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Physics 2 > Physics of Solids > Flashcards

Physics of Solids Flashcards

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1
Q

principle quantum number

A

n
from 1 to infinity

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2
Q

angular momentum quantum number (azimuthal)

A

l
between 0 and n-1

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3
Q

magnetic quantum number

A

m
between -l and l

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4
Q

spin quantum number

A

s
-1/2 or +1/2

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5
Q

greater distance so appear

A

point like

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6
Q

two atoms get close

A

repel each other

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7
Q

what forces can exist between two neutral atoms?

A

mutual, non uniform repulsion of electrons, creates charge distribution

this attraction is the van der waals force

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8
Q

force for point charges

A

F prop. to 1/r^2

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9
Q

force for dipoles

A

F prop. to 1/r^7

ie much much smaller

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10
Q

cooling atoms so that their kinetic energy is low enough allows..

A

van der waals forces to bind them together as a liquid or a van der waals solid

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11
Q

van der waals solids unstable because

A

forces very weak

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12
Q

when atoms get really close

A

wave functions overlap

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13
Q

symmetric eigenstate

A

1/root2(1+2)

energy of the joint state is lowered
this is a bonding state

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14
Q

anti-symmetric eigenstate

A

1/root2 (1-2)

energy of the joint state is riased
this is an anti-bonding state

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15
Q

most elements bond

A

metallically

when there is no longer an energetic advantage of bonding covalently

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16
Q

metallic bonding - each orbital overlaps several other orbitials. Collections of states overlap to form

A

bands

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17
Q

metallic bonding - provided some of the bands are not full…

A

an infinitesimal change in energy allows the electron to change state

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18
Q

metallic - treat system as

A

continuum of electron states surrounding a regular grid or lattice of positive ions

take into account Pauli - different quantum states

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19
Q

why beryllium is stronger than lithium

A

Be gives 2 electrons to the lattice leaving a 2+ ion

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20
Q

why aren’t elements that form large scale covalent structures metallic

A

either have band gaps which come from their lattice structure or completed outer orbitals which prevent delocalised electron cloud from forming

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21
Q

why aren’t elements like Nitrogen and Oxygen metallic

A

covalently bond into stable molecules with full bonding states

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22
Q

why aren’t noble gases metallic

A

full outer electron shells

can still show van der waals bonding and can be made solid if cold enough

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23
Q

electronegativity describes

A

how much atoms attract electrons

two atoms with different electronegativity can ‘take’ electrons from each other

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24
Q

ionisation potential

A

energy it costs to remove electron

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25
Q

electron affinity

A

energy gained by gaining electron

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26
Q

binding energy per bond

A

energy released when a positive and negative ion combine

work out from electromagnetism due to the electric field between them

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27
Q

all outer shells are full so how does this form a solid?

A

because it is very polarised

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28
Q

in carbon, the four spatially oriented covalent bonds allow it to

A

act like a scaffold for all sorts of structures

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29
Q

what covalent bonding depends on

A

unfilled anti-bonding states

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30
Q

I angstrom

A

10^-10m

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31
Q

crystalline solids

A

atoms have regular periodic arrangement

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32
Q

amorphous solids

A

atoms are disordered though can be ordered on a short range

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33
Q

DVD-RAMs

A

laser heats phase change material allowing it to go from crystalline to amorphous phase and vice versa

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34
Q

pretty much all elements will form crystals if

A

they are allowed to cool slowly enough and to a low enough temp

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35
Q

most pure substances will form

A

crystals

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36
Q

if you cool things too quickly, even pure substances

A

you get an amorphous solid

there is a timescale required for the ordered structure to form

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37
Q

unit cell

A

pattern that repeats without transformation

ie no flips

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38
Q

what is a unit cell made up of

A

a basis (eg an atoms or ions)

a lattice

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39
Q

lattice

A

array of points periodically repeated in space

each lattice point can have one or more atoms associated with it

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40
Q

most efficient packing

A

hexagonal

eg honeycomb

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41
Q

hexagonal close packing

A

hexagonal sheets will overlap in alternating layers
ABAB layer structure
has hexagonal symmetry

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42
Q

Face centred cubic

A

ABC layer structure
next later goes in the space that hasn’t been used
has cubic symmetry

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43
Q

body centred cubic

A

alternating layers of cubic atoms not truly close packed, no hexagonal symmetry

next layer above spaces in previous. ABAB

produces a cubic lattice with one extra atom in the middle

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44
Q

simple cubic

A

directly above previous layer

aka primitive cubic

looks like regular cube

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45
Q

lattice constant, a

A

gives size of unit cell

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46
Q

crystal structure is a convolution of

A

a lattice and a basis

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47
Q

how many non-degenerate lattice symmetries are there in nature

A

14

these are the bravais lattices

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48
Q

how many atoms in the unit cell

A

work out how many cells the corners and faces are shared with

8 x corner share + 6 x face share

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49
Q

coordination number

A

nearest neighbours

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50
Q

packing fraction

A

fraction of the structure occupied by atoms
=volume of atoms / volume of cell

use lattice parameter =a and atomic radius = r0

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51
Q

characteristics of simple cubic

A

coordination =6
atoms per unit cell =1
packing fraction=52%

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52
Q

characteristics of body centred cubic

A

coordination=8
atoms per unit cell=2
packing fraction=68%

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53
Q

characteristics of face-centred cubic

A

coordination=12
atoms per unit cell=4
packing fraction=74%

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54
Q

characteristics of hexagonal close packed

A

coordination=12
atoms per unit cell=6
packing fraction=74%

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55
Q

‘face’ atom is shared between

A

two unit cells

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56
Q

‘corner’ atoms is shared among

A

eight unit cells

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57
Q

coordination number

A

number of nearest neighbours

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58
Q

lattice can be described by three vectors

these vectors are chosen such that

A

the lattice looks identical for an integer translation along these vectors

r’=r+sa+tb

a and b ‘primitive lattice vectors’

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59
Q

if the cell is defined by primitive vectors, we can find any point inside the cell as

A

a fraction of the primitive vectors

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60
Q

drawing unit cells

A

collapse 3D cell on to xy-plane

mark each atom/ion with its z coordinates

don’t draw top layer if it is a repeat of bottom layer

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61
Q

miller indices are used to

A

identify atomic planes

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62
Q

miller indices steps

A

pick a cell
identify the intercepts (if never intercepts, intercept at infinity)
write down intercepts
take reciprocals
multiply through to get integers
reduce to lowest common fraction
replace -ve signs with bars

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63
Q

normal distance between planes from the miller index

A

d=a/ sqrt(h^2+l^2+k^2)

64
Q

crystal directions are denoted

A

[hkl] rather than (hkl)

65
Q

we can specify direction in crystals by

A

T=Ua1+Va2+Wa3

where [UVW] is defined such that [100] is x-axis, [010] is y-axis

66
Q

for cubic crystals only, [hkl] direction is

A

perpendicular to face of (hkl) plane

67
Q

equivalent lattice directions

A

directions that are identical under symmetry operations

there can also be equivalent lattice planes

68
Q

notations

A

miller indices for planes (hkl)
notation for directions [hkl]
equivalent planes {hkl}
equivalent directions <hkl></hkl>

69
Q

the lennard-jones potential

A

atoms have an equilibrium spacing

as atoms get closer, pauli exclusion principle forces electrons to fill higher energy states

attractive potential energy from van der waals force

70
Q

real crystals - if system cools quickly, likely that

A

sometimes crystals will get stuck in local minima

don’t have energy to overcome the potential barrier

71
Q

when atoms end up in the ‘wrong’ place

A

they create defects which propagate through the structure as grain boundaries

this can also be caused by impurities

72
Q

the size of the crystal grain tends to correlate to

A

how fast they cool

quick cooling = lots of defects = lots of small grains

73
Q

glasses (like obsidian) are

A

amorphous solids
they have no crystalline order

molten material –> flash freezing –> snapshot of liquid state

74
Q

water expands as it freezes due to

A

frustration and residual entropy in its crystal structure

polar so +ve must be next to -ve
no way to do this across crystal
millions of ways to almost do it - raise the entropy of the system

75
Q

normally increased pressure

A

holds solids together

for water, increased pressure breaks the solid apart

76
Q

quasi crystals

A

crystals that have order, but no repetition

based on odd-number symmetry (pentagons, heptagons etc)

77
Q

bulk modulus of elasticity quantifies

A

how much the solid deforms

(kapa has dimensions of pressure)

78
Q

real tensile strength values are mostly

A

around 100x lower than prediction

only break this way in perfect crystals

79
Q

before solids break, they

A

bend

due to elastic distortion

80
Q

to be ductile, a solid needs to to able to

A

change the position of atoms without much change in energy

(metals tend to be ductile)

81
Q

in general, alloys and compounds are less ductile than

A

pure metals but not always - structure dependent

82
Q

covalent and ionically bonded materials tend to be very

A

brittle since bonding is directionally dependent

83
Q

the difference between yield stress and ultimate tensile strength is a measure of

A

ductility, ie how much a material can be plastically deformed

84
Q

x-ray diffraction - the bragg law

A

atoms act as 3D diffraction grating

pattern of diffracted radiation allows for determination of internal structure of solid

85
Q

consider two planes separated by distance, d

for reflected radiation to be in phase with incident, the anlge of incidence must

A

equal the angle of reflection

86
Q

for diffraction, need

A

lambda < or = 2d

87
Q

a collimated beam has

A

parallel wavefronts

if they reflect off different planes we can calculate the path difference

88
Q

general equation for a plane

A

hx+ky+lz=a

miller indices tell us where planes cut the axes

89
Q

the distance between miller planes is

A

the length of the vector normal to the plane that goes from the origin to the plane

90
Q

separation of miller planes, d=

A

a / sqrt(h^2+k^2+l^2)

91
Q

bright x-ray scattering when

A

n lambda = 2asin theta / sqrt(h^2+k^2+l^2)

92
Q

x-ray generated by projecting

A

accelerated electrons at a metal target

electrons ejected from lower energy states

x-rays are produced by e in higher state dropping

93
Q

spectrum of x-rays has sharp lines due to

A

electron transitions

94
Q

rotation photography

A

crystal alligned in particular direction and rotated with x-ray detector

uses monochromatic x-rays

95
Q

laue photography

A

continuum of x-rays directed at thin sample

bragg condition always met at perpendicular angles, creating spots on screen

96
Q

powder photography

A

uses monochromatic x-rays on sample of fine powder

some grains will be at correct angle to satisfy bragg

x-rays emitted in series of cones

97
Q

destructive interference can arise from

A

equivalent planes in more complex crystal structures

98
Q

if we take the square of both sides of the Bragg law

A

not all values of {hkl} are visible

98
Q

for FCC and BCC latices, destructive interference within unit cell

A

cuts out certain reflections

99
Q

general rules for destructive interference cutting out certain reflections

A

FCC: h,k,l must all be odd or all even (0 counts as even)

BCC: h+k+l must be even

100
Q

making a monochromatic x-ray beam

A

at certain angle, only one wavelength will be diffracted

this separates a single wavelength from a spread

101
Q

relativistic momentum, E=

A

p^2c^2 + m^2c^4

102
Q

electron microscopy

A

charged so interact strongly with ions in the crystal

comparing wavelength to diameter of an atom, small diffraction angles

103
Q

neutron diffraction

A

no electric charge
magnetic dipole moment

need large samples as have a weak interaction with matter

can be used to probe magnetic atoms

104
Q

conduction electrons

A

in metals, free electrons can carry energy around the metal and also electric current

105
Q

free electron model

A

ignore the positive ions

106
Q

fermi energy

A

corresponds to the highest occupied energy level

intrinsic property of the metal (more electrons = higher Ef)

electrons near fermi energy dominate electric current

107
Q

density of states

A

the number of states per unit energy

108
Q

when electric field applied to electron sea in metals

A

each e accelerates

acquires a drift velocity in addition to fermi velocity

109
Q

resistivity

A

intrinsic property, independent of shape

110
Q

conductivity

A

1/resistivity

111
Q

current density units

A

coulombs per square metre per second

112
Q

current density

A

current across a unit area

113
Q

drude model

A

e accelerated by E field

in addition to normal motion

time between collisions small so gained v &laquo_space;normal v

114
Q

as well as collisions with the lattice, electrons will scatter from

A

defects in the crystal

important at low temperatures

115
Q

residual resistivity that depends on

A

material purity and quality

116
Q

hall effect

A

electron path between collisions is curved

charge builds up on one side of the conductor

this creates E field that opposes further transverse drift

steady electric potential maintained across material as long as current flowing

117
Q

momentum or k-space is known as

A

reciprocal space

118
Q

nearly free electron model

A

taking into accounts effects of lattice

119
Q

Brillouin zones

A

map all possible k-vectors into a range between -pi/a and pi/a (first B zone)

“folding back to the middle zone”

120
Q

the square of the wavefunction gives

A

probability of finding electron there

121
Q

symmetric state

A

electrons sit mainly at atom sites
lower energy

122
Q

anti-symmetric state

A

electrons sit away from atom sites
higher energy

123
Q

band gap

A

no e in this energy range - no solutions with this energy

124
Q

as wavelength gets closer to a, electron converges on two states:

A
  1. between atom sites

or

  1. bound to atom sites
125
Q

at long wavelengths its an average of the two so

A

they cancel and the electron behaves as if completely free

band gaps open up

126
Q

band gaps occur in all materials

the effect depends on

A

the filling of the bands

127
Q

an intrinsic semiconductor is typically considered conducting if

A

kbT is approx a tenth of the bandgap

then approx 0.1% of electrons are in conduction band which passes threshold for conductivity to start

128
Q

valence band

A

where electrons are involved in covalent bonds, but do not contribute to electric current

129
Q

n type doping

A

add atoms that have extra valence electron

donor atoms donate electron

provides excess of electrons to help with bonding

130
Q

p type doping

A

add atoms that have one less valence electron

results in a positive hole which can carry electric current

131
Q

dopant atoms add

A

extra ‘dopant bands’ which are closer to the conduction/valence band

smaller band gap

conduct better at lower temps

132
Q

for metals there is an overlap in conduction and valence bands so

A

conduction band partially filled by electrons

133
Q

for semiconductors there is

A

an energy gap between bands

134
Q

at absolute zero, the valence band of semiconductors

A

is full of electrons and conduction band empty

135
Q

principle energy gap

A

Eg=Ec-Ev

136
Q

shining long wavelength at a semiconductor

A

valence electrons cannot absorb photons and scatter to high energy states so photons will pass right through

137
Q

for wavelengths where the photon energy is greater than Eg, each photon will

A

raise a valence electron into conduction band

E=hv=hc/lambda > Eg

138
Q

indirect bandgaps

in some semiconductors there is an offset between the top of the valence band and the bottom of the conduction band (in momentum space)…

A

the change in p is too large for photon to take up so phonon also needed

photon carries almost all energy
phonon almost all momentum

139
Q

paramagnetic sample suspended in a magnetic field

A

due to electron spin interacting with magnetic field

stronger effect comes from interaction with unpaired electrons

140
Q

diamagnetic sample suspended in a magnetic field

A

weak effect due to the fact that electrons are paired with partners of opposite spin

141
Q

magnetic materials M

A

magnetisation of a material

A/m

142
Q

magnetic materials H

A

magnetic field strength

A/m

143
Q

magnetic materials B

A

magnetic induction or magnetic flux density

T

144
Q

paramagnetism

A

unpaired electrons

145
Q

diamagnetism

A

paired electrons in the same orbital

146
Q

ferromagnetism

A

d shells incompletely filled
atoms have permanent magnetic moments

147
Q

for ferro magnets, all atomic magnetic moments are

A

aligned in the same direction

148
Q

Curie temperature

A

critical temp above which the alignment of magnetic moments is destroyed and materials are no longer ferromagnetic

149
Q

examples of ferromagnetic materials

A

Fe, Co and Ni

150
Q

antiferromagnet materials

A

adjacent magnetic moments are aligned in opposite directions

151
Q

antiferromagnetic materials have no net

A

magnetic moment in the bulk, but neutron diffraction confirms that the materials are
magnetically ordered, but with a period of twice the inter-atomic spacing.

152
Q

The physics of magnetic ordering depends on

A

the coupling energy between neighbouring magnetic moments

E=-Ju1.u2 where J is the exchange coupling constant

153
Q

if J>0

A

parallel u1 and u2 give lowest possible energy which corresponds to ferromagnetic order

154
Q

if J<0

A

antiparallel moments give the lowest energy which leads to antiferromagnetism

155
Q

Neutron diffraction studies indicate

A

how atomic magnetic moments are distributed within
magnetic crystals.

Physics 2 (8 decks)

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