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Unit cells
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> Dear All,
>
> I have two data sets with cell dimensions
>
> a=118.806 b=126.818 c=85.610 alpha=90. beta=104.166 gamma=90.
> a=128.193 b=127.106 c=85.513 alpha=90. beta=115.994 gamma=90.
>
> both in the space group P21
>
> I have a suspicion that they are the same data indexed in two ways.
>
> can anyone tell me about some program to check it out.
I put both cells through the sg-init program in maXus (Designed for
small molecules but useful in this case). In particular it uses the LePage
method for examining metric symmetry. The results are:
> a=118.806 b=126.818 c=85.610 alpha=90. beta=104.166 gamma=90.
Niggli reduced cell: 85.610 118.806 126.818 90.00 90.00 104.17
Niggli matrix: 7329.0723 14114.8652 16082.8057
0.0000 0.0000 -2489.1650
Transformation matrix: 0.00 0.00 1.00
1.00 0.00 0.00
0.00 1.00 0.00
Niggli matrix indicates monoclinic cell of type P
Checking for higher metric symmetry via LePage method:
Possible 2-Fold Axes - 2-Axis Crit = 0.50, Exp. Error = 0.30 Deg., LATT = P:
Rows Products Angle Between Two Direct Axes
Nr D N Direct Recip Dot Delta 1 2 3 4 5 6 7 8 9
1126.818 0 0 0 1 0 0 1 1 0.000 0.
Transformation Matrix: Input (a,b,c) to Conventional Cell(a', b', c'):
(a') ( 0.00 0.00 1.00) (a) (x') ( 0.00 0.00 1.00) (x) Metrically
(b') = ( 0.00-1.00 0.00) (b). (y') = ( 0.00-1.00 0.00) (y). monoclinic
(c') ( 1.00 0.00 0.00) (c) (z') ( 1.00 0.00 0.00) (z) FOM: 0.000
Latt a b c Alpha Beta Gamma Volume
Input Cell P 118.806 126.818 85.610 90.00 104.17 90.00 1250639.62
Reduc Cell P 85.610 118.806 126.818 90.00 90.00 104.17 1250640.00
Conv. Cell mP 85.610 126.818 118.806 90.00 104.17 90.00 1250639.62
Possible alternative metric symmetry detected.
====> Gives you 85.610 126.818 118.806 90.00 104.17 90.00
------------------------------------------------------------------------------------
> a=128.193 b=127.106 c=85.513 alpha=90. beta=115.994 gamma=90.
Niggli reduced cell: 85.513118.899127.106 90.00 90.00 75.72
Niggli matrix: 7312.4731 14136.9834 16155.9355
0.0000 0.0000 2508.0068
Transformation matrix: 0.00 0.00 1.00
1.00 0.00 1.00
0.00 1.00 0.00
Niggli matrix indicates monoclinic cell of type P
Checking for higher metric symmetry via LePage method:
Possible 2-Fold Axes - 2-Axis Crit = 0.50, Exp. Error = 0.30 Deg., LATT = P:
Rows Products Angle Between Two Direct Axes
Nr D N Direct Recip Dot Delta 1 2 3 4 5 6 7 8 9
1127.106 0 0 0 1 0 0 1 1 0.000 0.
Transformation Matrix: Input (a,b,c) to Conventional Cell(a', b', c'):
(a') ( 0.00 0.00 1.00) (a) (x') (-1.00 0.00 1.00) (x) Metrically
(b') = ( 0.00 1.00 0.00) (b). (y') = ( 0.00 1.00 0.00) (y). monoclinic
(c') (-1.00 0.00-1.00) (c) (z') (-1.00 0.00 0.00) (z) FOM: 0.000
Latt a b c Alpha Beta Gamma Volume
Input Cell P 128.193 127.106 85.513 90.00 115.99 90.00 1252405.00
Reduc Cell P 85.513 118.899 127.106 90.00 90.00 104.28 1252404.62
Conv. Cell mP 85.513 127.106 118.899 90.00 104.28 90.00 1252405.00
Possible alternative metric symmetry detected.
====> Gives you 85.513 127.106 118.899 90.00 104.28 90.00
which is suspiciously close to 85.610 126.818 118.806 90.00 104.17 90.00
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=========================================================
Chris Gilmore Phone(44)(0)141 330 5947
Professor of Crystallography Lab (44)(0)141 330 6579
Department of Chemistry Fax (44)(0)141 330 4419
University of Glasgow
Glasgow G12 8QQ, Scotland, UK
E-mail: chris@chem.gla.ac.uk
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