An Analytical Self-consistent Solution for the Free Energy of a 1-D Chain of Atoms Including Anharmonic Effects

Journal of Statistical Physics

Volumn 148, Issue 5, 2012, Pages 951-971

  Kim, Woo Kyun ^a   Tadmor, Ellad B ^a  

^a University of Minnesota   (United States)

Author keywords

Anharmonic effects; Free energy; Lattice dynamics; One dimensional chain; Self consistent method; Statistical mechanics

Indexed keywords

EID: 84866444151     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-012-0559-x     Document Type: Article

References (19)

1. Agrawal, P., Rice, B., Thompson, D.: Predicting trends in rate parameters for self-diffusion on fcc metal surfaces. Surf. Sci. 515(1), 21-35 (2002).
2. Basile, G., Delfini, L., Lepri, S., Livi, R., Olla, S., Politi, A.: Anomalous transport and relaxation in classical one-dimensional models. Eur. Phys. J. Spec. Top. 151, 85-93 (2007).
3. Blanc, X., Bris, C. L., Legoll, F., Patz, C.: Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches. J. Nonlinear Sci. 20, 241-275 (2010).
4. Bonetto, F., Lebowitz, J., Lukkarinen, J.: Fourier's law for a harmonic crystal with self-consistent stochastic reservoirs. J. Stat. Phys. 116(1-4), 783-813 (2004).
5. Bonetto, F., Lebowitz, J. L., Lukkarinen, J., Olla, S.: Heat conduction and entropy production in anharmonic crystals with self-consistent stochastic reservoirs. J. Stat. Phys. 134(5-6), 1097-1119 (2009).
6. Guthikonda, V. S.: Thermodynamic modeling of martensitic phase transformations in shape memory alloys. Ph. D. thesis, University of Minnesota (2010).
7. Guthikonda, V. S., Elliott, R. S.: Modeling martensitic phase transformation in shape memory alloys with the self-consistent lattice dynamics approach. J. Mech. Phys. Solids (2012, submitted for publication).
8. Iacobucci, A., Legoll, F., Olla, S., Stoltz, G.: Thermal conductivity of the Toda lattice with conservative noise. J. Stat. Phys. 140(2), 336-348 (2010).
9. Leibfried, G., Ludwig, W.: Theory of anharmonic effects in crystals. In: Seitz, F., Turnbull, D. (eds.) Solid State Physics: Advances in Research and Applications, vol. 12, pp. 275-459. Academic Press, New York (1961).
10. Martyna, G. J., Klein, M. L., Tuckerman, M.: Nosé-Hoover chains: the canonical ensemble via continuous dynamics. J. Chem. Phys. 97, 2635-2643 (1992).
11. Monga, M. R., Jindal, V. K.: Free energy of an anharmonic linear lattice. Phys. Rev. B 11(4), 1718-1720 (1975).
12. Sethna, J. P.: Statistical Mechanics: Entropy, Order Parameters, and Complexity. Oxford University Press, Oxford (2006).
13. 4). IV. Thermodynamic properties of Kr and Xe for the Lennard-Jones, Morse, and Rydberg potentials. Phys. Rev. B 32(4), 2513-2521 (1985).
14. Tadmor, E. B., Miller, R. E.: Modeling Materials: Continuum, Atomistic and Multiscale Techniques. Cambridge University Press, Cambridge (2011).
15. Vlachos, K., Papatheou, V., Okopińska, A.: Perturbation and variational-perturbation method for the free energy of anharmonic oscillators. Can. J. Phys. 85, 13-30 (2007).
16. Wallace, D. C.: Thermodynamics of Crystals. Dover, Mineola (1972).
17. Yemélé, D., Kofané, T. C.: Temperature dependence of first lattice corrections to the free-energy of kink compacton-bearing systems. J. Phys. Condens. Matter 17, 1747-1762 (2005).
18. Zubov, V.: Unsymmetrized self-consistent field approximation for a crystal. 1. Linear-chain. Phys. Status Solidi (b) 72(1), 71-75 (1975).
19. Zubov, V.: Higher anharmonicities in improved unsymmetrized self-consistent field approximation for a crystal. 1. General consideration. Phys. Status Solidi (b) 87(1), 385-394 (1978).