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Quantum Theory of Atoms, Molecules and Solids > Solids (Morrison) > Flashcards

Solids (Morrison) Flashcards

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Organic Chemistry 101 flashcards
1
Q

what is the layer stacking pattern for hexagonal cp?

A

ABA

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2
Q

what is the layer stacking pattern for cubic cp?

A

ABC

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3
Q

How many tetrahedral sites in hcp?

A

2 x T+ 2 x T-

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4
Q

in ccp what do T+ and T- share?

A

faces

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5
Q

how many T // O sites per unit cell of ccp?

A

8 // 4

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6
Q

in hcp what do T+ and T+ share?

A

corners

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7
Q

in hcp what do T+ and T- share?

A

edges

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8
Q

in hcp what do O and T sites share?

A

faces

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9
Q

Rocksalt describe:

A

ccp (either Na or Cl)
all O sites filled; T sites empty
edge sharing NaCl6 and ClNa6 octahedra

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10
Q

Zinc Blende describe:

A

ccp S2- with Zn2+ in 1/2 T sites
all O and 1/2 T empty
corner sharing ZnS4 and SZn4 tetrahedra

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11
Q

Wurtzite describe:

A

hcp S2- with Zn2+ in 1/2 T sites
all O and 1/2 T empty
corner sharing ZnS4 and SZn4 tetrahedra

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12
Q

Nickel Arsenide describe:

A

hcp As with Ni in all O sites
all T sites empty
Face sharing NiAs6 octahedra, edge sharing AsNi6 trigonal bi-prisms

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13
Q

Fluorite describe:

A

ccp Ca2+ with F- in all T sites
all O sites empty
edge sharing CaF8 cubes, edge sharing FCa4 tetrahedra

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14
Q

Rutile describe:

A

hcp O with Ti in 1/2 O sites [distorted]
1/2 and all T sites empty
layers of edge sharing TiO6 octahedra and edge sharing OTi3 trigonal planar

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15
Q

ReO3 describe:

A

based on primitive cubic
cubic Re lattice with O2- on the midpoints
corner sharing RO6 octahedra

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16
Q

Perovskite describe:

A

ABO3 - based on primitive cubic
cubic B lattice with O on the midpoints and A central
face sharing AO12 cuboctahedra, corner sharing BO6 octahedra, face sharing OA4B2 distorted octahedra

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17
Q

Spinel describe:

A

ccp
AB2X4 array with A in 1/8 T sites, B2 in 1/2 O sites
T-T isolated, T-O corner, O-O edge
unconnected tetrahedra and edge sharing octahedral

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18
Q

Inverse spinel describe:

A

ccp
AB2X4 array with B in 1/8 T sites, A+B in 1/2 O sites
edge sharing BO6 + AO6 octahedra, BO4 tetrahedra unconnected, corner shared with octahedra.

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19
Q

how do you find the radius ratio?

A

r+/r-

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20
Q

What are some rules to determine radius ratios? (6 things)

A

based purely on ionic model
hard spheres // only electrostatic forces // maximise CN // avoid C+C+ and A-A- interactions // maintain local electroneutrality

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21
Q

What are some general size relationships for atomic radii? (7 things)

A

radii increase down a period // isoelectric series - size decreases with increased charge // radius decreases with increased oxidation state // radius increases with increasing CN // for a given OxS radius decreases –> // for a given 3D element, r(HS) > r(LS) // diagonal relationships: r(Na+)~r(Ca2+)

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22
Q

what is the minimum cation size for an octahedral site?

A

0.414

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23
Q

what is the minimum cation size for an 8-coordination site?

A

0.732

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24
Q

what is the minimum cation size for a tetrahedral site?

A

0.225

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25
Q

what is the minimum cation size for a trigonal site?

A

0.155

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26
Q

what is the minimum cation size for a dodecahedral site?

A

1.000

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27
Q

What is a mooser-pearson plot?

A

a graph of n (principle quantum number) vs dx (electronegativity difference between ions) which looks at the type of bonding - non-directional to idealised.

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28
Q

What is Pauling’s electrostatic valence rule?

A

for a cation Mm+ surrounded by n anions Xx-, the electrostatic bond strength, s = m/n; then for each anion the sum of s = x

this determines the stability of the complex.

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29
Q

What is the tolerance factor?

A

To determine if something is a perovskite or not.
a perovskite wants to be a perfect cube - when t = 1.
t = (ra + ro)/sqrt2(rb+ro) (for ABO3)
a perovskite has t = 1 +/- 0.05.

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30
Q

what is a simple substitution?

A

an isovalent substitution where there is no change in charge or interstitial sites or vacancies

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31
Q

in Kroger-Vink notation what is the symbol for filling a vacancy?

A

v in small

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32
Q

in Kroger-Vink notation what is the symbol for making a vacancy?

A

V in big

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33
Q

KV what is the symbol for positive effective charge?

A

.

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34
Q

KV what is the symbol for negative effective charge?

A

’

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35
Q

KV what is the symbol for neutral effective charge?

A

x

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36
Q

KV what is the symbol in subscript?

A

the environment - so what is being replaced in the substitution

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37
Q

KV what is the main symbol?

A

the type of atom - element or vacancy

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38
Q

KV what is before the arrow vs what is on top of the arrow?

A

before is what is being substituted in

on top is what is being substituted for

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39
Q

electronic effects: which d orbitals does cfse apply to?

A

3d (4d and 5d are only low spin)

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40
Q

what is the cfse difference between tetrahedral and octahedral?

A

dt = 4/9 do

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41
Q

which is bigger (cfse) do or p (pairing energy)

A

do

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42
Q

in an interstitial mechanism what do you want to maintain?

A

electroneutrality

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43
Q

what 3 factors do interstitial mechanisms apply to?

A

thermodynamics, structure and electronic configuration

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44
Q

What are the requirements for a substitutional mechanism of solid solution formation?

A 
same charge
similar size (dr~15%)
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45
Q

What is extra the requirement for a continuous substitution mechanism for solid solution formation?

A

isostructural end members

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46
Q

what are the requirements for an interstitial/vacancy solid solution formation?

A

ions of similar size but different charge
minimise vacancy formation energy
interstitial sites available (avoid face sharing)

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47
Q

Explain a cation vacancy substitution

A

introduce new cations with too much positive charge - so you make some vacancies to remove charge to compensate

48
Q

explain a cation interstitial substitution

A

introduce cations with insufficient positive charge - so you need to fill some vacant sites with different positive charges or change the oxidation state of the metal to add charge.

49
Q

give some examples of a cation vacancy substitution

A

Fe(1-x)O –> balance charge by adding Fe2O3 into FeO
Ca2+ doped NaCl
Al2O3 in MgAl2O4

50
Q

give some examples of a cation interstitial substitution

A 
stuffed quartz (SiO2 replaced by LiAlO2)
tungsten bronze (NaxW(V, 1-x)W(IV, x)O3)
51
Q

explain an anion vacancy substitution

A

introduce a less positive cation - need to make vacancies to remove some of the more negative feelings by introducing some positive feeling vacancies where the anion used to be

52
Q

explain an anion interstitial substitution

A

either introducing an extra anion and balancing with an extra positive cation which increases number of atoms so need to fill an interstitial site; or balancing by changing the oxidation state of the metal and filling an extra interstitial with the extra atoms.

53
Q

give some examples of an anion vacancy substitution

A

ZrO2 replaced by CaO
ZrO2 replaced by Y2O3
CeO2-Ce2O3

54
Q

give some examples of an anion interstitial substitution

A

CaF2 - YF3

UO2+x

55
Q

what is a double substitution?

A

when both a cation and an anion can switch

56
Q

give some examples of double substitutions

A

AgBr-NaCl
Olivine Mg2SiO4
Feldspars CaAl2Si2O4-NaAlSi3O4
Sialons Si3N3-Al2O3

57
Q

What is Vegard’s law?

A

describes the effects of replacing A atoms for B atoms and the effects this has on the cell parameters - related to the A-B repulsion (up) and attraction (down)

58
Q

What causes positive deviations from Vegards law?

A

due to A-A and B-B forming clusters which increases repulsive energy so curve goes concave up.

59
Q

what main factors determine electronic properties of transition metal oxides?

A

extension of transition metal complexes
all about d electrons
in solids d e- are localised in AOs or delocalised in bands

60
Q

What are the two models used in band theory?

A

tight binding model and nearly free electron model

61
Q

what is the tight binding model?

A

bases electrons in a solid on MO theory.

62
Q

what is the nearly-free electron model?

A

analogous to particle in a box –> delocalised electrons are travelling as waves

63
Q

what type of bonding is present in tight binding model when |ca|^2=|cb|^2

A

pure covalent

64
Q

what type of bonding is present in tight binding model when ca=0 and cb=1?

A

pure ionic

65
Q

what is quantum number k?

A

the wave vector = k=2pi/lambda = pi/a

66
Q

what is e^ikna?

A

the Bloch function - which is the eigenfunction of the translational operator

67
Q

is anti bonding or bonding orbitals dominated by anions or cations?

A

bonding = anion

anti bonding = cation

68
Q

what is DOS?

A

density of states

69
Q

what is the wavelength for the most bonding or most anti bonding orbitals?

A

infinity

70
Q

What shape is the energy potential graph for the nearly free electron model and what is on the axes?

A

E vs k parabola

71
Q

what is Bragg’s law?

A

n[lambda]=2asin[theta]

72
Q

what is the equation for a in braggs law?

A

a = n[lambda]/2

73
Q

what is the equation for k in the nfe- model?

A

k = +/- n[pi]/a

74
Q

what is then central portion of the band structure graph called for nfe- model?

A

1st brillouin zone

75
Q

what are the equations for standing waves in nfe- model?

A 
[psi]+ = exp (ipix/a) + exp (-ipix/a) = 2cos(pix/a)
[psi]- = exp (ipix/a) - exp (-ipix/a) = 2isin(pix/a)
76
Q

what type of orbitals make up the TM valence band?

A

(low number) p (from oxygen)

77
Q

what type of orbitals make up TM conduction band

A

d

78
Q

what type of orbitals make up the TM anti bonding band?

A

metal s-, p- bands

79
Q

what do you do if the conduction band isn’t accurate?

A

fill it with normal d orbital MOs.

80
Q

what is d-d overlap?

A

many orbitals of the same energy overlap = to make a band of orbitals covering a range of energies over the entire crystal. (called the d band)

81
Q

what is d-p ovelap?

A 
eg orbitals on TM can sigma overlap with p orbitals on an anion ---> splits into a bonding and anti bonding band
and t2g (dxy, dxz, dyz) orbitals can pi overlap with with O2- 2p orbitals
82
Q

how does a band form?

A

continuous overlap of d-p-d-p-d orbitals

83
Q

what are the conditions for d-d orbital overlap?

A

size of d orbitals must be large enough to overlap with neighbouring cations (favours LHS)

84
Q

what are the conditions for d-p orbital overlap?

A

size not important but energy of d and p is the controlling factor - if d orbitals are low in energy - similar to near the top of the O2- 2- band - gives strong overlap (favours RHS)

85
Q

what are the two criteria for the theory of the hubbard model?

A

electron transport would require transfer of an electron and spin pairing –> energetically unfavourable
e-e repulsion favours e- localisation in atomic orbitals —> opposed band formation

86
Q

What does the Hubbard Parameter, U, require for electron transfer?

A

the opening of an energy gap

87
Q

what is the equation for the quantum hubbard? and what does it explain

A

U = Ie- - x (ionisation energy minus electronegativity)

to move an electron around it costs energy which is measured by U

88
Q

what is the equation for charge fluctuation?

A

U = dn + dn —-> dn-1 + dn+1

89
Q

what is the Hubbard hamiltonian? and which is the potential term and the kinetic term?

A

H = t(sum)c+c + U(sum)n(up)n(down)

kinetic potential

90
Q

in the Hubbard Hamiltonian, what does it mean when t>U

A

delocalisation occurs –> solid conducts

91
Q

in the Hubbard Hamiltonian, what does it mean when t<u></u>

A

localisation occurs –> solid insulates

92
Q

what is the equation for bandwidth?

A

w = 2zb (where z = number of nearest neighbours)

93
Q

in the equation for bandwidth, what is b?

A

the exchange integral - degree of interaction/overlap
bij = (psi, H’psi) = eij(psii, psij)

eij = one e- energy; psii, psij is the overlap integral; H’ is the perturbation of atomic potential bt neighbouring atoms at ri and rj

94
Q

At what point in the hubbard model does an insulator become a conductor?

A

when U=W –>

95
Q

what are the two conditions for electron delocalisation according to hubbard model?

A

d orbitals are diffuse and overlap AND U is small

d-p overlap is continuous AND U is small

96
Q

what is the alternative classification? (ZSA)

A

for charge transfer insulators: delta dn —> dn+1 + L+

97
Q

U or delta control - two options

A

Mott-Hubbard insulators - U

charge transfer semiconductors - delta

98
Q

what is a mott-hubbard insulator? and some examples

A

when Eg~U - there is a hole and e- in d band (p d d)

v2O3, Ti2O3, Cr2O3 + halides

99
Q

what is a charge transfer semiconductor? and some examples

A

Eg~delta - hole in p band, electron in d band (d p d)

CuX2, NiX2

100
Q

what are some examples of a mixture of the U or delta control?

A

NiO, NiF2, CuF2

101
Q

what are the five types of magnetism?

A

dia, para, ferro, antiferro, ferri

102
Q

what is the magnetic susceptibility of the 5 types?

A

small and neg; small and pos; large and pos; small and pos; large and pos

103
Q

what are the magnetic behaviours of the 5 magnetic types?

A

no moment; random; parallel; antiparallel; mixed (anti)parallel

104
Q

what type of magnetism has the curie temperature?

A

ferromagnetism

105
Q

what type of magnetism has the Niell temperature?

A

ferrimagnetism

106
Q

What is the Heisenberg exchange hamiltonian?

A

Hex = -(sum)JijSiSj

107
Q

in the HEH, what happens when J>0

A

parallel spin –> ferromagnetic ordering

108
Q

in the HEH, what happens when J<0

A

antiparallel spin –> antiferromagnetic ordering

109
Q

what is the equation fo rJ in the HEH

A

J = -2t^2/U

110
Q

What are the 3 types of exchange?

A

direct (cation-cation), indirect (double exchange e- transfer), superexchange (cation-anion-cation)

111
Q

how do unpaired electron spins couple?

A

through covalent interactions with intervening ligand

112
Q

what type of magnetism present in a 1/2 filled metal - 1/2 filled metal orbital interaction?

A

AFM

113
Q

what type of magnetism present in a 1/2 filled metal - empty metal orbital interaction?

A

FM

114
Q

what happens to the strength of the superexchange interaction as covalency increases?

A

it increases

115
Q

how does delocalisation occur in neighbouring atoms

A

spins must be aligned in a certain way (usually ferromagnetically)

116
Q

what are the two main mechanisms for determining the magnetism of magnetic oxides?

A

superexchange and indirect double exchange

Quantum Theory of Atoms, Molecules and Solids (2 decks)

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