Crystal Unit Cell Question

[Bev Vincent]

"Uncle Al" <UncleAl0 at hate.spam.net> wrote in message
news:3BF42339.6F5822E at hate.spam.net...
> Uncle Al asks a probably silly and very obvious question about some
> crystal data...
>
> REFERENCE STRUCTURE = 20626   A,B,C =   5.482   5.482   5.173
>    ALPHA,BETA,GAMMA =  90.000  90.000 120.000    SPGR =173 P63
>    3   0 CODEN=   46025 SYMOPS=  389
>   40     RFAC= 2.1 ERRFLAG=0 (C-C)ESD=0
>    1 Li1    0.00000   0.00000   0.07830
>    2 O1     0.24750   0.34220  -0.16200
>    3 I1     0.33333   0.66667   0.00000
>
> Lithium iodate, LiIO(3), has two formula units in its unit cell:
>
> 2 lithiums
> 2 iodines
> 6 oxygens
>
>   ----- Where are the rest of the atoms? -----

Space Group P63 (#173) has the following symmetry operators:

1)    +X,    +Y,    +Z           2)    -Y,    +X-Y,    +Z
 3)    -X+Y,    -X,    +Z       4)    -X,    -Y, 1/2+Z
 5)    +Y,    -X+Y, 1/2+Z    6)    +X-Y,    +X, 1/2+Z

Take the above coordinates for Li1, I1 and O1 and apply these operations. If
an atom is on a special position, some of these operations will return the
same coordinates (e.g. 0, 0, .0783 produces the same coordinates for
operators 1-3 and the second position -- 0, 0, 0.5783 -- for operators 4-6).

>  REFERENCE STRUCTURE = 47670   A,B,C =   4.913   4.913   5.405
>    ALPHA,BETA,GAMMA =  90.000  90.000 120.000    SPGR =154 P3221
>    2   0 CODEN=   83849 SYMOPS=  398
>   40     RFAC= 2.4 ERRFLAG=0 (C-C)ESD=0
>    1 Si1     0.46980   0.00000   0.16667
>    2 O1      0.41380   0.26510   0.28710
>
> Alpha-quartz, SiO(2), has three formula units in its unit cell,
>
> 3 silicons
> 6 oxygens
>
>    ----- Where are the rest of the atoms? -----

P3221 (#154) has these operators:

1)    +X,    +Y,    +Z           2)    -Y,    +X-Y, 2/3+Z
 3)    -X+Y,    -X, 1/3+Z     4)    +Y,    +X,    -Z
 5)    -X,    -X+Y, 2/3-Z      6)    +X-Y,    -Y, 1/3-Z

Same game as before.

Bev Vincent
Rigaku/MSC
http://www.RigakuMSC.com