Thermodynamics of the System Ag 2 se-Ag 2 s: A Molecular Dynamics Study
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Recent experimental studies of these systems and its solid solutions have reported a decrease in the transition temperature from non-conducting (a-phase) to superconducting (/3- phase) phase as a function of substitutional concentration of Se in Ag 2S and of S in Ag 2Se [5]. This reduction in the transition temperature with concentration is accompanied by a reduction in the a - /3 entropy difference. In order to understand the fundamental mechanisms involved in the observed changes in entropy and transition temperature in these systems, we have undergone a series of Molecular Dynamics studies of Ag 2S and Ag 2 Se and have calculated free energies and vibrational entropies in these systems as function of temperature. The obtained entropy, enthalpy and volumetric differences between a - /3 phases agree quite well with experimental values. We will discuss the methods employed in calculating free energies and entropies and discuss the nature of the differences in these quantities in terms of lattice structures and ion mobilities. SIMULATION The Molecular Dynamics (MD) calculations were carried out at both NVT (constant volume, constant temperature, and fixed number of particles) and NPT (constant pressure, constant
531 Mat. Res. Soc. Symp. Proc. Vol. 398 01996 Materials Research Society
temperature, and fixed number of particles) ensembles over temperatures between 50K and 800K. The Ag 2 Se simulations were comprised of 1344 particles while for Ag2 S we used 1744 particles. The low temperature structures [1,2] were created and checked via energy minimization using steepest-decent and simulating annealing. The radial pair distribution functions were calculated and compared with X-ray diffraction data. The simulations are based on an effective interparticle potential having the same functional form for Ag 2Se and Ag 2 S [3,6]. They are comprised of three terms: coulomb interaction, steric repulsion, and a charge-dipole interaction due to the large polarizability of Se-- and S-- ions. The functional form of the potentials can be written as follows -
r
exp (--r/r4,) + Aij
+
2
i
}
(1+
In the simulations, the coulomb term is handled using a standard ewald summation. All other terms were tabulated and truncated at a radius rcut = 12 Angstroms. This value gave a residue in the potential energy of less than 10-6 eV than the uncut values. The systems used were prepared by thermalizing samples using constant pressure MD from 50K to 600K in steps of 1OOK. The structures were checked by monitoring the radial pair distribution function, rms displacement, internal energy as well as volumetric changes. The free energy and entropy as a function of temperature were calculated employing two methods: a) internal energy integration and b) adiabatic switching in a MD framework [7]-[9]. Using internal energy integration, the free energy as a function of temperature can be computed if the free energy at a particular temperature is known provided the integration path is reversible: A(T)
A(To)
T
TO
TEJdT
(2)
T,ToI
The value of
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