Basic Crystallography Part 1 Theory and Practice of X-ray Crystal Structure Determination

1. Basic CrystallographyPart 1 Theory and Practice of X-ray Crystal Structure Determination Charles Campana, Ph.D. Senior Applications Scientist Bruker AXS

2. Course Overview Basic Crystallography – Part 1 • Introduction: Crystals and Crystallography • Crystal Lattices and Unit Cells • Generation and Properties of X-rays • Bragg's Law and Reciprocal Space • X-ray Diffraction Patterns from Crystals Basic Crystallography – Part 2 • Review of Part 1 • Selection and Mounting of Samples • Unit Cell Determination • Intensity Data Collection • Data Reduction • Structure Solution and Refinement • Analysis and Interpretation of Results

3. Introduction to Crystallography

4. What are Crystals?

5. Examples of Crystals

6. Examples of Protein Crystals

7. Growing Crystals Kirsten Böttcher and Thomas Pape

8. Crystal Systems and Crystal Lattices

9. What are Crystals? • A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly, repeating pattern extending in all three spatial dimensions.

10. Foundations of Crystallography • Crystallography is the study of crystals. • Scientists who specialize in the study of crystals are called crystallographers. • Early studies of crystals were carried out by mineralogists who studied the symmetries and shapes (morphology) of naturally-occurring mineral specimens. • This led to the correct idea that crystals are regular three-dimensional arrays (Bravais lattices) of atoms and molecules; a single unit cellis repeated indefinitely along three principal directions that are not necessarily perpendicular.

11. The Unit Cell Concept Ralph Krätzner

12. Unit Cell Description in terms of Lattice Parameters • a ,b, and c define the edge lengths and are referred to as the crystallographic axes. • a, b, and g give the angles between these axes. • Lattice parameters  dimensions of the unit cell. c a b

13. Choice of the Unit Cell

14. Choice of the Unit Cell A A B B C D C No symmetry - many possible unit cells. A primitive cell with angles close to 90º (C or D) is preferable. The conventional C-centered cell (C) has 90º angles, but one of the primitive cells (B) has two equal sides.

15. 7 Crystal Systems - Metric Constraints • Triclinic - none • Monoclinic -  =  = 90,  90 • Orthorhombic -  =  =  = 90 • Tetragonal -  =  =  = 90, a = b • Cubic -  =  =  = 90, a = b = c • Trigonal -  =  = 90,  = 120, a = b (hexagonal setting) or  =  =  , a = b = c (rhombohedral setting) • Hexagonal -  =  = 90,  = 120, a = b

16. Within each crystal system, different types of centering produce a total of 14 different lattices. P – Simple I – Body-centered F – Face-centered B – Base-centered (A, B, or C-centered) All crystalline materials can have their crystal structure described by one of these Bravais lattices. Bravais Lattices

17. Bravais Lattices Cullity, B.D. and Stock, S.R., 2001, Elements of X-Ray Diffraction, 3rd Ed., Addison-Wesley

18. Bravais Lattices Cullity, B.D. and Stock, S.R., 2001, Elements of X-Ray Diffraction, 3rd Ed., Addison-Wesley

19. Bravais Lattices

20. Bravais Lattices

21. Crystal Families, Crystal Systems, and Lattice Systems