X-ray Diffraction- Interpretation of Diffraction Patterns Flashcards
What can you measure from the diffraction pattern?
Reflection positions (2θ, d) Reflection intensities Reflection profiles (lone shapes
What properties can you interpret from measurements from a diffraction pattern?
Unit cell size/shape, phase analysis
Atomic arrangement (crystal structure)
Crystallite size and strain
What two key equations are needed for cubic symmetry?
nλ=2dsinθ
1/d^2=(h^2+k^2+l^2)/a^2
How to use 2 key equations for cubic symmetry
Rearrange both for 1/d^2 and put equal to each other. Assume n=1 Rearrange to:
(Sinθ)^2/(h^2+k^2+l^2)=λ^2/4a^2
What are the permissible values of h^2+k^2+l^2?
All apart from 7, 15, 23, 28…
Because h, k and l are integers
How is the quotient λ/4a^2 used?
It is a constant for any pattern as λ (from machine) and a are fixed. The sum h^2+k^2+l^2 is an integer. Need to determine the set of h^2+k^2+l^2 values which when divided into the observed (sinθ)^2 values gives a constant quotient. Then the correct Miller indices for each reflection can be assigned
Rules for primitive, body centred and face centred lattice types
Primitive: all values of h, k, l allowed
Body centred: values of h+k+l=2n allowed
Face centred: values h, k, l allowed if they are all odd or all even
Process for indexing powder diffraction patterns
Convert d or θ values to (sinθ)^2 values
Divide these values by allowed (h^2+k^2+l^2) for one lattice type. Inspect values of (sinθ)^2/(h^2+k^2+l^2) and check if constant. If no, try for allowed h^2+k^2+l^2 for another lattice type. If yes assign the Miller indices for each reflection. Determine cubic cell constant a
How to distinguish between primitive and body centred cubic diffraction patterns
There is a regular sequence of lines in both up to the 6th. 7th is forbidden for primitive but is allowed for body centred (h^2+k^2+l^2=14). Require at least 7 lines to distinguish
How to find lattice parameter a after Miller indices found
Use equation
(Sinθ)^2/(h^2+k^2+l^2)=λ^2/4a^2
Use values from largest value of (sinθ)^2 as systematic error decreases with increasing θ. Rearrange to find a
What parts of a diffraction pattern are almost unique for one substance?
Reflection positions (2θ or d spacings) Reflection intensities (peak height or area)
How can the diffraction pattern from an unknown sample be used to identify it?
Compare its diffraction pattern with reference patterns from known pure materials. These are on a reference database, the Powder Diffraction File (PDF), which is compiled by the International Commission for Diffraction Data (ICDD)
How are diffraction patterns reduced to a set of positions and intensities?
Positions: use d spacing because 2θ depends on λ used
Intensities: scale to the intensity of the strongest line, In/I1
Hanawaldt system
List every substance by the 3 strongest lines d1, d2, d3 and corresponding intensities I1, I2, I3. Groups substances within a certain range of d1 values in decreasing order. Within each group list substances by decreasing d2 values. Where d2 values identical list in order of decreasing d3 values
What does the subscript to d values mean in Hanawaldt search manual?
Intensity of reflection on scale of 1-10 where x means 10
