[Pw_forum] Fiorentini-Methefessel: Surface energy

[Ari P Seitsonen]

Dear Elliot,

   I am not sure if I understood correctly your description, but basically: 
You plot the energy per layer as a function of the inverse of number of 
layers, so starting from the definition

E_surf = [ E_slab(N) - N * E_bulk ] / ( 2 A ) ,

where

   Esurf = surface energy per unit area A - sometimes one plots the surface 
energy per unit cell; 2 because the slab has two surfaces,

   E_slab(N) = total energy of the slab of N layers

   E_bulk = the "unknown" bulk energy

Rewriting à la Fiorentini et Methfessel,

     E_slab(N)/N = 2A (1/N) E_surf + E_bulk

which is equivalent of an equation

     y = 2A E_surf x + E_bulk ^= a x + b

where E_surf and E_bulk are the unknowns, obtained from the fit. So how do 
you find E_bulk from this equation (hint: What happens when N -> 
infinity?)? And what does the slope yield?

     Greetings from Paris,

        apsi

-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-
   Ari Paavo Seitsonen / Ari.P.Seitsonen at iki.fi / http://www.iki.fi/~apsi/
     Ecole Normale Supérieure (ENS), Département de Chimie, Paris
     Mobile (F) : +33 789 37 24 25    (CH) : +41 79 71 90 935


On Fri, 25 Mar 2016, Elliot S. MENKAH wrote:

> 
> Hello Everyone,
> 
> In reference to the papers Extracting convergent surface energies from slab calculations, 1996, and Surface e
> nergies, work functions, and surface relaxations of low index metallic surfaces from first-principles, 2009,
>  I'm trying to compute surface energies with the Fiorentini-Methefessel technique. 
> 
> I'm extracting the bulk energy from a linear plot of total energy vrs N.
> 
> I computed the total energies of nickel surface (100) with 12, 14, 16,
> 18 and 20 atomic layers.
> 
> I made a plot of total energies vrs N(Number of layers) and i got the
> equation  y = 0.24897 - 171.79x
> 
> With the slope being -171.79, am I right to say the bulk energy is
> -171.79Ry?
> 
> Is this the right way of going about the Fiorentini-Methfessel technique?
> 
> Can someone please point me in the right direction
> 
> Thank you.
> 
> Kind Regards,
> 
> Elliot.
> 
> -- 
> Elliot Sarpong Menkah
> Graduate Student - Computational Chemistry / Computational Material Science.
> Theoretical and Computational Chemistry
> Dept. of Chemistry
> Kwame Nkrumah University of Science and Technology (KNUST),
> Private Mail Bag,
> Kumasi,
> Ghana.
> Mobile:+233-243-055-717,+233-202-929-058
> 
> 
> Alt. Email: 	esmenkah at knust.edu.gh
> 		elliotsmenkah at gmail.com
>                 elliotsmenkah at hotmail.com
> 
> webpage: http://chemistry.knust.edu.gh/MMC/group-members/ESMenkah
> 
>