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

GAO Zhe flux_ray12 at 163.com
Wed Nov 16 13:53:59 CET 2011

```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

how can I calculate the lattice parameter a and the angle (alpha)  ???