@mastersthesis{2014-Jaznusko,
  author={Aistis Jaznusko},
  title={Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen model},
  year={2014},
  abstract={Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately 
as the presence of the electron gas renders the total energy strongly dependent
on the electron density. The embedded atom method (EAM) addresses this issue by
expressing the total energy as a sum of pair-potentials and an explicitly density-
dependent term called the embedding function to simulate the band energy or the
energy of embedding an atom/ion in an electron gas of a given density. Finnis and
Sinclair proposed a model where the embedding function is taken to be proportional
to the square root of the electron density. This is based on the idea that the band en-
ergy is proportional to the band width which is the square root of the second moment
of the electron density of states. Models of this type are known as Finnis-Sinclair
many body potentials.

In this work we study a particular parametrization of the Finnis-Sinclair type
potential, called the ”Sutton-Chen” model, and a later version, called the ”Quantum
Sutton-Chen” model, to study the phonon spectra and the temperature variation
thermodynamic properties of fcc metals. Both models give poor results for thermal
expansion, which can be traced to rapid softening of transverse phonon frequencies
with increasing lattice parameter. We identify the power law decay of the electron
density with distance assumed by the model as the main cause of this behaviour and
show that an exponentially decaying form of charge density improves the results significantly. 
Results for Sutton-Chen and our improved version of Sutton-Chen models
are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are
the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic
and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen
parameter. For the sake of comparison we have also considered two other models
where the distance-dependence of the charge density is an exponential multiplied by
polynomials. None of these models exhibits the instability against thermal expansion
(premature melting) as shown by the Sutton-Chen model.

We also present results obtained via pure pair potential models, in order to identify
advantages and disadvantages of methods used to obtain the parameters of these
potentials.},
school={Brock University}
}