Crystal structures

Question 1

Lattice pattern of cubic close packed structures

Answer 1

ABC

Question 2

Lattice pattern of hexagonal close packed structures

Answer 2

ABA

Question 3

Number of tetrahedral holes and octahedral holes per ion

Answer 3

two tetrahedral, one octahedral

Question 4

How are distances measured in a unit cell projection

Answer 4

From the bottom up. 0 is bottom, 1 is at the top

Question 5

Calculating occupancy from unit cell projections

Answer 5

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.

Question 6

Pauling’s rules

Answer 6

1. The coordination number of the cation will be maximised to maintain cation-anion contact (radius ratio laws). 2. ebs = m/n.

Question 7

How to calculate radius ratio?

Answer 7

r2/r1 assuming cations are small with radius r2 and anions are large with radius r1

Question 8

Outline the equation for electrostatic bond strength

Answer 8

m/n where m is the charge on the cation and n is the number of anions that surround it

Question 9

what is the sum of ebs = x

Answer 9

x is the anion charge. The sum of all electrostatic bond strengths must equal this charge

Question 10

What is the born-mayer equation used for

Answer 10

determining lattice enthalpy of crystal structures

Question 11

Assign every member in the Born-Mayer equation

Answer 11

Look at notes

Question 12

What is the Madelung constant

Answer 12

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

Question 13

Important to consider when calculating d0

Answer 13

It is the sum of both the ionic radii. Not just one or the difference

Question 14

Schottky defect

Answer 14

Holes for both a cation and anion

Question 15

Frenkel defect

Answer 15

The movement of a ion to a different location leaving a hole in the crystal

Question 16

What is maintained in the simplest defected crystal structures

Answer 16

electrical neutrality

Question 17

Two mechanisms for Frenkel defects

Answer 17

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

Question 18

Ion migration for Schottky defects

Answer 18

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

Question 19

Draw an energy diagram for ion migration

Answer 19

See notes

Question 20

Equation for the equilibrium number of defects

Answer 20

n = Nexp(-Ev/kbT) where Ev is the energy to remove an atom

Question 21

When does the equilibrium number of defects not work

Answer 21

when N is very small

Question 22

Other name for colour centres

Answer 22

F centres

Question 23

Formation of F centres

Answer 23

X-ray bombardment, ionising the surface of crystals which gives rise to electrons that can diffuse to occupy vacant sites

Question 24

What causes the colour from an F centre

Answer 24

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

Question 25

How does radioactive decay make crystal defects

Answer 25

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

Question 26

Overall thermodynamics of defects

Answer 26

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.

Question 27

Effect of temperature on the number of defects

Answer 27

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