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Theoretical investigation of phase equilibria by the continuous displacement cluster variation method

Published/Copyright: June 11, 2013
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International Journal of Materials Research
From the journal International Journal of Materials Research Volume 100 Issue 3

Abstract

By employing the continuous displacement cluster variation method, order – disorder transition behavior of a two-dimensional square lattice is investigated. It is demonstrated that the distribution of displaced atoms around a Bravais lattice point continuously changes with temperature. The additional freedom of atomic displacement contributes to the entropy and thermal lattice expansion is confirmed. Finally, it is shown that the order – disorder transition temperature decreases as compared with the one by the conventional cluster variation method in which no local atomic displacements are allowed.

Keywords: Continuous displacement cluster variation method; Lattice relaxation; Thermal expansion; Two-dimensional square lattice
* Correspondence address, Professor Tetsuo Mohri, Division of Materials Science and Engineering, Graduate School of Engineering, Hokkaido University, Kita-13 Nishi-8, Kita-ku, Sapporo 060-8628, Japan, Tel.: +81 11 706 6348, Fax: +81 11 706 6348, E-mail:

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Received: 2008-8-25
Accepted: 2008-12-18
Published Online: 2013-06-11
Published in Print: 2009-03-01

© 2009, Carl Hanser Verlag, München

Articles in the same Issue

  1. Contents
  2. Contents
  3. Editorial
  4. 11th ISPMA in Prague
  5. Feature
  6. Physical aspects of plastic deformation in Mg–Al alloys with Sr and Ca
  7. Review
  8. Fe–Al materials for structural applications at high temperatures: Current research at MPIE
  9. Basic
  10. Very high cycle fatigue behaviour of as-extruded AZ31, AZ80, and ZK60 magnesium alloys
  11. Phase composition and morphology development in WE-type alloys modified by high Zn content
  12. Microstructural investigation of the failure mechanisms after creep exposure of Mg–Y–Nd–Zn–Mn alloy
  13. Theoretical investigation of phase equilibria by the continuous displacement cluster variation method
  14. Alloying behaviour of binary transition metal systems
  15. Surface composition of a Ag-5.1Cu (mass%) alloy
  16. Temperature and strain rate dependent flow criterion for bcc transition metals based on atomistic analysis of dislocation glide
  17. Strain-hardening behaviour of AZ31 magnesium alloys
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  19. Core structure of screw dislocations in hcp Ti: an ab initio DFT study
  20. Long-range internal stresses in monotonically and cyclically deformed metallic single crystals
  21. Energetic formulation of nonlocal crystal plasticity
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  23. Mechanical anisotropy and ideal strength in a multifunctional Ti–Nb–Ta–Zr–O alloy (Gum Metal)
  24. Low-cycle fatigue properties of TiAl alloy with high Nb content
  25. Mechanism and kinetics of the intermediary phase formation in Ti–Al and Ti–Al–Si systems during reactive sintering
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  29. Influence of titanium volume fraction on the mechanical properties of Mg–Ti composites
  30. Applied
  31. Effects of prior homogenization treatments on microstructure development and mechanical properties of the extruded wrought magnesium alloy ZK60
  32. Annealing effects after various thermo-mechanical treatments on microstructure and mechanical properties of the wrought magnesium alloy AZ80
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  37. High-rate plastic deformation of a copper single crystal under loading by spherical converging shock waves
  38. Hardening and softening in an Mg–Al–Ca matrix alloy reinforced with short graphite fibres
  39. Deformation behaviour of microcrystalline magnesium reinforced by alumina nano- and microparticles
  40. Thresholds in creep of magnesium alloy AX41 composites reinforced with short fibers
  41. Recovery processes in magnesium alloy AX41 and AX41-12 vol.% C-fibre composite studied by dilatometry
  42. Directional crystallisation of Ti–Al–Si in-situ composites
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https://doi.org/10.3139/146.110030
Keywords for this article
Continuous displacement cluster variation method; Lattice relaxation; Thermal expansion; Two-dimensional square lattice

Articles in the same Issue

  1. Contents
  2. Contents
  3. Editorial
  4. 11th ISPMA in Prague
  5. Feature
  6. Physical aspects of plastic deformation in Mg–Al alloys with Sr and Ca
  7. Review
  8. Fe–Al materials for structural applications at high temperatures: Current research at MPIE
  9. Basic
  10. Very high cycle fatigue behaviour of as-extruded AZ31, AZ80, and ZK60 magnesium alloys
  11. Phase composition and morphology development in WE-type alloys modified by high Zn content
  12. Microstructural investigation of the failure mechanisms after creep exposure of Mg–Y–Nd–Zn–Mn alloy
  13. Theoretical investigation of phase equilibria by the continuous displacement cluster variation method
  14. Alloying behaviour of binary transition metal systems
  15. Surface composition of a Ag-5.1Cu (mass%) alloy
  16. Temperature and strain rate dependent flow criterion for bcc transition metals based on atomistic analysis of dislocation glide
  17. Strain-hardening behaviour of AZ31 magnesium alloys
  18. Bauschinger effect in thin metal films simulated by the continuum dislocation-based model
  19. Core structure of screw dislocations in hcp Ti: an ab initio DFT study
  20. Long-range internal stresses in monotonically and cyclically deformed metallic single crystals
  21. Energetic formulation of nonlocal crystal plasticity
  22. Austenite–martensite interfaces in strained foils of CuAlNi alloy
  23. Mechanical anisotropy and ideal strength in a multifunctional Ti–Nb–Ta–Zr–O alloy (Gum Metal)
  24. Low-cycle fatigue properties of TiAl alloy with high Nb content
  25. Mechanism and kinetics of the intermediary phase formation in Ti–Al and Ti–Al–Si systems during reactive sintering
  26. Influence of the dynamic crystallization conditions on the martensitic transformation in the Ti40.7Hf9.5Ni39.8Cu10 shape memory alloy
  27. Isostructural phase transition in hexagonal Ce1–xYxPdAl compounds
  28. Structural and phase transformations in Zr and Zr–Nb alloys under loading by spherical converging stress waves
  29. Influence of titanium volume fraction on the mechanical properties of Mg–Ti composites
  30. Applied
  31. Effects of prior homogenization treatments on microstructure development and mechanical properties of the extruded wrought magnesium alloy ZK60
  32. Annealing effects after various thermo-mechanical treatments on microstructure and mechanical properties of the wrought magnesium alloy AZ80
  33. Vacancy–solute interaction in magnesium alloy WE54 during artificial ageing: a positron annihilation spectroscopy study
  34. FeAl-based alloys cast in an ultrasound field
  35. High-temperature mechanical properties of Fe-40 at.% Al based intermetallic alloys with C or Ti addition
  36. The influence of dispersoids on the recrystallization of aluminium alloys
  37. High-rate plastic deformation of a copper single crystal under loading by spherical converging shock waves
  38. Hardening and softening in an Mg–Al–Ca matrix alloy reinforced with short graphite fibres
  39. Deformation behaviour of microcrystalline magnesium reinforced by alumina nano- and microparticles
  40. Thresholds in creep of magnesium alloy AX41 composites reinforced with short fibers
  41. Recovery processes in magnesium alloy AX41 and AX41-12 vol.% C-fibre composite studied by dilatometry
  42. Directional crystallisation of Ti–Al–Si in-situ composites
  43. Microstructure and mechanical properties of the AA6082 aluminium alloy with small additions of Sc and Zr
  44. Microstructure of a ternary Al–Pd–Rh alloy
  45. Effect of annealing on microstructure and properties of twin-roll-cast Al–Mn alloys with different copper content
  46. Quantitative characterization of the orientation spread within individual grains in copper after tensile deformation
  47. Effect of crystallization on the deformation behavior of a Zr-based bulk metallic glass
  48. Changes in structure and properties of carbide-steel cermets resulted from a heat treatment
  49. Comparative study of the high-temperature behaviour of Mg–Al and Mg–Zn wrought alloys
  50. Notification
  51. DGM News
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