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crystalline solids > Ride or Die > Flashcards

Ride or Die Flashcards

1
Q

structure factor

A

factor within diffraction scattering intensity equation that accounts for scattering power of basis atoms within conventional unit cell

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2
Q

what effect does structure factor have on diffraction pattern?

A

structure factor alters relative intensity of scattering from different reciprocal lattice vector

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3
Q

assumptions of tight binding theory of atomic bonding? (3)

A
  1. surrounding atoms only weakly perturb electrons of each atom (electrons are tightly bound to atomic nucleus)
  2. electron states in a solid are well approximated by sums of atomic orbitals and the wavefunction has the periodicity of lattice + satisfies Bloch’s equation
  3. coulomb interaction between electrons is ignored
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4
Q

Born-Oppenhaimer approximation

A

the fixing of nuclei positions in a crystal with respect to the motion of electrons

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5
Q

why is Born-Oppenheimer a good approximation?

A

electrons are 2000x smaller than a proton and 50x slower

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6
Q

Bloch’s theorem states…

A

eigenfunctions of a Hamiltonian = plane wave x periodic function (translational periodicity)

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7
Q

dispersion relation

A

relation between wavevector and associated energy of a particle

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8
Q

Fermi energy

A

chemical potential at T=0. energy level at which occupied energy states and unoccupied energy states are divided

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9
Q

Fermi-surface

A

surface in reciprocal k-space for which all points on the surface have magnitude equal to that of the Fermi wavevector

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10
Q

allowed k-state

A

value for wavevector in reciprocal space that satisfies the constraints places on the system

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11
Q

why does x-ray diffraction measured from a crystalline material in powder form produce conical shaped beams?

A

crystalline powers contains polycrystalline randomly oriented crystal grains so they can be oriented in any possible direction. there is always some angle at which the crystal can be oriented. the resulting diffraction pattern = combination of diffraction for all possible orientations of a single crystal. multiple conical beams are observed where each corresponds to diffraction from a single Bragg reflection from a single crystal

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12
Q

crystal properties that can be determined from X-ray diffraction?

A

reciprocal lattice vector length, crystal structure (in cubic case), temperature and pressure dependence

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13
Q

energy of free electron

A

E = hbar^2k^2/2m_e

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14
Q

assumptions for free electron (jellium) model? (3)

A
  1. QM obeyed
  2. electrons are free to move inside the material
  3. each electron only feels an average potential from the others (that’s included in total potential energy)
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15
Q

electron mobility

A

drift velocity per unit applied electric field = parametrises how fast electrons travel in an electric field

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16
Q

electron conductivity

A

electric field inside a material per unit current density

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17
Q

steady state condition?

A

m dv_d/dt = 0

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18
Q

how many atoms in unit cell for FCC lattice?

A

4

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19
Q

how to find electron number density knowing type of lattice and side length of unit cell?

A

n = atoms in unit cell/(length of unit cell)^3

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20
Q

paramagnetism

A

magnetic phenomenon where already existing magnetic moments align parallel to B field. can arise from atoms/ions with permanent magnetic moments or free electrons = magnetic response linear with B field at low magnetic fields with a positive susceptibility

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21
Q

equation describing paramagnetism

A

mu_0M = XB

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22
Q

ferromagnetism

A

significant observable magnetic permeability allowing the material to form a permanent magnet = permanent magnetic dipoles even in absence of external B field for T<Tc. above Tc = material is paramagnetic with susceptibility that doesn’t follow Curie’s law

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23
Q

magnetic susceptibility

A

= X = parametrises magnetisation M due to an applied magnetic field B

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24
Q

what are 2 physical mechanisms described by:
Be = B0 + λM ?

A
  1. mean field approximation to the exchange interaction between electrons
  2. also describes magnetic moment due to all other magnetic moments in the material in form of Be
25
Q

Curie-Weiss law =

A

X = C/(T-Tc)

26
Q

how to find electron number density knowing type of lattice and lattice constant, a in Armstrong?

A

n = number of atoms in unit cell/ (a x 10^-10)^2

27
Q

where does free electron model breakdown?

A

it does not allow for electronic band gap

28
Q

example of free electron model breakdown with Copper

A

plasma frequency found is bigger than visible light frequency, but we know copper has a reddish colour. copper has interbond transitions in visible range of EM spectrum which results in absorption of light at these frequencies

29
Q

quasi-particle for charge oscillations

A

plasmon. has energy hbar*omega_p

30
Q

why do we use quasiparticles to describe excitations in solids? (2)

A
  1. allows description of collective behaviour of a material as though it’s due to a single particle
  2. can assign QM values of real particles to quasi-particles
31
Q

quasi-particles examples

A

phonon -> vibration of atoms in solids
electron hole -> nearly full electronic band
electron-quasi-particle -> electron
exciton -> bound electron-hole

32
Q

how is a covalent bond formed between two neutral atoms?

A

electrons are equally shared between the two atoms. nucleus of atom A attracts electrons of atom B and the atoms are bound together by Coulomb forces (electrons and nuclei repel each other)#

33
Q

bonding orbital

A

sum of linear combinations. maximises charge density between nuclei and forms a stable bound state

34
Q

antibonding orbital

A

difference of linear combinations. zero charge density at midpoint

35
Q

why do we get bonding and antibonding orbitals?

A

when electron distributions around 2 neutral atoms overlap we need new orbitals to describe those states

36
Q

diamagnetism

A

repelled by a B field. no unpaired spins or permanent moments in structure. distortion of electron orbits produces weak negative susceptibility

37
Q

Bloch wavevector

A

describes a phase variation of wavefunction from cell to cell

38
Q

crystal momentum =

A

ħk

39
Q

crystal momentum

A

behaves like momentum of an excitation state modified by diffraction of the lattice

40
Q

why can all possible Bloch states be described by wavevectors within first Brillouin zone?

A

k and k+G describe the same phase variation from cell to cell.
exp(i(k+G).R) = exp(ikRn)exp(iGRn)= exp(ik.R) x 1. all distinct values of k are found in 1 unit cell of reciprocal lattice

41
Q

how does structure factor affect directions of scattered beams?

A

no effect

42
Q

how does structure factor affect intensities of scattered beams?

A

controls distribution of intensity between different order G

43
Q

when do ‘missing order’ appear in a diffraction pattern?

A

when there are several identical atoms in the atomic basis. they result from destructive interference of waves scattered out of phase from planes of atoms midway between lattice points

44
Q

layers of atoms in square, lattice constant a. primitive translation vectors of the space lattice?

A

a1 = ax, a2 = ay

45
Q

layers of atoms in square, lattice constant a. primitive translation vectors of the reciprocal lattice?

A

a1* = 2π/a x, a2* = 2π/a y

46
Q

what’s the electronic ground state of a 2D free electron fermi gas like?

A
  1. due to Pauli exclusion principle, 1 electron can occupy a single particle orbital and 2 electrons can occupy each k-state (spin-1/2)
  2. allowed k-states form a rectangular lattice (2π)^-2 per unit area k-space per unit area box
  3. ground state of fermi gas fill up single electron states in order of increasing energy
47
Q

what happens to Fermi function at T=0?

A

it becomes a step function

48
Q

when does a Fermi surface just touch 1st Brillouin zone?

A

1 bisector of primitive reciprocal lattice vector = Brillouin zone boundary

49
Q

how will diffraction by atom affect the shape of fermi surface?

A

fermi surface is drawn out into nucleus to track BZ boundaries (dispersion relation affected by diffraction close to boundary)

50
Q

condition for a crystal to form a diffracted beam

A

wavevector of diffracted radiation changes by an amount equal to a reciprocal lattice translation vector of crystal

51
Q

condition for a crystal to forma diffracted beam =

A

for some integer p,
G.Rn = 2πp

52
Q

why are neutrons rather than X-rays used to investigate magnetic ordering of crystals and to investigate lattice vibrations? (2)

A
  1. magnetic moment of neutrons interacts differently with up and down spins
  2. at a given energy, neutrons has a much larger k-vector than X-ray (as it has mass) so allows for inelastic scattering and probing vibrational quarks across BZ
53
Q

what’s the defining property of a semiconductor?

A

dispersion relation has an energy gap at the BZ boundary, separating filled and unfilled energy bands in ground state. Eg > kT

54
Q

intrinsic semiconductor

A

no defect/impurity state concentrations = crystal is insulating

55
Q

extrinsic semiconductor

A

defect states are thermally ionised = crystal is conducting

56
Q

n-type semiconductor

A

defects use donors; levels below conduction band edge

57
Q

p-type semiconductor

A

defects use acceptors; levels above valence edge

58
Q

why are minority carriers always present in an extrinsic semiconductor?

A

electron-hole pairs are thermally generated and recombined. they balance in equilibrium. product of electron and hole concentrations = constant at given T. even in presence of strong doping and large electron/hole concentration, minority population persists

59
Q

why do extrinsic carriers in a semiconductor doped with acceptor impurities appear to be positively charged?

A
  1. ionised acceptor creates a vacant state in otherwise filled valence band
  2. E field applied in x-direction accelerates all band electrons to states of higher k_x
  3. sum of filled band k = 0. properties of band with unfilled state at k_x are the same as properties of unpaired state at -k_x
  4. unpaired state accelerated in k-space in the opposite direction to the unfilled state

crystalline solids (2 decks)

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