[Wien] specific heat factor

[Peter Blaha]

> Seems like I am to blame here:

and I'm to be blamed for my ignorance of your questions. Since I trusted Georg
completely, I just tried to "explain" these factors and overlooked a
13.6/2 factor

I've now put the following (hopefully more readable):

            fermDEN(ind)=fermDEN(ind)*(pi**2)/3.d0*(6.3336303d-6)**2*6.0221d23*13.6058d0*1.60219d-19*1000.d0

and this gives for fcc Cu: 0.72 mJ/K^2/mol; which is hopefully ok.

An updated version is also on the web.

Thank's for the questions and for "persisting" that there is an error,
even when we think, everything is ok.

>
> Checking it I guess the line should read
> gamma=N(E_F)*(6.333D-6)**2*pi**2/3.d0*2.6255D3/2.d0
> where N(E_F) is in 1/(Ry uc)
> k_b=6.333D-6 Ry/K
> and 2.6255D3/2.d0 is the conversion factor between Ry and kJ/mol. The result
> will then be in kJ/(mol K**2) and 1 mol refeers to one mol of primitive unit
> cells. If spin polarized it is also pr. spin like N(E_F) is.
>
> This is what comes from putting something in and never applying it. Sorry.
> Best wishes
>   Georg
>
> Quoting Ruben Weht <ruweht at cnea.gov.ar>:
>
> > Dear Peter,
> >
> > I think Jan is right and there is an error in the gamma formula.
> >
> > I think Gamma is  (1/3).pi^2.kb^2.Na
> >
> > where kb is the Bolztmann constant and Na Avogadro's number.
> >
> > As Gamma is in general in units of  mJ/k^2.mol
> > and density of states in   states/Ry
> > you can take one kb in each energy unit.
> >
> > In this way   kb = 1.3806503.10^-20  mJ/K
> > and           kb = 6.3336303.10^-6   Ry/K
> >               Na = 6.0221.10^23      1/mol
> >
> > So   Gamma = 0.17324706  mJ.Ry/K^2/mol
> >
> > I hope it helps,
> > Best,
> >
> >    Ruben
> >
> > >> There is the electronic specific heat C_v/T, which is for
> > >> non-interacting electrons propotional to the density of states
> > >> at Fermi level, printed out in the output of tetra. I find the
> > >> convesion factor from N(E_F) in 1/Ry to gamma in mJ/(K^2 mol)
> > >> strange:
> > >>
> > >> gamma=N(E_F)/2.d0*(8.617D-5)
> > **2*pi**2)/3.d0*2.6255D6/27.212d0*1000.d0
> > >>
> > >> does anybody know where the 2.6255D6 comes from? By the way
> > >> conversion factor I normally use is
> > >> gamma[mJ/K^2/mol]=0.173*N(E_F)[1/Ry] (quite different from wien
> > >> value).
> > >
> > > Well, Georg seems to have programmed a "secret" here.
> > >
> > > To my understanding the conversions require k_B, Avogadros number
> > > and E-conversions into J
> > >
> > > 2.6255D6:  This factor arises from two (or actually 3) numbers:
> > > Avogadros number (6.022 10^23 /mol)
> > > the energy conversion from "atomic units" to Joule, which is
> > >
> > > 27.212 * 1.60219 10^-19    (first converts hartree into eV, than
> > > eV into J)
> > >
> > > PS: The (8.617D-5)**2 is k_B in (eV/K)^2   and this leads to this
> > > additionl factor of 1/27.212 ....
> > >
> > > And somewhere are hidden the factors of 2 from Ry to hartree....
> > >
> > > Hope it fits like this. Just check it on a simple case (Cu or
> > > so), where the gamma0 is well known.
> > >
> > >                                       P.Blaha
> > > -------------------------------------------------------------------
> > -------
> > > Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060
> > > Vienna Phone: +43-1-58801-15671             FAX:
> > > +43-1-58801-15698
> > > Email: blaha at theochem.tuwien.ac.at    WWW:
> > > http://info.tuwien.ac.at/theochem/
> > > -------------------------------------------------------------------
> > -------
> > >
> > > _______________________________________________
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> >
> >
> > --
> > *===============================================*
> > |  Ruben Weht                                   |
> > |  Departmento de Fisica - CNEA                 |
> > |  Avda. General Paz y Constituyentes           |
> > |  1650 - San Martin - ARGENTINA                |
> > |  Email:  ruweht at cnea.gov.ar                   |
> > |  Tel: (54-11) 6772-7104                       |
> > |  Fax: (54-11) 6772-7121                       |
> > *===============================================*
> >
> >
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>
>
> --
> Georg Madsen
> Department of Chemistry
> Aarhus University
> DK-8000 Århus C
> Denmark
> tlf (+45) 89423885
>
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                                      P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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