8.1) Inorganic solids: close packing structures

Why do many solids form close packing structures

most efficient method of packing spheres

What are the two types of interstitial sites

tetrahedral: cations sit with one atom above and three below; CN=4; octahedral: cation sits with three atoms above and below; CN=6

How many interstitial sites exist for each atom

one octahedral and two tetrahedral

How does cation size affect interstitial sites

larger cations can’t fit into lower CN tetrahedral sites (eg Ti)

What structures can we have depending on cation/anion size

larger anions (cations) form close packing lattice with smaller cations (anions) on interstitial sites (tetra/octahedral); can also have perovskites with compounds on lattice and one smaller cation on interstitials

Where are the octahedral sites in fcc

edge centres and body centre

Where are the tetrahedral sites in fcc

split cell into 8 cubes; tetrahedral sites are at the centre of each cube

What distinguishes T+ and T- sites

they point in (111) and -(111) directions respectively

Describe the structure of rocksalt

ccp anions with cations in all octahedral sites; edge sharing octahedra

Describe the idea of space filling polyhedra

structures are built of polyhedra with ccp lattice at the corners; structure made by sharing faces, edges and vertices

MX6 octahedron

6 corners; 12 edges; 8 faces

MX4 tetrahedron

4 corners; 6 edges; 4 faces

Describe the spinel structure AB2X4

ccp anions with octahedral (B) and (partially filled) tetrahedral (A) cations; unit cell 8 times larger than typical fcc; framework of edge sharing BX6 octahedra share corners with isolated AX4 tetrahedra

Describe the structure of Fluorite (eg CaF2)

ccp cations with tetrahedral anions; X has CN=4; M has CN=8 (cube); common due to alternate cation, edge sharing cubes

Describe the cubic perovskite (ABX3) structure

ccp of AX3 layers (A at corners and X on edges) with smaller B cations on octahedral sites (centre of fcc cube); A site has CN=12 (edge centres); B site has CN=6; corner (O) sharing octahedra (B); space filled by AX12 cuboctahedra

How do the polyhedra vary for ccp and hcp ABX3 perovskites

ccp: AO3 layers in (111) plane, corner sharing octahedra; hcp: AO3 layers (0001) plane; face sharing octahedra

Pauling’s third rule

shared edges and faces decrease the distance between like charges; decreasing stability due to stronger electrostatic repulsion (especially for small tetrahedra with highly charged cations)

Why is NaCl structure more common than NiAs

longer MM distance in rocksalt due to edge sharing vs face sharing octahedra (NiAs is hcp) increases stability

Why are cubic perovskites more common than hexagonal

sharing corners vs faces leads to reduced B site cation repulsion

What about metallic bonding

delocalisation of e between cations greatly reduces repulsion for face sharing octahedra

Intermetallics

atoms can occupy all tetrahedral and octahedral sites in the same unit cell; Li3Bi does this due to small Li fitting into all interstitial sites (and due to metallic bonding)

General rule for CNs

formula MaXb dictates CNs of M and X must be in ratio b:a

What does the tolerance factor tell us

if the A or B cations in a perovskite are too big or small to perfectly fit in the 12 and 6 CN sites respectively;

Give the equation for the tolerance factor

t = (rA + rO) / (sqrt(2) (rB+rO)); rA,B,O = radius of A, B and O ions

If t<1

perovskite structure collapses slightly around A cations reducing CN (usually to 8) by partial rotation of the BO6 octahedra; orthorhombic unit cell

If t=1

perfect fit; ABO ions sit on ideal positions; cubic unit cell

If t>1

BO bond lengths become stretched; B ion displaces from centre of octahedron to reduce CN (to 5) and bond lengths; tetragonal unit cell

How does the structure of a perovskite affect its properties

larger A cation (or smaller B) produces t>1 displacing B from the centre, this produces a dipole moment and results in very high permittivity required for dielectrics in multi layer capacitors; smaller A cation (or larger B) produces t<1 tilting octahedra (reducing A CN) and producing a lower permittivity (good for microwave dielectrics)

Why is the fluorite structure a good host for anionic conduction

ccp of cations with tetrahedral holes filled with anions; large octahedral holes vacant allowing anions to migrate

How can fluorites be doped to increase anionic conductivity (ionic vacancy compensation mechanism)

replace some of the cations with ones of similar size but less charge; generates O vacancies; O ions can therefore diffuse more easily via these vacancies

How can fluorites be doped to increase anionic conductivity (ionic interstitial occupation mechanism)

replace some of the cations with ones of similar size but greater charge; requires an extra F- ion which occupies an octahedral interstitial site;