Topic 3 - Characterisation Methods

Question 1

What information does X-ray crystallography provide?

Answer 1

It provides information on the time and volume averaged long-range ordered structure of the solid

Question 2

What causes the scattering of X-rays?

Answer 2

Electron density that is associated with the atoms regularly arranged in the crystal

Question 3

How does increases the grating spacing affect x-ray diffraction?

Answer 3

As the grating spacing increases, x-ray diffraction spacing decreases - and vice versa.

This is because of the reciprocal lattice generated by the diffraction pattern

Question 4

Whats the significance of the incident angle of diffracted x-rays?

Answer 4

Waves passing through a grating interfere constructively at certain angles for a particular d-spacing, constructive interference
- results in a diffraction pattern

Question 5

What causes the dark areas observed in a diffraction pattern?

Answer 5

When the incident angle for the particular d-spacing is ‘not correct’ and results in destructive interference
- the diffracted waves are out of phase

Question 6

Whats the significance of the path difference length?

Answer 6

The path difference must be an integer multiple of the wavelength (lamda) to produce a diffraction pattern

This is determined by the d-spacing of the crystal and the incident angle

Question 7

What does Bragg’s law relate?

Answer 7

Bragg’s law relates the spacing of the crystal planes with the angles at which diffraction is observed

Diffraction is a function of spacing & angle incident of diffracted wave

Question 8

What is the formula for Bragg’s law?

Answer 8

Lamda = 2d(hkl)sin(theta)

Question 9

What is the reciprocal lattice?

Answer 9

The reciprocal lattice is the representation of the diffraction pattern generated when waves are scattered by a periodic array of points.

It is a representation of the real lattice. Each point in the reciprocal lattice corresponds to the diffraction from a particular set of planes (hkl) in the real (direct) lattice.

Question 10

How are x-rays generated?

Answer 10

X-rays are formed when high energy particles (e-) collide with matter
- e- are typically fired at a Cu anode

This produces white radiation (or Brehmsstrahlung) and some sharp peaks superimposed with characteristic wavelengths.

Question 11

Why are synchrotrons used as x-ray sources?

Answer 11

Extremely intense x-ray source
- fast experiments, time-resolved studies, in situ, in operando measurements (more data)

Tunable wavelength
- can vary energy of radiation depending on the materials studied and experiment (not just x-rays)

Highly collimated, parallel x-rays
- give excellent resolution assuming material is highly crystalline

Question 12

What information does the reflection position of a single crystal give?

Answer 12

The reflection position give info on the plane distances, and hence the unit cell

Question 13

What information does the intensity of the diffraction pattern give?

Answer 13

Diffraction intensities provides information on the atom positions within the crystal
- technically its the position of electron density for x-rays

Question 14

How does the diffraction pattern of powders differ to that of single crystals?

Answer 14

Powder diffraction produces rings instead of isolated spots
- lower resolution

Question 15

Why is it harder to fully determine crystal structures using PXRD?

Answer 15

Peak positions are usually still accessible but extracting intensities of individual reflections can be difficult because of overlap

Question 16

What’re the advantages of PXRD?

Answer 16

Simple, fast, non-destructive experiment

Does not require high quality sample (large single crystal)

Doe not require sample remains a single under changing conditions

Bulk characterisation technique

Question 17

What’re the disadvantage of PXRD?

Answer 17

Data analysis to fully determine structure can be more complex than for single crystal diffraction

Question 18

What information does PXRD give?

Answer 18

Polymorph identification
Crystalline size and shape information
Microstructural analysis
Unit cell determination
Crystal structure determination

Question 19

Whats the benefit of comparing PXRD of known solids to new solids?

Answer 19

PXRD patterns of known solids can be used to fingerprint a new solid.

Both the positions and relative intensities of peaks of the new material’s profile are taken into account when comparing to known solids.

Question 20

What are crystallites?

Answer 20

Crystallites, or scattering domains, (smaller than ~200nm) give rise to broadening of diffraction reflections in the diffraction pattern

Question 21

What equation provides a way to approximate crystalline size from the width of a diffraction pattern?

Answer 21

The Scherrer equation

Question 22

What equation relates the d-spacing and unit cell parameters for cubic structures?

Answer 22

Question 23

What equation relates the d-spacing and unit cell parameters for orthorhombic structures?

Answer 23

Question 24

Why do systematic absences occur in diffraction patterns?

Answer 24

They occur because of destructive interference of reflections from certain planes

Translational symmetry elements can also cause systematic absences
- screw axis, glide planes

Question 25

What do systematic absences tell you?

Answer 25

Systematic absences tell you about the centring of the lattice - FCC, BCC, primitive, etc.

Question 26

What are the allowed reflections for primitive, P, centred lattices?

Answer 26

All reflections are allowed

Question 27

What are the allowed reflections for body centred, I, lattices?

Answer 27

h+k+l = 2n

Question 28

What are the allowed reflections for face centred, F, lattices?

Answer 28

h, k, l must be all odd or all even

Question 29

What does it mean if a reflection breaks the rules of the miller indices of a lattice?

Answer 29

If a reflection breaks the rules for a given lattice centring, it cannot be observed if a lattice has that centring
- i.e. it is systematically absent

Question 30

Between what planes does destructive interference occur in the Rocksalt structure, why?

Answer 30

Destructive interference occurs between reflections from (111) and (222).

This is because the ions on these close-packed planes are exactly out of phase with he interleaving planes

If the ions are isoelectronic, the interference is complete, and so no intensity is observed for the (111) reflection

Question 31

How do you index a cubic crystal using Braggs’ law?

Answer 31

Convert 2(theta) to sin^2
- or d to 1/d^2

Find the common factor to give integer ratios.

Divide all sin^2 (or 1/d^2) values by this factor to give the ratio that is equal to h^2+k^2+l^2.

Look at the equation (h^2+k^2+l^2) and assign miller indices

Determine centring, P, I or F based on systematic absences

If required, calculate a (UC length) using d-spacing equation.

Question 32

What equation gives the structure factor for a particular reflection?

Answer 32

Where fj is the scattering factor of atom j at position (xj, yj, zj) in the unit cell

Question 33

What is the intensity of a reflection given by?

Answer 33

Hence, the intensities can be quantitatively related to the positions of the atoms in the unit cell

Question 34

Is the scattering factor of Cr equal to that of Cr(III)?

Answer 34

No, as they have a different number of electrons

Question 35

What is Rietveld refinement?

Answer 35

Rietveld refinement is the process of varying the structural model to fit the whole experimental powder profile of a material.