Glide Planes
Recall:
•Glide is the combination of a mirror (reflection) and a translation.
•Glide must be compatible with the translations of the Bravais lattice, thus the
translation components of glide operators must be rational fractions of lattice vectors.
•In practice, the translation components of a glide operation are always ½ or ¼ of
the magnitude of translation vectors.
•If the translation is parallel to a lattice vector, it is called axial glide (glide planes with
translations a/2, b/2 or c/2 are designated with symbols a, b or c, respectively).
•Another type of glide is diagonal glide (n) and has translation components of a/2+b/2, b/2+c/2 or
a/2+c/2. Last type is diamond glide (d) w/ translation components of a/4+b/4, b/4+c/4 or a/4+c/4.
two b-glide operations:
A
or in
2-D:
A
two n-glide operations:
a, b
and
d:
[110]
[010]
d
[100]
A’
(or c)
(b or c-axis is ┴ to g)
(a or c-axis is ┴ to g)
(a or b-axis is ┴ to g)
(c-axis is ┴ to g)
(displacement
vector)
Glide plane
can’t be ┴ to
glide direction
= net
(a-axis is ┴ to g)
(b-axis is ┴ to g)
*Diamond glides (d-glide) can only occur in F and
I-centered lattices, e.g. diamond cubic crystal (C,
Si, Ge) structure is Fd3m (see next slide
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Diamond Glide Planes in Diamond Cubic
d = 1/4b + 1/4c
d = 1/4a + 1/4b
[011]
[011]
[101]
d = 1/4a + 1/4c
[101]
[110]
[110]
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Conversion of Space Group (SG) to
Point Group (PG) Symbolism
•Eliminate translation from symbol.
•Example: Space group #62: Pnma (Mg,Fe)2SiO4 belongs to point group mmm:
•P=primitive lattice type does not apply to PG symmetry.
•n(net glide plane perpendicular to x or a-axis)=m because the reflection of a net
glide plane has no meaning in PG symmetry.
•m(mirror plane perpendicular to y or b-axis)=m
•a(axial glide plane perpendicular to z or c-axis)=m because the reflection of an
axial glide plane has no meaning in PG symmetry.
•Example: Space group #167: R3c (Al2O3) belongs to point group 3m:
•R=rhombohedral lattice type does not apply to PG symmetry.
•3(3-fold roto-inversion axis)=3(3-fold roto-inversion axis).
•c(axial glide plane parallel to 3)=m because the reflection of an axial glide plane
has no meaning in PG symmetry.
The 13 unique monoclinic
space groups that are
derived from the 3
monoclinic point groups
and the 2 monoclinic
Bravais lattices:
You should be able to
look at any one of the
230 3-D Space groups
and identify its 3-D
Point group and
3-D Bravais lattice
3
The 230 3-D Space Groups categorized
according to crystal system
from Rohrer
Also good website:
http://img.chem.ucl.ac.uk/sgp/large/sgp.htm
4
Alternative Notation for Crystal Structures
Also listed in DeGraef
Structure appendix .pdf
The 230 space groups categorized
according to crystal system with examples:
http://web.archive.org/web/20100531072811/http://cst-www.nrl.navy.mil/lattice/spcgrp/index.html
5
Example from International Tables
for Crystallography
(a)
(b)
a. Identify all the symmetry elements in (a) and describe which
operation they include.
1. Diads-indicate a two-fold rotation about the axis
2. Screw tetrads (42)-indicate a rotational axis of a tetrad plus a
translation of T=½ where T is the lattice translation fraction parallel to
the axis.
3. Axial glide plane(
)-indicates that the translation glide vector is
½ lattice spacing along line parallel to the projection plane
4. Axial glide plane(
)-indicates that the translation glide vector is
½ lattice spacing along line normal to the projection plane.
5. Diagonal glide plane(
)-indicates a translation of ½ of a face
diagonal.
b. In separate plots, apply each symmetry element to a general point
(equipoint) and show which of the points in (b) are generated:
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More Examples from International
Tables for Crystallography
•No. 122 has Chalcopyrite (E11) Structure
(CuFeS2, AgAlTe2, AlCuSe2, CdGeP2,etc.
•No. 60 has no examples of real crystals
at all!
http://web.archive.org/web/20100531072811/http://cst-www.nrl.navy.mil/lattice/spcgrp/index.html
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