Home Thermodynamics of dilute binary solid solutions using the cluster variation method
Article
Licensed
Unlicensed Requires Authentication

Thermodynamics of dilute binary solid solutions using the cluster variation method

  • Bandikatla N. Sarma , Shreyansh N. Shah , Manoj Kumar and Shrikant Lele
Published/Copyright: June 11, 2013
Become an author with De Gruyter Brill
Author Information
International Journal of Materials Research
From the journal International Journal of Materials Research Volume 103 Issue 10

Abstract

A transformation of correlation functions used in the cluster variation method is introduced, such that the transformed correlation functions represent departures of the untransformed correlation functions from their values corresponding to ideal solutions. Analytical solutions for the transformed correlation functions and their derivatives with respect to composition in the infinite dilution limit are obtained for the first time for disordered binary bcc (under irregular tetrahedron approximation), fcc, and cph (both under tetrahedron-octahedron approximation) phases using the framework of the cluster variation method. These results are utilized to obtain the configurational contribution to self-interaction coefficients which occur in the expansion of the logarithm of the activity coefficient.

Keywords: Thermodynamics; Cluster expansion method; Cluster variation method; Dilute solutions
2 Correspondence address: Professor B. Nageswara Sarma, Department of Metallurgical Engineering, Institute of Technology, Banaras Hindu University, Varanasi, 221005, India, Mobile: +919454784898, Fax: +915422369478, E-Mail: ,

Refrences

[1]R.Kikuchi: Phys. Rev.81 (1951) 988. 10.1103/PhysRev.81.988Search in Google Scholar

[2]J.A.Barker: Proc. Roy. Soc. London A216 (1953) 45. 10.1098/rspa.1953.0005Search in Google Scholar

[3]C.M.van Baal: Physica64 (1973) 571. 10.1016/0031-8914(73)90010-4Search in Google Scholar

[4]J.M.Sanchez, D.de Fontaine: Phys. Rev. B17 (1978) 2926. 10.1103/PhysRevB.17.2926Search in Google Scholar

[5]J.M.Sanchez, F.Ducastelle, D.Gratias: Physica A128 (1984) 334. 10.1016/0378-4371(84)90096-7Search in Google Scholar

[6]S.Lele, B.N.Sarma: J. Mater. Sc.44 (2009) 2334. 10.1007/s10853-008-3197-6Search in Google Scholar

[7]T.Mohri, in: W.Pfeiler (Ed.), Alloy Physics, Wiley-VCH, Weinheim (2007) 525. 10.1002/9783527614196.ch10Search in Google Scholar

[8]D.de Fontaine: Solid State Phys.34 (1979) 73. 10.1016/S0081-1947(08)60360-4Search in Google Scholar

[9]D.de Fontaine: Solid State Phys.47 (1994) 33. 10.1016/S0081-1947(08)60639-6Search in Google Scholar

[10]G.Inden, in: G.Kostorz (Ed.), Phase Transformations in Materials, Wiley-VCH, Weinheim (2001) 519.10.1002/352760264XSearch in Google Scholar

[11]C.Colinet: Calphad25 (2001) 607. 10.1016/S0364-5916(02)00011-1Search in Google Scholar

[12]T.Tanaka: Methods of Statistical Physics, Cambridge University Press, Cambridge (2002). 10.1017/CBO9780511755675Search in Google Scholar

[13]R.Kikuchi, C.M.van Baal: Scripta Metall.8 (1974) 425. 10.1016/0036-9748(74)90148-3Search in Google Scholar

[14]R.Kikuchi, H.Sato: Acta Metall.22 (1974) 1099. 10.1016/0001-6160(74)90065-0Search in Google Scholar

[15]N.S.Golosov, A.M.Tolstik: J. Phys. Chem. Solids36 (1975) 899. 10.1016/0022-3697(75)90165-1Search in Google Scholar

[16]N.S.Golosov, A.M.Tolstik: J. Phys. Chem. Solids36 (1975) 903. 10.1016/0022-3697(75)90166-3Search in Google Scholar

[17]N.S.Golosov, A.M.Tolstik: J. Phys. Chem. Solids37 (1976) 273. 10.1016/0022-3697(76)90087-1Search in Google Scholar

[18]H.Ackerman, G.Inden, R.Kikuchi: Acta Metall.37 (1989) 1. 10.1016/0001-6160(89)90259-9Search in Google Scholar

[19]B.N.Sarma, S.Lele: Bull. Mater. Sci.28 (2005) 293. 10.1007/BF02711263Search in Google Scholar

[20]C.H.P.Lupis: Chemical Thermodynamics of Materials, North Holland, Amsterdam (1983).Search in Google Scholar

[21]C.Wagner: Thermodynamics of Alloys, Addison-Wesley, Reading (1962).Search in Google Scholar

[22]J.Chipman, in: J.F. Elliott, T.R. Meadowcroft (Eds.), The Chipman Conference, MIT Press, Cambridge (1965) xvii.Search in Google Scholar

[23]C.H.P.Lupis, J.F.Elliott: Acta Metall.14 (1966) 529. 10.1016/0001-6160(66)90320-8Search in Google Scholar

[24]S.K.Aggarwal, T.Tanaka: Phys. Rev. B16 (1977) 3963. 10.1103/PhysRevB.16.3963Search in Google Scholar

[25]D.Gratias, J.M.Sanchez, D.de Fontaine: Physica A113 (1982) 315. 10.1016/0378-4371(82)90023-1Search in Google Scholar

[26]M.Asta, R.McCormack, D.de Fontaine: Phys. Rev. B48 (1993) 748. 10.1103/PhysRevB.48.748Search in Google Scholar

[27]R.McCormack, M.Asta, D.de Fontaine, G.Garbulsky, G.Ceder: Phys. Rev. B48 (1993) 6767. 10.1103/PhysRevB.48.6767Search in Google Scholar

[28]A.F.Kohan, P.D.Tepesch, G.Ceder, C.Wolverton: Comp. Mater. Sci.9 (1998) 389. 10.1016/S0927-0256(97)00168-7Search in Google Scholar

[29]G.S.Gupta, G.Vamsi Madhav, A.Pandey, B.N.Sarma, S.Lele: Bull. Mater. Sci.28 (2005) 173. 10.1007/BF02704237Search in Google Scholar

[30]H.Lukas, S.G.Fries, B.Sundman: Computational Thermodynamics: The CALPHAD Method, Cambridge University Press, Cambridge (2007). 10.1017/CBO9780511804137Search in Google Scholar

[31]G.S.Gupta: Estimation of Energy Parameters for Optimization using Cluster Variation Method, Ph. D. Thesis, Banaras Hindu University, Varanasi, India (2008).Search in Google Scholar

[32]B.Fultz: Prog. Mater. Sci.55 (2010) 247. 10.1016/j.pmatsci.2009.05.002Search in Google Scholar

[33]P.Cenedese, J.W.Cahn: Prog. Theor. Phys. Suppl.115 (1994) 95.Search in Google Scholar

Received: 2010-10-13
Accepted: 2012-2-6
Published Online: 2013-06-11
Published in Print: 2012-10-01

© 2012, Carl Hanser Verlag, Munich

Articles in the same Issue

  1. Contents
  2. Contents
  3. Original Contributions
  4. Phase equilibria in the Gd–Ni binary and Mg–Ni–Gd ternary systems
  5. Thermodynamics of dilute binary solid solutions using the cluster variation method
  6. Thermal stability of coherent Pd/TiAl interfaces studied from first-principles calculations and experiments
  7. Electropulsing-induced phase transformations and their effects on the single point diamond turning of a tempered alloy AZ91
  8. Study of the mechanism of ductile-regime grinding of SiCp/Al composites using finite element simulation
  9. Investigations on laser welding of magnesium alloys
  10. Investigation of the surface of a laser-treated cast iron cylinder bore
  11. Solidification behaviour of an AA5754 Al alloy ingot cast with high impurity content
  12. Study of the structural evolution of crystalline zinc oxide films prepared by PLD
  13. Effects of sintering temperature on pore characterization and strength of porous cordierite–mullite ceramics by a pore-forming in-situ technique
  14. Sol–gel synthesis of Eu3+, Tb3+ co-doped Y2O3 scintillating nanopowders
  15. Morphological study of SiC coating developed on 2D carbon composites using MTS precursor in a hot-wall vertical reactor
  16. Self-assembling behavior and corrosion inhibition properties of TDPA films on differently structured surfaces of 2024 and 1060 aluminum alloys
  17. Photocatalytic activity of MnWO4 powder in highly effective hydrogen generation from H2O and H2O2
  18. Rheology and microstructure of polymer-modified asphalt nanocomposites
  19. Short Communications
  20. Microstructure and phase composition in a die cast Mg–Nd alloy containing Zn and Zr
  21. DGM News
  22. DGM News
https://doi.org/10.3139/146.110755
Keywords for this article
Thermodynamics; Cluster expansion method; Cluster variation method; Dilute solutions

Articles in the same Issue

  1. Contents
  2. Contents
  3. Original Contributions
  4. Phase equilibria in the Gd–Ni binary and Mg–Ni–Gd ternary systems
  5. Thermodynamics of dilute binary solid solutions using the cluster variation method
  6. Thermal stability of coherent Pd/TiAl interfaces studied from first-principles calculations and experiments
  7. Electropulsing-induced phase transformations and their effects on the single point diamond turning of a tempered alloy AZ91
  8. Study of the mechanism of ductile-regime grinding of SiCp/Al composites using finite element simulation
  9. Investigations on laser welding of magnesium alloys
  10. Investigation of the surface of a laser-treated cast iron cylinder bore
  11. Solidification behaviour of an AA5754 Al alloy ingot cast with high impurity content
  12. Study of the structural evolution of crystalline zinc oxide films prepared by PLD
  13. Effects of sintering temperature on pore characterization and strength of porous cordierite–mullite ceramics by a pore-forming in-situ technique
  14. Sol–gel synthesis of Eu3+, Tb3+ co-doped Y2O3 scintillating nanopowders
  15. Morphological study of SiC coating developed on 2D carbon composites using MTS precursor in a hot-wall vertical reactor
  16. Self-assembling behavior and corrosion inhibition properties of TDPA films on differently structured surfaces of 2024 and 1060 aluminum alloys
  17. Photocatalytic activity of MnWO4 powder in highly effective hydrogen generation from H2O and H2O2
  18. Rheology and microstructure of polymer-modified asphalt nanocomposites
  19. Short Communications
  20. Microstructure and phase composition in a die cast Mg–Nd alloy containing Zn and Zr
  21. DGM News
  22. DGM News
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 16.11.2025 from https://www.degruyterbrill.com/document/doi/10.3139/146.110755/pdf
Scroll to top button