This course is offered in Spring every alternate year.

Instructor: Stephen Guggenheim

Office hours: I have an open door policy. Alternatively, an appointment may be arranged.

Class hours:       Lecture are 1 1/2 hours long, twice a week, tentatively scheduled for 1-2:30 on Monday and Wednesday.
                         New times may need to be decided the first day of class. Laboratories are also to be scheduled (for 2
                         hours per week).   Expect to spend additional time on the labs, either in the X-ray lab or as
                         homework. Expect tp spend about 2 hours for every hour spent in class.

Text:                X-ray Diffraction Methods by E.W. Nuffield. J. Wiley and Sons, 1966. This book is out-of-print, but I have
                        permission from the author to duplicate it. I have one Xerox copy that can be used to easily produce others on
                        the Xerox. Please see me to make a copy for yourself.

                        X-ray Structure Determination: A Practical Guide by G. Stout and L. Jensen. MacMillan and Co., 1968.

                        This text will be used for more advanced topics near the end of the course. I recommend that the few copies
                        be shared, rather th an purcahsed. I have several copies that may be borrowed, and a couple
                        of copies are available in the library.

Prerequisites:    E&ES 220 (Mineralogy) or its equivalent or by consent of the instructor. With a short review, it is assumed
                        that you have a basic understanding of crystal systems, simple symmetry, Miller indices, unit
                        cells, and point groups. A good book for review is Bloss, Elementary Crystallography and Crystal Chemistry,
                        Chapters 1, 2 and 7 and Nuffield, Chapter 1.

Topic Assignment (Reading)

1. Review of symmetry: External - types of symmetry,                       (Review mineralogy 200 notes, Bloss, Ch. 1, 2 and 7),
     combination of symmetry, point groups, symbols,                            Nuffield, Ch.1.
     derivation; Internal - types of lattices, Bravais

2. Review of symmetry: Derivation of Bravais lattices, Nuffield, Ch. 1
effect of space lattices, screw axes, glide planes

3. Space groups, equipoints, the International Tables,
examples involving space group derivations: rechoosing
origins and axes, general and special positions

4. The nature and generation of x-rays: spectra,                                Nuffield, Ch. 2
     absorption edges, fluorescence, comments on
     practical aspects; The diffraction of x-rays

5. The diffraction of x-rays; The Bragg Equation,                              Nuffield, Ch. 3 (p. 46-62)
     The Reciprocal Lattice Concept, Ewald's Sphere                         and Ch. 8
     and the geometric model

6. The intensity of diffraction: The Structure Factor,                         Nuffield, Ch. 3 (p 62-73, 84-86)
     (Effects of temperature, absorption, geometry, and
     atomic scattering power) Laue Symmetry

7. Symmetry elements and the structure factor: Systematic              Nuffield, Ch. 4
     absences, a physical interpretation for systematic
     absences

Methods for Intensity Collection and Symmetry Determination: Experimental Techniques

8. Debye-Scherrer Powder Method: geometry                               Nuffield, Ch. 5 (103-149)
     experimental procedure, appearance of reflections,
     film measurement

9. Debye-Scherrer Powder Method: choice of radiation,                Nuffield, Ch. 5 (149-207)
     fluorescence, indexing cubic patterns, reflection
     multiplicity, sight indexing, other systems

10. Debye-Scherrer-Powder Method: obtaining accurate
       cell parameters, effects of measuring errors, absorption,
       film shrinkage, Gandolfi and Parafocusing cameras

11. Debye-Scherrer Method: intensities, Lorentz-polarization,
Powder diffractometer, optical arrangement

Exam 1: Covering topics through Debye-Scherrer method

13. Return of exams: Powder diffractometer, optical
arrangement (cont.), monochromator/filters

14. Powder diffractometer: detectors, dead time, pulse-height
analyzer, 0:0 diffractometers, optics, intensity of diffraction

15. Comparison of diffractometer to Debye-Scherrer method,
special techniques: crystallite size, quantitative analysis

16. Buerger Precession Method: geometry and motion Nuffield, Ch. 9

17. Buerger Precession Method: Photographing the zero and
       upper levels, Interpreting zero level photos, cone axis photos
       and determining d*, orientation photos, measuring axes in
       non-orthogonal cases

18. No class, spring break

19.   Buerger Precession Method: Compared to other methods,        Nuffield, Ch. 10
        special applications in twinning, exsolution, etc. Rotation
        Methods: geometry, cell dimension data, disadvantages
        and advantages

20 Measuring intensities: Film methods and 4-circle Nuffield, Ch. 12 (p. 342-3, 345-7)
diffractometers S & J, Ch. 6

The Interpretation of Intensities: Crystal Structure Determinations

21. Use of symmetry to simplify data collection and calculations,        S. & J., Ch. 8 (p. 212-230),
        F(hkl) sample calculations, centric structures, the R factor,          Ch. 10
        the phase problem

22. Exam covering Powder Diffractometer through 4-Circle
Diffractometers

23. Return of exams: Fourier transforms, Heavy atoms                     S. & J., Ch. 11 (p. 270-288)
       methods: the Patterson Function, characteristics of the
       Patterson, interpretation of the Patterson, Harker sections
       and lines, Special Pattersons (sharpened, etc.)

24. Other Fourier coefficients: Fourier Synthesis, Difference            S. & J., Ch. 15
       Synthesis, interpreting difference maps, use of special data;
       Anomalous Scattering and effects on symmetry, Argand
       diagrams

25. Direct Methods: objective, inequalities, probabilities S. & J., Ch. 13, handout

26. Direct Methods: Choosing an origin, E maps

27. Synchrotron radiation: Basis of X-ray production; uses:
small crystal techniques, spectroscopy

28. Refinement procedures and accuracy S. & J., p. 385-97, 399-408, 416-21

29. Primary and secondary extinction, Rietveld Analysis,                 S. & J., 449-50, 409-12
       basis of the technique, effect of preferred orientation,
       special data problems (phyllosilicates)

30. Rietveld Analysis, data-to-parameter ratio and the effect
of special data, R, systematic errors, esd, use of bond
distances in refinements

Laboratory Schedule

Week 1. Safety Lecture by Radiation Safety
Week 2. Three dimensional space groups, 1at Home problem due
Week 3. Three dimensional space groups
Week 4. Using space groups
Week 5. Using space groups

Take home exam on space groups

Week 6. Debye-Scherrer Method: Taking and measuring a photograph, sample identification
Week 7. Debye-Scherrer Method: Careful measurements of a photograph
Week 8. Debye-Scherrer Method: Computer assisted indexing/cell refinement
Week 9. Scanning Debye-Scherrer Patterns, use of PhotoShop, FilmScan, and Jade
Week 10. Powder diffractometer 1 - Sample preparation and identification
Week 11. Powder diffractometer 2 - Quantitative analysis of mixtures
Week 12. Powder diffractometer 3 - Multiple phases analysis using thin sections and poor samples
Week 13. Buerger Precession Camera - Orientation procedures
Week 14. Buerger Precession Camera - Final photographs Class demonstration of 4-Circle diffractometer
Week 15. Return/discussion of Patterson maps problem set

Homework Problem Sets

Week 1. Bravais lattices
Week 4. Systematic absences - Calculations using the structure factor formula
Week 5. Indexing cubic powder patterns/correction of errors
Week 9. Systematic absences - Determining a space group from precession photographs
Week 12. Patterson maps