The XRD technique involves taking a powdered sample and illuminating it with x-rays of fixed wavelength. The intensity of the reflected radiation is recorded using a goniometer and analyzed to calculate the inter-atomic spacing based on reflection angle. Spacings are compared to known data to identify possible mineral matches. Samples are powdered finely and randomly oriented to give a statistical representation of all atomic planes. Problems can arise with preferentially oriented minerals like mica and clay.

2. The XRD Technique
• Takes a sample of the material and places aTakes a sample of the material and places a
powdered sample which is then illuminatedpowdered sample which is then illuminated
with x-rays of a fixed wave-length.with x-rays of a fixed wave-length.
• The intensity of the reflected radiation isThe intensity of the reflected radiation is
recorded using a goniometer.recorded using a goniometer.
• The data is analyzed for the reflection angleThe data is analyzed for the reflection angle
to calculate the inter-atomic spacing.to calculate the inter-atomic spacing.
• The intensity is measured to discriminate theThe intensity is measured to discriminate the
various D spacing and the results arevarious D spacing and the results are
compared to known data to identify possiblecompared to known data to identify possible
matches.matches.

3. Powdering SamplesPowdering Samples
• The samples are powdered to give a randomThe samples are powdered to give a random
sampling of ALL atomic planes (crystal faces)sampling of ALL atomic planes (crystal faces)
• Statistically accurate given samples areStatistically accurate given samples are
powdered finely AND randomly oriented onpowdered finely AND randomly oriented on
sample holdersample holder
– Intensities are a reflection of d-spacing abundanceIntensities are a reflection of d-spacing abundance
• Problems arise with minerals that mayProblems arise with minerals that may
preferentially orient on sample holderpreferentially orient on sample holder
– Micas and clays have special preparation techniquesMicas and clays have special preparation techniques

4. X-Rays
Wavelengths used
for XRD

6. What is X-Ray Diffraction??
• Crystalline
substances (e.g.
minerals) consist of
parallel rows of atoms
separated by a
‘unique’ distance
• Simple Example:
– Halite (Na and Cl)

8. • Crystalline substances (e.g. minerals) consist of parallel
rows of atoms separated by a ‘unique’ distance
• Diffraction occurs when radiation enters a crystalline
substance and is scattered
• Direction and intensity of diffraction depends on
orientation of crystal lattice with radiation

10. Schematic X-Ray Diffractometer
X-Ray
Source
Powdered
sample
Detector

15. Sample XRD Pattern

16. background radiation
strong intensity = prominent crystal plane
weak intensity = subordinate crystal plane

17. Determine D-Spacing from XRD patterns
Bragg’s Law
nλ = 2dsinθ
• n = reflection order (1,2,3,4,etc…)
• λ = radiation wavelength (1.54 angstroms)
• d = spacing between planes of atoms
(angstroms)
• θ = angle of incidence (degrees)

20. background radiation
strong intensity = prominent crystal plane
nλ = 2dsinθ
(1)(1.54) = 2dsin(15.5 degrees)
1.54 = 2d(0.267)
d = 2.88 angstroms

21. d-spacing Intensity
2.88 100
2.18 46
1.81 31
1.94 25
2.10 20
1.75 15
2.33 10
2.01 10
1.66 5
1.71 5

22. Factors that affect XRD data
• Sample not powdered fine enough
– May not give all d-spacing data (not random
enough)
• Analysis too fast (degrees/minute)
– May not give accurate peak data
• Mixture of minerals??
• Not crystalline – glass!!

23. Mixture of 2 Minerals

24. Applications of XRDApplications of XRD
• Unknown mineral IDUnknown mineral ID
• Solid solution ID (e.g. feldspars, olivine)Solid solution ID (e.g. feldspars, olivine)
• Mixtures of mineralsMixtures of minerals
• Clay analysesClay analyses
• ZeolitesZeolites
• Crystallographic applicationsCrystallographic applications
• Material ScienceMaterial Science