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
What error should you allow when looking up a sample diffraction pattern?
+/- 0.01Å
Phase identification procedure
List data in decreasing dn and associate relative intensities. Locate appropriate d1 group. Read down d2 values to get closest match. Read down d3 column to get closest matching set of candidates. Compare experimental and tabulated intensities. Compare remaining experimental and tabulated line positions and intensities, if near full agreement is reached, identification complete
Why is identification of components in a multi-phase system difficult using Hanawaldt method?
Cannot determine a priori which lines belong to which phase. Critical lines may overlap. 3 strongest lines may belong to 2 or 3 phases
Other problems with Hanawaldt method
Preferred orientation in sample may give misleading intensities (need special care in sample preparation). Poorly filtered radiation may give spurious weak lines (e.g diffraction of Kβ). Inaccurate PDF data for old reference patterns
How does computer based phase identification work?
Based on Hanawaldt method. Use sample chemistry to narrow down possible candidate matches. Allow background fitting and subtraction (useful if substantial amorphous content). Candidate matches ranked on a figure of merit indicator.
What is good about computer based phase identification?
Rapid and efficient searching of entire database. Invaluable for multiphase samples with more than 3 components
