi.org/10.1103/PhysRevB.68.134110.

    Article  CAS  Google Scholar 

  47. K. Ali, A. Arya, P. Ghosh, and G. Dey, A first principles study of cohesive, elastic and electronic properties of binary Fe-Zr intermetallics. Comput. Mater. Sci. 112, 52 (2016). https://doi.org/10.1016/j.commatsci.2015.09.012.

    Article  CAS  Google Scholar 

  48. M. Rösner-Kuhn, J. Oin, K. Schaefers, U. Thiedemann, and M.G. Frohberg, Temperature dependence of the mixing enthalpy and excess heat capacity in the liquid system iron-zirconium/temperaturabhängigkeit der mischungsenthalpie und der Exzeßwärmekapazität flüssiger Eisen-Zirkonium-Legierungen. Int. J. Mater. Res. 86(10), 682 (1995). https://doi.org/10.1515/ijmr-1995-861005.

    Article  Google Scholar 

  49. B. Mukhamedov, I. Saenko, A. Ponomareva, M. Kriegel, A. Chugreev, and A. Udovsky, Thermodynamic and physical properties of Zr3Fe and ZrFe2 intermetallic compounds. Intermetallics 109, 189 (2019). https://doi.org/10.1016/j.intermet.2019.01.018.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zahid Ali.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Murad, M., Ali, Z. DFT Study of the Structural Stability, Electronic, Magnetic, and Elastic Properties of the Binary Intermetallic Compounds AB2 (A = Ti, Zr; B = Cr, Mn and Fe). J. Electron. Mater. 52, 4091–4105 (2023). https://doi.org/10.1007/s11664-023-10370-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11664-023-10370-5

Keywords

Navigation