[Wien] Wien2k: Rhombohedral lattice

[Jian-Xin Zhu]

Dear Wien Users, 

This is an earlier communication I made with Peter.
It might be useful to be documented in the archive.

Regards, 

Jianxin

Begin forwarded message:

> From: Peter Blaha <pblaha at theochem.tuwien.ac.at>
> Date: September 18, 2010 1:31:45 AM MDT
> To: Jian-Xin Zhu <jxzhu at lanl.gov>
> Subject: Re: Wien2k: Rhombohedral lattice
> 
> Yes, everithing is as statet in the UG (even if it is very unlogical
> to specify hexagonal lattice parameters and rhombohedral coordinates).
> 
> PS: This is an IDEAL question for the mailing list. Others could learn
> from the answer too and I do not have to  answer this 15 times/year.
> 
> Jian-Xin Zhu schrieb:
>> Dear Peter, I am trying to calculate a system of rhombohedral lattice.  From the UG, I  am advised that special care should be taken for preparing the structure file, e.g., rhomb.struct. ---
>> 1/ On page 39,  for the input of unit cell parameters (a,b,c), it reads "...
>> for rhombohedral (R) lattices the hexagonal lattice constants must be specified. (The following may help you to convert between hexagonal and rhombohedral specifications:
>> 	 	$a_{hex} = 2 cos (\frac{\pi- \alpha_{rhomb}}{2} ) a_{rhomb}$
>> 	 	$c_{hex} = 3 \sqrt{a_{rhomb}^2 - \frac{1}{3} a_{hex}^2 } $
>> 	 	and (for fcc-like lattices) $a_{rhomb}=a_{cubic}/\sqrt{2} $
>> "
>> It means I should put in the lattice parameter of the corresponding hexagonal lattice. So in the above formula, alpha_rhomb is the angle between any of two rhombohedral  primitive unit vectors, for example, alpha_homb=60 degree. Is it correct?
>> 2/ Then for the position of atom in internal units (x,y,z), it reads "...
>> For R lattice use rhombohedral coordinates. (To convert from hexagonal into rhombohedral coordinates use the auxiliary program *hex2rhomb*, which can be called at a command-line:
>> 	 	$ \vec X_{ortho} = \vec X_{hex} \left ( \begin{array}{ccc} 0 & 1 & 0 \\ \frac{\sqrt{3}}{2} & \frac{-1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right ) $
>> 	 	$ \vec X_{rhomb} = \vec X_{ortho} \left ( \begin{array}{ccc} \frac{1}{\sqrt{3}}... ...rt{3}} & \frac{-2}{\sqrt{3}}\\ -1 &1 & 0 \\ 1 & 1 & 1 \end{array} \right ) $
>> "
>> Here when you say "For R lattice use rhombohedral coordinates". Does it means I should use the following x,y,z values  in
>> vecr = x veca_rhombohedral + y vecb_rhombohedral + z vecc_rhombohedal
>> rather than in
>> vecr = x veca_hexagonal + y vecb_hexagonal + z vecc_hexagonal
>> although we use the hexagonal lattice constants for the unit cell parameters of the rhombohedral lattice? Here veca_rhombohedral, vecb_rhombohedral, vecc_rhombohedral, are three primitive translation vectors for the rhombohedral lattice I am going to study while veca_hexagonal, vecb_hexagonal, vecc_hexagonal, are those for the hexagonal lattice mentioned in the above point 1.
>> I want to make sure I really understand these points of care correctly.
>> Best regards, Jian-Xin
>> P.S.: Since it is not about the code itself and also might be too trivial for other users, I don't post it to the mailing list.   --
>> ###############################
>> Jian-Xin Zhu, Ph.D
>> Theorertical Division, MS B262
>> Los Alamos National Laboratory
>> Los Alamos, NM 87545
>> Phone: (505) 667 2363
>> Fax: (505) 665 4063
>> Emai: jxzhu at lanl.gov <mailto:jxzhu at lanl.gov>
>> Email (backup): physjxzhu at gmail.com <mailto:physjxzhu at gmail.com>
>> URL: http://theory.lanl.gov
>> ###############################
> 
> -- 
> -----------------------------------------
> 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
> -----------------------------------------

-- 
###############################
Jian-Xin Zhu, Ph.D
Theoretical Division, MS B262
Los Alamos National Laboratory
Los Alamos, New Mexico 87545
Phone: (505) 667 2363
Fax: (505) 665 4063
Email (main): jxzhu at lanl.gov
Email (backup): physjxzhu at gmail.com
URL: http://theory.lanl.gov
###############################






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