Topic 2 - Higher Order Structures Flashcards
What assumptions are made of ionic solids?
We assume their structure is determined by electrostatic considerations:
- Arrangement is stabilised by maximising anion-cation interactions and minimising anion-anion repulsion
- Size of ions is important in determining structure
What is the sphere:hole ratio of tetrahedral holes and what is the size of these holes?
1:2 sphere:hole ratio
Size = 0.225r
What is the sphere:hole ratio of octahedral holes and what is the size of these holes?
1:1 sphere:hole ratio
Size = 0.414r
What’s significant about eutactic structures?
Eutactic structures are formed when the structure expands to accommodate ions in interstitial sites, forces original ions to no longer touch.
What is the radius rule? (Radius ratio)
The radius rule predicts the coordination (preferred interstitial sites) of the secondary ion
What assumptions are made in the radius rule?
Electrostatic bonding dominates
Ions are perfect hard spheres of a known radius
What does the radius rule not account for?
Does NOT account for attractive and repulsive forces between ions, considerations of orbital overlap and covalency.
It is simply a geometric rule used as a guide to determine stability
What’re the threshold values of the radius rule for determining the preferred interstitial site?
What is the structure and CN of Rocksalt?
AB
FCC array of anions with all octahedral holes filled by cations
6,6 coordination
What is the structure and CN of Nickel arsenide?
AB
HCP array of anions (As) with all octahedral holes occupied by cations (Ni)
6,6 coordination
- Octahedral Ni
- Trigonal prismatic As
What’s significant about Nickel arsenide?
Charge separation:
- As exists as 1- and 3-, giving As^2- overall
Short M-M contact:
- preferred as compound is not strongly ionic, As is large and is polarisable
- also depends on covalency
What is the structure and CN of Fluorite and Antifluorite?
AB2 or A2B
FCC array of cations (Ca2+) with all tetrahedral holes occupied by anions (F-).
- Oct holes are vacant
8,4 coordination
- 2:1 ration for tetrahedral holes
What’s significant about the Fluorite and Antifluorite structures?
Structure gives Bight Blue colour
When coordination of Fluorite is inverted, it gives Antifluorite structure
There is no HCP equivalent of these structures
What is the structure and CN of Zinc blende and Wurtzite?
AB
Zinc blende:
FCC array of anions with half tetrahedral holes occupied by cations
Wurtzite:
HCP array of anions with half tetrahedral holes occupied by cations
4,4 coordination in both structures
What’s significant about Zinc blende and Wurtzite?
Is also known as sphalerite or cubic ZnS
3-5 semiconductors adopt this structure
- isoelectronic compounds
Zinc blende and Wurtzite are polymorphs of ZnS
What is the structure and CN of Lithium bismuthide?
AB3
FCC array of Bi^3- anions with all Oct and Tet holes filled by Li+
CN of Bi^3-:
14 coordinate
- 8 from cube
- 6 from FC
CN of Li+:
4 and 6 coordinate
What application does the lithium bismuthide structure have?
K3C60 is a superconductor
- FCC disordered C60 (4 per UC)
- K+ in all Oct and Tet holes (12 per UC)
What is the structure and CN of Caesium chloride?
AB
Simple cubic (primitive) array of Cl- anions with large Cs+ cation occupying cubic hole
8,8 coordination
What’s significant about CsCl structure?
That it is NOT BCC, as large Cs+ cation occupies central cubic hole in UC
What is the structure and CN of Rhenium trioxide?
AB3
Simple (primitive) cubic array of cations (Re6+)
6 coordinate octahedral Re6+
Linear 2 coordinate O2-
Corner sharing ReO6 octahedra
What’s significant about the structure of Rhenium trioxide?
It is a substructure of perovskite
- ion can be inserted inside structure
- ABX3 where A & B are both cations, X is anion
What structures covered are FCC/CCP?
Rocksalt
Zinc blende
Fluorite / Antifluorite
Lithium bismuthide
What structures covered are HCP?
Nickel arsenide
Wurtzite
Rutile
.
What structures covered are simple cubic?
CsCl
Rhenium trioxide
Determine the FCC structure of MBr using the radius ratio rule.
M+ radius = 0.6A
Br- radius = 1.96A
0.6 / 1.96 = 0.306
0.414 - 0.225 = tetrahedral holes occupied by cation
Hence M+ must occupy tetrahedral holes
Zinc blende - cation occupies half of Tet holes, matches stoichiometry of 1:1, as Tet holes have 2:1 ratio of close packed ions.
Whats the general formula of spinels?
AB2X4
MgAl2O4 - parent mineral
What is the structure of spinels?
FCC array of anions (O2-)
A cations (Mg2+) in 1/8 tetrahedral holes
B cations (Al3+) in 1/2 octahedral holes
How many formula units are there per unit cell in spinels?
8 formula units per UC
- gives 8Mg 16Al 16O2
How many spheres (atoms) and holes are there in a spinel unit cell?
32 spheres (atoms) per UC
- 64 tetrahedral holes (2:1)
- 32 octahedral holes (1:1)
What different types of spinels are there? What do they mean?
2-3 spinels
- A cation is 2+, B cations is 3+
4-2 spinels
- A cation is 4+, B cation is 2+
How do inverse spinels differ to regular spinel structures?
The distribution in the two types of cations is different
However, the overall occupancy of sites are the same in each structure.
- 1/2 Oct and 1/8 Tet holes occupied
What is the cation distribution in regular spinels?
8 A in 1/8 Tet holes
16 B in 1/2 Oct holes
What is the cation distribution of inverse spinels?
8 A in 1/4 Oct holes
8 B in 1/8 Tet holes
8 B in 1/4 Oct holes
(1/2 Oct and 1/8 Tet holes filled total)
What factors determine spinel or inverse spinel structure?
Ionic radius:
- Tet holes are smaller
- Suggests smaller, highly charged cation occupancy
Electrostatics:
- Highly charged cation should prefer higher coordination.
(Ionic radius and Electrostatic factors compete w/each other)
CFSE (TM cations):
- Relative stabilisation due to partially occupied d-orbitals affects preference for Oct sites.
- Dominates when relevant.
How do you determine the octahedral site preference due to CFSE of a TM cation?
Octahedral site preference energy (OSPE)
OPSE = CFSEoct - CFSEtet (for each cation)
Greater ∆Oct CFSE = greater stability of crystal when in octahedral site
How do lithium ion batteries work on charging and discharging power?
On charging, Li+ diffuses through the electrolyte from the cathode to the anode - the reverse occurs on discharge
What key factors determine the usability of a lithium ion battery?
Li+ must be mobile in electrode material & materials must be able to store Li+ ions
Key factors for cathodes:
- charge density
- charge rates
- stability
- cost
- toxicity
LiCoO2 is the most common cathode material, why?
LiCoO2 forms a layered solid with an ordered Rocksalt structure
Li+ can diffuse in two dimensions between layers of Co octahedra
It allows for reversible interact action of Li+ ions with high cycling efficiency
Also has a low thermal runaway temperature - tho Co is expensive
Whats an issue with LiMn2O4 for use as a cathode?
they have poor cycling stability partially due to Jahn-Teller distortion from Mn3+
- also undergoes side reactions with electrolyte
What’re the benefits of using LiMn2O4 as a Li+ ion cathode?
Mn is cheaper and less toxic than Co
Also have higher thermal runaway temperatures
When are perovskites often formed?
Often formed when the difference in size of A and B cations is large
What’s the general formula of perovskites?
ABX3
What combinations of cations can be used in perovskites?
1+/5+
2+/4+
3+/3+
Whats the structure of perovskites?
A and X ions form FCC array
B cations reside in octahedral holes
What factors cause distortion in perovskites?
Charge, size & coordination/geometry
Why does distortion occur in perovskites?
The structure distorts to better accommodate the preferences of the ions
The composition and stoichiometry is unchanged
What can be used to determine the extent of distortion in perovskites?
The Tolerance factor, t
What’re the thresholds for the tolerance factor?
1 < t < 1.06 = hexagonal / tetragonal perovskite
0.9 < t < 1 = ideal cubic structure
0.8 < t < 0.9 = orthorhombic perovskite
t < 0.8 = other structure types
- e.g. LiNbO3, ilmenite
What happens when a tolerance factor of a crystal falls outside the thresholds?
The compound is unstable
What is the tolerance factor based on?
The tolerance factor is only based on ion size
- no account for electrostatic interactions
Whats the significance of lead perovskites?
Lead-containing perovskites have important technological applications which relate to their dielectric, ferroelectric and piezoelectric (converts mechanical stress to electrical energy) properties.
How is polarisation of lead-containing perovskites achieved?
Pb2+ cations occupy the A-site (central) where the 6s lone pair drives the displacement from the centre of its coordination, polarising the material.
Ti4+ is also off-centred, contributing to polarisation.
Both cations are displaced in the same direction, with O2- anions shifting the opposite direction.
Whats the problem with Pb-containing perovskites?
Lead is highly toxic and affects the environment
This makes Pb-free ferroelectrics a priority target for new materials
Why have organic-inorganic halide perovskite seen research interest recently?
Because of their potential applications as absorbers in solar cells
(>22% energy conversion from solar energy - 3.8% in 2009)
How can the band gap in organic-inorganic halide perovskites be tuned?
By varying alkyl chain length
What is the chemical formula of YBCO?
YBa2Cu3O7-∂
(Where ∂ = sigma)
Whats the significance of YBCO?
It is the first high temperature superconductor
Tc = 90K for ∂=0
What does changing the oxygen content (∂) in YBCO do?
As ∂ increases, oxygen content decreases.
This causes greater +ve charge across the material. Hence, Cu oxidation state changes to accommodate
