Topic 3 - Characterisation Methods Flashcards
What information does X-ray crystallography provide?
It provides information on the time and volume averaged long-range ordered structure of the solid
What causes the scattering of X-rays?
Electron density that is associated with the atoms regularly arranged in the crystal
How does increases the grating spacing affect x-ray diffraction?
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
Whats the significance of the incident angle of diffracted x-rays?
Waves passing through a grating interfere constructively at certain angles for a particular d-spacing, constructive interference
- results in a diffraction pattern
What causes the dark areas observed in a diffraction pattern?
When the incident angle for the particular d-spacing is ‘not correct’ and results in destructive interference
- the diffracted waves are out of phase
Whats the significance of the path difference length?
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
What does Bragg’s law relate?
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
What is the formula for Bragg’s law?
Lamda = 2d(hkl)sin(theta)
What is the reciprocal lattice?
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.
How are x-rays generated?
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.
Why are synchrotrons used as x-ray sources?
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
What information does the reflection position of a single crystal give?
The reflection position give info on the plane distances, and hence the unit cell
What information does the intensity of the diffraction pattern give?
Diffraction intensities provides information on the atom positions within the crystal
- technically its the position of electron density for x-rays
How does the diffraction pattern of powders differ to that of single crystals?
Powder diffraction produces rings instead of isolated spots
- lower resolution
Why is it harder to fully determine crystal structures using PXRD?
Peak positions are usually still accessible but extracting intensities of individual reflections can be difficult because of overlap
What’re the advantages of PXRD?
Simple, fast, non-destructive experiment
Does not require high quality sample (large single crystal)
Does not require sample remains a single under changing conditions
Bulk characterisation technique
What’re the disadvantage of PXRD?
Data analysis to fully determine structure can be more complex than for single crystal diffraction
What information does PXRD give?
Polymorph identification
Crystalline size and shape information
Microstructural analysis
Unit cell determination
Crystal structure determination
Whats the benefit of comparing PXRD of known solids to new solids?
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.
What are crystallites?
Crystallites, or scattering domains, (smaller than ~200nm) give rise to broadening of diffraction reflections in the diffraction pattern
What equation provides a way to approximate crystallite size from the width of a diffraction pattern?
The Scherrer equation
What equation relates the d-spacing and unit cell parameters for cubic structures?
What equation relates the d-spacing and unit cell parameters for orthorhombic structures?
Why do systematic absences occur in diffraction patterns?
They occur because of destructive interference of reflections from certain planes
Translational symmetry elements can also cause systematic absences
- screw axis, glide planes
What do systematic absences tell you?
Systematic absences tell you about the centring of the lattice - FCC, BCC, primitive, etc.
What are the allowed reflections for primitive, P, centred lattices?
All reflections are allowed
What are the allowed reflections for body centred, I, lattices?
h+k+l = 2n
What are the allowed reflections for face centred, F, lattices?
h, k, l must be all odd or all even
What does it mean if a reflection breaks the rules of the miller indices of a lattice?
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
Between what planes does destructive interference occur in the Rocksalt structure, why?
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 the interleaving planes
If the ions are isoelectronic, the interference is complete, and so no intensity is observed for the (111) reflection
How do you index a cubic crystal using Braggs’ law?
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.
What equation gives the structure factor for a particular reflection?
Where fj is the scattering factor of atom j at position (xj, yj, zj) in the unit cell
What is the intensity of a reflection given by?
Hence, the intensities can be quantitatively related to the positions of the atoms in the unit cell
Is the scattering factor of Cr equal to that of Cr(III)?
No, as they have a different number of electrons
What is Rietveld refinement?
Rietveld refinement is the process of varying the structural model to fit the whole experimental powder profile of a material.
