Rotation of Premitive lattice

[ezaztaw]

Hi,

I am a naive user of ATK and trying to build a bulk material with different premitive lattice vector using builder in ATK.  For example, suppose, I made a fcc with a A=[1 0 0], B=[0 1 0], c=[ 0 0 1] premitive lattice vector, so that all the faces of the cube are perpendicular to those direction.

Now, I want to transform the premitive lattice A to be in [-2 1 1], B in [ 1 1 1] and C in [0 1 -1], thus want to get the coordinates in using these premitive lattice vector. A simple rotation matrix can do this, but as there any way to make this calculation using the builder in ATK?

 

[zh]

First, only thing should be clarified. The lattice vectors of a primitive cell of FCC are usually written as A = a[0,  1/2,  1/2], B= a[1/2,  0, 0], C=a[1/2, 1/2, 0]. The lattice vectors listed by you are used for a conventional cell of a FCC.

Second, to achieve what you want,  you may construct a supercell with those lattice vectors by cleaving a bulk to get the slab model of a (01-1) surface of FCC. In such slab model, the vacuum thickness is set as the layer distance of (01-1) surface.

Alternatively,  a tool for the construction of supercell is provided here for the VASP code, but it can be easily used to construct a supercell. The obtained coordinates in supercell can be easily transfered to the format of ATK.
http://www.freeware.vasp.de/VASP/
For example: the followings are demonstrated for constructing a supercell of FCC copper.
The primitive cell of copper and the atomic positions:

Cu   # title to indicate the system
   3.52293    # lattice constant
    0.0   0.5   0.5      # primitive lattice vector 1
    0.5   0.0   0.5      # primitive lattice vector  2
    0.5   0.5   0.0      #primitive lattice vector 3
   1                        # Number of atoms in the cell
Direct                     #indicate that the fractional coordinates of atoms are given
  0.0000000000000000  0.0000000000000000  0.0000000000000000

The supercell with  lattice vectors A= a[-2, 1, 1], B=a[1,1,1], and C=a[0,1,-1] are constructed by the tool provided in that webpage:

Cu
    3.52293000000000
   -2.00000000000000    1.00000000000000    1.00000000000000
    1.00000000000000    1.00000000000000    1.00000000000000
    0.00000000000000    1.00000000000000   -1.00000000000000
   24
Direct
    0.00000000000000    0.00000000000000    0.00000000000000
    0.16666666666667    0.33333333333334    0.00000000000000
    0.33333333333334    0.66666666666667    0.00000000000000
    0.50000000000000    0.00000000000000    0.00000000000000
    0.66666666666667    0.33333333333334    0.00000000000000
    0.83333333333334    0.66666666666667    0.00000000000000
    0.91666666666667    0.33333333333334    0.75000000000000
    0.08333333333334    0.66666666666667    0.75000000000000
    0.25000000000000    0.00000000000000    0.75000000000000
    0.41666666666667    0.33333333333334    0.75000000000000
    0.58333333333334    0.66666666666667    0.75000000000000
    0.75000000000000    0.00000000000000    0.75000000000000
    0.83333333333334    0.66666666666667    0.50000000000000
    0.00000000000000    0.00000000000000    0.50000000000000
    0.16666666666667    0.33333333333334    0.50000000000000
    0.33333333333334    0.66666666666667    0.50000000000000
    0.50000000000000    0.00000000000000    0.50000000000000
    0.66666666666667    0.33333333333334    0.50000000000000
    0.75000000000000    0.00000000000000    0.25000000000000
    0.91666666666667    0.33333333333334    0.25000000000000
    0.08333333333334    0.66666666666667    0.25000000000000
    0.25000000000000    0.00000000000000    0.25000000000000
    0.41666666666667    0.33333333333334    0.25000000000000
    0.58333333333334    0.66666666666667    0.25000000000000

A online tool for the transformation of any unit cell is provided by Bilbao Crystallographic Server:
http://www.cryst.ehu.es/cryst/metric.html
Bilbao Crystallographic Server also provides a online tool to transform Structure, see here:
http://www.cryst.ehu.es/cryst/transtru.html

[ezaztaw]

Dear ZH,

Thanks a lot for the elaborative mail and helping me out. The alternative solution is exactly what we need. With the fcc, I tried to gave a sample example. Actually,  We are trying to apply shear in different planes in a bulk alloy NiTi and trying to understand its behavior. In martensite phase, it has a monoclinic structure  ([tex]P2_{1}/m[/tex] space group). I generated the POSCAR (input file for vasp) file for it.


B19relaxed NiTirelaxed NiTi 
1.000000
   4.10799320000000   0.00000000000000   0.00000000000000
   0.00000000000000   2.90156295462098   0.00000000000000
   0.00000000000000   0.62786873794988   4.60337885122496
2 2
Cartesian(4)
   2.05399660000000   1.38769180295539   0.49900626747279       
   0.00000000000000   1.39182072490922   2.11203021694201       
   0.00000000000000   0.00000000000000   0.00000000000000       
   2.05399660000000   2.77951252786461   2.61103648441480       


in this POSCAR, the premitive lattice is in [010], [100] and [001] direction. However, I need to rotate in [011], [1 1 -1] and [-2 1 -1] direction. I am hoping the vasp code will give me the supercell in this direction.

The problem I am facing, I could not compile the makefile (supercell.F and others)  in poscar directory. I was able to compile the Makefile in the vasp directory though. The problem is, the makefile includes library ldmy4, llapack64 and lblas which I don't have in my local machine (ubuntu). In the parallel computer (fedora 12) we do not have pgf90. Also, I am a novice in terms of compiling files in linux.

Thus, I am wondering, if you have a compiled version of the supercell.F file which I can run. Or is there any way to bypass the library during the build.

Sorry for these question, As I know it is completely not relating to the Builder. It would be great if you can answer my questions.

Thanks

Tawhid


 

[zh]

Sorry, in this forum I can not offer more supports related to vasp code. If you can not build the supercell in the second way, please try other solutions, as listed in my last reply. Especially, the 1st and 3rd ones can work without compiling any code.