User:Benjah-bmm27/degree/3/MFH
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Crystallography, MFH
[edit]Texts
[edit]- Otterbein College: learn molecular symmetry with Jmol
- Werner Massa, Crystal Structure Determination (2004)
- Bill (William) Clegg, Crystal Structure Determination (Oxford Chemistry Primer) (1998)
- Glusker, J. P.; Lewis, M.; Rossi, M. Crystal Structure Analysis for Chemists and Biologists.
- International Tables for Crystallography Volume C. doi:10.1107/97809553602060000103.
- Book review: Acta Cryst. (2007). A63, 483
Topics
[edit]Unit cells, lattices and symmetry
[edit]- Molecular structure and crystal structure
- Crystal shapes, including symmetry axes
- Calcite — cubic
- Molybdenite — hexagonal
- Diamond — cubic
Crystal symmetry
[edit]- Symmetry
- Point symmetry
- Translational symmetry
- Symmetry groups
- In one dimension: 7 frieze groups
- In two dimensions: 17 wallpaper groups
- In three dimensions: 230 space groups (list)
- Crystallographic restriction theorem — cannot have 5-fold rotation symmetry in crystal lattices (pentagons don't tessellate)
- Symmetry elements in crystallography
Crystal systems
[edit]crystal system | cell edge restriction | cell angle restriction |
---|---|---|
triclinic | none | none |
monoclinic | none | α = γ = 90° |
orthorhombic | none | α = β = γ = 90° |
tetragonal | a = b | α = β = γ = 90° |
trigonal, hexagonal | a = b | α = β = 90°, γ = 120° |
cubic | a = b = c | α = β = γ = 90° |
Bravais lattices
[edit]pearson symbol | lattice name | commonly called |
---|---|---|
aP | triclinic | ? |
mP | monoclinic primitive | ? |
mC | monoclinic C-centred | ? |
oP | orthorhombic primitive | ? |
oA | orthorhombic A-centred | ? |
oI | orthorhombic body centred | ? |
oF | orthorhombic (all-)face centred | ? |
tP | tetragonal primitive | ? |
tI | tetragonal body centred | ? |
hP | trigonal or hexagonal primitive | ? |
hR | rhombohedral, hexagonal setting | ? |
cP | cubic primitive | simple cubic |
cI | cubic body-centred | body-centred cubic |
cF | cubic (all-)face centred | face-centred cubic |
Miller indices
[edit]- Lattice planes
- Miller indices (hkl) and all that - http://www.doitpoms.ac.uk/tlplib/miller_indices/index.php
Bragg's law
[edit]Misc
[edit]Systematic absences
[edit]absence | when this is odd | indicates presence of this symmetry element |
---|---|---|
h00 | h | 21 screw axis parallel to the a-axis |
0k0 | k | 21 screw axis parallel to the b-axis |
00l | l | 21 screw axis parallel to the c-axis |
h0l | h | a-glide perpendicular to the b-axis |
h0l | l | c-glide perpendicular to the b-axis |
h0l | h+l | n-glide perpendicular to the b-axis |
hkl | k+l | A-centred |
hkl | h+l | B-centred |
hkl | h+k | C-centred |
hkl | h+k+l | I-centred |
hkl | one or two but not all three of h, k, and l |
F-centred |
Solving the Phase Problem, Refinement of the Solution and Interpretation of the Results
[edit]A cautionary tale: the quest for cyclopentadienyl cation
[edit]- Cyclopentadienyl cation, [C5H5]+
- Pentamethylcyclopentadienyl cation, [C5Me5]+, AKA [Cp*]+, should be stable, thought they'd determined a crystal structure containing it
- Turned out to be the pentamethylcyclopentenyl cation, [(CMe)3(CHMe)2]+
- http://www.benjamin-mills.com/chemistry/structures/Cp*-cation/
C10H15+ pentamethylcyclopentadienyl cation |
C10H17+ pentamethylcyclopentenyl cation |
---|
See also
[edit]- User:Benjah-bmm27/degree#Crystallography
- Symmetry in Crystallography from the University of Oklahoma Chemical Crystallography Lab
- X-ray Diffraction Techniques, an interactive tutorial from the University of Cambridge