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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
------------------------------------------------------------------------------------


 =========================================================
 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  
 =========================================================