# [Pw_forum] Inconsistencies in the CELL_PARAMETERS - ibrav=5

Stefano de Gironcoli degironc at sissa.it
Thu Dec 23 19:49:13 CET 2010

```if you are interested in comparing with the definition of in INPUT.PW
you should apply the definition in INPUT.PW...
which is not the one you are using.
There is a value of "a" missing in your definition.

stefano

Marino Vetuschi Zuccolini wrote:
> stefano,
> thanks but can you explain a little bit more exhaustively, because I do not understand. It seems that tx and ty and the cos(alpha) derived from them are numerically exact and I suppose the algorithm are right.
>
> ...
>        v_1=sqrt(at(1,1)**2+at(2,1)**2+at(3,1)**2)
>        cell_edge=alat*v_1
>        c_tx=(1-2*(at(1,1))**2)
>        c_ty=(-6*at(2,1)**2)+1
>        c_tz=((3*at(3,1)**2-1)/(2))
> ....
>
>        tx=sqrt((1-c)/2)
>        ty=sqrt((1-c)/6)
>        tz=sqrt((1+2*c)/3)
> ...
>
> m.
>
>
> On 23 Dec 2010, at 17:28, Stefano de Gironcoli wrote:
>
>
>> Dear  Marino Vetuschi Zuccolini wrote:
>>
>>> trigonal(r)
>>>                   ===================
>>>                   for these groups, the z-axis is chosen as the 3-fold axis, but the
>>>                   crystallographic vectors form a three-fold star around the z-axis,
>>>                   and the primitive cell is a simple rhombohedron. The crystallographic
>>>                   vectors are:
>>>                         v1 = a(tx,-ty,tz),   v2 = a(0,2ty,tz),   v3 = a(-tx,-ty,tz).
>>>                   where c=cos(alpha) is the cosine of the angle alpha between any pair
>>>                   of crystallographic vectors, tc, ty, tz are defined as
>>>                        tx=sqrt((1-c)/2), ty=sqrt((1-c)/6), tz=sqrt((1+2c)/3)
>>>
>>>
>> in order to extract c you are forgetting to divide v1 by a=|v1|.
>>
>> stefano
>>
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>
>
>
> *******************************************************
> Marino Vetuschi Zuccolini
> zucco at dipteris.unige.it
> Researcher / Geochemist
> Laboratory of Geochemistry
>
> DIPartimento per lo studio della TErra e delle sue RISorse - Università  di Genova
> Tel. ++39 010 3538136 Fax. ++39 010 352169
> Corso Europa 26, 16132 - Genova - Italy
>
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```