Metallurgical and Materials Transactions A

, Volume 37, Issue 12, pp 3403–3409 | Cite as

Thermodynamic properties and phase diagram by the statistical moment and cluster variation methods: Application to pure metals and Ta-W alloys

  • K. Masuda-Jindo
  • Vu Van Hung
  • P. E. A. Turchi


The thermodynamic quantities of metals and alloys are studied using the moment method in the quantum statistical mechanics, going beyond the quasi-harmonic (QH) approximations. Including the power moments of the atomic displacements up to the fourth order, the free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The configurational entropy term is taken into account by coupling the moment expansion scheme with the cluster variation method (CVM). The energetics of the binary (TaW) alloys are treated within the framework of the first-principles tight-binding linear muffin-tin orbital (TB-LMTO) method coupled to the coherent potential approximation (CPA) and generalized perturbation method (GPM). The equilibrium phase diagrams are calculated for the refractory Ta-W bcc alloys.


Material Transaction Thermodynamic Quantity Atomic Displacement Linear Thermal Expansion Equilibrium Phase Diagram 


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Copyright information

© ASM International & TMS-The Minerals Metals and Materials Society 2006

Authors and Affiliations

  • K. Masuda-Jindo
    • 1
  • Vu Van Hung
    • 2
  • P. E. A. Turchi
    • 3
  1. 1.Department of Materials Science and EngineeringTokyo Institute of TechnologyYokohamaJapan
  2. 2.Department of PhysicsHanoi National Pedagogic UniversityHanoiVietnam
  3. 3.Lawrence Livermore National LaboratoryLivermore

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