[Wien] Determine primitive cell and positions, CXZ LATTICE 15_B2/b
Peter Blaha
pblaha at theochem.tuwien.ac.at
Thu Mar 19 19:29:33 CET 2015
For low symmetry structures (eg. monoclinic) one can generate several unit cells
which are absolutely equivalent (same volume, same number of atoms, ...)
This happens with sgroup, which transforms your structure such that the
monoclinic angle is less than 90. In addition the fractional coordinates
have been changed austomatically. Nevertheless, these two cells will give
identical neighbor-distances, which you can verify with nn and comparing the
resulting outputnn files. There is nothing wrong with either your original cell
or the one from sgroup. You can use either one for the calculations.
If you want the conventional cell (which contains of course 2x as many atoms),
you can use x supercell (1x1x1, no shifts/vacuum). It simply changes
the lattice type to "P", and adds the centered atoms.
With this struct file, however, you cannot make the calculations unless you
make these atoms "non-equivalent" and break symmetry, eg. by labeling one
atom as "Al1".
What you have been trying was to express the lattice vectors/positions in carthesian
coordinates.
You can check your calculations again using the distances of outputnn and
compare them to your own calculations.
Am 19.03.2015 um 17:03 schrieb David Olmsted:
> 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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--
-----------------------------------------
Peter Blaha
Inst. Materials Chemistry, TU Vienna
Getreidemarkt 9, A-1060 Vienna, Austria
Tel: +43-1-5880115671
Fax: +43-1-5880115698
email: pblaha at theochem.tuwien.ac.at
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