Rhombohedral graphite?

[Quantamania]

Friends,

I am continuing my research into graphite and hexagonal boron nitride modeling with Virtual NanoLab 2008.10.  When I looked through the default Crystal Cupboard to look for a particular form of graphite, it was not there.

This form is rhombohedral graphite, which is 40% or less of natural graphite.  It has the ABCABC stacking of graphene sheets and a two-atom unit cell.  The dimensions of this cell, according to IUPAC, are a = 256.6 pm and c = 1006.2 pm (in angstroms they are a = 2.566 A and c = 10.006 A).  The space group this crystal belongs to is R(3 bar)m.  The Schoenflies symbol it belongs to is D_3d⁵.  A similar structure can be found at the Naval Research Laboratory crystal structure database.

I want to use this model to make mixed carbon/boron nitride models that mimic the ABCABC stacking structure, and also to calculate band structures of both carbon and boron nitride versions.  I have already used the Bernal and simple hexagonal structures of graphite with both C and BN.  If you know how to make rhombohedral graphite on your program, I would appreciate your help.  I would also like to see coordinates of the atoms in both fractional and Cartesian coordinates, as well as supercells (so I can mix the elements together in them).

Thank you for your help.

[zh]

As you have said, a similar structure rhombohedral graphite can be found in the Naval Research Laboratory crystal structure database.  For the primitive vectors for rhombohedral graphite in a rhombohedral lattice and the atomic positions within primitive unit cell, you also can found them there:
http://cst-www.nrl.navy.mil/lattice/struk.xmol/rgr.pos

The following information is copied from there:

Primitive vectors
a(1) =   1.22832727 -0.70917508  3.34686537
a(2) =   0.00000000  1.41835016  3.34686537
a(3) =  -1.22832727 -0.70917508  3.34686537

Basis Vectors:
Atom    Lattice Coordinates                Cartesian Coordinates

C   0.16666667  0.16666667  0.16666667     0.00000000  0.00000000  1.67343269
C  -0.16666667 -0.16666667 -0.16666667     0.00000000  0.00000000 -1.67343269


In your question, the lattice parameters for rhombohedral graphite are  given in a hexagonal lattice, they (i.e. a_hex, c_hex) can be converted to the ones(a_rho, theta) of a rhombohedral lattice:
You may convert them by an online tool here:
http://qpeng.org/tools/r2h.html

or by the formula listed here:
http://cst-www.nrl.navy.mil/lattice/struk/rgr.html
 
Since you want to mix cabon and BN in the structure of rhombohedral graphite, it is better to  first create a crystal structure of rhombohedral graphite in a hexagonal lattice. The atomic positions in hexagonal lattice of  rhombohedral graphite can also be found here:
http://cst-www.nrl.navy.mil/lattice/struk/rgr.html
i.e.
Atomic positions of carbon given in fractional coordinate type:
(0,0,z)    (0,0,-z), where z= 0.1666666667.

Once you know the atomic positions and lattice parameters for  rhombohedral graphite in hexagonal and rhombohedral lattices, you can easily create a crystal structure of rhombohedral graphite by using "Bulk Builder" in Virtual NanoLab, and then get the atomic positions in the primitive unit cell and the supercell. Please try it by yourself.