Ionic Lattices And Close Packing Flashcards
What is the opposite of a periodically ordered array of atoms know as?
An amorphous solid lacking long-range order
Define what a unit cell is
A unit cell is the smallest repeating unit of a periodic structure
What do we need to describe the pattern of a crystalline structure?
The unit cell parameters and the contents of the unit cell
What is the shape of a 3 dimensional unit cell?
Parallelepiped - cuboid
How many crystal lattice structures are known as Bravias lattices?
14
What are the 3 types of cubic packing?
Primitive cubic
Body-centred cubic
Face-centred cubic
Draw out a body-centred cubic projection presentation
When counting atoms in a unit cell, what is the relative value of each position to the unit cell?
Inside = 1
Face = 1/2
Edge = 1/4
Corner = 1/8
What effect does metals being electropositive have on the structure they form?
Their valence electrons are less tightly held - hence bonding is non-directional
As a result atom tend to pack as densely as possible
How does cubic close packing differ from hexagonal close packing?
CCP is where you have a stacking sequence of ABC - with C directly above A
HCP is where you have a stacking sequence of AB - with B in the gaps created by the A spheres below
What unit cell does cubic close packing show?
Face-centred unit cell
How do you find the packing efficiency of a unit cell?
Packing efficiency = (number of spheres per unit cell x volume of sphere) / volume of unit cell
What is the coordination number and coordination of a simple cubic structure?
CN = 6
Coord = octahedral
What is the coordination number and coordination of a body-centred cubic structure?
CN = 8
Coord = cubic
What is the coordination number and coordination of a face-centred cubic structure?
CN = 12
Coord = cube-octahedral
What holds ions together?
Electrostatic forces
Why do ions form crystalline structures?
Because they tend to pack in such a way that maximises attractive forces between opposite ions, and repelling forces from same ions are minimised
Resulting in a crystalline solid packed in a regular periodic fashion
Which are generally bigger anions or cations?
Anions are usually bigger, they form the sphere packing
Cations occupy the interstitial holes between them as they’re smaller
What are the two types of interstitial holes in close-packing of equal spheres?
Octahedral holes and tetrahedral holes
What is the coordination of octahedral holes?
Coordinated by 6 anions
What is the coordination of tetrahedral holes?
Coordinated by 4 anions
Give the coordination numbers of Rocksalt
NaCl
Both cations and anions have CN = 6
All octahedral holes in cubic close packing of anions is occupied by cations
Give the coordination numbers of Fluorite
CaF2
Cations = 8
Anions = 4
Cation form the cubic close packing while anions fill all tetrahedral holes
Give the coordination numbers of Antifluorite
LiO2
Cations = 4
Anions = 8
Anions form the cubic close packing while cations fill all tetrahedral holes
Give the coordination numbers of Sphalerite
Cubic cp ZnS
Both cations and anions have CN = 4
Half of tetrahedral holes in cubic close packing are occupied
Give the coordination numbers of Wurtzite
Hexagonal cp ZnS
Both cations and anions have CN = 4
Half of tetrahedral holes are filled
Give the coordination numbers of CsCl type packing
Simple body-centred cubic CsCl
Both cations and anions have CN = 8
(Primitive cubic not bcc as it is 2 simple cubic cubes interpenetrating each other)
What are the coordination numbers of CdCl2
Distorted ccp CdCl2
Cation = 6
Anion = 3
Half of octahedral holes filled
Give the coordination numbers of Rutile
Distorted hcp TiO2
Cation = 6
Anion = 3
Half of octahedral holes filled
Give the coordination numbers of NiAs
hcp NiAs
Both cations and anions have CN = 6
All octahedral holes filled
How does the size of an ion change with its charge respectively?
Cations generally are much smaller while anions become much larger than their neutral atoms
r(Na) = 191 pm vs r(Na+) = 102 pm
r(Cl)=99pm vs r(Cl-)=181pm
( 2x larger due to extra electron)
What does the ionic radius depend on?
The charge of the ion
The coordination number of the ion (especially for cations)
- the higher the CN the larger the ionic radius
What structures does the number of interstitial holes increase in order of?
Tetrahedral —> Octahedral —> Cubic
What are the radius ratios of the 3 interstitial hole types?
Tetrahedral - 0.225
Octahedral - 0.414
Cubic - 0.732
How do you find the radius ratio of a binary ionic solid?
¥ = radius small ion / radius large ion
What does the coordination number of the cation reflect?
Due to cations usually being smaller they fill the interstitial holes
Hence the cation coordination number indicates the interstitial hole type.
4 = tetrahedral
6 = octahedral
8 = cubic
Why is the structure of Fluorite a special case?
Because F- ions are larger than Ca2+ ions, so F- anions should make up the sphere packing
The structure is usually referred to as a cubic close packing of cations in which anions fill the holes because the structure is face-centred cubic
