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Merge pull request #2433 from athomps/eamfs-doc 

Clarified order of rho_alpha_beta density functions
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Axel Kohlmeyer 2020-10-20 20:13:35 -04:00 committed by GitHub
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doc/src/pair_eam.rst
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@ -345,8 +345,11 @@ given by
\rho_{\alpha\beta} (r_{ij})\right) +
\frac{1}{2} \sum_{j \neq i} \phi_{\alpha\beta} (r_{ij})
where :math:`\rho_{\alpha\beta}` refers to the density contributed
by a neighbor atom J of element :math:`\beta` at the site of atom I
of element :math:`\alpha`.
This has the same form as the EAM formula above, except that rho is
now a functional specific to the atomic types of both atoms I and J,
now a functional specific to the elements of both atoms I and J,
so that different elements can contribute differently to the total
electron density at an atomic site depending on the identity of the
element at that atomic site.
@ -393,20 +396,20 @@ have an ".eam.fs" suffix. They are formatted as follows:
The 5-line header section is identical to an EAM *setfl* file.
Following the header are Nelements sections, one for each element I,
Following the header are Nelements sections, one for each element :math:`\beta`,
each with the following format:
* line 1 = atomic number, mass, lattice constant, lattice type (e.g. FCC)
* embedding function F(rho) (Nrho values)
* density function rho(r) for element I at element 1 (Nr values)
* density function rho(r) for element I at element 2
* density function :math:`\rho_{1\beta} (r)` for element :math:`\beta` at element 1 (Nr values)
* density function :math:`\rho_{2\beta} (r)` for element :math:`\beta` at element 2
* ...
* density function rho(r) for element I at element Nelement
* density function :math:`\rho_{N_{elem}\beta} (r)` for element :math:`\beta` at element :math:`N_{elem}`
The units of these quantities in line 1 are the same as for *setfl*
files. Note that the rho(r) arrays in Finnis/Sinclair can be
asymmetric (i,j != j,i) so there are Nelements\^2 of them listed in the
file.
asymmetric (:math:`\rho_{\alpha\beta} (r) \neq \rho_{\beta\alpha} (r)` )
so there are Nelements\^2 of them listed in the file.
Following the Nelements sections, Nr values for each pair potential
phi(r) array are listed in the same manner (r\*phi, units of