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 (bibtex)

by Aistis Jaznusko

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 Grüneisen 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.

Reference:

Aistis Jaznusko, "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", Master's thesis, Brock University, 2014.

Bibtex Entry:

@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} }

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