Some questions/issues to guide your reading

Chaps. 4, 7:

What is a Bravais lattice? Point-group operations: inversion, reflection, rotation. How do they distinguish the 7 (in 3D) crystal systems?

Primitive unit cell & Wigner-Seitz; conventional unit cell; primitive vectors--What is unique?

Types: sc, bcc, fcc, hcp (close-packed, why different from fcc), hex, diamond; non-cubic: tetragonal, orthorhombic

Basis, 2-element structures: NaCl, CsCl, ZnS (zincblende, wurtzite)

2D Bravais net from array of 1D Bravais chains; 3D Bravais lattice from array of 2D Bravais nets

Chaps. 5, 6:

Reciprocal lattice: what does it mean? how to construct it (e.g. find its primitive vectors):

Algebraic (exp(iK•R) = 1, all R), constructive interference of lattice planes (decompose 3D into families of planes)

Miller index labels of surface planes; relaxation, reconstruction

Why are the Bragg and Laue descriptions of scattering equivalent?

What is the Ewald construction and why is it useful? What happens for 2D nets or surfaces?

How does the geometric structure factor account for bases? How does it reconcile using conventional vs. primitive unit cells? How is it modified by atomic form factors for non-point atoms and for atoms of different elements?

Chaps. 19, 20:

What does Fig. 19.3 mean?

For ionics, how does the ratio of radii affect crystal structure?

Just skim comments on metals; we will return to them after doing the electron gas.

What are the properties of a crystal dominated by Lennard-Jones interactions?

In summing interactions in an ionic crystal, how best to arrange terms in the conditionally convergent series?

Chap. 22:

What does eqn. 22.11 mean? What are the symmetries of D?

Understand the normal modes of a 1D chain: dispersion relation, nature of displacements for various k.

What does quasicontinuous k (eq. 22.27) mean? How to go between it and continuous k?

In the 1D chain with 2-atom basis, understand the general solution and the limits of very similar and very different spring (or masses). Acoustic vs. optical, & why these labels?

What does the [group] velocity of a lattice vibration mean? How do individual atoms displace?

Generalizing to 3D: how many branches? L vs. T along symmetry directions? How can a T mode evolve into an L mode when crossing a zone boundary?

What can you learn from measured or calculated phonon dispersion relations?

What are "soft modes"? "localized modes"?

What about non-sinusoidal pulses? frequency-wavevector pairs not on a branch?

Chap. 23:

Understand phonons in terms of lattice vibrations and quantum treatment of SHO (simple harmonic oscillator)

Understand DOS (density of states), what it means, why bother, how to compute it.

How to go between k-space integrations and sums of quasicontinuum k's?

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