GSFE curves

Here, we calculate the generalized stacking fault energy (GSFE) curves on {110}, {112}, and {123} planes in CrMoNbTa, CrNbTaW, MoNbTaV, and MoNbTaW. Since there are three types of planes and four MPEAs, you need to prepare 12 directories on your local computer and on Pod, respectively.

{110} GSFE curves in CrMoNbTa

Take the {110} GSFE curve in CrMoNbTa as an example. First, on your local computer, download the six files in CrMoNbTa/110/ from this GitHub repository to a local directory CrMoNbTa/110. These six files are

• lmp_gsfe.batch, which is for job submission
• 110-gsfe.lmp, which is the LAMMPS data file
• lmp_gsfe_110.in, which is the LAMMPS input file
• CrMoNbTaVW_Xu2022.eam.alloy, which is an interatomic potential file made by Xu et al.
• gsfe_curve.sh, which is the post-processing bash script
• usfe_iss.m, which is the MATLAB code used for calculating the unstable stacking fault energy (USFE) and ideal shear strength

Then on Pod, create a new directory in your $HOME. Say the directory is also CrMoNbTa/110. The commands are

mkdir CrMoNbTa

cd CrMoNbTa

mkdir 110

cd 110

Then upload, via Filezilla, the six files from your local computer to 110 on Pod.

One {110} GSFE curve in CrMoNbTa

In your terminal emulator, submit the job by typing

sbatch lmp_gsfe.batch

then hit Return. To check the status of the job, type

squeue -u $USER

then hit Return. Once the job is finished successfully, you will find a lot of files in the directory 110. One file is called gsfe_ori. In the same directory on Pod, type

sh gsfe_curve.sh

then hit Return. You will find a new file called gsfe. The first and second columns of this file, respectively, are the x and y axes of the GSFE curve.

Download gsfe to your local computer. Run usfe_iss.m in MATLAB to calculate the USFE and ideal shear strength T_is. For more on these two quantities, read Section 3.2 of this paper.

More {110} GSFE curves in CrMoNbTa

So far you have obtained one {110} GSFE curve, but for MPEAs, multiple GSFE curves exist even for the same type of slip plane. It is suggested that 20 GSFE curves be calculated for the {110} plane. To calculate another curve, in your terminal emulator, go to the 110 directory, edit the LAMMPS input file lmp_gsfe_110.in. In lines 14, 15, and 16, there are three random number seeds 1239, 3534, 4678, respectively. Change any of the seeds to another integer, e.g., 6873. For more information, please refer to this page.

Then resubmit the job. Once it is finished, run gsfe_curve.sh, you will get another GSFE curve in a file gsfe. Save it to your local computer. Note: do not overwrite the previous gsfe file. Again, calculate USFE and T_is.

Repeat the steps above 18 more times. Each time, change at least one random seed before you resubmit the job. Eventually, you will get 20 {110} GSFE curves, which would give you 20 USFE values, and 20 T_is values. Calculate the mean and standard deviation of the 20 USFE values, as well as those of the 20 T_is values. The mean should be close to the USFE based on the A atom potential, which is the peak GSFE value in the file CrMoNbTa/110/gsfe_A in this GitHub repository.

{112} and {123} GSFE curves in CrMoNbTa

Repeat the steps above to get 20 {112} and 20 {123} GSFE curves in CrMoNbTa. Instead of CrMoNbTa/110/ in this GitHub repository, you will need the files in CrMoNbTa/112/ and CrMoNbTa/123/. Again, calculate mean and standard deviation of:

• 20 {112} USFE
• 20 {112} T_is
• 20 {123} USFE
• 20 {123} T_is

Note: the two mean USFEs should be close to the peak GSFE values in the files CrMoNbTa/112/gsfe_A and CrMoNbTa/123/gsfe_A, respectively.

GSFE curves in CrNbTaW

Repeat the steps above to get 20 {110}, 20 {112}, and 20 {123} GSFE curves in CrNbTaW. Go to the three subdirectories under CrNbTaW/ in this GitHub repository. Obtain the mean and standard deviation of USFE and T_is. Again, compare the mean USFE with the peak GSFE value in respective file gsfe_A.

GSFE curves in MoNbTaV

Repeat the steps above to get 20 {110}, 20 {112}, and 20 {123} GSFE curves in MoNbTaV. Go to the three subdirectories under MoNbTaV/ in this GitHub repository. Obtain the mean and standard deviation of USFE and T_is. Again, compare the mean USFE with the peak GSFE value in respective file gsfe_A.

Note: the interatomic potential file for this MPEA is different from that for the other three MPEAs.

GSFE curves in MoNbTaW

Repeat the steps above to get 20 {110}, 20 {112}, and 20 {123} GSFE curves in MoNbTaW. Go to the three subdirectories under MoNbTaW/ in this GitHub repository. Obtain the mean and standard deviation of USFE and T_is. Again, compare the mean USFE with the peak GSFE value in respective file gsfe_A.

Results

Eventually, you will have 20 x 3 x 4 = 240 different GSFE curves. You will also have 3 x 4 = 12 different mean and standard deviation of USFE, and those of T_is.

References

If you use the interatomic potential file from this GitHub repository, please cite

• Shuozhi Xu, Saeed Zare Chavoshi, Yanqing Su, On calculations of basic structural parameters in multi-principal element alloys using small atomistic models, Comput. Mater. Sci. 202 (2022) 110942

If you use any other files from this GitHub repository, please also cite

• Rebecca A. Romero, Shuozhi Xu, Wu-Rong Jian, Irene J. Beyerlein, C.V. Ramana, Atomistic calculations of the local slip resistances in four refractory multi-principal element alloys, Int. J. Plast. 149 (2022) 103157
• Shuozhi Xu, Emily Hwang, Wu-Rong Jian, Yanqing Su, Irene J. Beyerlein, Atomistic calculations of the generalized stacking fault energies in two refractory multi-principal element alloys, Intermetallics 124 (2020) 106844