[Pw_forum] calculation of lattice parameter and angle of rhombohedral structure

[Gabriele Sclauzero]

Dear all,

I think that (using GAO Zhe's notation) both
b (*) c / (|b| |c|)
and
a (*) b / (|a| |b|)
should give the same result, because in the rhombohedral lattice the
three basis vectors form equal angles with each other.
Obviously, a (*) b / (|a (*) b|) is not correct because it would always
give 1 or -1 (and I believe it was just a typo).


HTH

GS


On 11/17/2011 06:49 AM, Huiqun Zhou wrote:
> I'm afraid the formula for calculating cosA should be
> cosA = b (*) c / (|b| | c|)
> dr. zhou huiqun
> @earth sciences, nanjing university, china
>
>     ----- Original Message -----
>     *From:* GAO Zhe <mailto:flux_ray12 at 163.com>
>     *To:* PWSCF Forum <mailto:pw_forum at pwscf.org>
>     *Sent:* Wednesday, November 16, 2011 8:53 PM
>     *Subject:* Re: [Pw_forum] calculation of lattice parameter and
>     angle of rhombohedral structure
>
>     the three basis vectors of rhombohedral are (after relaxation) :
>     a = ( 0.636439417 -0.367448469 0.640642896 )
>     b = ( 0.000000000 0.734896938 0.640642896 )
>     c = ( -0.636439417 -0.367448469 0.640642896 )
>     then the lattice paremeter should be: A = sqrt (a1^2+a2^2+a3^2) *
>     alat = 8.05092296 a.u. .
>     The angle between two vectors can be calculated by:
>     cosA = a (*) b / |a (*) b|,
>     where a and b are basis vectors, (*) represents the dot product.
>
>     --
>     GAO Zhe
>     CMC Lab, MSE, SNU, Seoul, S.Korea
>
>     At 2011-11-16 20:14:38,"yedu kondalu" <nykondalu at gmail.com> wrote:
>
>         Dear users,
>
>         I did the optimization for a compound using variable cell
>         approximation using PWSCF, which belongs to the space group
>         R3m(160) Rhombohedral representation. The primitive vectors in
>         terms of lattice parameter a = 8.25791360 a.u.
>         a(1) = ( 0.619505 -0.357671 0.698774 )
>         a(2) = ( 0.000000 0.715343 0.698774 )
>         a(3) = ( -0.619505 -0.357671 0.698774 )
>
>         after completion of optimization step, the primitive vectors
>
>         CELL_PARAMETERS (alat= 8.25791360)
>         0.636439417 -0.367448469 0.640642896
>         0.000000000 0.734896938 0.640642896
>         -0.636439417 -0.367448469 0.640642896
>
>         can u please explain me
>
>         how can I calculate the lattice parameter *a* and the *angle
>         (alpha)* ???
>
>         Thanks in advance
>
>         Regards
>         Yedukondalu
>


-- 

Gabriele Sclauzero, EPFL SB ITP CSEA
PH H2 462, Station 3, CH-1015 Lausanne

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