This thesis presents calculations done on germanium dioxide. These have been done with interatomic pair potentials developed with the aid of a fitting procedure. Results for the crystalline modifications and the glassy state are presented. This includes static and dynamic properties of the GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ modifications.

Germanium dioxide is an intriguing compound, not only because it has not undergone the same vast computational exploration as has silicon dioxide, but also because it possesses some quite interesting features. One is the coexistence of two radically different crystal structures at ambient conditions. Another trait is that GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ readily forms a glass when cooling the melt. The nature behind the phase transition between the crystal modifications is not fully understood, which therefore poses a challenge. A starting point is the creation of a suitable interatomic potential that can model GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ reasonably well. The study of the glassy state is interesting because it serves as an additional check on the quality of the pair potential modeling and because the theory of glasses is currently still under development.

After an introduction, chapter 2 presents the known modifications of GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$. Chapter 3 discusses how the interatomic potential used in this work is constructed. The method is adopted from other workers who did similar fitting on SiO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ and works well despite the fact that GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ should be a less promising compound when developing pair potentials. Chapter 4 gives a discussion about molecular-dynamics simulation and how it is applied to validate the interatomic potentials used in this work. Chapter 5 presents results from two of the best interatomic potentials that were found in the previous chapters and compares results of calculations with other GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ potentials. Chapter 6 discusses the vibrational properties of the pair potentials discussed in the previous chapter. The dynamical properties of the pair potential compare favourably well with experiments. Chapter 7 discusses the effect of an angle-dependent three-body potential on the vibrational spectrum of α-quartz GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$. Chapter 8 presents a new method, selective molecular dynamics, which can elucidate anharmonicity and demonstrate the nature of some phase transitions. The existence of an α−β quartz phase transition is shown. Chapter 9 presents results from calculations done on the glassy state of GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ with the best potential obtained from the fitting procedure. These results are compared with experiments. Chapter 10 contains the conclusions and suggestions for future work. The appendices mainly consist of specific details of selected programming implementation, viz. the Ewald sum and the Hessian matrix.