, Volume 67, Issue 8, pp 1876–1880 | Cite as

Calculation of 2D and 3D Phase Diagrams

  • Shuanglin Chen
  • Weisheng Cao
  • Fan Zhang
  • Qian Li
  • Jieyu Zhang
  • Chuan Zhang
  • Jun Zhu


The algorithms for calculating two-dimensional (2D) phase diagrams and three-dimensional (3D) phase diagrams are described. While the concept of the zero-phase-fraction is used to calculate 2D phase diagrams, the concept of one-phase fraction is applied to calculate 3D phase diagrams. 3D phase diagrams can be better viewed with contour lines such as isothermal lines on the 3D phase boundary surfaces. The concepts of zero-phase fraction and one-phase fraction have also been generalized to a contour line of any property.


Phase Diagram Contour Line Phase Fraction Liquidus Projection Integrate Computational Material Engineering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



One of the authors, Q. Li, would like to thank the financial supports from the National Natural Science Foundation of China (51222402), “Shu Guang” project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation (13SG39).


  1. 1.
    J.E. Allison, P. Collins, and G. Spanos (eds.), Proceedings of the 1st World Congress on Integrated Computational Materials Engineering (Hoboken: Wiley Inc., 2011).Google Scholar
  2. 2.
    M. Li, C. Campbell, and K. Thornton (eds.), Proceedings of the 2nd World Congress on Integrated Computational Materials Engineering (Hoboken: Wiley Inc., 2013).Google Scholar
  3. 3.
    R. Schmid-Fetzer, J. Phase Equilib. Diff. 35, 735–760 (2014).CrossRefGoogle Scholar
  4. 4.
    M. Hansen, Constitution of Binary Alloys, 2nd ed. (New York: McGraw-Hill, 1958).Google Scholar
  5. 5.
    Handbook of Ternary Alloy Phase Diagrams, 10 vols., (Materials Park, ASM International, 1995).Google Scholar
  6. 6.
    J.J. van Laar and Z. Phys, Chem. 63, 216 (1908).Google Scholar
  7. 7.
    J.J. van Laar and Z. Phys, Chem. 64, 257 (1908).Google Scholar
  8. 8.
    J.L. Meijering, Philips Res. Rep. 18, 318 (1963).Google Scholar
  9. 9.
    L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams, (Academic Press, 1970).Google Scholar
  10. 10.
    ASM Handbook, Vol. 3, Alloy Phase Diagrams, (Materials Park, ASM International, 1992).Google Scholar
  11. 11.
    iPandatLive Phase Diagram, CompuTherm, LLC.
  12. 12.
    Alloy Phase Diagrams Database, ASM International.
  13. 13.
  14. 14.
    MIST, Phase Online, The American Ceramic Society and NIST.
  15. 15.
    CALPHAD, 33,(2009).Google Scholar
  16. 16.
    G. Eriksson, C.W. Bale, and A.D. Pelton, J. Chem. Therm. 67, 63–73 (2013).CrossRefGoogle Scholar
  17. 17.
    J.E. Morral and H. Gupta, Scr. Met. 25, 393–396 (1991).CrossRefGoogle Scholar
  18. 18.
    J.E. Morral and H. Gupta, J. Chim. Phys. 90, 421–427 (1993).Google Scholar
  19. 19.
    F.N. Rhines, Phase Diagrams in Metallurgy (New York: McGraw-Hill, 1956).Google Scholar
  20. 20.
    Pandat Software, CompuTherm, LLC (2015).Google Scholar
  21. 21.
    J. Zhu, C. Zhang, W. Cao, S. Chen, and F. Zhang, JOM, (2015). doi: 10.1007/s11837-015-1493-6.

Copyright information

© The Minerals, Metals & Materials Society 2015

Authors and Affiliations

  • Shuanglin Chen
    • 1
    • 2
  • Weisheng Cao
    • 1
  • Fan Zhang
    • 1
  • Qian Li
    • 2
    • 3
  • Jieyu Zhang
    • 2
  • Chuan Zhang
    • 1
  • Jun Zhu
    • 1
  1. 1.CompuThermLLCMadisonUSA
  2. 2.State Key Laboratory of Advanced Special SteelsShanghai UniversityShanghaiChina
  3. 3.Institute of Genomic MaterialShanghai UniversityShanghaiChina

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