bl6: translational symmetrygoodwin.chem.ox.ac.uk/goodwin/teaching_files/bl6.pdf ·...
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BL6: Translational Symmetry
Pure translational symmetry:
Unit cell translations
Centred lattices
A / B / C
(x,y,z) ⟼(x+½,y+½,z)
I
(x,y,z) ⟼(x+½,y+½,z+½)
R
(x,y,z) ⟼(x+⅓,y+⅔,z+⅓),(x+⅔,y+⅓,z+⅔)
F
(x,y,z) ⟼(x+½,y+½,z),(x+½,y,z+½),(x,y+½,z+½)
The Bravais lattices represent the absolute minimum number of primitive and centred lattices
for all 7 crystal systems
Centred unit cells are used in lieu of primitive unit cells only when needed to represent the
true crystal symmetry
Translational symmetry+ point symmetry:
Screw axesGlide planes
21 screw axis ∥ x
(x,y,z) [ ⟼ (x,−y,−z) ](x,y,z) [ ⟼ (x + ½,−y,−z)
a-glide ⊥ b
(x,y,z) [ ⟼ (x,−y,z) ](x,y,z) [ ⟼ (x + ½,−y,z)
b
a
n
M T DoveStructure and Dynamics
§ 3.5
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