Skip to main content
SpringerLink
Log in

Study of Collective Excitations in Cu60Zr20Hf10Ti10 Quaternary Bulk Metallic Glass

  • Published:
Glass Physics and Chemistry Aims and scope Submit manuscript

Abstract

The vibrational dynamics of quaternary Cu60Zr20Hf10Ti10 bulk metallic glass (BMG) in terms of the longitudinal and transverse phonon Eigen frequencies of the localized collective excitations using Show’s optimized model pseudopotential at room temperature is reported in the present study. The theoretical pseudo alloy atom (PAA) model with WH-approach is used for the computation of the interatomic pair potential V(r) and pair correlation function (PCF) g(r). The phonon dispersion curves (PDCs) are theoretically generated through Hubbard-Beeby (HB), Takeno-Ghoda (TG) and Bhatia-Singh (BS) models, where the screening dependency is studied by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) local field correction functions. Important elastic and thermodynamic properties have been reported from the elastic limits of the phonon dispersion curves.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

REFERENCES

  1. Suryanarayana, C. and Inoue, A., Bulk Metallic Glasses, London: CRC, 2011.

    Google Scholar 

  2. Gandhi, A.L. and Vora, A.M., Theoretical study of thermodynamic and elastic properties of Ti50Be34Zr16 BMG - a pseudopotential method, Int. J. Trend. Sci. Res. Dev., 2019, vol. 3, no. 2, pp. 1076–1080.

    Google Scholar 

  3. Vora, A.M. and Gandhi, A.L., Collective dynamics of Zr-based bulk metallic glasses, Chin. J. Phys., 2019, vol. 62, pp. 284–295.

    Article  CAS  Google Scholar 

  4. Gandhi, A.L. and Vora, A.M., Theoretical study of Pd39Ni10Cu30P21 bulk metallic glass using TG and BS approaches, KCG e-J. Sci., 2019, vol. 19, pp. 1–8.

    Google Scholar 

  5. Vora, A.M., Vibrational dynamics of bulk metallic glasses studied by pseudopotential theory, in Computational Materials, Oster, W.U., Ed., New York: Nova Science, 2009, pp. 119–176.

    Google Scholar 

  6. Gandhi, A.L. and Vora, A.M., A theoretical study of vibrational dynamics of Ti60Zr16V9Cu3Al3Be9 hexanary bulk metallic glass by pseudopotential theory and estimation of thermodynamic and elastic properties using BS approach, AIP Conf. Proc., 2020, vol. 2224, pp. 030010-1–5.

    Article  CAS  Google Scholar 

  7. Gandhi, A.L. and Vora, A.M., Study of collective mode excitations in Zr41Ti14Cu12.5Be22.5 Fe10 bulk metallic glass, Mater. Today Proc., 2021, vol. 42, no. 4, pp. 1685–1688.

    Article  CAS  Google Scholar 

  8. Gandhi, A.L. and Vora, A.M., A pseudopotential study on the thermodynamic and elastic properties of Pd39Ni10Cu30P21 bulk metallic glass, Res. Guru, 2019, vol. 12, pp. 1–10.

    Google Scholar 

  9. Vora, A.M. and Gandhi, A.L., Phonon dynamics of bulk metallic glass using Takeno-Goda approach, Armen. J. Phys., 2019, vol. 12, no. 4, pp. 289–294.

    CAS  Google Scholar 

  10. Vora, A.M. and Gandhi, A.L., Phonon dynamics of Zr67Ni33 and Fe80B20 binary glassy alloys, BIBECHANA, 2021, vol. 18, no. 1, pp. 33–47.

    Article  Google Scholar 

  11. Gandhi, A.L. and Vora, A.M., A computational study of phonon dynamics of Pd77.5Si16.5Cu6 bulk metallic glass by pseudopotential method, KCG e-J. Sci., 2019, vol. 21, pp. 1–7.

    Google Scholar 

  12. Vora, A.M., Phonon dispersion in binary metallic glasses, Glass Phys. Chem., 2008, vol. 34, no. 6, pp. 671–682.

    Article  CAS  Google Scholar 

  13. Wang, Z.X., Zhao, D.Q., Pan, M.X., Wen, P., Wang, W.H., Okada, T., and Utsumi, W., Crystallization mechanism of Cu-based supercooled liquid under ambient and high pressure, Phys. Rev. B, 2004, vol. 46, pp. 092202–1–4.

    Article  CAS  Google Scholar 

  14. Wang, Z.X., Zhao, D.Q., Pan, M.X., Wang, W.H., Okada, T., and Utsumi, W., Formation and crystallization of CuZrHfTi bulk metallic glass under ambient and high pressure, J. Phys.: Condens. Matter, 2003, vol. 15, pp. 5923–5932.

    CAS  Google Scholar 

  15. Wang, Z.X., Elastic properties of Cu60Zr20Hf10Ti10 BMG under high pressure, Matter. Lett., 2006, vol. 60, pp. 831–833.

    Article  CAS  Google Scholar 

  16. Agarwal, P.C., Dynamics of bulk metallic glass: Cu60Zr20Hf10Ti10, Mater. Sci. Eng. A, 2005, vol. 404, nos. 1–2, pp. 301–304.

    Article  CAS  Google Scholar 

  17. Soto, C.E.B., Vargas, I.A.F., Velázquez, J.R.F., Rodriguez, G.A.L., and Martíne, J.A.V., Composition, elastic property and packing efficiency predictions for bulk metallic glasses in binary, ternary and quaternary systems, Mater. Res., 2016, vol. 19, no. 2, pp. 285–290.

    Article  CAS  Google Scholar 

  18. Wang, W.H., Dong, C., and Shek, C.H., Bulk metallic glasses, Mater. Sci. Eng., 2004, vol. 44, pp. 45–89.

    Article  CAS  Google Scholar 

  19. Rouxel, T., Elastic properties and short-to-medium range order in glasses, J. Am. Ceram. Soc., 2007, vol. 90, no. 10, pp. 3019–3039.

    Article  CAS  Google Scholar 

  20. Wang, W.H., The elastic properties, elastic models and elastic perspectives of metallic glasses, Prog. Mater. Sci., 2011, vol. 57, no. 3, pp. 487–656.

    Article  CAS  Google Scholar 

  21. Wang, W.H., Correlation between elastic moduli and properties in bulk metallic glass, J. Appl. Phys., 2006, vol. 99, pp. 093506-1–10.

    Article  CAS  Google Scholar 

  22. Ke, H.B., Liu, C.T., and Yang, Y., Structural heterogeneity and deformation rheology in metallic glasses, Sci. China Tech. Sci., 2015, vol. 58, pp. 47–55.

    Article  Google Scholar 

  23. Li, S., Xi, X.K., Wei, Y.X., Luo, Q., Wang, Y.T., Tang, M.B., Zhang, B., Zhao, Z.F., Wang, R.J., and Pan, M.X., Formation and properties of new heavy rare-earth-based bulk metallic glasses, Sci. Technol. Adv. Mater., 2005, vol. 6, p. 823.

    Article  CAS  Google Scholar 

  24. Wang, Z.X., Elastic properties of Cu60Zr20Hf10Ti10 BMG under high pressure, Mater. Lett., 2006, vol. 60, pp. 831–833.

    Article  CAS  Google Scholar 

  25. Wills, J.M., and Harrison, W.A., Interionic interactions in transition metals, Phys. Rev. B, 1983, vol. 28, pp. 4363–4373.

    Article  CAS  Google Scholar 

  26. Shaw, R.W., Jr., Optimum form of a modified Heine-Abarenkov model potential for the theory of simple metals, Phys. Rev., 1968, vol. 174, no. 3, pp. 769–781.

    Article  Google Scholar 

  27. Harrison, W.A., Elementary Electronic Structure, Singapore: World Scientific, 1999.

    Book  Google Scholar 

  28. Taylor, R., A simple, useful analytical form of the static electron gas dielectric function, J. Phys. F: Metal Phys., 1978, vol. 8, pp. 1699–1702.

    Article  CAS  Google Scholar 

  29. Ichimaru, S. and Utsumi, K., Analytic expression for the dielectric screening function of strongly coupled electron liquids at metallic and lower densities, Phys. Rev. B, 1981, vol. 24, no. 12, pp. 7385–7388.

    Article  Google Scholar 

  30. Farid, B., Heine, V., Engel, G., and Robertson, I., External properties of the Harris-Foulkes functional and an improved screening calculation for the electron gas, Phys. Rev. B, 1993, vol. 48, no. 16, pp. 11602–11621.

    Article  CAS  Google Scholar 

  31. Sarkar, A., Sen, D.S., Haldar, S., and Roy, D., Static local field factor for dielectric screening function of electron gas at metallic and lower densities, Mod. Phys. Lett. B, 1998, vol. 12, no. 6, pp. 639-648.

    Article  CAS  Google Scholar 

  32. Hubbard, J. and Beeby, J.L., Collective motion in liquids, Theor, J. Phys. C: Solid State Phys., 1969, vol. 2, pp. 556–571.

    Article  Google Scholar 

  33. Takeno, S. and Goda, M., A theory of phonons in amorphous solids and its implications to collective motion in simple liquids, Prog. Theor. Phys., 1971, vol. 45, no. 2, pp. 331–352.

    Article  CAS  Google Scholar 

  34. Takeno, S. and Goda, M., A theory of phonon-like excitations in non-crystalline solids and liquids, Prog. Theor. Phys., 1972, vol. 47, no. 3, pp. 790–806.

    Article  CAS  Google Scholar 

  35. Bhatia, A.B. and Singh, R.N., Phonon dispersion in metallic glasses: A simple model, Phys. Rev. B, 1985, vol. 31, no. 8, pp. 4751–4758.

    Article  CAS  Google Scholar 

  36. Shukla, M.M. and Campanha, J.R., Lattice dynamics of metallic glass Ca70Mg30 on the model of Bhatia and Singh, Acta Phys. Polon., A., 1998, vol. 94, no. 4, pp. 655–660.

    Article  CAS  Google Scholar 

  37. Bretonnet, J.L. and Derouiche, A., Variational thermodynamic calculations for liquid transition metals, Phys. Rev. B, 1990, vol. 43, pp. 8924–8929.

    Article  Google Scholar 

  38. Thorpe, M.F., Continuous deformation in random networks, J. Non-Cryst. Sol., 1983, vol. 57, no. 3, pp. 355–370.

    Article  CAS  Google Scholar 

Download references

ACKNOWLEDGMENTS

The computer facility established under DST-FIST programme from DST, Government of India, New Delhi, India and financial assistance under DRS-SAP-I & II from UGC, New Delhi, India are acknowledged by the author (AMV).

Author information

Authors and Affiliations

  1. Department of Physics, University School of Sciences, Gujarat University, 380009, Ahmedabad, Gujarat, India

    Aditya M. Vora

  2. Department of Physics, B. V. Shah (Vadi-Vihar) Science College, C. U. Shah University, 363002, Wadhwan, Gujarat, India

    Alkesh L. Gandhi

Authors
  1. Aditya M. Vora
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alkesh L. Gandhi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aditya M. Vora.

Ethics declarations

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aditya M. Vora, Alkesh L. Gandhi Study of Collective Excitations in Cu60Zr20Hf10Ti10 Quaternary Bulk Metallic Glass. Glass Phys Chem 47, 431–440 (2021). https://doi.org/10.1134/S1087659621050163

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1087659621050163

Keywords:

Search

Navigation