B6 Condensed matter

Dulong petit law ?

C = 3Kb

Einstein method of calculating C

Consider N potential wells with frequency w and use stat mech

how does debye calculate C?

what form are metal heat capacity in?

C = aT + bT³

Drude theory calculation - electrons in metals

Drude theory assumptions

Kinetic theory model, with average scattering time t and resulting momentum of a collision P=0

Hall coefficient?

success/failures of drude thoery?

• valence is accurate for a lot of metals

• k/Tomega is accurate

• fails to account for QM so fails at heat transfer equations

Ionic bonding

Covalent bonding

Metallic bonding

Molecular (Van Der Waals) bonding

Hydrogen Bonds

Compressibility, Bulk Modulus and speed of sound

Reason for thermal expansion in solids (reverence potential of atoms in straight line / xeq )

Magnetic susceptibility for pauli paramagnetism

how to find basis’ for lattice

Just take the coords of the first one lol and add them to a[n1,n2,n3] to generate any point

Coordination number z

Reciprocal lattice definition

how to find b, reciprocal lattice vectors

Structure factor definition

Brillouin zone definition and pattern for 2d square lattice

Brillouin zone is a primative unit cell in reciprocal space

Lattice plane and miller indices definition

Calculating the difference between lattice planes

Laue condition for crystal diffraction derivation

structure factor for diffraction intensity

Structure and form factors for x-ray scattering

Form factor for BCC, FCC and SC lattices

Compare x-ray and neutron scattering

Table we should draw for x-ray power diffraction techniques to determine lattice structure

Monatomic chain setup

Total number of modes in a brillouin zone

Density of states for oscillations in 1d monatomic chain. (hint: 2 polarisations)

Diatomic chain setup and solution

Optical and acoustic mode definition

Bloch’s theorem

Tight bindingn model setup and hamiltonian

Solving tight binding model

solving nearly free electron case

Definition of conductors, insulators and semiconductors

Fermi surfaces for monovalent and divalent atoms in varying potentials

Techniques to find effective mass of electrons and holes

Doping definitions n/p

Law of mass action

find using n=1/V integral(g(E)nfdE)

Lattice and structure definition

lattice - a mathematical construct of periodic features which is typically related to crystal structure via a basis.

Structure = lattice x basis

what comprises the structure factor?

Sstructure = Slattice x Sbasis

Either one can be responsible for sending Sstructure to 0 and causes missing orders

What stuff is bcc and fcc?

inc NaCl and CsCl + diamond

elemental metals can be anything but simple cubic

NaCl is FCC

CsCl is simple cubic

Diamond is FCC

Phonon def + max energy of phonon

a quanta of a normal mode within a lattice

wmax = Csound/a

Emax = wmax hbar

what is the significance of v( r ) = -A/r^6 + B / r^12?

r^-6 term represents the electron dipole interaction between atoms. r^-12 is a ‘brick wall’ used to represent the pauli exclusion principle. -12 is used as it is the square of the dipole term.

How to improve precision in x-ray scattering experiments?

increase the angle of incident x-rays to higher orders.

Number of acoustic or optical modes within a system?

For M atoms (or modes / K vectors etc), in 3d there is 3M - 3 optical modes and 3 acoustic modes

how to sketch lattice planes?

Reciprocal of (hkl) is intersection coords: e.g (123) intersects axis at (1,0,0) , (0, 1/2 , 0) and (0, 0, 1/3) then join points.

Finding density of states g(k)

In k -space, g(k) = (area of K surface)/(2pi/L)^N where N is number of dimensions. For 1D, area of K surface is 1.

Fermi surface definition