## Density Functional Calculations of Physical Properties of Sodium Oxide

##### Abstract

Sodium is the sixth most abundant crustal element; as such, it is found throughout a variety of mineral systems where it is typically represented as an oxide (Na<sub>2</sub>O). However, due to high reactivity, neither Na nor Na<sub>2</sub>O are naturally occurring and are volatile. The difficulties in acquisition and safe handling present challenges to traditional experiments. However, these difficulties can be overcome by advances in computational methods in solid state physics. While such computational experiments are demanding, the relative simplicity of structure makes Na<sub>2</sub>O a reasonable candidate for this type of analysis. This thesis presents a Density Functional Theory (DFT) based study of Na<sub>2</sub>O in both the Local Density Approximation (LDA) and the Generalized Gradient Approximation (GGA). We calculate significant physical properties and find that in cases where experimental data exist, LDA and GGA form lower and upper bounds that bracket experimental values, so while quantities determined using DFT may not be exact, performing calculations within both approximations may at least provide upper and lower bounds. We find that LDA predicts a lattice parameter of 5.398 ? , while GGA predicts 5.583 ? ; and cohesive energy is calculated to be 0.7383 and 0.6356 Ry for LDA and GGA, respectively. Electronic band structure calculations yield an LDA band gap of 0.161 Ry and a GGA band gap of 0.143 Ry, both lower than expected for an ionic insulator, but consistent with electronic structure calculations performed by others. Phonon dispersion and phonon density of states (P-DOS) are determined which allows calculation of longitudinal and transverse acoustic wave velocities and elastic constants. Bulk modulus (K) is calculated from both elastic constants and from the second derivative of total energy vs. volume and found to be consistent with other calculations. Finally, we calculate Debye temperature (&theta<sub>0</sub>) to be 559 and 545 K for LDA and GGA, respectively. In addition to providing previously unrecorded data for Na<sub>2</sub>O, our calculations also present an unconventional way of determining the geologically significant but historically computationally expensive elastic constants and bulk modulus from the relatively inexpensive phonon calculations.

##### Description

37 pg.