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

Huiqun Zhou hqzhou at nju.edu.cn
Thu Nov 17 06:49:25 CET 2011

```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
To: PWSCF Forum
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

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

Regards
Yedukondalu

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