Abstract
Graham scan, a computational geometric algorithm for finding a two-dimensional convex hull, is introduced to calculate binary phase diagrams. This algorithm is modified and applied to find the convex hull of discrete points in the space of Gibbs energy vs mol fraction. The modified Graham scan algorithm has a very low computational cost, which improves efficiency in binary phase diagram calculation.
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S.-L. Chen, K.-C. Chou, and Y. A. Chang, On a New Strategy for Phase Diagram Calculation, 1. Basic Principles, CALPHAD, 1993, 17, p 237–250
S.-L. Chen, K.-C. Chou, and Y. A. Chang, On a New Strategy for Phase Diagram Calculation, 2. Binary Systems, CALPHAD, 1993, 17, p 297–302
S.-L. Chen, S. Daniel, F. Zhang, Y. A. Chang, X.-Y. Yan, and F.-Y. Xie, The PANDAT Software Package and Its Applications. CALPHAD, 2002, 26, p 175–188
S.-L. Chen, F. Zhang, S. Daniel, F.-Y. Xie, X.-Y. Yan, Y. A. Chang, R. Schmid-Fetzer, and W. A. Oates, Calculating Phase Diagrams Using PANDAT and PanEngine, J. Metals, 2003, 55, December, p 48–51
T.H. Cormen, C.E. Leiserson, and R.L. Rivest, Introduction to Algorithms, MIT Press, Cambridge, MA, 1989
R.L. Graham. An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set, Inf. Process. Lett., 1972, 1, p 132–133
F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction, Springer-Verlag, New York, 1988
M.J. Laszlo, Computational Geometry and Computer Graphics in C++, Prentice Hall, Englewood Cliffs, NJ, 1996
J. O'Rourke, Computational Geometry in C, Cambridge University Press, New York, 1993
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Chen, SL., Zhang, JY., Lu, XG. et al. Application of Graham scan algorithm in binary phase diagram calculation. J Phs Eqil and Diff 27, 121–125 (2006). https://doi.org/10.1007/s11669-006-0034-y
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DOI: https://doi.org/10.1007/s11669-006-0034-y