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Basic Crystallography Part 1 Theory and Practice of X-ray Crystal Structure Determination. Charles Campana, Ph.D. Senior Applications Scientist Bruker AXS. Course Overview. Basic Crystallography – Part 1 Introduction: Crystals and Crystallography Crystal Lattices and Unit Cells
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Basic CrystallographyPart 1 Theory and Practice of X-ray Crystal Structure Determination Charles Campana, Ph.D. Senior Applications Scientist Bruker AXS
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
Growing Crystals Kirsten Böttcher and Thomas Pape
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.
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.
The Unit Cell Concept Ralph Krätzner
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
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.
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
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
Bravais Lattices Cullity, B.D. and Stock, S.R., 2001, Elements of X-Ray Diffraction, 3rd Ed., Addison-Wesley
Bravais Lattices Cullity, B.D. and Stock, S.R., 2001, Elements of X-Ray Diffraction, 3rd Ed., Addison-Wesley