Crystal Unit Cell Question
Bev Vincent
brv at RigakuMSC.com
Thu Nov 15 15:35:24 EST 2001
"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
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