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

Éric Germaneau germaneau at gucas.ac.cn
Thu Nov 17 20:02:19 CET 2011

```Actually it's

cos(alpha) = *b* . *c* / ( |*b*||*c*| )

Éric.

On 11/17/2011 12:49 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)*  ???
>
>
>                  Regards
>              Yedukondalu
>
>
>
>
>     ------------------------------------------------------------------------
>     _______________________________________________
>     Pw_forum mailing list
>     Pw_forum at pwscf.org
>     http://www.democritos.it/mailman/listinfo/pw_forum
>
>
>
> _______________________________________________
> Pw_forum mailing list
> Pw_forum at pwscf.org
> http://www.democritos.it/mailman/listinfo/pw_forum

--
/Be the change you wish to see in the world
/ --- Mahatma Gandhi ---

Dr. Éric Germaneau

College of Physical Sciences