[Wien] Determine primitive cell and positions, CXZ LATTICE 15_B2/b
David Olmsted
olmsted at berkeley.edu
Thu Mar 19 17:03:34 CET 2015
Dear reader,
I am trying to determine the primitive cell and positions for a
case.struct file I am running. But I am not determining the either
primitive cell or the conventional cell correctly.
I need to either:
1. Figure out what I am doing wrong. or
2. Find a place in the code where I can print out the positions in terms
of the primitive cell.
Does anyone know the answer to either question?
This is a base-centered monoclinic system, space group 15.
>From case.struct:
MODE OF CALC=RELA unit=bohr
35.704486 13.533274 13.533274 90.000000 90.000000 99.990000
The full case.struct is given below.
sgroup reports 15 (C 2/c) [unique axis c] cell choice 2.
The struct file output from sgroup is:
CXZ LATTICE,NONEQUIV.ATOMS: 14 15 C2/c
MODE OF CALC=RELA unit=bohr
35.704486 13.533274 13.533274 90.000000 90.000000 80.010000
The case.struct file I am using has the 99.99 degree entry as above.
In angstroms, my lattice constants (and angles in degrees) are
18.894 7.1615 7.1615 90 90 99.99
The userguide gives (on page 39) the primitive cell as:
CXZ [a sin(\gamma)/2, a cos(\gamma)/2, -c/2], [0, b, 0], [a
sin(\gamma)/2, acos(\gamma)/2, c/2]
So I have for a primitive cell (each row is a vector):
9.3038 -1.6388 -3.5808
0 7.1615 0
9.3038 -1.6388 3.5808
With lengths of 10.1029 7.1615 10.1029 and angles 99.34 41.52 99.34.
The positions in case.struct are given in terms of the conventional unit
cell, and I must convert them to the primitive cell. So I need the
conventional cell in cartesian coordinates.
The README file in SRC_sgroup talks about base-centered monoclinic being
restricted to A centered. Page 39 of the userguide shows only
B-base-centered,
which is what I have. The README gives:
The vectors of the conventional cell in cartesian basis
( 1 vector is 1 column ... )
a b*Cos[gamma] 0
0 b*Sin[gamma] 0 A - centred
0 0 c
This is a valid conventional cell in my case, and switching to each row
being a vector, I have:
18.894 0 0
-1.24235 7.0529 0
0 0 7.1615
However the location of the second primitive cell is (0.5, 0, 0.5) in terms
of the conventional cell. When transformed to primitive cell coordinates it
must be a lattice vector. But it is not. So one of my cells is wrong. (I
believe the vector for the second primitive cell is correct because it is
what is given in the International Tables, page 199, for unique axis c, cell
choice 2. And it matches to the neighbor positions in case.outputnn.)
Quite possibly the conventional cell is different for B-centered than for
A-centered, but I do not find it described anywhere.
My thanks for any help.
David
David Olmsted
Assistant Research Engineer
Materials Science and Engineering
210 Hearst Memorial Mining Building
University of California
Berkeley, CA 94720-1760
------- case.struct
troll_icsd
CXZ LATTICE,NONEQUIV.ATOMS: 14 15_B2/b
MODE OF CALC=RELA unit=bohr
35.704486 13.533274 13.533274 90.000000 90.000000 99.990000
ATOM -1: X=0.16778000 Y=0.32059000 Z=0.00654000
MULT= 4 ISPLIT= 8
-1: X=0.83222000 Y=0.67941000 Z=0.99346000
-1: X=0.83222000 Y=0.17941000 Z=0.00654000
-1: X=0.16778000 Y=0.82059000 Z=0.99346000
Al NPT= 781 R0=0.00010000 RMT= 1.6300 Z: 13.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -2: X=0.07570000 Y=0.41714000 Z=0.72882000
MULT= 4 ISPLIT= 8
-2: X=0.92430000 Y=0.58286000 Z=0.27118000
-2: X=0.92430000 Y=0.08286000 Z=0.72882000
-2: X=0.07570000 Y=0.91714000 Z=0.27118000
Al NPT= 781 R0=0.00010000 RMT= 1.6300 Z: 13.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -3: X=0.00000000 Y=0.25000000 Z=0.11731000
MULT= 2 ISPLIT= 8
-3: X=0.00000000 Y=0.75000000 Z=0.88269000
P NPT= 781 R0=0.00010000 RMT= 1.3000 Z: 15.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -4: X=0.16844000 Y=0.08109000 Z=0.63272000
MULT= 4 ISPLIT= 8
-4: X=0.83156000 Y=0.91891000 Z=0.36728000
-4: X=0.83156000 Y=0.41891000 Z=0.63272000
-4: X=0.16844000 Y=0.58109000 Z=0.36728000
P NPT= 781 R0=0.00010000 RMT= 1.3000 Z: 15.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -5: X=0.06458000 Y=0.32611000 Z=0.98827000
MULT= 4 ISPLIT= 8
-5: X=0.93542000 Y=0.67389000 Z=0.01173000
-5: X=0.93542000 Y=0.17389000 Z=0.98827000
-5: X=0.06458000 Y=0.82611000 Z=0.01173000
O NPT= 781 R0=0.00010000 RMT= 0.8700 Z: 8.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -6: X=0.02064000 Y=0.09579000 Z=0.23728000
MULT= 4 ISPLIT= 8
-6: X=0.97936000 Y=0.90421000 Z=0.76272000
-6: X=0.97936000 Y=0.40421000 Z=0.23728000
-6: X=0.02064000 Y=0.59579000 Z=0.76272000
O NPT= 781 R0=0.00010000 RMT= 0.8700 Z: 8.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -7: X=0.23738000 Y=0.16861000 Z=0.53512000
MULT= 4 ISPLIT= 8
-7: X=0.76262000 Y=0.83139000 Z=0.46488000
-7: X=0.76262000 Y=0.33139000 Z=0.53512000
-7: X=0.23738000 Y=0.66861000 Z=0.46488000
O NPT= 781 R0=0.00010000 RMT= 0.8700 Z: 8.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -8: X=0.11140000 Y=0.00803000 Z=0.49156000
MULT= 4 ISPLIT= 8
-8: X=0.88860000 Y=0.99197000 Z=0.50844000
-8: X=0.88860000 Y=0.49197000 Z=0.49156000
-8: X=0.11140000 Y=0.50803000 Z=0.50844000
O NPT= 781 R0=0.00010000 RMT= 0.8700 Z: 8.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -9: X=0.14191000 Y=0.23708000 Z=0.75449000
MULT= 4 ISPLIT= 8
-9: X=0.85809000 Y=0.76292000 Z=0.24551000
-9: X=0.85809000 Y=0.26292000 Z=0.75449000
-9: X=0.14191000 Y=0.73708000 Z=0.24551000
O NPT= 781 R0=0.00010000 RMT= 0.8700 Z: 8.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -10: X=0.18216000 Y=0.92446000 Z=0.76484000
MULT= 4 ISPLIT= 8
-10: X=0.81784000 Y=0.07554000 Z=0.23516000
-10: X=0.81784000 Y=0.57554000 Z=0.76484000
-10: X=0.18216000 Y=0.42446000 Z=0.23516000
O NPT= 781 R0=0.00010000 RMT= 0.8700 Z: 8.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -11: X=0.00000000 Y=0.25000000 Z=0.63572000
MULT= 2 ISPLIT= 8
-11: X=0.00000000 Y=0.75000000 Z=0.36428000
O NPT= 781 R0=0.00010000 RMT= 0.8700 Z: 8.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -12: X=0.16141000 Y=0.06966000 Z=0.12100000
MULT= 4 ISPLIT= 8
-12: X=0.83859000 Y=0.93034000 Z=0.87900000
-12: X=0.83859000 Y=0.43034000 Z=0.12100000
-12: X=0.16141000 Y=0.56966000 Z=0.87900000
O NPT= 781 R0=0.00010000 RMT= 0.8700 Z: 8.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -13: X=0.00000000 Y=0.25000000 Z=0.51600000
MULT= 2 ISPLIT= 8
-13: X=0.00000000 Y=0.75000000 Z=0.48400000
H NPT= 781 R0=0.00010000 RMT= 0.4700 Z: 1.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -14: X=0.19000000 Y=0.07200000 Z=0.19100000
MULT= 4 ISPLIT= 8
-14: X=0.81000000 Y=0.92800000 Z=0.80900000
-14: X=0.81000000 Y=0.42800000 Z=0.19100000
-14: X=0.19000000 Y=0.57200000 Z=0.80900000
H NPT= 781 R0=0.00010000 RMT= 0.4700 Z: 1.0
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
4 NUMBER OF SYMMETRY OPERATIONS
-1 0 0 0.00000000
0-1 0 0.00000000
0 0-1 0.00000000
1
1 0 0 0.00000000
0 1 0 0.00000000
0 0 1 0.00000000
2
-1 0 0 0.00000000
0-1 0 0.50000000
0 0 1 0.00000000
3
1 0 0 0.00000000
0 1 0 0.50000000
0 0-1 0.00000000
4
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