Pressure-dependent linewidth and Grüneisen parameter calculated from the soft Raman mode in zirconia.

Authors

  • Nazan Kara Middle East Technical University, Ankara 06790, Turkey
  • Ali Kiraci Intercurricular Courses Department, Cankaya University, Ankara 06790, Turkey
  • Hamit Yurtseven Department of Computer Engineering, Baskent University, Ankara 06790, Turkey

DOI:

https://doi.org/10.17308/kcmf.2026.28/13820

Keywords:

Linewidth, Grüniesen parameter, Raman frequency, ZrO2

Abstract

Objectives: The halfwidth at half maximum (HWHM or linewidth) of the soft Raman Eg mode at 260 cm-1 in Zirconia (ZrO2) was quantitatively interpreted as a function of pressure at room temperature using the Ising pseudospin-phonon coupled model predictions, namely the pseudospin-phonon coupled (PS) the energy fluctuation (EF) models.

Experimental: The soft Raman Eg mode frequency, associated to the order parameter, is used to determine the inverse of relaxation time as a function of pressure in ZrO2. Furthermore, the activation energy calculation for ZrO2 was carried out from our obtained values of HWHM from both PS and EF models. Moreover, the temperature dependence of this Eg mode was predicted through the two models studied here. Finally, the volume-pressure phase diagram of zirconia from the literature was used to estimate the isothermal Grüinesen parameter of the Raman modes at 150, 260, 320, 480, 602, and 650 cm-1 of ZrO2 as a function of pressure.

Conclusions: Our results indicate that both the PS and EF models adequately describe the increasing and decreasing behavior of the observed HWHM as a function of pressure and temperature, respectively for the soft Raman Eg mode in ZrO2

Downloads

Download data is not yet available.

Author Biographies

  • Nazan Kara, Middle East Technical University, Ankara 06790, Turkey

    PhD in Physics, Graduated from Middle East Technical University (Ankara, Türkiye)

  • Ali Kiraci, Intercurricular Courses Department, Cankaya University, Ankara 06790, Turkey

    Professor, Intercurricular Courses Department, Cankaya University (Ankara, Türkiye)

  • Hamit Yurtseven, Department of Computer Engineering, Baskent University, Ankara 06790, Turkey

    Professor, Department of Computer Engineering, Baskent University (Ankara, Türkiye)

References

1. Gorelov V. P. High-temperature phase transitions in ZrO2. Physics of the Solid State 2019;61: 1288–1293. https://doi.org/10.1134/S1063783419070096

2. Terki R., Bertrand G., Aourag H., Coddet C. Structural and electronic properties of zirconia phases: a FP-LAPW investigations. Materials Science in Semiconductor Processing. 2006; 9: 1006–1013. https://doi.org/10.1016/j.mssp.2006.10.033

3. Ohtaka O., Yamanaka T., Yagi T. New high-pressure and -temperature phase of ZrO2 above 1000 °C at 20 GPa. Physical Review B. 1994;49: 9295–9298. https://doi.org/10.1103/PhysRevB.49.9295

4. Haines J., Léger J. M., Atouf A. Crystal structure and equation of state of cotunnite-type zirconia. Journal of the American Ceramic Society. 1995;78: 445–448. https://doi.org/10.1111/j.1151-2916.1995.tb08822.x

5. Arashi H., Yagi T., Akimoto S., Kudoh Y. New highpressure phase of ZrO2 above 35 GPa. Physical Review B. 1990; 41: 4309–4313. https://doi.org/10.1103/PhysRevB.41.4309

6. Desgreniers S., Lagarec K. High-density ZrO2 and HfO2: Crystalline structures and equations of state. Physical Review B. 1999;59: 8467–8472. https://doi.org/10.1103/PhysRevB.59.8467

7. Haines J., Léger J. M., Hull S., … da Jornada J. A. H. Characterization of the cotunnite-type phases of zirconia and hafnia by neutron diffraction and Raman spectroscopy. Journal of the American Ceramic Society. 1997;80: 1910–1914. https://doi.org/10.1111/j.1151-2916.1997.tb03073.x

8. Ohtaka O., Fukui H., Funakoshi K., Utsumi W., Irifune T., Kikegawa T. Phase relations and EOS of ZrO2 and HfO2 under high-temperature and high-pressure. High Pressure Research. 2002;22: 221–226. https://doi.org/10.1080/08957950211347

9. Léger J. M., Tomaszewski P. E., Atouf A., Pereira A. S. Pressure-induced structural phase transitions in zirconia under high pressure. Physical Review B. 1993;47: 14075–14083. https://doi.org/10.1103/physrevb.47.14075

10. Howard C. J., Hill R. J., Reichert B. E. Structures of ZrO2 polymorphs at room temperature by high-resolution neutron powder diffraction. Acta Crystallographica Section B Structural Science. 1988;44: 116–120. https://doi.org/10.1107/S0108768187010279

11. Teufer G. The crystal structure of tetragonal ZrO2. Acta Crystallographica. 1962;15: 1187. https://doi.org/10.1107/S0365110X62003114

12. Yoshimura M. Phase stability of zirconia. American Ceramic Society Bulletin. 1988;67: 1950–1955.

13. Lityagina L. M., Kabalkina S. S., Pashkina T. A., Khzyainov A. Polymorphism of ZrO2 at high pressures. Fizika Tverdogo Tela. 1978;20: 3475–3477. (In Russ.)

14. Liu L. New high pressure phases of ZrO2 and HfO2. Journal of Physics and Chemistry of Solids. 1980;41:331–334. https://doi.org/10.1016/0022-3697(80)90205-X

15. Leger J. M., Atouf A., Tomaszewski P. E., Pereira A. S. Pressure-induced structural phase transitions in zirconia under high pressure. Physical Review B. 1993;47: 14075–14083. https://doi.org/10.1103/PhysRevB.47.14075

16. Zhao X., Vanderbilt D. Phonons and lattice dielectric properties of zirconia. Physical Review B. 2002;65: 075105. https://doi.org/10.1103/PhysRevB.65.075105

17. Sternik M., Parlinski K. Lattice vibrations in cubic, tetragonal, and monoclinic phases of ZrO2. The Journal of Chemical Physics. 2005;122: 064707. https://doi.org/10.1063/1.1849157

18. Fadda G., Colombo L., Zanzotto G. First-principles study of the structural and elastic properties of zirconia. Physical Review B. 2009;79: 214102. https://doi.org/10.1103/PhysRevB.79.214102

19. Milman V., Perlov A., Refson K., Clark S. J., Gavartin J., Winkler B. Structural, electronic and vibrational properties of tetragonal zirconia under pressure: a density functional theory study. Journal of Physics: Condensed Matter. 2009;21: 485404. https://doi.org/10.1088/0953-8984/21/48/485404

20. Parlinski K., Li Z. Q., Kawazoe Y. First-principles determination of the soft mode in cubic ZrO2. Physical Review Letters. 1997;78: 4063–4066. https://doi.org/10.1103/PhysRevLett.78.4063

21. Souvatzis P., Rudin S. P. Dynamical stabilization of cubic ZrO2 by phonon-phonon interactions: Ab initio calculations. Physical Review B. 2008;78: 184304. https://doi.org/10.1103/PhysRevB.78.184304

22. Caravaca M. A., Miño J. C., Pérez V. J., Casali R. A., Ponce C. A. Ab initio study of the elastic properties of single and polycrystal TiO2, ZrO2 and HfO2 in the cotunnite structure. Journal of Physics: Condensed Matter. 2009;21: 015501. https://doi.org/10.1088/0953-8984/21/1/015501

23. Rignanese G. M., Detraux F., Gonze X., Pasquarello A. First-principles study of dynamical and dielectric properties of tetragonal zirconia. Physical Review B. 2001;64: 134301. https://doi.org/10.1103/PhysRevB.64.134301

24. Fadda G., Zanzotto G., Colombo L. First-principles study of the effect of pressure on the five zirconia polymorphs. I. Structural, vibrational, and thermoelastic properties. Physical Review B. 2010;82: 064105. https://doi.org/10.1103/PhysRevB.82.064105

25. Block S., Jornada J. A., Piermarini G. J. Pressuretemperature phase diagram of zirconia. Journal of the American Ceramic Society. 1985;68: 497–499. https://doi.org/10.1111/j.1151-2916.1985.tb15817.x

26. Bouvier P., Djurado E., Lucazeau G., Le Bihan T. High-pressure structural evolution of undoped tetragonal nanocrystalline zirconia. Physical Review B. 2000;62: 8731–8737. https://doi.org/10.1103/PhysRevB.62.8731

27. Park J. H., Bang I. H., Lee S. J. Phase transition and thermal expansion behavior of zirconia setter fabricated from fused CaO stabilized zirconia. Journal of the Korean Ceramic Society. 2019;56: 184–190. https://doi.org/10.4191/kcers.2019.56.2.08

28. Bouvier P., Lucazeau G. Raman spectra and vibrational analysis of nanometric tetragonal zirconia under high pressure. Journal of Physics and Chemistry of Solids. 2000;61: 569–578. https://doi.org/10.1016/S0022-3697(99)00242-5

29. Li C. W., Smith H. L., Lan T., … Fultz B. Phonon anharmonicity of monoclinic zirconia and yttrium-stabilized zirconia. Physical Review B. 2015;91: 144302. https://doi.org/10.1103/PhysRevB.91.144302

30. Bouvier P., Godlewski J., Lucazeau G. A Raman study of the nanocrystallite size effect on the pressure–temperature phase diagram of zirconia grown by zirconiumbased alloys oxidation. Journal of Nuclear Materials. 2000;300: 118–126. https://doi.org/10.1016/S0022-3115(01)00756-5

31. Kiraci A., Yurtseven H. Pressure-dependent Raman modes near the cubic-tetragonal transition in strontium titanate. Journal of the American Ceramic Society. 2018;101: 1344–1355. https://doi.org/10.1111/jace.15279

32. Kiraci A., Yurtseven H. Damping constant calculated as a function of temperature for the tetragonal Raman mode close to the paraelectric-ferroelectric transition in BaTiO3. Ferroelectrics. 2013;450: 93–98. https://doi.org/10.1080/00150193.2013.838500

33. Kiraci A., Yurtseven H. Damping constant and the relaxation time calculated for the lowest-frequency soft mode in the ferroelectric phase of Cd2Nb2O7. Optik. 2016;127: 11497. https://doi.org/10.1016/j.ijleo.2016.09.023

34. Yurtseven H., Kiraci A. Damping constant (linewidth) and the relaxation time of the brillouin LA mode for the ferroelectric-paraelectric transition in PbZr1-xTixO3. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 2016;63: 1647–1655. https://doi.org/10.1109/TUFFC.2016.2572044

35. Kara N., Kiraci A., Yurtseven H. Phenomenological approaches on the Nd3+ doped ferroelectric LaBGeO5. Ferroelectrics. 2021;572: 13–26. https://doi.org/10.1080/00150193.2020.1868869

36. Kara N., Kiraci A., Yurtseven H. Calculation of the spin-lattice relaxation time and the activation energy near the IV–III phase transition in pyridinium fluorosulfonate (C5NH6)FSO3. Ferroelectrics. 2022;589: 45–54. https://doi.org/10.1080/00150193.2022.2061216

37. Yamada Y., Mori N., Noda Y. A microscopic theory on the phase transitions in NH4Br -an ising spin phonon coupled system. Journal of the Physical Society of Japan. 1972;32: 1565–1576. https://doi.org/10.1143/JPSJ.32.1565

38. Matsushita M. Anomalous temperature dependence of the frequency and damping constant of phonons near Tλ in ammonium halides. The Journal of Chemical Physics. 1976;65: 23–29. https://doi.org/10.1063/1.432804

39. Laulicht I., Luknar N. Internal-mode line-broadening by proton jumps in KH2PO4. Chemical Physics Letters. 1976;47: 237–240. https://doi.org/10.1016/0009-2614(77)80008-0

40. Schaack G., Winterfeldt V. Temperature behaviour of optical phonons near Tc in triglycine sulphate and triglycine selenate, II. Evidence of non-linear pseudospinphonon interaction. Ferroelectrics. 1977;15: 35–41. https://doi.org/10.1080/00150197708236718

41. Laulicht I. The drastic temperature broadening of hard mode Raman lines of ferroelectric KDP type crystals near Tc. Chem. Solids. 1978; 39:901-906. https://doi.org/10.1016/0022-3697(78)90153-1

42. Yurtseven H., Karacali H. Temperature dependence of the damping constant and the order parameter close to the λ phase transitions in ammonium halides. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy. 2006;65: 421–427. https://doi.org/10.1016/j.saa.2005.10.054

43. Lahajnar G., Blinc R., Zumer S. Proton spin-lattice relaxation by critical polarization fluctuations in KH2PO4. Physics of Condensed Matter. 1974;18: 301–316. https://doi.org/10.1007/BF01464399

44. Rakov A. V. The influence of intermolecular interaction on line width in the Raman spectra of liquids. Optics and Spectroscopy. 1959;7: 128–131.

45. Bartoli F. F., Litovitz T. A. Raman scattering: orientational motions in liquids. The Journal of Chemical Physics. 1972;56: 413–425. https://doi.org/10.1063/1.1676883

46. Cochran W. Crystal stability and the theory of ferroelectricity. Advances in Physics. 1960;9: 387–423. https://doi.org/10.1080/00018736000101229

47. Kittel C. Introduction to solid state physics. Wiley, New York; 1976.

48. Yurtseven H., Senol M. G. Temperature and pressure dependence of the linewidth for an internal mode in the solid phases of benzene. Acta Physica Polonica A. 2013;124: 698–701. https://doi.org/10.12693/APhysPolA.124.698

Published

2026-09-22

Issue

Section

Original articles

How to Cite

Pressure-dependent linewidth and Grüneisen parameter calculated from the soft Raman mode in zirconia. (2026). Kondensirovannye Sredy I Mezhfaznye Granitsy = Condensed Matter and Interphases, 28(3), 363-375. https://doi.org/10.17308/kcmf.2026.28/13820