[ase-users] spacegroup question

[Lasse Bjerg]

> If I understand you right, you're suggesting that
> I should be trying this:
>
> bulk = crystal(['Cu','Au'],[(0,0,0),(0.5,0.5,0.5)], spacegroup=123,
> cellpar=[a/sqrt(2),a/sqrt(2),c,90,90,90])
>
> where (0,0,0) and (.5,.5,.5) are the Wyckoff positions 1a and 1d of
> spacegroup 123, respectively. While this makes sense and the values can
> all be found in this online database
> http://cst-www.nrl.navy.mil/lattice/struk/l1_0.html it doesn't produce
> the right output. I get a lattice that resembles a BCC structure and not
> FCC.

The structures are the same. The "body centeret unit cell" contains one 
Au and one Cu, while the "fcc unit cell" contains two of each. I have 
tried to illustrate it in the attached drawing. The fcc like unit cell 
is not a true unit cell, since it is a C-centered tetragonal/cubic cell. 
These can always be reduced to smaller unit cells without reducing the 
symmetry, and thus C-centered tetragonal and cubic Bravais lattices do 
not exist 
(http://en.wikipedia.org/wiki/Bravais_lattice#Bravais_lattices_in_3_dimensions).

> I guess I don't really understand how to use the information from the
> crystal structure database as input to the ase spacegroup package. A
> simpler example is the HCP structure for which I find:
> http://cst-www.nrl.navy.mil/lattice/struk/a3.html
>
> • Primitive Vectors:
> A1= ½ a X - ½ 31/2 a Y
> A2= ½ a X + ½ 31/2 a Y
> A3= c Z
> • Basis Vectors:
> B1= 1/3 A1 + 2/3 A2 + ¼ A3= ½ a X + ½ 3-1/2 a Y + ¼ c Z(Mg) (2c)
> B2= 2/3 A1 + 1/3 A2 + ¾ A3= ½ a X - ½ 3-1/2 a Y + ¾ c Z(Mg) (2c)
>
> On the ASE spacegroup documentation website there is an example how to
> make the HCP structure and it is as simple as:
>
> mg = crystal('Mg', [(1./3., 2./3., 3./4.)], spacegroup=194, cellpar=[a,
> a, c, 90, 90, 120])
>
> How does one relate to the other? Sorry if the answer should be obvious!

The relations of space group no. 194 can be found here:
http://img.chem.ucl.ac.uk/sgp/large/194az1.htm

B1 and B2 are related e.g. by relation 6. That they are related can also 
be seen from the fact, that they have the same position name (2c).
I hope this helps.

Lasse


>
> Thanks a lot in advance!
>
> Lars
>
> On Sep 7, 2011, at 5:07 PM, Lasse Bjerg wrote:
>
>> Furthermore, the space group no. 123 must refer to the primitive (and
>> also tetragonal) unit cell with a = b = 1./sqrt(2) * old_a, c = old_c;
>> and Au at (0, 0, 0) and Cu at (½, ½, ½).
>>
>> On 2011-09-07 17:56, Lasse Bjerg wrote:
>>> Hi Lars
>>>
>>> Space group no. 123 does not connect (0,0,0) to (0.5,0.5,0.0), so the
>>> two positions are two distinct positions, and both should be given
>>> when creating the structure. The connections of space group no. 123
>>> can be seen here:
>>> http://img.chem.ucl.ac.uk/sgp/large/123az1.htm
>>> Putting an atom on position (x,y,z) will automatically give you atoms
>>> on positions 2-16.
>>>
>>> Lasse
>>>
>>> On 2011-09-07 16:06, Lars Grabow wrote:
>>>> Hi,
>>>>
>>>> I tried to use the ase spacegroup package to make the L_10 bulk
>>>> structure (http://cst-www.nrl.navy.mil/lattice/struk/l1_0.html)
>>>>
>>>> I expected to get the correct results with this command:
>>>>
>>>> bulk = crystal(['Cu','Au'],[(0,0,0),(0.5,0.0,0.5)], spacegroup=123,
>>>> cellpar=[a,a,c,90,90,90])
>>>>
>>>> However, when I build this bulk structure, one Cu atom seems to be
>>>> missing.
>>>> The correct structure is obtained when I add an extra Cu atom like this:
>>>>
>>>> bulk =
>>>> crystal(['Cu','Cu','Au'],[(0,0,0),(0.5,0.5,0.0),(0.5,0.0,0.5)],
>>>> spacegroup=123, cellpar=[a,a,c,90,90,90])
>>>>
>>>> Am I using the spacegroup package correctly, or is this possibly a bug?
>>>>
>>>> Thanks!
>>>> Lars
>>>>
>>>> -------------------------------------------------------------------------------------------------------------
>>>> Lars C. Grabow
>>>> Assistant Professor of Chemical and Biomolecular Engineering
>>>> University of Houston
>>>> S341 Engineering Building 1
>>>> Houston, TX 77204-4004
>>>> email: grabow at uh.edu <mailto:grabow at uh.edu>web:
>>>> http://www.chee.uh.edu/faculty/grabow
>>>> phone: (+1) 713-743-9899fax: (+1) 713-743-4323
>>>>
>>>>
>>>>
>>>>
>>>> _______________________________________________
>>>> ase-users mailing list
>>>> ase-users at listserv.fysik.dtu.dk
>>>> https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users
>>>
>>> --
>>> Lasse Bjerg
>>> Visiting PhD Student
>>> Massachusetts Institute of Technology
>>> 77 Massachusetts Avenue
>>> Room 13-4042
>>> Cambridge, MA 02139
>>> office (+1) 617-258-0222
>>> mobile (+1) 857-272-0769
>>> emailbjerg at mit.edu
>>>
>>>
>>>
>>> _______________________________________________
>>> ase-users mailing list
>>> ase-users at listserv.fysik.dtu.dk
>>> https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users
>>
>> --
>> Lasse Bjerg
>> Visiting PhD Student
>> Massachusetts Institute of Technology
>> 77 Massachusetts Avenue
>> Room 13-4042
>> Cambridge, MA 02139
>> office (+1) 617-258-0222
>> mobile (+1) 857-272-0769
>> emailbjerg at mit.edu
>>
>>
>> _______________________________________________
>> ase-users mailing list
>> ase-users at listserv.fysik.dtu.dk <mailto:ase-users at listserv.fysik.dtu.dk>
>> https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users
>
>

-- 
Lasse Bjerg
Visiting PhD Student
Massachusetts Institute of Technology
77 Massachusetts Avenue
Room 13-4042
Cambridge, MA 02139
office (+1) 617-258-0222
mobile (+1) 857-272-0769
email bjerg at mit.edu

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