Comparison of Monte Carlo and anharmonic-lattice-dynamics results for the thermodynamic properties and atomic mean-square displacement of Xe using the Morse potential

R. C. Shukla, S. K. Bose, and R. F. Delogu
Phys. Rev. B 45, 12812 – Published 1 June 1992
PDFExport Citation

Abstract

Monte Carlo (MC) and anharmonic-lattice-dynamics [the λ2 and λ4 perturbation-theory (PT)] calculations of the thermodynamic properties of Xe are presented for the temperature range 60–160 K using a nearest-neighbor central-force (NNCF) model of the fcc crystal with atoms interacting via a Morse potential. In particular, we calculate the equilibrium lattice parameter at zero pressure and the corresponding specific heats at constant volume and at constant pressure, volume expansivity, adiabatic and isothermal bulk moduli, and Gru¨neisen parameter. We also calculate the atomic mean-square displacement (MSD) from the MC method and the lowest-order (λ2) PT for the same NNCF model and the Morse potential. For the thermodynamic properties, the MC results are found to agree more closely with the λ2 PT than the λ4 PT results. Similarly the MSD results from the MC method agree quite well with those from the λ2 theory. This may be due to the fact that the exact solution of the Schro¨dinger equation for the vibrational states of the Morse potential for a one-dimensional or an isotropic three-dimensional model agrees exactly with the λ2 PT. We show that this is indeed true by evaluating the λ2 and λ4 contributions to vibrational energy for the above model of the Morse potential and showing that all the λ4 contributions add up to zero and that the total λ2 contribution is in agreement with the solution of the Schro¨dinger equation.

  • Received 9 September 1991

DOI:https://doi.org/10.1103/PhysRevB.45.12812

©1992 American Physical Society

Authors & Affiliations

R. C. Shukla, S. K. Bose, and R. F. Delogu

  • Physics Department, Brock University, St. Catharines, Ontario, Canada L2S 3A1

References (Subscription Required)

Click to Expand
Issue

Vol. 45, Iss. 22 — 1 June 1992

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×