All Questions
Tagged with symmetry crystallography
16
questions
2
votes
1
answer
73
views
Identifying Type of Symmetry Operations
From the given set of symmetry operations for a space group, say, P-3m1 or Cmma, how can one identify the type of all symmetry operations. For example, how to distinguish the axis of rotation symmetry ...
- 123
2
votes
1
answer
134
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Why are certain lattices compatible with only certain point groups and not all point groups?
I will limit this discussion to 2 dimensions for ease of intuition. My understanding of the 17 crystallographic plane groups is that these 17 groups represent all the possible symmetry groups of any ...
- 241
3
votes
1
answer
305
views
Relation between symmetry of a reciprocal vector and lattice planes perpendicular to it
What is the relation the symmetry of a high-symmetry point in the first Brillouin zone and lattice planes perpendicular to it? Are the two symmetries equivalent?
I have this question because I want to ...
- 273
2
votes
1
answer
405
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What is m.2m point group?
I'm using Bilbao Crystallographic Server to find 3D crystallographic point groups of the K points of anatase TiO2.
Since the space group of anatse TiO2 is $I4_1/amd$, on this page, I found the point ...
- 273
6
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2
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Why are there only 14 types of Bravais lattices and not 28 when there are 7 types of unit cells and each can have four variations?
As the title suggests, I can't understand why certain kinds of variations (like Face-centred or Body-centred) are restricted to certain types of unit cells. An orthorhombic unit cell has Primitive, ...
- 317
5
votes
2
answers
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Why is the base-centered orthorhombic crystal lattice a unique crystal system?
I'm having difficulty understanding why the base-centered orthorhombic crystal system is a unique crystal system. When I draw two base-centered orthorhombic unit cells next to each other there appears ...
2
votes
2
answers
2k
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Conventional unit cell for a hexagonal crystal system
The figure shows a unit cell of a hexagonal crystal system. Drawn in bold, is the unit cell. The lightly shaded one is a unit cell as well and has a six fold symmetry along an axis, hence is more ...
- 313
3
votes
1
answer
108
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Why should the scalar product of the components along two axes remain unchanged after transformation?
A couple of proofs from Chapter 2 of "Space Groups for Solid State Scientists" are giving me a hard time (see attached image).
So what I understand is:
"r" was the original ...
- 31
2
votes
2
answers
2k
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Why rutile structure have primitive unit cell instead of body centered?
In the literature (Wikipedia), I read that $\ce{MgH2}$ have a structure of rutile. Then, I looked at its space group which is $P4_2/mnm$. From this notation, I understood that it possesses a (...
- 37
3
votes
1
answer
171
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Origin in a crystal
I am trying to understand the International Tables for Crystallography.
How can I identify the origin in the image on the left?
Without knowing the origin, I cannot identify the position of the ...
- 203
4
votes
2
answers
2k
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Sulfuric acid symmetry point group
On the following page: https://cccbdb.nist.gov/pglist.asp It appears that the point symmetry group of sulphuric acid is $C_2$. I know that $C_2$ means that there is an axis of symmetry of order 2 (180 ...
- 607
1
vote
1
answer
83
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Reading Stereographs
On an old paper, I found an interesting representation of some symmetry operations: stereographs.
Online I found a set of symmetry operations and related stereographs (see: http://newton.ex.ac.uk/...
user32223
5
votes
1
answer
603
views
What is the diagram of the roto-inversion of $\bar 6$?
Using the standard way of representation:
Here we have a rotation followed by an inversion (technically called 'rotational inversion'). So as to represent it, what I have done is:
1) Both rotation ...
- 351
2
votes
0
answers
78
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What system of nomenclature can I use to indicate the positions of specific kinds of atoms of a surface reconstruction?
I was reading a journal based on SiC reconstructions, and they seem to mention that every dangling bond in the $(1\times 1)$ unreconstructed Si face or the $(0001)$ direction bonds up with a Si adatom ...
- 501
3
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0
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What is the symmetry of the cuboctahedron (FCC metal)?
The background to this is that I've recently given a tutorial wherein we had to go through the determination of point groups for atoms in various lattices (BCC, FCC/CCP and HCP). BCC and HCP, I have ...
