Computing Binary Phase Diagram in MD++

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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. 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.tc 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.tc 1 1 Si4 1701 2.70 After the two scripts finish four MATLAB scripts are produced in the Binary_AuSi_3 folder:

Input files

INCAR


POTCAR

In this example, we currently choose the US-LDA PP of Au provided by VASP. We will provide results of simulations with Au PAW-LDA PP in the later section.

Run VASP

To compute the elastic constants, we prepared the following PBS scripts to submit the jobs to MC2 cluster. vasp.pbs.C11 is used to to run vasp repeated with different values for the first component of the first Bravais lattice vector, $a. Here we put 4.067877 as the length of the lattice constant in the script, which is obtained from our previous VASP calculation. In generally, you are expected to put a reliable value from your lattice constant calculation with the same PP. The script automatically creates the POSCAR file for every a specified in the script in the range from 0.997 to 1.003. For C44 calculation, the PBS script vasp.pbs.C44 changes the value of $a for the first and second component of the first Bravais lattice vector.


Analyze data

After running the two scripts above for C11 and C44, the data files: Elatt.C11.dat and Elatt.C44.dat will be created.

If you choose your POTCAR for US-LDA PP, the date should be similar to

Elatt.C11.dat 

0.997 1  -.17546258E+02  -.17546235E+02 -.175463E+02
0.998 1  -.17546476E+02  -.17546452E+02 -.175465E+02
0.999 1  -.17546606E+02  -.17546580E+02 -.175466E+02
1.000 1  -.17546649E+02  -.17546622E+02 -.175466E+02
1.001 1  -.17546605E+02  -.17546577E+02 -.175466E+02
1.002 1  -.17546476E+02  -.17546446E+02 -.175465E+02
1.003 1  -.17546261E+02  -.17546229E+02 -.175463E+02

Elatt.C44.dat 

0.997 1  -.35092701E+02  -.35092739E+02 -.350927E+02
0.998 1  -.35093172E+02  -.35093210E+02 -.350932E+02
0.999 1  -.35093440E+02  -.35093474E+02 -.350934E+02
1.000 1  -.35093511E+02  -.35093539E+02 -.350935E+02
1.001 1  -.35093392E+02  -.35093411E+02 -.350934E+02
1.002 1  -.35093087E+02  -.35093098E+02 -.350931E+02
1.003 1  -.35092601E+02  -.35092607E+02 -.350926E+02


C44 of 36 GPa is a bit lower than the paper's result of 47 GPa (The experimental value is 45 GPa).

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