Solid state exam Flashcards
Bravais lattice
a set of points generated by multiples of “primitive vectors”
Primitive unit cell
The volume of space which, when translated through all the vectors of a BL, fills space without overlapping or leaving voids
Wigner-Seitz cell
the region of space which is closer to one given lattice point than any other (a special primitive unit cell)
Basis
the atom(s) that we place on each lattice point
Packing fraction
the volume percentage of a unit cell occupied by atoms as hard spheres - higher is better!
Kinematic approximation
that x-rays are only scattered once in a solid
Bragg condition
the condition for constructive interference when x-rays specularly reflect by successive lattive planes nl = 2dsin(x)
Lattice plane
a plane containing at least three non-colinear points of a given Bravais lattice, characterised by “Miller indices”
Reciprocal lattice
A set of vectors G for which G.R = 2PiL (L = integer)
G vectors
Plane waves that are periodic with the reciprocal lattice (frequencies)
Laue condition
When K = G. Physical meaning is constructive interference
Phase problem
Rho-G (the structure factor) is complex, so intensity measurements tell us the modulus, not the phase
Ewald construction
a geometrical construction which helps to visualise the Laue condition
Structure factor
takes the atomic basis into account mathematically
Atomic form factor
fj, describes the scattering power of the atom
Brillouin condition
2k.G = G^2 (comes from Laue condition)
Independent electrons
no interaction with each other
Free electrons
no interaction with ion cores
Born-Oppenheimer approximation
ignore motion of ions
Born-von-Karman boundary conditions
like a box wrapping round on itself (periodic)
Density of states
How many allowed states there are within dE at E
Fermi energy
maximum energy level (at 0K) occupied when all electrons are assigned levels
Fermi wavevector
maximum wavevector at Ef
How can we get the Fermi energy from the density of states?
By integrating the density of states from 0 up to the Fermi energy
Fermi surface
Surface of constant energy in reciprocal space which separates occupied states from unoccupied ones
Soft zone
smearing of electron distribution at finite temperature (approx 4kBT)
Thomas-Fermi screening length
the distance at which the potential is no longer infinitely ranged
Mott transtition
the amount of doping which causes as insulator to become a conductor
Bloch’s theorem
For a particular k, there is a “Bloch wave” which is a plane wave x a function with the periodicity of the lattice
Central equation
the SE in a periodic lattice written as algebraic, (rather than differential) equations
Band structure
E eigenvalues of Bloch states, E(k)
Band gaps
gaps in band structure when U = 0
