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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
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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
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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
Introduction to
Crystallography
What are Crystals?
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Examples of Crystals
Examples of Protein Crystals
Growing Crystals
Kirsten Böttcher and Thomas Pape
Crystal Systems and
Crystal Lattices
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.
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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 threedimensional arrays (Bravais lattices) of atoms and
molecules; a single unit cell is 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.
c
a



b
 , , and  give the
angles between these
axes.
 Lattice parameters 
dimensions of the
unit cell.
Choice of the Unit Cell
Choice of the Unit Cell
A
B
A
B
C
D
No symmetry - many possible
unit cells. A primitive cell with
angles close to 90º (C or D) is
preferable.
C
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
Bravais Lattices
 Within each crystal system, different types of
centering produce a total of 14 different lattices.
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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
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
Bravais Lattices
Bravais Lattices
Crystal Families, Crystal Systems,
and Lattice Systems