Chapter 7 X-Ray diffraction
Chapter 7
X-Ray diffraction
Contents
Basic concepts and definitions Waves and X-rays Crystal structure Bragg’s law X-ray techniques
Basic concepts Crystal chemistry: study of relationship of internal
crystal structure to the physical and chemical properties of minerals
Crystals:• Lattice structure, with unit cell as basic building block• Atoms and inter-atomic distances: 0.1 – 0.5 nm• For investigation of crystals - waves with wavelengths in
this order Visual light: wavelength 400 – 700 nm X-Rays and neutron waves: 0.01 – 0.5 nm
Basic concepts
Quantum shells orbits wherein electrons move:• K, L, M, N, O, P, Q• No of electrons: 2N2 (N = 1,2,3,4,5,6 or 7)• M: 2 x 32 = 18
Sub-shells – dividing quantum shells• s, p, d, f• No of electrons: 4K – 2 (K = 1, 2, 3 or 4)• d: (4 x 3) – 2 = 10
Basic concepts Generation of X-rays
• Electrons emitted by source (heated W filament) • Accelerate electrons by using an electric field (control
strength of electric field to control speed of electrons)• Electrons collide with metal anode (Cu or Mo)• Very high-energy radiation emitted: X-rays*
How:• Accelerated electrons displace electrons of inner shell of
atom• Electron from higher shell fills electron ‘gap’ and release
excess energy as X-ray photons• Energy and wavelength of these photons correspond to
particular electronic transition of given atom of the metal anode
Generation of X-rays
Waves Amplitude Wavelength Path/phase difference
• Fig 7.4 Interference of waves
• Constructive• Destructive
Interference of waves
Bragg’s Law Based on the diffraction of X-rays or neutrons
from crystal surfaces at certain angles Basis of developing powerful tool for studying
crystals in the form of X-ray and neutron diffraction
How:• When X-rays (or neutrons) hit an atom the movement of
electrons (or spinning of nuclei) cause re-radiation of waves with the same frequency
Rayleigh scattering• Scattered waves interfere with each other constructively
or destructively to produce peaks at certain angles• Produces a diffraction pattern from which the analyses of
the crystal structure is done
Bragg’s law When X-rays are scattered from a crystal lattice, peaks of
scattered intensity are observed which correspond to the following conditions:
1. The angle of incidence = angle of scattering2. The path length difference is equal to an integer number of
wavelengths.
The condition for maximum intensity contained in Bragg's law above allow us to calculate details about the crystal structure, or if the crystal structure is known, to determine the wavelength of the x-rays incident upon the crystal.
Bragg’s equation: nλ = 2dsinθ• n: integer determined by the order given• λ: the wavelength of x-rays• d: spacing between atomic lattice planes• θ: angle between the incident ray and the scattering planes
Bragg’s law
Techniques: X-ray diffractometer
The x-rays are collimated into a strong X-ray absorber (usually lead)
Narrow resulting x-ray beam strike the crystal
Rotate crystal and detector to satisfy Braggs law for diffraction
Techniques: Diffractometer
Techniques: Diffractometry of powders
Randomly oriented small crystals or ‘crystallites’
Reflections scanned and record intensity as function of diffraction angle
The list of θ angles with different intensities are converted to d-spacings
Identify crystals by comparing with diffractions patterns of known minerals
Techniques: Diffraction pattern
Chapter 8
Physical properties of crystals
Definitions(Further self-study of this
chapter is optional)
Definitions
Thermal conductivity:• Transfer of heat through a mineral
through thermal vibrations• High in metals and minerals with
significant metallic bonding Thermal expansion
• Expansion of a crystal (increase in volume) with an increase in temperature
Definitions Piezoelectricity:
• The ability of a crystal to change its shape slightly (undergoes strain) when an electrical field is applied to it (also vice versa: applying stress can induce an electric field on these crystals)
Only possibly with some crystals with no centre of symmetry
Pyroelectricity• The ability of a prismatic crystal to develop opposite
electric charges on opposite ends when heated Common in trigonal tourmaline crystals
Magnetisism• The ability of a crystal to produce a magnetic moment
when a magnetic field is applied to it Only possible when crystal contains atoms or ions with unpaired
electrons• Strongest: Fe3+ and Mn2+ - has five unpaired 3d-electrons• Fe2+ - has four unpaired 3d-electrons
Chapter 3Q2
Chapter 3Q5
Chapter 4
Q8