Crystal structures Flashcards
Lattice pattern of cubic close packed structures
ABC
Lattice pattern of hexagonal close packed structures
ABA
Number of tetrahedral holes and octahedral holes per ion
two tetrahedral, one octahedral
How are distances measured in a unit cell projection
From the bottom up. 0 is bottom, 1 is at the top
Calculating occupancy from unit cell projections
Each ion has an occupancy depending on its location (centre = 1, corner = 1/8). By working out the ratio of cations to anions, you can work out how many of each hole type are filled.
Pauling’s rules
- The coordination number of the cation will be maximised to maintain cation-anion contact (radius ratio laws). 2. ebs = m/n.
How to calculate radius ratio?
r2/r1 assuming cations are small with radius r2 and anions are large with radius r1
Outline the equation for electrostatic bond strength
m/n where m is the charge on the cation and n is the number of anions that surround it
what is the sum of ebs = x
x is the anion charge. The sum of all electrostatic bond strengths must equal this charge
What is the born-mayer equation used for
determining lattice enthalpy of crystal structures
Assign every member in the Born-Mayer equation
Look at notes
What is the Madelung constant
Sum of all the electrostatic interactions between ions in the crystal. Each contribution is the number of equidistant ions divided by their distance from the initial ion relative to an initial distance d
Important to consider when calculating d0
It is the sum of both the ionic radii. Not just one or the difference
Schottky defect
Holes for both a cation and anion
Frenkel defect
The movement of a ion to a different location leaving a hole in the crystal
What is maintained in the simplest defected crystal structures
electrical neutrality
Two mechanisms for Frenkel defects
Direct in which the cation jumps into an already empty interstitial site. Interstitialcy mechanism by which the cation moves into an occupied hole forcing the other cation to move into an empty interstitial space
Ion migration for Schottky defects
The ion must ‘hop’ through a small region with high electrostatic interactions to make it to the empty site. The energy of this ‘transition state’ determines ease of migration
Draw an energy diagram for ion migration
See notes
Equation for the equilibrium number of defects
n = Nexp(-Ev/kbT) where Ev is the energy to remove an atom
When does the equilibrium number of defects not work
when N is very small
Other name for colour centres
F centres
Formation of F centres
X-ray bombardment, ionising the surface of crystals which gives rise to electrons that can diffuse to occupy vacant sites
What causes the colour from an F centre
The electron in an empty site is essentially an electron in a box. This electron has allowed energy levels depending on the size of the box which gives rise to different colours
How does radioactive decay make crystal defects
The production of the daughter nuclei. This will cause a reasonably large amount of damage if in contact with the crystal structure which will ionise and displace surrounding atoms
Overall thermodynamics of defects
The overall reaction is endothermic. Moving the ion is exothermic, but in interstitial sites, there will be fewer bonds made than were broken and hence the overall process is endothermic.
Effect of temperature on the number of defects
dG = dH - TdS
dH will be positive and therefore, as T increases, the spontaneity of the formation of defects increases.
The number of defects increases with temperature
