Abstract
The advent of quantum mechanical codes implementing density functional theory within the local density approximation for periodic systems has made it possible to predict their properties ab-initio, without the use of empirical data. This chapter will use these invaluable tools to calculate some of the properties of microwave dielectric ceramics. Calculation of the complex permittivity of a material at microwave frequencies requires knowledge of harmonic properties such as phonon eigenfrequencies, Born effective charges and electronic permittivity. This chapter will report detailed modelling of the crystal structure and harmonic lattice dynamical properties of MgO, LaAlO\(_3\), TiO\(_2\) and Al\(_2\)O\(_3\) using density functional perturbation theory (DFPT). For each material the convergence of the ground-state energy with respect to plane-wave cut-off energy and electronic k-point sampling will be investigated. The equilibrium crystal structure and lattice parameters will then be found by minimization of the total energy with respect to lattice parameter and the ionic positions. Phonon dispersion relations and the response to electric fields will be used to calculate the low-frequency permittivity of each material and then compared to low-temperature experimental data.
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Breeze, J. (2016). Harmonic Properties of Metal Oxide Dielectrics. In: Temperature and Frequency Dependence of Complex Permittivity in Metal Oxide Dielectrics: Theory, Modelling and Measurement. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-44547-2_5
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