[ase-users] spacegroup question

Thu Sep 8 16:19:46 CEST 2011

Thanks Lasse! The attached drawing helped immensely and I can see that the 2 structures are the same.

I still have to look into the HCP structure a bit more...

Thanks a bunch!
Lars

On Sep 8, 2011, at 8:38 AM, Lasse Bjerg wrote:

>> 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
> 
> <body_centeret.png>

-------------------------------------------------------------------------------------------------------------
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			web: http://www.chee.uh.edu/faculty/grabow
phone: (+1) 713-743-9899		fax: (+1) 713-743-4323

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