SS - Crystal structure determination

Question 1

Describe the process of crystal structure determination

Answer 1

X-rays, neutrons and electrons can be used to probe structure. X-rays have a wavelength of approx 10-10m which is a typical internuclear distance in crystals. X-rays are diffracted by planes of atoms.

Question 2

Describe how X-ray radiation is generated

Answer 2

High energy electrons are fired at metal samples (eg Cu). The electrons excite core elctrons, leaving a vacancy. As the excited electron drops back down, X-ray radiation is emitted.

The emitted radiation is usually filtered to produce monochromatic X-rays with a given wavelength.

Question 3

Describe the diffraction pattern obtained using X-ray diffraction

Answer 3

For a signal to be produced, the X-rays must be coherent, ie there is no path difference, the waves are in phase. If there is even a small path difference no signal is produced.

Question 4

State and describe Braggs law

Answer 4

2dsinθ = nλ

• n is an integer
• λ is the wavelength of the X-ray
• d is the interlayer separation, ie the Miller plane with dhkl
• Bragg’s law can be derived using trigonometry

Question 5

Describe the meaning of ‘n’ in Bragg’s law

Answer 5

n is the order of diffraction, ie how many wavelengths difference there are between the two incident rays. We can assume.

Question 6

Describe how XRD helps determine crystal structure

Answer 6

The XDR experiment gives the relation between diffraction intensity and diffraction angle. d is otherwise known as the lattice parameter a.

Question 7

State what reflections are allowed for body centred cubic lattices

Answer 7

Only when h + k + l is even is the reflection allowed. Iron is an example of a BCC lattice

Question 8

Give the relationship between d and h, k and l for a cubic cell

Answer 8

Question 9

Give the relationship between d and h ,k and l for an orthorhombic cell

Answer 9

Question 10

Describe how the intensity of a reflection helps in crystal structure determination

Answer 10

Each reflection has an associated intensity which is proportional to the electron density of the atom which scatters the radiation. Atoms with dissimilar electron density can be distinguished. The intensity can be used to show all atom positions in a cell.

Note: hydrogen has such a low scattering power that its position cannot be resolved using X-rays - neutrons are used instead.

Question 11

Describe how d_hkl can be used to predict the external form of a crystal

Answer 11

• Large interlayer separations between planes implies weak interactions
• It is easier to cleave between planes which are weakly interacting
• Crystal shape is determined by minimising the free energy of a crystal