Physics 322 – 2007 Walter F. Smith

Exam 1 coverage

Coverage: Kittel Chapters 1 and 2 or equivalents

Livingston Chapter 7

Problem sets 1-5

Classes 1-12

Equation sheet: You will be allowed to create an equation sheet with up to 20 equations to refer to during the exam. No text or pictures allowed.

Critical Topics:

Crystal Structure Basics

Lattice translation vectors and primitive vectors

Lattice + Basis = crystal structure

How symmetries distinguish Bravais lattice types

Miller indices: be ready calculate the Miller indices from a sketch of the plane (even for a non-cubic crystal), or vice versa

Memorize the following structures: fcc, bcc, diamond, hexagonal

fcc and hcp are close-packed structures

Primitive cell vs. conventional cell

Reciprocal lattice

Definition in terms of plane waves that match crystal periodicity

Definition in terms of the wavevectors that could be used for Fourier analysis of a function with periodicity of the lattice (e.g. the electron density)

How to find reciprocal lattice primitive vectors from direct lattice primitive vectors (both graphically and with the equations; i.e. be ready to do this if I just sketch the direct lattice for you, but also if I instead give you the primitive vectors of the direct lattice)

(integer)

Know that r.l. for bcc is fcc & vice-versa

Brillouin zones: definition, importance for Brillouin formulation of diffraction, fact that k-space volume of higher zones is the same as that of the 1BZ.

X-ray diffraction

Bragg & von Laue formulations

Brillouin construction

Know the connections between the Bragg and the Brillouin/von Laue constructions, i.e. if given one, be ready to construct the other, including being able to make k-space drawings to scale showing the reciprocal lattice, k, k’, and G. Here are the most important equations that illustrate the connections:

, G is perpendicular to the Bragg planes which are separated by d

For diffraction off the family of planes (hkl),

Powder diffraction

Math

Complex exponential version of Fourier analysis

Expression for plane waves propagating in an arbitrary direction

Phonons

Dispersion relation

Know it, be ready for problems relating to it.

Be able to explain why each wavevector outside the 1BZ is equivalent to one inside the 1BZ

Know that these equivalent wavevectors differ by a reciprocal lattice vector

Be ready to prove the above two things mathematically for a three-dimensional crystal

Phase velocity and group velocity

Know meanings, definitions, and graphical representations (on the dispersion curve)

Phonon direction: understand the indexing system, e.g. [110]

Transverse and longitudinal phonons

Optical phonons

Know what they are, where the name comes from, and remember that the two parts of the basis need not have opposite charge.

Phonon energy

Know and understand

Know how the phonon occupancy relates to the amplitude of vibration

Einstein and classical models for the phonon heat capacity