Re: [ccp4bb] Question on Symmetry Axis Notation Convention
James,
The IUCr report that Ethan referred to distinguishes carefully between
a "symmetry element" and a "symmetry operation". A symmetry element
corresponds to a set of coaxial rotation or screw axes (assuming we're
limiting the discussion to enantiomorphic space groups) in a unit cell
related by allowed origin shifts, as shown in the space group diagram.
A symmetry element set consists of a number of symmetry operations
(i.e. the operations are the members of the set). To distinguish
symmetry operations from element sets, the symbol for all element sets
starts with the letter 'E' (for 'element').
So space group P2_1 consists of two symmetry element sets: 'E1' and
'E2_1' which together form a group obeying the usual group rules. The
symmetry element set 'E2_1' (two-fold screw axis) is a set with 4
symmetry operations as members: the defining '2_1' operation plus 3
other coaxial 2_1 operations related by origin shifts. Note that the
identity operation 1 is not a member of the E2_1 set, contrary to what
you might think, i.e. E2_1 is indeed a set, not a group (the identity
operation 1 is the only member of the element set E1).
This might seem like a lot redundancy at first sight, until you
consider higher order axes; so for example the symmetry element set
'E4_1' (4-fold screw axis) contains the 3 operations '4_1' and '4_1^2'
and '4_1^3' (where e.g. the operation '4_1^n' is the operation '4_1'
repeated n times in succession) plus other coaxial 4_1^n operations
related by origin shifts. Note that '4_1^2' is NOT the same as '4_2'
& similarly for the other 'power' operations. In fact the set 'E4_2'
which represents the 4_2 axis in space groups P4_2, P4_2 2_1 2 etc.
contains the operations 4_2, 4_2^2, 4_2^3 plus other coaxial 4_2 axes
related by origin shifts.
Now to get back to your question, a "2-fold screw axis parallel to the
a axis" would be "E2_1 parallel to (100)". Unfortunately the IUCr
report doesn't seem to suggest a symbol for "parallel to" so you'll
have to be inventive: parallel bars ('||') being the usual symbol for
this relationship would seem the obvious choice. So the whole symbol
then becomes 'E2_1 || (100)'. On the other hand, if you want to
symbolise a symmetry operation the most concise notation would seem to
be the usual (1/2+x,1-y,-z), or whatever.
Cheers
-- Ian
On 14 June 2012 20:06, James Stroud wrote:
> Hello All,
>
> I would like to discuss symmetry axes, but I'm not sure what the notation
> convention is. For example, I'd like to say something about a 2(1) along the
> x-axis, but the phrase "the 2(1) symmetry axis along x" is a bit cumbersome
> to repeat many times or to put in a table. So I'd like a shorthand, maybe
> something like "x(2_1)" (where the preceding "_" means that the "1" is
> subscript. Another way I like is "x_{2(1)}" (where the curly braces mean that
> all of "2(1)" is subscript).
>
> Does anyone know what the convention is or if there is one?
>
> Thanks in advance for any help.
>
> James
[ccp4bb] Fw: [ccp4bb] Question on Symmetry Axis Notation Convention
The standard notation is 21 axis parallel to [100]?
Rex Palmer
http://www.bbk.ac.uk/biology/our-staff/emeritus-staff
http://rexpalmer2010.homestead.com
From: James Stroud
To: CCP4BB@JISCMAIL.AC.UK
Sent: Thursday, 14 June 2012, 20:06
Subject: [ccp4bb] Question on Symmetry Axis Notation Convention
Hello All,
I would like to discuss symmetry axes, but I'm not sure what the notation
convention is. For example, I'd like to say something about a 2(1) along the
x-axis, but the phrase "the 2(1) symmetry axis along x" is a bit cumbersome to
repeat many times or to put in a table. So I'd like a shorthand, maybe
something like "x(2_1)" (where the preceding "_" means that the "1" is
subscript. Another way I like is "x_{2(1)}" (where the curly braces mean that
all of "2(1)" is subscript).
Does anyone know what the convention is or if there is one?
Thanks in advance for any help.
James
Re: [ccp4bb] Question on Symmetry Axis Notation Convention
Ethan Merritt writes:
> On Thursday, June 14, 2012 12:06:13 pm James Stroud wrote:
>> Hello All,
>>
>> I would like to discuss symmetry axes, but I'm not sure what the
>> notation convention is. For example, I'd like to say something about
>> a 2(1) along the x-axis, but the phrase "the 2(1) symmetry axis
>> along x" is a bit cumbersome to repeat many times or to put in a
>> table. So I'd like a shorthand, maybe something like "x(2_1)" (where
>> the preceding "_" means that the "1" is subscript. Another way I
>> like is "x_{2(1)}" (where the curly braces mean that all of "2(1)"
>> is subscript).
>>
>> Does anyone know what the convention is or if there is one?
>
> One would think that this document would have the answer:
>
>
> http://www.iucr.org/resources/commissions/crystallographic-nomenclature/symel
>
> But it's too cryptic for me.
>
> I'd go with the full expression in the text.
> For table entries, I'd want something shorter.
> International Tables for Crystallography, Vol A defines the glyph used to
> indicate
> 2_1 screws in the space group diagrams (a solid oval with two flagella).
> But finding a font to print it in your table could be challenging.
> There is a cryst.mf font for TeX if that helps.
>
Re: [ccp4bb] Question on Symmetry Axis Notation Convention
Hi,
Isn't there a notation 2 subscript 1 superscript x (one on top of the other)
for "2-fold screw along x" for example? and likewise for y and z?
Boaz
Boaz Shaanan, Ph.D.
Dept. of Life Sciences
Ben-Gurion University of the Negev
Beer-Sheva 84105
Israel
E-mail: bshaa...@bgu.ac.il
Phone: 972-8-647-2220 Skype: boaz.shaanan
Fax: 972-8-647-2992 or 972-8-646-1710
From: CCP4 bulletin board [CCP4BB@JISCMAIL.AC.UK] on behalf of James Stroud
[xtald...@gmail.com]
Sent: Thursday, June 14, 2012 10:06 PM
To: CCP4BB@JISCMAIL.AC.UK
Subject: [ccp4bb] Question on Symmetry Axis Notation Convention
Hello All,
I would like to discuss symmetry axes, but I'm not sure what the notation
convention is. For example, I'd like to say something about a 2(1) along the
x-axis, but the phrase "the 2(1) symmetry axis along x" is a bit cumbersome to
repeat many times or to put in a table. So I'd like a shorthand, maybe
something like "x(2_1)" (where the preceding "_" means that the "1" is
subscript. Another way I like is "x_{2(1)}" (where the curly braces mean that
all of "2(1)" is subscript).
Does anyone know what the convention is or if there is one?
Thanks in advance for any help.
James
Re: [ccp4bb] Question on Symmetry Axis Notation Convention
On Thursday, June 14, 2012 12:06:13 pm James Stroud wrote:
> Hello All,
>
> I would like to discuss symmetry axes, but I'm not sure what the notation
> convention is. For example, I'd like to say something about a 2(1) along the
> x-axis, but the phrase "the 2(1) symmetry axis along x" is a bit cumbersome
> to repeat many times or to put in a table. So I'd like a shorthand, maybe
> something like "x(2_1)" (where the preceding "_" means that the "1" is
> subscript. Another way I like is "x_{2(1)}" (where the curly braces mean that
> all of "2(1)" is subscript).
>
> Does anyone know what the convention is or if there is one?
One would think that this document would have the answer:
http://www.iucr.org/resources/commissions/crystallographic-nomenclature/symel
But it's too cryptic for me.
I'd go with the full expression in the text.
For table entries, I'd want something shorter.
International Tables for Crystallography, Vol A defines the glyph used to
indicate
2_1 screws in the space group diagrams (a solid oval with two flagella).
But finding a font to print it in your table could be challenging.
There is a cryst.mf font for TeX if that helps.
[ccp4bb] Question on Symmetry Axis Notation Convention
Hello All,
I would like to discuss symmetry axes, but I'm not sure what the notation
convention is. For example, I'd like to say something about a 2(1) along the
x-axis, but the phrase "the 2(1) symmetry axis along x" is a bit cumbersome to
repeat many times or to put in a table. So I'd like a shorthand, maybe
something like "x(2_1)" (where the preceding "_" means that the "1" is
subscript. Another way I like is "x_{2(1)}" (where the curly braces mean that
all of "2(1)" is subscript).
Does anyone know what the convention is or if there is one?
Thanks in advance for any help.
James
