High Pressure Effects on the Structural Properties of GaN Compound Using Equations of State

Abstract

The present study is a theoretical calculation for the effects of high pressure on thermodynamic properties on GaN up to 40Gpa at room temperature. Volume compression ratio (V0/Vp), lattice constant (a) and elastic bulk modulus(B) have been established. Furthermore, lattice frequencies and disruptions function by analyzing phonon frequency spectrum (PFS) at (0 K). The entire calculations rely on using of two equation of state (EOS) "Birch-Murnaghan and modified Lennard-Jones" equation of state and with the integration of Grüneisen approximation theory. From the considered equations of state, formulation of bulk modulus was derived, that predicts a rising trend of bulk modulus. The large bulk modulus value of GaN has made a small fraction of change in volume (less than 15%) of the material even under an extreme pressure up to 45Gpa. It was also found that the results of phonon frequency spectrum obtained from Birch-Murnaghan equation of state in a better agreement with the experimental data than that of modified Lennard-Jones equation of state. Given that the Birch-Murnaghan equation of state developed according to Eulerian strain theory accounted as a universal equation of state. Moreover, good agreement between theoretically present calculations and experiment data of phonon frequency spectrum, reveals the validity of the equations of state used in the present study.

Keywords

• compression volume;
• Bulk modulus;
• lattice constant;
• phonon frequency spectrum;

References

1. K.M. Benali, “First-Principles study of structural, elastic and electronic properties of AlN and GaN semiconductors under pressure effect and magnetism in AlN:Mn and GaN:Mn systems,” PhD. Thesis. Abou-bakrbelkaiduniversity – Tlemcen faculty of sciences- Physics department, 2004.
2. M. Ferhat, A.Zaoui, M.Certier and B. Khelifa, “ Empirical tight- binding band structure of zinc-blende nitrides GaN, AlN, and BN,” Phys. Stat. sol. (b) 195, 415,1996.
3. S. Berrah, H. Abid, A. Boukortt and M. Sehil, “Band gap of cubic AlN, GaNandInN compounds under pressure,” Turk J Phys. 30, 513-518, 2006.
4. S.K. Jalal, A.M. Al-Sheikh, R.H. Al-Saqa, “ High Pressure Effects on the Phonon Frequency Spectrum of Silicon Nanoparticle,” Iran J Sci Technol Trans Sci 45, 391–396 , 2021.
5. S. K. J, S. mawood, “Size dependent thermodynamic properties of nanoparticles, ” International Journal of Thermodynamics, Vol. 23 (No. 4), 245-250,2020.
6. R. J. Angel, F. Miozzi, M. Alvaro,” Limits to the Validity of Thermal-Pressure Equations of State” Minerals 9, 562,2019.
7. F. Birch, “Finite elastic strain of cubic crystals,” phys. Rev. 71 ; 809 – 824,1947
8. S. Jiuxun, “ A modified Lennard-Jones type equation of state for solids strictly satisfying the spinodal condition,” J. Phys.: Condens. Matter 17; L103-L111,2005.

9. I. O. Radi; , M.A.Abdulsatter; M. Abdul-Lettif,“ Semiemperical LUC- INDO calculations on the effect of pressure on the electronic structure of diamond,” Phys. Stat. Sol. b, 244(4), 1304-1317,2007.
10. S. K. Jalal, A. M. Al-Sheikh, “heoretical High Pressure Study for Thermoelastic Properties of NaCl-B1. Raf. J. Sci., Vol. 25, No.3, pp. 80- 89, 2014.
11. F. D. Murnaghan, “Finite deformations of an elastic solid,” Am. J. Math.,49. 235- 260,1937.
12. S. Adachi, “Properties of Group IV, III-VI and II-VI semiconductors,” Wiley, N. Y., chap.2,2005.
13. N.E.Christensen and I. Gorczyca,“Optical and structural properties of III-V nitrides under pressure,” Physical Review B. 0163-1829/94/50(7)/4397(19), 1994.
14. Xiao-wei Sun et al, “Heat Capacity and GrÄuneisen Parameter for GaN with Zinc-Blende Structure” Chinese journal of chemical physics,(20),3,2007.
15. A. M.AL-sheikh, R. H. AL-Saqa, “Evaluation of High Pressure Effect of Phonon Frequency Spectrum for Gold by Using Different Equations of State (EOS), ” Global Proceedings Repository, American Research Foundation, http://proceedings.sriweb.org ISSN 2476-017X, pp 58-278, 2019.
16. J. E. Herriman, O. Hellman, and B. Fultz, “Phonon thermo dynamics and elastic behavior of GaN at high temperatures and pressures,” physical review B 98, 214105,2018.
17. R. H. AL-Saqa, S. J. AL-Taie, “Theoretical Study of Mechanical, Elastic and Phonon Frequency Spectrum Properties for GaAs at High Pressure,”Journal of Siberian Federal University. Mathematics & Physics, 12, (3), 371–378,2019.
18. D. L. Anderson,“Theory of the Earth. Blackwell Scientific Publications, ” Oxford, UK,1989.
19. R. Boehler; J.Ramakrishnan, “Experime ntal results on the pressure dependence of the Grüneisen parameter,” A review. J. Geophy. Res., 85 (B12), 6996-7002,1980.