Exploring the electronic, elastic, optical, thermal, and structural characteristics of silicon nitride (Si3N4) ceramic by employing the FP-LAPW method

R. Mahdjoubi; L. Tairi; F. Chouit; M. Laouamer; H. Meradji; S. Ghemid; S. Djellab; Y. Mgdoud; S. Remha; Y. Benkrima

doi:10.22399/ijcesen.5301

Authors

R. Mahdjoubi
L. Tairi
F. Chouit
M. Laouamer
H. Meradji
S. Ghemid
S. Djellab
Y. Mgdoud
S. Remha
Y. Benkrima

DOI:

https://doi.org/10.22399/ijcesen.5301

Keywords:

polymorph-type ceramic, β-Si₃N₄,, elastic constants, FPLAW

Abstract

This paper presents a comprehensive firstــprinciples investigation into the structural, electronic, elastic, optical, thermal, and mechanical characteristics of the polymorphic ceramic β−Si₃N₄. The analysis employs the highly reliable fullــpotential linearized augmented plane wave (FP-LAPW) approach, executed within the robust context of density functional theory (DFT) using the WIEN2k package. Structural optimization utilizes the PerdewــBurkeــErnzerhof (PBE) version of the generalized gradient approximation (GGA). Notably, the electronic band gap is accurately determined using the superior modified Becke–Johnson (mBJ) functional, which offers enhanced predictive power over conventional approximations. The six independent elastic constants are derived directly from the stress–strain responses under minute deformations, which subsequently informs the prediction of the overall mechanical behavior of β−Si₃N₄. Band structure analysis confirms the intrinsic semiconducting nature of the compound. Optical behavior is explored by calculating the complex dielectric function ϵ(ω) and its related parameters, including the refractive index, extinction coefficient k(ω), absorption coefficient α(ω), reflectivity R(ω), and the electron energy-loss function L(ω). Furthermore, thermal features are meticulously examined through the quasi-harmonic Debye model, enabling the determination of critical thermodynamic properties such as the equilibrium volume, bulk modulus, and specific heat capacity as a function of temperature and pressure. The computed results demonstrate excellent consistency with established theoretical and experimental data, thereby validating the methodological rigor. These findings establish the critical reliability of β−Si₃N₄and underscore its immense potential for advanced technological and scientific applications, offering a valuable benchmark for future research in materials science.

References

[1]Pradhan G. K., Kumar A., Deb S. K., Waghmare U. V., Narayana C., Phys. Rev. B82,144112 (2010);

DOI: 10.1103/PhysRevB.82.144112 DOI: https://doi.org/10.1103/PhysRevB.82.144112

[2] Yi Zhang., Sun Hong., Changfeng Chen., Phys. Rev. B 76,144101 (2007); DOI: https://doi.org/10.1103/PhysRevD.76.061901

DOI: https://doi.org/10.1103/PhysRevB.76.144101 DOI: https://doi.org/10.1103/PhysRevB.76.144101

[3] StanVepřek., J. Vac. Sci. Technol. A 17, 2401 (1999);

DOI :10.1116/1.581977

[4] Serghiou G., Miehe G., Tschauner O., Zerr A., Boehler R., J. Chem. Phys.111, 4659 (1999);

https://doi.org/10.1063/1.479227 DOI: https://doi.org/10.1063/1.479227

[5] Yang P., Fun H. K., Rahma I. A., Saleh M. I., Ceram.Int.21, 137 (1995); DOI: https://doi.org/10.1016/0272-8842(95)95885-L

DOI :10.1016/0272-8842(95)95885-l

[6]Ben-Hai Y., Dong Chin., Chin. Phys. B 21, 060508 (2012);

DOI:10.1088/1674-1056/21/6/060508 DOI: https://doi.org/10.1088/1674-1056/21/6/060508

[7]Anderson O. K., Phys Rev. B 12,3060 (1975); DOI: https://doi.org/10.1103/PhysRevB.12.3060

DOI :10.1103/physrevb.12.306

[8] Hohenberg P., Kohn W., Phys Rev. 136B 864 (1964);

DOI: https://doi.org/10.1103/PhysRev.136.B864 DOI: https://doi.org/10.1103/PhysRev.136.B864

[9] Kohn W., Sham L. J., Phys Rev A 140, A1133 (1965);

http://dx.doi.org/10.1103/PhysRev.140.A1133 DOI: https://doi.org/10.1103/PhysRev.140.A1133

[10]Blaha P., Schwarz K., Madsen G. K. H., Kvasnicka D., Luitz J., WIEN2K,Vienna. (2001);

http://www.wien2k.at

[11]Perdew J. P., Burke K., Ernzerhof M., Phys. Rev. Lett. 77, 3865 (1996);

DOI:https://doi.org/10.1103/PhysRevLett.77.3865 DOI: https://doi.org/10.1103/PhysRevLett.77.3865

[12] Tran F., Blaha P., Phys Rev Lett. 102, 226401 (2009);

DOI: https://doi.org/10.1103/PhysRevLett.102.226401 DOI: https://doi.org/10.1103/PhysRevLett.102.226401

[13]Murnaghan F. D., Proc. Natl. Acad. Sci. USA 30, 244 (1944);

DOI: 10.1073/pnas.30.9.244 DOI: https://doi.org/10.1073/pnas.30.9.244

[14] Xu Y. N., Ching W. Y., Phys. Rev. B 51, 17379 (1995); DOI: https://doi.org/10.1103/PhysRevB.51.17379

DOI: https://doi.org/10.1103/Phys.RevB.51.17379

[15] Cem Sevik., Ceyhun Bulutay., J. Mater Sci. 42,6555 (2007);

DOI: 10.1007/s10853-007-1526-9 DOI: https://doi.org/10.1007/s10853-007-1526-9

[16] Idrobo J. C., Iddir H., Ögut S., Ziegler A., Browning N. D., Ritchie R. O., Phys.Rev. B 72, 241301 (2005);

DOI: https://doi.org/10.1103/PhysRevB.72.241301 DOI: https://doi.org/10.1103/PhysRevB.72.241301

[17] Benhai Yu., Chen D., Yingbin Li., Yonglei Jia., Acta Metall. Sin. (Engl. Lett) 25, 131 (2012);

DOI: 10.11890/1006-7191-122-131

[18] Ching W. Y., Xu Y. N., Gale J. D., Rϋhle M., J.Am.GranSoc81, 3189 (1998);

https://doi.org/10.1111/j.1151-2916.1998.tb02755.x DOI: https://doi.org/10.1111/j.1151-2916.1998.tb02755.x

[19] Hirosaki N., Ogata S., Kocer C., Kitagawa H., Nakamura Y., Phys.Rev B 65, 134110 (2002);

DOI: 10.1103/PhysRevB.65.134110 DOI: https://doi.org/10.1103/PhysRevB.65.134110

[20] Marian C. M., Gastreich M., Gale J. D., Phys.Rev B 62, 3117 (2000);

DOI: https://doi.org/10.1103/PhysRevB.62.3117 DOI: https://doi.org/10.1103/PhysRevB.62.3117

[21] Priest H. F., Burns F. C., Priest G. L., Skaar E. C. J Am Ceram Soc 56, 395 (1973);

https://doi.org/10.1111/j.1151-2916.1973.tb12700.x DOI: https://doi.org/10.1111/j.1151-2916.1973.tb12700.x

[22] Yashima M., Ando Y., Tabira Y., J.Phys.Chem B 111, 3609 (2007);

https://doi.org/10.1021/jp0678507 DOI: https://doi.org/10.1021/jp0678507

[23] He H., Sekine T., Kobayashi T., Hirosaki H., Phys. Rev. B 62, 11412 (2000); DOI: https://doi.org/10.1103/PhysRevB.62.5281

DOI: https://doi.org/10.1103/PhysRevB.62.11412 DOI: https://doi.org/10.1103/PhysRevB.62.11412

[24] Vogelgesang R., Grimsditch M., Wallace J. S., Appl. Phys. Lett.76, 982 (2000);

DOI: 10.1063/1.125913 DOI: https://doi.org/10.1063/1.125913

[25] Jong De., Chen M., Angsten W., Jain T., Notestine A., Gamst R., Sluiter A., Krishna M., Van der Zwaag C., Curtarolo S., Toher S., Plata C., Ceder J., Persson G., Asta M., Dryad M., Scientific Data, 2, 150009 (2015);

DOI :10.1038/sdata.2015.9

[26] Born M., Vol. 36, 160 (1940); DOI: https://doi.org/10.1017/S0305004100017138

DOI :10.1017/S0305004100017138

[27] Voigt W., Lehrbuch der Kristallphysik, Teubner, Leipzig., Advances in Earth., (1928).

[28] Reuss A., Angew Z., Math.Mech.9, 49 (1929);

https://doi.org/10.1002/zamm.19290090104 DOI: https://doi.org/10.1002/zamm.19290090104

[29] Hill R., Proc. Phys. Soc. London.65, 350 (1952); DOI: https://doi.org/10.1088/0370-1298/65/5/307

DOI 10.1088/0370-1298/65/5/307

[30] Pugh S. F., Philos. Mag. 45, 823 (1954);

https://doi.org/10.1080/14786440808520496 DOI: https://doi.org/10.1080/14786440808520496

[31] Benyelloul K., Bouhadda Y., Bououdina M., Faraoun H. I., Aourag H., Seddik L., Int. J. Hydrogen Energy.39,12667 (2014);

https://doi.org/10.1016/j.ijhydene.2014.05.190 DOI: https://doi.org/10.1016/j.ijhydene.2014.05.190

[32] Liu A. Y., Cohen M. L., Phys. Rev.B41, 10 727 (1990);

DOI: https://doi.org/10.1103/PhysRevB.41.10727 DOI: https://doi.org/10.1103/PhysRevB.41.10727

[33] Ren S. Y., Ching W. Y., Phys. Rev.B23, 5454 (1981);

DOI: https://doi.org/10.1103/PhysRevB.23.5454 DOI: https://doi.org/10.1103/PhysRevB.23.5454

[34] Iqbal A., Jackson W. B., Tsai C. C., Allen J. W., Bates C. W., J.Appl. Phys. 61, 2947 (1987);

https://doi.org/10.1063/1.337842 DOI: https://doi.org/10.1063/1.337842

[35] Carson R. D., Schnatterly S. E., Phys. Rev. B 33, 2432 (1986);

DOI: https://doi.org/10.1103/PhysRevB.33.2432 DOI: https://doi.org/10.1103/PhysRevB.33.2432

[36] Sénémaud C., Driss-khodja M., Gheorghiu A.,Harel S., Dufour G., Roulet H., J. Appl. Phys. 74, 5042 (1993); DOI: https://doi.org/10.1063/1.354286

DOI :10.1063/1.354286

[37] Kurata H., Hirose M., Osaka Y., J. Appl. Phys. 20, L811 (1981); DOI: https://doi.org/10.1143/JJAP.20.L811

DOI :10.1143/JJAP.20L811

[38] Goodman A. M. Appl. Phys. Lett. 13, 275(1968);

DOI:10.1063/1.1652607 DOI: https://doi.org/10.1063/1.1652607

[39] Bauer J., Phys.Status Solidi 39, 411 (1977); DOI: https://doi.org/10.1002/pssa.2210390205

DOI :10.1002/pssa.2210390205

[40] Milek J. T., Handbook of Electronic MateriaIs (IFIfPlenutn, New York, 1971), Vol. 3(1971);

DOI :10.1007/978-1-4684-6162

[41] Knoll R. W., Henager C. H., J. Mater. Res.7, 1247 (1992); DOI: https://doi.org/10.1557/JMR.1992.1247

DOI :10.1557/jmr.1992.1247

[42] Shabalov A. L., Feldman M. S., Bashirov M. Z., Phys. Status Solidi. B 145, K71 (1988);

https://doi.org/10.1002/pssb.2221450150 DOI: https://doi.org/10.1002/pssb.2221450150

[43] Bovard B. G., Ramm J., Hora R., Hanselmann F., Appl. Opt.28, 4436 (1989);

https://doi.org/10.1364/AO.28.004436 DOI: https://doi.org/10.1364/AO.28.004436

[44] Singh J., Charles Darwin University, Darwin, Australia, John Wiley, Ltd, Copyright (2006);

DOI: 10.1002/0470021942 DOI: https://doi.org/10.1002/0470021942

[45] Wooten F., Optical Properties of Solid, Academic, New York, (1972).

[46] Tao S. X., Anne M M G Theulings., Violeta Prodanovié., John Smedley., Harry Van der Graaf, Computation 3, 657 (2015);

https://doi.org/10.3390/computation3040657 DOI: https://doi.org/10.3390/computation3040657

[47] Blanco M. A., Francisco E., Luaña V., Comput. Phys. Commun. 158, 57 (2004);

DOI: 10.1016/J.COMPHY.2003.12.001 DOI: https://doi.org/10.1016/j.comphy.2003.12.001

[48] Blanco M. A., Martín Pendás A., Francisco E., Recio J. M., Franco R., J. Mol. Struct. Theochem.368, 245 (1996); DOI: https://doi.org/10.1016/S0166-1280(96)04658-1

https://doi.org/10.1016/S0166-1280(96)90571-0Get rights and content

[49] Florez M., Recio J. M., Francisco E., Blanco M. A., Pendás A. M., Phys. Rev. B 66, 144112 (2002);

DOI: https://doi.org/10.1103/PhysRevB.66.144112 DOI: https://doi.org/10.1103/PhysRevB.66.144112

[50] Debye P., Ann. Phys. 39, 789 (1912); DOI: https://doi.org/10.1248/yakushi1881.1912.365_789

http://dx.doi.org/10.1002/andp.19123441404 DOI: https://doi.org/10.1002/andp.19123441404

[51]Dulong P. L., Petit A. T., Recherches de la Théorie de la Chaleur. Ann. Chim. Phys., 10, 395 (1819).