First-principles study of the phonon, dielectric, and piezoelectric response in Bi2ZnTiO6 supercell

Computational Materials Science - Tập 101 - Trang 227-232 - 2015
Jian-Qing Dai1, Yu-Min Song1, Hu Zhang1
1School of Materials Science and Engineering, Kunming University of Science and Technology, Kunming, 650093, PR China

Tài liệu tham khảo

Suchomel, 2005, Appl. Phys. Lett., 86, 262905, 10.1063/1.1978980 Grinberg, 2007, Phys. Rev. Lett., 98, 107601, 10.1103/PhysRevLett.98.107601 Chen, 2007, Appl. Phys. Lett., 91, 171907, 10.1063/1.2794742 Zhang, 2008, Appl. Phys. Lett., 92, 082906, 10.1063/1.2884321 Zhang, 2010, J. Appl. Phys., 107, 114110, 10.1063/1.3431387 Wang, 2007, Phys. Rev. B, 75, 245209, 10.1103/PhysRevB.75.245209 Baettig, 2005, Chem. Mater., 17, 1376, 10.1021/cm0480418 Inaguma, 2003, Ferroelectrics, 286, 833, 10.1080/00150190390206293 Azuma, 2005, J. Am. Chem. Soc., 127, 8889, 10.1021/ja0512576 Khalyavin, 2006, Chem. Mater., 8, 5104, 10.1021/cm061129w Suchomel, 2006, Chem. Mater., 18, 4987, 10.1021/cm061085r Qi, 2009, Phys. Rev. B, 79, 094114, 10.1103/PhysRevB.79.094114 Wang, 2009, J. Appl. Phys., 105, 053713, 10.1063/1.3086628 Ju, 2009, J. Chem. Phys., 129, 194704, 10.1063/1.3009623 Dai, 2012, J. Appl. Phys., 111, 114101, 10.1063/1.4720440 The bond angle variance is defined as σ2=1m-1∑i=1mϕi-ϕ02, where m is number of bond angles, ϕi is the ith bond angle, and ϕ0 is the ideal bond angle for a regular polyhedron (for example, 90° for an octahedron). Kresse, 1993, Phys. Rev. B, 47, R558, 10.1103/PhysRevB.47.558 Kresse, 1996, Phys. Rev. B, 54, 11169, 10.1103/PhysRevB.54.11169 Gajdoš, 2006, Phys. Rev. B, 73, 045112, 10.1103/PhysRevB.73.045112 Perdew, 2008, Phys. Rev. Lett., 100, 136406, 10.1103/PhysRevLett.100.136406 Wahl, 2008, Phys. Rev. B, 78, 104116, 10.1103/PhysRevB.78.104116 Blöchl, 1994, Phys. Rev. B, 50, 17953, 10.1103/PhysRevB.50.17953 Elsässer, 1994, Phys. Rev. B, 49, 13975, 10.1103/PhysRevB.49.13975 Monkhorst, 1976, Phys. Rev. B, 13, 5188, 10.1103/PhysRevB.13.5188 Baroni, 2001, Rev. Mod. Phys., 73, 515, 10.1103/RevModPhys.73.515 Hamann, 2005, Phys. Rev. B, 71, 035117, 10.1103/PhysRevB.71.035117 Wu, 2005, Phys. Rev. B, 72, 035105, 10.1103/PhysRevB.72.035105 H.T. Stokes, D.M. Hatch, B.J. Campbell, ISOTROPY, 2007, <http://stokes.byu.edu/isotropy.html>. Venkataraman, 1975 The involvement of each atom in eigendisplacements is quantified from individual contributions to the norm: 〈η|η〉=∑i=110ηi2=1. Cockayne, 2000, Phys. Rev. B, 62, 3735, 10.1103/PhysRevB.62.3735 He, 2002, Phys. Rev. B, 65, 214112, 10.1103/PhysRevB.65.214112 Wang, 2008, Phys. Rev. B, 77, 134113, 10.1103/PhysRevB.77.134113 Choudhury, 2005, Phys. Rev. B, 71, 125134, 10.1103/PhysRevB.71.125134 According to equation (52) in Ref. [Phys. Rev. B 55, 10335 (1997) 27], lattice dielectric tensor is the summation over atom and eigenmode m. By first summing on all modes m and using the orthonormalization of eigenvectors, we can get the dielectric contribution from individual ions. de Gironcoli, 1989, Phys. Rev. Lett., 62, 2853, 10.1103/PhysRevLett.62.2853 Cockayne, 1998, Phys. Rev. B, 57, 13973, 10.1103/PhysRevB.57.R13973 Wu, 2005, Phys. Rev. Lett., 95, 037601, 10.1103/PhysRevLett.95.037601 Rabe, 2007