The volume as a variable in the Cluster Variation Method.

Author(s)

Luiz Tadeu Fernandes Eleno

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Escola Politécnica (EP/BC)
• Defense date: 2003-08-19

Examining board members

Claudio Geraldo Schon; Tania Tome Martins de Castro; Helio Goldenstein

• Advisor: Claudio Geraldo Schon

Abstract

The Cluster Variation Method (CVM), used in thermodynamical calculations, is based in the mean-field approximation to the free energy. The CVM was originally devised to treat configurational-only cases. The scope of the present work is to enhance the method's capabilities, introducing other free energy components. The volumetric contributions, either dilatacional or vibrational, are believed to be of great importance, and are therefore incorporated here in the method. Another aim is to verify whether this approach would solve the temperature range calculated with CVM using ab initio data. In this kind of calculation, the phase diagram temperature range is usually twice or three times as large as experimentally verified or, equivalently, as the ones obtained in CVM calculations using experimental data. Therefore, a new minimisation algorithm was proposed to handle with the vibrational effects and the volume as a variable. The algorithm is based on the NIM (Natural Iteration Method), which is used for the minimization in the configurational case. The Debye-Grüneisen approximation has been adapted, with elastical considerations, for multicomponent systems (i.e., alloys). The method is based on Anderson model, when ab initio elastic constants are available, or on Moruzzi-Janak-Schwarz model otherwise. In ab initio calculations it is possible to determine the elastic constants for each structure considered. Using these data, Debye temperature and bulk modulus at 0K are determined with greater accuracy. First-principles cohesion/formation energies in function of volume for the b.c.c. Fe-Al (body-centered cubic iron-aluminum) system were used as an example to derive parameters to the model. (AU)