University of the Punjab.

Overview

STATIC LATTICE MODEL:

Periodic arrays of atoms, fundamental types of lattices, position and orientations of planes in crystals, simple crystal structures, the limitations of static lattice model

FORMATION OF LATTICE DYNAMICS:

Classical theory of lattice vibrations, Periodic boundary condition and dispersion relation for point masses and spring constant, Quantum picture as a set of independent harmonic oscillator, the adiabatic approximations, Born-Oppenheimer approximation, Harmonic approximation, Normal co-ordinate transformation, Quantization of lattice vibrations, phonons

DISPERSION RELATION AND NATURE OF MODES:

Dispersion relation for a monoatomic linear chain with nearest neighbor interaction, Extension to all neighbors, linear diatomic chain, acoustic and optic modes

Dispersion relation for transverse vibrations in a two dimensional square lattice, dispersion relation and nature of modes along symmetry directions for a two dimensional square lattice with central force interaction, dispersion relation and nature of modes for a hexagonal lattice

Dynamics of three dimensional crystals, atomic vibrations and normal mode frequencies for a monatomic simple cubic lattice, dynamic matrix for a bcc lattice, two atoms per unit cell, extension to fcc lattice

DENSITY OF STATES:

Monoatomic linear chain, diatomic linear chain, monoatomic planar lattice, three dimensional crystals, cut off frequencies

THERMODYNAMICS OF PHONONS:

Bose-Einstein function, Einstein model of lattice, heat capacity, Debye model of lattice, heat capacity

PHOTON PHONON INTERACTION:

Optical absorption due to phonons, Lyddane-Sachs-Teller relation, zeroes and poles of the dielectric function, local phonon modes, polaritons, Reststrahlen band

SIMULATION OF PHONON DISPERSION CURVES AND DENSITY OF STATES:

Phonon density of states and dispersion relations for 3D lattices using Quantum Espresso, a simulation software.