Solid state exam

Question 1

Bravais lattice

Answer 1

a set of points generated by multiples of “primitive vectors”

Question 2

Primitive unit cell

Answer 2

The volume of space which, when translated through all the vectors of a BL, fills space without overlapping or leaving voids

Question 3

Wigner-Seitz cell

Answer 3

the region of space which is closer to one given lattice point than any other (a special primitive unit cell)

Question 4

Basis

Answer 4

the atom(s) that we place on each lattice point

Question 5

Packing fraction

Answer 5

the volume percentage of a unit cell occupied by atoms as hard spheres - higher is better!

Question 6

Kinematic approximation

Answer 6

that x-rays are only scattered once in a solid

Question 7

Bragg condition

Answer 7

the condition for constructive interference when x-rays specularly reflect by successive lattive planes nl = 2dsin(x)

Question 8

Lattice plane

Answer 8

a plane containing at least three non-colinear points of a given Bravais lattice, characterised by “Miller indices”

Question 9

Reciprocal lattice

Answer 9

A set of vectors G for which G.R = 2PiL (L = integer)

Question 10

G vectors

Answer 10

Plane waves that are periodic with the reciprocal lattice (frequencies)

Question 11

Laue condition

Answer 11

When K = G. Physical meaning is constructive interference

Question 12

Phase problem

Answer 12

Rho-G (the structure factor) is complex, so intensity measurements tell us the modulus, not the phase

Question 13

Ewald construction

Answer 13

a geometrical construction which helps to visualise the Laue condition

Question 14

Structure factor

Answer 14

takes the atomic basis into account mathematically

Question 15

Atomic form factor

Answer 15

fj, describes the scattering power of the atom

Question 16

Brillouin condition

Answer 16

2k.G = G^2 (comes from Laue condition)

Question 17

Independent electrons

Answer 17

no interaction with each other

Question 18

Free electrons

Answer 18

no interaction with ion cores

Question 19

Born-Oppenheimer approximation

Answer 19

ignore motion of ions

Question 20

Born-von-Karman boundary conditions

Answer 20

like a box wrapping round on itself (periodic)

Question 21

Density of states

Answer 21

How many allowed states there are within dE at E

Question 22

Fermi energy

Answer 22

maximum energy level (at 0K) occupied when all electrons are assigned levels

Question 23

Fermi wavevector

Answer 23

maximum wavevector at Ef

Question 24

How can we get the Fermi energy from the density of states?

Answer 24

By integrating the density of states from 0 up to the Fermi energy

Question 25

Fermi surface

Answer 25

Surface of constant energy in reciprocal space which separates occupied states from unoccupied ones

Question 26

Soft zone

Answer 26

smearing of electron distribution at finite temperature (approx 4kBT)

Question 27

Thomas-Fermi screening length

Answer 27

the distance at which the potential is no longer infinitely ranged

Question 28

Mott transtition

Answer 28

the amount of doping which causes as insulator to become a conductor

Question 29

Bloch's theorem

Answer 29

For a particular k, there is a "Bloch wave" which is a plane wave x a function with the periodicity of the lattice

Question 30

Central equation

Answer 30

the SE in a periodic lattice written as algebraic, (rather than differential) equations

Question 31

Band structure

Answer 31

E eigenvalues of Bloch states, E(k)

Question 32

Band gaps

Answer 32

gaps in band structure when U = 0