Formulas Flashcards
Density
bello
M/V = M/a^3
where a is the lattice constant
packing fraction
Packing fraction = Vsphere/Vlattice
lattice constant of an FCC
a = 4r/sqrt(2)
lattice constant of a BCC
a = [4r/sqrt(3)]^3
Monoclinic
|a1| ≠ |a2| ≠ |a3| and alpha = gamma = 90 but beta ≠ 90
Orthorhombic
|a1| ≠|a2| ≠|a3| alpha = beta = gamma = 90
Tetragonal
|a1| = |a2| ≠ |a3| alpha = beta = gamma = 90
Hexagonal
|a1|=|a2| ≠|a3| alpha = beta = 90, gamma = 120
Structure factor
F(K) = Σj fj exp(iK.rj)
where G is the reciprocal lattice vector
and r is (x,y,z)
Intensities of diffraction peaks
I ∝ Ψ(K)^2 = F(K)^2
where F(K) is the structure factor
number density / number of free electrons per unit volume
n = zp(Na)/A
where Na is Avogadro’s number and only used if p is in mol.
or
n = n.atoms z/a^3
Fermi temperature
EF = kB TF
Fermi velocity
vF = pF/m
where pF = ℏkF
electronic specific heat constant
cel,V = gamma T
where gamma = π^2nkB^2/2EF
Volume
V = M/p
First brillouin zone
kF = |G|/2
cyclotron frequency
ω = eB/m
Resistivity
p = 1/σ
where σ is conductivity
conductivity
σ = 1/p
where p is resistivity
scattering rate
1/τ
Hall voltage
VH = -IB/dne
where d is the thickness
Resistance
R = L/σA
fermi sphere from the origin to the Brillouin zone
kF/kBZB
estimating the temperature of the intrinsic carrier concentration
use ni formula and where mc and mv are omitted use me for both
effective mass
m* formula on the formula sheet
The probability of a vacancy at energy Ev is equivalent to the probability of finding a hole at energy Eh if
Eh - μ = μ - Ev
where μ is the chemical potential
Band gap energy
E = hf
intrinsic limit
~ ni