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

GAO Zhe flux_ray12 at 163.com
Thu Nov 17 11:34:40 CET 2011

```Yes, that is my mistake. The denominator should be (|a| |b|).
Furthermore, I just wanted to say A as the angle between vector a and b~~~ Definitely, in rhombohedral structure, alpha = beta = gamma~

--
GAO Zhe
CMC Lab, MSE, SNU, Seoul, S.Korea

At 2011-11-17 18:15:17,"Gabriele Sclauzero" <gabriele.sclauzero at epfl.ch> wrote:
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
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

can u please explain me

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

Regards
Yedukondalu

--

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