Computing Binary Phase Diagram in MD++

Binary Phase Diagram Construction from Free Energy Calculation

Yanming Wang, Adriano Santana and Wei Cai

Created Nov, 2015

This tutorial discusses how to perform a series of simulations that generate free energy data of pure solid, solid with impurity and binary liquid alloy with different mixing ratio. Based on these data, the binary phase diagram can be obtained from common tangent construction using the free energy curves. As an example this tutorial explains how to produce the binary phase diagram for the Au-Si system.

Au-Si with impurities

The first script, wcrAuSi_Solid_imp.tcl, run MC simulations and produces the free energy raw data for Au with Si impurities and Si with gold impurities. First calculate the free energy of Au fcc crystal with Si impurity:

meam-lammps_gpp wcrAuSi_Solid_imp.tcl 1 1 Au1 1701 2.70 

The script takes four arguments, the first one ranges from 1-7. the second is the number of repetitions. The third one is the label for the chemical element: 'Au1', 'Si4', etc. which are all found inside the script. The fourth argument is a division factor, 1701/2.70 equals 629 . Hence, the range of temperatures will be from 1701 to 629 K.

Simultaneously one can also calculate the free energy of Si DC crystal with a gold impurity as:

meam-lammps_gpp wcrAuSi_Solid_imp.tcl 1 1 Si4 1701 2.70

After the two scripts finish four MATLAB scripts are produced in the Binary_AuSi_3 folder:

AuSi binary alloy

This tcl scripts, wcr_AuSi_Liquid.tcl, calculates the data needed for the binary system mixture:

meam-lammps_intel scripts/work/si_au/wcr_AuSi_Liquid.tcl 1 1 0 1701 2.704

where the third argument from the left represents the silicon fraction in the mixture, in this example 0%. The other arguments have similar meaning as above.

Plot binary phase diagram

Finally, place in the same folder all the *.dat files from the previous simulations, Au with Si impurity, Si with Au impurity and the AuSi files for for the binary alloy with the range of compositions. you'll also need these three scripts: plot_liquid_free_energy.m, comtan.m and polyfunc.m create

Launch MATLAB and run plot_liquid_free_energy.m and you should get the binary phase diagram.

Step3

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