Document AM-97-648
Structure and dynamics of protonated Mg2SiO4: An ab-initio molecular dynamics study
Michael Haiber, Pietro Ballone, and Michele Parrinello
American Mineralogist 82(9-10)913-922

Table 5. Optimized lattice parameters and atomic positions for beta spinel

**************
* BetaSpinel *
**************

We chose the conventions of 

H. Horiuchi and H. Sawamoto, Amer. Miner. Vol.66, (1981), p568-575

to name inequivalent positions. A different way of naming them was adopted by

Werner H. Baur, Nature Physical Science Vol.233, (1971), p135-137
and
P.B. Moore and J.V. Smith, Phys. Earth Planet. Interiors Vol.3, (1970), p166-177
to which we refer as case2.


Space group:    Ibmm    (No. 74) 

Atomic coordinates:
						case2
Mg1     in  4(d):     3/4, 1/4, 1/4		Mg2	
Mg2     in  4(e):       u,   0, 1/4		Mg1
Mg3     in  8(f):       0,   v,   0		Mg3
Si      in  8(i):       u,   v, 1/4		Si
O1      in  4(e):       u,   0, 1/4		O2
O2      in  4(e):       u,   0, 1/4		O1
O3      in  8(i):       u,   v, 1/4		O3
O4      in 16(j):       u,   v,   w		O4



Positions as function of pressure:

a[A]          b/a         c/a           P[Kbar]

7.419062    1.387488  	.690592		1313.284664
Mg2    u=.225798
Mg3 		      v=.372881 
Si     u=.131657  v=.128240
O1     u=.523988
O2     u=.024557
O3     u=.000313  v=.238393
O4     u=.254050  v=.374537  w=.011059

7.630732  1.387488  .690592		 789.889857
Mg2    u=.225798
Mg3               v=.372881
Si     u=.131657  v=.128240
O1     u=.523988
O2     u=.024557
O2     u=.024557
O3     u=.000313  v=.238393
O4     u=.254050  v=.374537  w=.011059

7.778902  1.395234377  .700868850	 447.674989
Mg2    u=.225581
Mg3               v=.374468
Si     u=.132320  v=.128926
O1     u=.523248
O2     u=.023541
O3     u=-.000146 v=.23707
O4     u=.253936  v=.374101  w=.010237

8.202244  1.387488  .690592		  60.520383
Mg2    u=.225526
Mg3               v=.375247
Si     u=.132245  v=.128506
O1     u=.526302
O2     u=.029275
O3     u=.002841  v=.237430
O4     u=.256045  v=.373512  w=.013013

8.466832  1.387488  .690592		 -99.918707
Mg2    u=.223609
Mg3               v=.375822
Si     u=.132821  v=.128719
O1     u=.531868
O2     u=.033593
O3     u=.004732  v=.235858
O4     u=.257674  v=.373016  w=.015089