Absences

Question 1

What is an absence?

Answer 1

When F(hkl) = 0

Question 2

Reasons why absences arise

Answer 2

Lattice centring (i.e. anything other than a P lattice)
Presence of translational symmetry elements in the space group

Question 3

Why are all absences referred to as systematic absences?

Answer 3

Because they are governed by patterns/rules

Question 4

How is the presence of symmetry elements in a unit cell/crystal lattice resolved?

Answer 4

By examination of diffraction spot intensities
Symmetry elements can be determined by looking at reflections for which I(hkl) = 0
The Miller indices for which I(hkl) = 0 often form patterns, called absences

Question 5

What does space group determination involve?

Answer 5

Relating the absences to the symmetry elements that govern the spatial relationships between molecules in the unit cell to each other

Question 6

Lattice-centring absence conditions

Answer 6

Result from any lattice type other than P
Destructive interference of the X-rays will take place according to a selection rule that affects the entire set of intensities (i.e. all h, k, l values)

Question 7

Systematically absent reflections for P lattice type

Answer 7

None

Question 8

Systematically absent reflections for I lattice type

Answer 8

When h+k+l = 2n+1

i.e. sum of indices is odd

Question 9

Systematically absent reflections for F lattice type

Answer 9

Mixed odd/even values for h, k, and l are not allowed

i.e. the reflection conditions is that h, k, l must be all odd or all even

Question 10

Systematically absent reflections for A lattice type

Answer 10

When k+l = 2n+1

i.e. sum of k and l is odd

Question 11

Systematically absent reflections for B lattice type

Answer 11

When h+l = 2n+1

i.e. sum of h and l is odd

Question 12

Systematically absent reflections for C lattice type

Answer 12

When h+k = 2n+1

i.e. sum of h and k is odd

Question 13

Reflection condition

Answer 13

Opposite of a systematic absence

Question 14

Absences due to translational symmetry elements

Answer 14

Result from screw axes and glide planes present in the space group symmetry
Affects only small groups of reflections (subsets) within the data set

Question 15

Systematically absent reflections for a 2(1) screw axis along a

Answer 15

For (h, 0, 0) when h = 2n+1

i.e. h odd

Question 16

Systematically absent reflections for a 2(1) screw axis along b

Answer 16

For (0, k, 0) when k = 2n+1

i.e. k odd

Question 17

Systematically absent reflections for a 2(1) screw axis along c

Answer 17

For (0, 0, l) when l = 2n+1

i.e. l odd

Question 18

Systematically absent reflections for c glide perpendicular to b

Answer 18

For (h, 0, l) when l = 2n+1

i.e. l odd

Question 19

Systematically absent reflections for a glide perpendicular to b

Answer 19

For (h, 0, l) when h = 2n+1

i.e. h odd

Question 20

Systematically absent reflections for a glide perpendicular to c

Answer 20

For (h, k, 0) when h = 2n+1

i.e. h odd

Question 21

Why do mirror planes, inversion centres, rotation axes and rotary-inversion axes not give rise to absent reflections?

Answer 21

They are non-translational symmetry elements

Question 22

Systematically absent reflections for a 4(1) screw axis along c

Answer 22

For (0, 0, l) when l=/=4n

i.e. reflection condition is l = 4n

Question 23

When does an absence occur?

Answer 23

When the I(hkl) of a ‘reflection’ from a set of Miller planes has a mathematical value of 0
(This is the same as destructive interference)
This means the F(hkl) for a given Miller index is also 0

Question 24

When does the imaginary part of the structure factor expression = 0?

Answer 24

When the space group is centrosymmetric (has a centre of symmetry)

Question 25

Cos(pi x odd number)

Answer 25

= -1

Question 26

Cos(pi x even number)

Answer 26

= 1

Question 27

d-spacing equation for cubic

Answer 27

1/d^2 = (h^2+k^2+l^2)/a^2

Question 28

d-spacing equation for tetragonal

Answer 28

1/d^2 = (h^2+k^2)/a^2 + l^2/c^2

Question 29

d-spacing equation for orthorhombic

Answer 29

1/d^2 = h^2/a^2 + k^2/b^2 + l^2/c^2

Question 30

Method for calculating the structure factor for a given Miller set when given scattering factors (fj) as a function of sin(theta)/lambda

Answer 30

1. Determine sin(theta)/lambda for the given Miller set using the d-spacing equation for that particular unit cell type
2. Calculate the atomic scattering factors for the atoms in the unit cell at the sin(theta)/lambda value for the given Miller set (read off graph)
3. Sub all terms into structure factor equation