1. Practice of analysis and interpretation of X-ray diffraction data
Power Point presentation from lecture # 2 is available at:
Power Point presentation from lecture # 4 is available at:
Power Point presentation from lecture # 5 is available at:
Lecture # 5 software and files can be downloaded from:

2. Structure determination
Structure identification
“Logical” choices
Search and match
Indexing-based
Structure refinement (requires the structure model to be approximately known)
Rietveld method
Single-crystal refinement
Structure solution (ab initio)
direct methods
charge flipping
simulated annealing

3. High pressure apparatus
Metal gasket
Incident x-ray beam
Diffracted x-ray beam
Diamond anvil
Beryllium seats
Steel frame
Steel frame
Metal gasket
Incident x-ray beam
Diamond anvil
Diffracted x-ray beam
Sample is immersed in hydrostatic liquid, which freezes at some point during compression (usually below 10 GPa).
Diffraction pressure calibrant is placed in the sample chamber along with the sample.
Both incident and diffracted beam travel though diamonds, Be disks, pressure medium, and sample.

5. High-pressure crystallography challenges
Experimental challenges:
Very small sample (<0.01mm)
Angular access restricted (low completeness)
Absorption limits the incident energy to >15 keV
Absorption and extinction affect intensity measurement
High background (scattering, Compton, etc.)
Multiple SXD diffraction signal
Contamination by PXD signal
Poor sample quality (strain, multi-grain assemblages)
More challenging sample centering
Beam size vs. sample size

6. Tasks for today From 1-d diffraction pattern to refined structure
Rietveld-based quantitative analysis
From 2d powder diffraction image to solved and refined structure
Single crystal data processing
Solution and refinement of crystal structure from single crystal data using simulated annealing

7. Typical flow of analysis of (2d) powder diffraction data
Diffraction image (2d)
Integrated 1-d pattern
Detector geometry calibration
Calibration diffraction image
from known standard

8. Calibration of detector geometry
Incident wavelength
Sample-to-detector distance
Beam center (point of intersection of incident beam and detector plane in detector pixel coordinates)
Detector nonorthogonality (tilt and rotation of tilting plane)
CeO2:
Pixel size:
Approximate sample-to-detector distance
400 mm
Incident energy E=37.07 keV
Density g/cm3
Space group Fm3m (#225)

10. Individual peak fitting and unit cell parameter refinement (GSE_shell)
CeO2
Identify phase with Rosetta using full database
Subtract background and refine unit cell from individual peaks in GSE_Shell
Save the pattern with subtracted background.

11. Rietveld refinement in PowderCell for single and multiple phase patterns
When does it make sense to refine a known crystal structure?
Define the phase present in the sample by looking up the corresponding crystal structure in the American mineralogist Crystal Structure database (you can search by mineral name). Either type the unit cell parameters, space group number, and fractional atomic coordinates for all the atoms, or download a .cif file. Cif format from AMCSDB may not be readable in PowderCell. In such case you can use Endeavour to convert the file format to SHELX .ins. You may need to add ZERR and UNIT lines in the ins file.
Read in experimental diffraction pattern. The best import format is Diffrac AT&Plus .raw. You can use the CONVX program for diffraction pattern format conversion.
Make sure the wavelength is set correctly.
Define proper 2theta range.
Modify selection of parameters in refinement gui. Start with just refining background and scale. Then include peak profiles and unit cell parameters. Refinement of atomic coordinates, ADPs and occupancies comes last.
Look at refinement statistics. Check bond lengths.
Save refined structure as ins file.

12. Visualization and interpretation of structure model using Endeavour
Create polyhedral representation of the structure.
Display table of interatomic distances.
Import the pattern with subtracted background.
How does the fit statistics compare with the Rietveld refinement statistics? How does a refinement in Endeavour differ from a rietveld refinement?
Try to erase the atoms and solve the structure using simulated annealing.

13. Processing of single crystal x-ray diffraction data with GSE_ADA/RSV
Define detector calibration
Search for peaks in the wide rotation image and refine their detector coordinates.
Assign omega angles by analyzing step scan images. Save a peak table file with proper Cartesian coordinates of reciprocal vectors.
RSV
Index peak and find orientation matrix.
Convert to conventional setting, if necessary.
Refine unit cell parameters.
Save the refined orientation matrix.
Open the wide rotation image again
Open the orientation matrix
Define the range of rotation
Predict peaks
Verify if all peaks are observed and if they fit correctly.
Save peak table with fitted intensities.
Analyze systematic absences with XPREP and assign space group. If necessary tarnsform the unit cell to the correct setting.
Export SHELX hkl file.
Create a corresponding ins file with structure model and refinement instructions.
SHELXL
Refine the structure in SHELX

14. Structure solution from single crystal XRD data using Simulated Annealing (Endeavour)
Structure solution with single-crystal peak intensity data works in Endeavour just the same was as structure solution from powder data.
Composition NiP
Z=8
Space group Pbca
Unit cell a=4.8810A, b=6.8900A, c=6.0500°
Find fractional atom coordinates by solving the structure. Use peak intensities from all three available detector positions.
Refine the structure in SHELX.

15. Single crystal refinement with SHELXL

16. Homework (due 9/27)
Perform Rietveld refinement for all six powder patterns from the homework of lecture #4.
Try to solve the structures of minerals in the single-phase patterns using Endeavour.
Based on the crystal structure models refined with PowderCell prepare structure drawings showing the coordination polyhedra using Endeavour.