Sciencemadness Discussion Board

Space groups and equivalent positions

jam640 - 17-10-2007 at 06:57

Hi!
I'm taking a course in advanced inorganic chemistry which covers amongst other topics space groups, symmetry elements and equivalent positions. I have always had problems visualisings three dimensional structures etc and quite frankly I find this particular subject a bit hard to get a hold off. I have been to the library, but information on the subject is pretty absent. Does anybody know of a good website, prefferably with interactive demos which could give me some pointers? Especially the generation of equivalent positions feels abstract and animated 3D visulizations of this would be awesome, but probably very hard to find. :D

Thanks!

KemiRockarFett - 11-3-2009 at 14:23

http://en.wikipedia.org/wiki/Space_group
You got around 230 spacegroups. Its more but these are imaginary.
Actually its just all basic symetries. Cubic, tetragonal, hexagonal etc..
A higher symmetri ---> less lines on a x- ray diffractogram meaning cubik will give less reflexis then monochlin.
The general positions and the special ones are depending on the spacegroup.
Depending of the centering of the unit cell you will have different reflexis visible. For exampe F centered meaning a lot of losses in h k l meanwhile a primitive setting have all visible. A lof of reflexis could be lost depending on screwaxis etc.
The crystalograic space groups are importat in characterisation of materials in the solid state.
To practice you could just learn what the letters in PNMA and P3m1 are...
Buy the international tables...

turd - 11-3-2009 at 22:21

Ouch - the post of KemiRockarFett is so incoherent that it should be moved to detritus, if it is possible to move single posts. The whole thread is not in the correct place, BTW, since this is not about chemistry, but mathematics. It's a really unfortunate trend that crystallography is hidden in chemistry classes (and therefore often taught by people who know next to nothing about it).
Quote:
http://en.wikipedia.org/wiki/Space_group
You got around 230 spacegroups. Its more but these are imaginary.

There are 230 (219 if you don't care about handedness) crystallographic space groups, period. There are other symmetry groups for the description of magnetic, modulated or quasi-crystalline structures. And even groupoids for the description of OD-families. But they are in no way any more "imaginary" than the 230 crystallographic space groups.
Quote:
Actually its just all basic symetries. Cubic, tetragonal, hexagonal etc..

This sentence is devoid of any meaning.
Quote:
To practice you could just learn what the letters in PNMA and P3m1 are...
.
"PNMA" doesn't exist in the context of crystallography. The correct Hermann-Mauguin symbol is "Pnma".
Quote:
Buy the international tables...

The International Tables for Crystallography are an excellent resource (the description of the space groups being only a small part of it), but definitely not useful to someone who is unable to grok the basics and who doesn't want to spend weeks on working through the maths. Recommending it as an introductory text is very unhelpful.

turd - 11-3-2009 at 22:40

Quote:
Originally posted by jam640
[...]Especially the generation of equivalent positions feels abstract and animated 3D visulizations of this would be awesome, but probably very hard to find. :D[...]

Unfortunately I cannot be of much help, since this all seems so obvious to me, that I have a hard time imagining where you have problems.

Is it that you don't see what the different symmetry elements (translation, mirror, rotation axis, glide plane and screw axis) do? I'm not sure 3D animations would be of much help there, just because 3D is hard to imagine. That is why in crystallographic texts you will often see symmetry represented by two dimensional geometric objects. The classic is a triangle which is black on one and white on the other side or grey if both sides are equivalent. The classic text about symmetry is Shubnikov's "Symmetry in Science and Art", but if your interest lies only in chemistry, this is probably overkill.

Or don't you see what equivalent positions are? If you have a crystal structure which has let's say mirror symmetry, then it should be obvious that given an atom which does not lie on the mirror plane, there must be another atom which is the mirror image. These two atoms are called equivalent, because if you change the location of one, so you must change the location of the other. And therefore the locations of all equivalent atoms are described by the location of just one. So generating the equivalent atoms just means applying all the symmetries of the space group of the crystal.

You really should just get an introductory crystallography textbook..

JohnWW - 12-3-2009 at 01:07

International Tables For Crystallography: - mostly from http://university.arabsbook.com/forum61/thread32933.html which describes the volumes:

http://rs78cg.rapidshare.com/files/92795640/itca.zip 9,239 Kb - Vol. A - Space Group Symmetry
http://rs19cg.rapidshare.com/files/92796630/itca1.zip 6,601 Kb - Vol. A1: Symmetry relations between space groups
http://rs337gc2.rapidshare.com/files/92796282/itcb.zip 7,664 Kb - Vol. B - Reciprocal Space
http://rs263tg2.rapidshare.com/files/92795113/itcc.zip 20.58 Mb - Vol. C - Mathematical, Physical & Chemical Tables
http://rs383tg2.rapidshare.com/files/92796900/itcd.zip 10.35 Mb - Vol. D - Physical Properties Of Crystals
http://rs90gc.rapidshare.com/files/92796983/itce.zip 11.25 Mb - Vol. E - Subperiodic Groups
http://rs70tg.rapidshare.com/files/92796412/itcf.zip 18.00 Mb - Vol. F - Crystallography Of Biological Macromolecules
http://rs226tl3.rapidshare.com/files/92793836/itcg.zip 6,004 Kb - Vol. G - Definition & Exchange Of Crystallographic Data

I thought that there were 32 crystallographic groups, divided among the 7 crystal systems. I am not sure, offhand, how the further division into 230 crystallographic space groups arises, but no doubt this is covered in the International Tables For Crystallography.

For an introductory textbook on the subject, see:
http://rs390l32.rapidshare.com/files/162710088/ChristopherHa... 27.91 Mb

[Edited on 12-3-09 by JohnWW]

turd - 12-3-2009 at 02:55

Quote:

I thought that there were 32 crystallographic groups, divided among the 7 crystal systems.


There's an infinity of POINT groups, i.e. devoid of symmetry operations with translational component.
There's 32 crystallographic POINT groups, i.e. without translations and only operations compatible with an infinite lattice.
There's 11 Laue groups, i.e. crystallographic POINT groups containing inversion symmetry (that's the symmetry of a diffraction pattern if you ignore anomalous dispersion).
There's 7 crystal systems, i.e symmetry groups of LATTICES.
There's 230 crystallographic SPACE groups, i.e. with translations in three linear independent directions.

HTH

PS: People relying on the Tables should buy them. Or search for "Bilbao crystallographic server" on google.
PPS: Do never rely on wikipedia - many crystallography articles there are incomplete or wrong.

[Edited on 12-3-2009 by turd]

KemiRockarFett - 12-3-2009 at 03:38

Quote:
Originally posted by turd
Ouch - the post of KemiRockarFett is so incoherent that it should be moved to detritus, if it is possible to move single posts. The whole thread is not in the correct place, BTW, since this is not about chemistry, but mathematics. It's a really unfortunate trend that crystallography is hidden in chemistry classes (and therefore often taught by people who know next to nothing about it).

Quote:
http://en.wikipedia.org/wiki/Space_group
You got around 230 spacegroups. Its more but these are imaginary.

There are 230 (219 if you don't care about handedness) crystallographic space groups, period. There are other symmetry groups for the description of magnetic, modulated or quasi-crystalline structures. And even groupoids for the description of OD-families. But they are in no way any more "imaginary" than the 230 crystallographic space groups.
Quote:
Actually its just all basic symetries. Cubic, tetragonal, hexagonal etc..

This sentence is devoid of any meaning.
Quote:
To practice you could just learn what the letters in PNMA and P3m1 are...
.
"PNMA" doesn't exist in the context of crystallography. The correct Hermann-Mauguin symbol is "Pnma".
Quote:
Buy the international tables...

The International Tables for Crystallography are an excellent resource (the description of the space groups being only a small part of it), but definitely not useful to someone who is unable to grok the basics and who doesn't want to spend weeks on working through the maths. Recommending it as an introductory text is very unhelpful.


What is the problem with the mathematics? Its really easy matrix mathematics. I dont see your point.

chief - 12-3-2009 at 09:04

Has anyone the CCSD (Cambridge Crystal Structure Database) as a download at hand ?

turd - 12-3-2009 at 11:23

Quote:
Originally posted by KemiRockarFett
What is the problem with the mathematics? Its really easy matrix mathematics. I dont see your point.

My point was that it's sad that crystallography is nowadays often taught by people without intimate knowledge of crystallography and therefore crystallographic knowledge suffers tremendously.

It's only "easy matrix mathematics" (the word you're looking for is linear algebra, I guess) in that you need little mathematical pre-knowledge, but it quickly gets quite mind bending, with things like trigonal vs. rhombohedral or relations of symmetry groups with different lattices.
Quote:
Originally posted by chief
Has anyone the CCSD (Cambridge Crystal Structure Database) as a download at hand ?

Sometimes this feels more like a warez forum than a science forum. :P I wonder how this request is related to this thread.

JohnWW - 12-3-2009 at 11:36

Quote:
Originally posted by chief
Has anyone the CCSD (Cambridge Crystal Structure Database) as a download at hand ?

It is free to use online at http://www.ccdc.cam.ac.uk/ or
http://www.ccdc.cam.ac.uk/products/csd/
but it looks as if download of its entirety requires a payment, see http://www.ccdc.cam.ac.uk/support/purchasing_information/#cs... although that page gives some free downloads of utilities..

There are some exceptions to their storage, being stored instead at these locations:
Polypeptides and polysaccharides having more than 24 units are recorded in the Protein Data Bank http://www.rcsb.org/pdb/
Oligonucleotides are stored in the Nucleic Acids Data Bank http://ndbserver.rutgers.edu/
Inorganic structures are stored in the Inorganic Crystal Structure Database http://www.fiz-karlsruhe.de/icsd_content.html
Metals and Alloys are stored in CRYSTMET® http://www.tothcanada.com/

chief - 12-3-2009 at 14:14

The KarlsRuhe ICSD is only with a limited subset of 3000 (out of 100 000) compounds usable without charge ; purchase usually costs a 4 digit $-amount, absurdly high for data which have been set into public for free by the publishing gentlemen of the last maybe 7 decades ... .

The same is probably valid for the CCSD ; it's not much use to work only with the subset, since if you calculate a compound and want to verify it's existence it may well be in the 97 % of data which you don't have ...

Also you don't want to use it online, but you want to have it in your own fast database, ready for use by your self-made software ...

[Edited on 12-3-2009 by chief]

[Edited on 12-3-2009 by chief]