First principles study of the structural, electronic, elastic, mechanical, thermal, and vibrational properties in pyrochlores and temperature-dependent phonon properties in pyrochlores and SrTiO3 perovskite

Abstract

In this thesis, first-principles density functional theory (DFT) calculations are used to study the structural, electronic, elastic, mechanical, and thermal properties in a series of pyrochlore materials. The vibrational properties in these materials are also studied using density functional perturbation theory. Furthermore, and most importantly, a combination of DFT and many-body Green’s function approach is employed to study the temperature-dependence of the vibrational properties arising from anharmonic interactions in some of the pyrochlore compounds and in tetragonal SrTiO3 perovskite. Chapters 1 and 2 of the thesis contain introductory material. Chapter 1 provides a brief introduction to the properties of pyrochlores and perovskites and motivates the work undertaken in this thesis. A brief description of the theoretical background for the calculations in the thesis – DFT, Density functional perturbation theory, lattice dynamics, and elasticity theory – are given in Chapter 2. The structural, electronic, and vibrational properties of a series of rare-earth pyrochlores, RE2B2O7 (RE = Sm, Gd, Tb, Dy, Ho, Er, Yb, Lu and B = Ti, Zr, Hf) are explored in Chapter 3, using both LDA and GGA frameworks. A comparative analysis of how these properties depend on the rare-earth and transition metal cation radii is presented. Interesting findings include the presence of anomalous dynamical charges and structural instabilities which manifest as imaginary phonon frequencies. A small distortion of the atomic positions in the unit cell stabilizes the structure in the sense that the frequencies for all the modes become real. A comparative and comprehensive analysis of Raman and infrared active modes is also given. In Chapter 4, a similar comparative study of the elastic, mechanical, and thermal properties of the same series of rare-earth pyrochlores as in the previous chapter is presented. Furthermore, results for the bulk modulus, elastic constants, shear and Young’s moduli to study the hardness of the materials, Poisson’s ratio to characterize their ionicity, Pugh’s ratio to understand their ductile and brittle nature, sound velocities, Debye temperature, and the minimum thermal conductivity are also discussed. Chapter 5 contains results from high-pressure studies of the structural, elastic, and the vibrational properties of Dy2Ti2O7. A brief discussion of the isostructural phase transition observed around 9 GPa pressure in this compound is provided. Chapter 6 presents a comparative discussion of the structural, electronic, vibrational, elastic, mechanical, and thermal properties in the Y2B2O7 (B = Ti, Zr, Hf) pyrochlores. Chapters 7-10, all devoted to studies of the temperature dependence of vibrational properties arising from phonon anharmonic effects in several pyrochlores as well as in tetragonal SrTiO3 using DFT and many-body Green’s function approach, present the most sophisticated calculations of this thesis. Chapter 7 contains studies which use an approximate form for the third-order interatomic force constant matrix elements (IFC3MEs) using one overall fitting parameter for all the modes to get a qualitative understanding of temperature-dependent phonon behaviour in Y2Ti2O7 pyrochlore. In Chapter 8, the temperature-dependent phonon properties in Y2B2O7 (B = Ti, Zr) pyrochlores are re-examined using the same DFT plus Green’s function approach, but this time calculating the IFC3MEs ab initio, using the “2n+1” theorem, implemented within density functional linear response theory. An interesting finding in both sets of calculations is the anomalous behaviour (of softening with decreasing temperature) of two high frequency phonon modes in case of Y2Ti2O7, whereas, no anomaly is found in case of Y2Zr2O7. In Chapter 9, the temperature dependence of phonon properties in RE2Ti2O7 (RE = Dy, Lu) pyrochlores is investigated using the same procedure as in Chapter 7. It is found that the third-order anharmonic shift in frequency for some of the phonon modes in these systems shows an anomalous behaviour, which is likely to be a signature of an anomalous temperature dependence of phonons in these materials that one will find if one calculates the IFC3MEs exactly. Chapter 10 contains an exploration of the temperature-dependent phonons in tetragonal SrTiO3 perovskite using the methods of Chapter 8, but in this case no anomalous behaviour is found. The vibrational properties in the high temperature cubic phase of SrTiO3 are also studied, and strong structural instabilities as indicated by the imaginary frequencies for several of the optical modes are found. Finally, Chapter 11 summarizes all the work presented in the thesis, together with some concluding comments and future outlook. The appendices present some technical details related to the thesis content.