Confined layer slips

Foreword

The purpose of this project is to calculate the confined layer slip (CLS) process in nanolaminated Ag and two types of Ag/Cu nanolaminates.

Read the following journal articles to learn more about nanolaminates

• Irene J. Beyerlein, Zezhou Li, Nathan A. Mara, Mechanical properties of metal nanolaminates, Annu. Rev. Mater. Sci 52 (2022) 281--304
• Mohammad Nasim, Yuncang Li, Ming Wen, Cuie Wen, A review of high-strength nanolaminates and evaluation of their properties, J. Mater. Sci. Tech. 50 (2020) 215--244
• I.J. Beyerlein, J. Wang, Interface-driven mechanisms in cubic/noncubic nanolaminates at different scales, MRS Bull. 44 (2019) 31--39
• Samikshya Subedi, Irene J. Beyerlein, Richard LeSar, Anthony D. Rollett, Strength of nanoscale metallic multilayers, Scr. Mater. 145 (2018) 132--136
• Jian Wang, Qing Zhou, Shuai Shao, Amit Misra, Strength and plasticity of nanolaminated materials, Mater. Res. Lett. 5 (2017) 1--19
• A. Misra, J.P. Hirth, R.G. Hoagland, Length-scale-dependent deformation mechanisms in incoherent metallic multilayered composites, Acta Mater. 53 (2005) 4817--4824

Read the following journal articles to understand how the CLS process can be calculated:

• Weisen Ji, Wu-Rong Jian, Yanqing Su, Shuozhi Xu, Irene J. Beyerlein, Role of stacking fault energy in confined layer slip in nanolaminated Cu, J. Mater. Sci. 59 (2024) 4775--4787
• Wu-Rong Jian, Shuozhi Xu, Yanqing Su, Irene J. Beyerlein, Role of layer thickness and dislocation distribution in confined layer slip in nanolaminated Nb, Int. J. Plast. 152 (2022) 103239
• Wu-Rong Jian, Yanqing Su, Shuozhi Xu, Weisen Ji, Irene J. Beyerlein, Effect of interface structure on dislocation glide behavior in nanolaminates, J. Mater. Res. 36 (2021) 2802--2815

None of the three papers above are in the Ag/Cu system. The following are some prior work on Ag/Cu nanolaminates, although none of them focused on CLS:

• Experiments
  • X.F. Kong, N. Gao, I.J. Beyerlein, B.N. Yao, S.J. Zheng, X.L. Ma, D. Legut, T.C. Germann, H.J. Zhang, R.F. Zhang, Interface facilitated transformation of voids directly into stacking fault tetrahedra, Acta Mater. 188 (2020) 623-634
  • Min Wang, Irene J. Beyerlein, Jian Zhang, Wei-Zhong Han, Bi-metal interface-mediated defects distribution in neon ion bombarded Cu/Ag nanocomposites, Scr. Mater. 171 (2019) 1--5
  • Min Wang, Irene J. Beyerlein, Jian Zhang, Wei-Zhong Han, Defect-interface interactions in irradiated Cu/Ag nanocomposites, Acta Mater. 160 (2018) 211--223
  • Shijian Zheng, Shuai Shao, Jian Zhang, Yongqiang Wang, Michael J. Demkowicz, Irene J. Beyerlein, Nathan A. Mara, Adhesion of voids to bimetal interfaces with non-uniform energies, Sci. Rep. 5 (2015) 15428
• Modeling
  • Yanxiang Liang, Aibo Luo, Lingwei Yang, Jianfeng Zhao, Luobing Wang, Qiang Wan, Effect of interface structure and layer thickness on the mechanical properties and deformation behavior of Cu/Ag nanolaminates, Phys. B Condens. Matter 661 (2023) 414933
  • X.F. Kong, I.J. Beyerlein, Z.R. Liu, B.N. Yao, D. Legut, T.C. Germann, R.F. Zhang, Stronger and more failure-resistant with three-dimensional serrated bimetal interfaces, Acta Mater. 166 (2019) 231--245
  • A. Kardani, A. Montazeri, Temperature-based plastic deformation mechanism of Cu/Ag nanocomposites: A molecular dynamics study, Comput. Mater. Sci. 144 (2018) 223--231

LAMMPS

LAMMPS on OSCER does not come with many packages. To build more packages into LAMMPS, please visit this page.

To finish this project, build our own LAMMPS version with the following two packages included:

• MANYBODY package. This is to use the manybody potential such as the embedded-atom method potential.
• VORONOI package. This is to calculate Voronoi tessellation of the atoms in the simulation cell. To learn more, please visit this page.

To build LAMMPS with these two packages, use the file lmp_mbvo.sh. First, cd to any directory on OSCER, e.g., $HOME, then

sh lmp_mbvo.sh

Note that the second command in lmp_mbvo.sh will load a module. If one cannot load it, try module purge first.

Once the sh run is finished, we will find a file lmp_mpi in the lammps-mbvo/mylammps/src/ directory on OSCER. And that is the LAMMPS executable with MANYBODY and VORONOI packages.

Note: All files for calculations can be found in this GitHub repository, except the data files which can be found here. The reason is that the data files are too large for GitHub. Feel free to increase the walltime (default: 300 hours) and/or number of nodes (default: 1) and/or number of cores (default: 32), as needed. That would require the modification of lmp.batch.

Each time we run a new type of simulation, create a new directory.

The interatomic potential is from this paper.

Nanolaminated Ag

Two grains are involved. Their crystallographic orientations are [1-10]-[11-2]-[111] and [1-10]-[112]-[-1-11], respectively, the same as the Cu/Cu case in Table 2 of this paper.

The interfacial energy is 407.16 mJ/m².

There are three different slip planes.

Plane 1

Run the simulation with files lmp.in, data.Ag_5nm_1, AgCu.eam.alloy, and lmp.batch.

Once it is finished, we will find a file shear.mobile.txt. Column 2 is the shear strain, which is unitless, while column 8 is the shear stress, in units of GPa. Plot a curve using the two columns as the x and y axes, respectively, and that is the stress-strain curve.

From the stress-strain curve, one can determine the critical stress for the dislocation to move by more than 1 nm. The critical stress is usually the first local maximum stress, excluding the first coupe of points. Specifically, the critical stress is 0.17096 GPa, taken at the strain of 0.00885.

All dump files, which contain atomistic structures, can be found in the directory /ourdisk/hpc/cm3atou/dont_archive/mahshad1994/Ag_1. The reason why dump files are in another place is because they are too large for $HOME, see LAMMPSatOU.

Visualize the dump files in OVITO and check if the dislocation climbs, following Figures 3 & 6 of this paper and Figure 7 of this paper.

Other planes

Repeat the simulation for the other two planes. Note that we should use the data file data.Ag_5nm_x, where x is either 2 or 3. In lmp.in, make two changes:

• Line 19, change the corresponding data file name.
• Line 28, change the last number 1 to 2 or 3.

Determine their respective critical stresses for dislocation glide. Check if the dislocation climbs. Again, note that the dump files can be found in the directory /ourdisk/hpc/cm3atou/dont_archive/mahshad1994/Ag_x, where x is 2 or 3.

Plot the three stress-strain curves in the same figure, similar to Figure 7 of this paper.

Ag/Cu Nanolaminate - type 1

The crystallographic orientations are [1-10]-[11-2]-[111] and [1-10]-[112]-[-1-11], respectively, in Cu and Ag.

The interfacial energy is 580.79 mJ/m².

The interface has a complex structure, making it difficult to determine how many different slip planes there are in each material (i.e., Ag or Cu). Therefore, we simply choose ten adjacent planes in each material and place a dislocation on each plane. Thus, in total, we study 20 different slip planes.

Plane 1 in Ag

The simulation requires files lmp.in, data.AgCu_type1_Ag_5nm_1, AgCu.eam.alloy, and lmp.batch. Make these changes in lmp.in:

• Line 19, change the data file name to the correct one
• Line 23, change Ag Ag to Cu Ag
• Line 28, change the last directory name to AgCu_type1_Ag_1. In fact, we can set the directory name as anything; just need to distinguish it from other directories.

In each case, determine (i) value of the critical stress and (ii) whether the dislocation climbs.

Other planes

Follow the steps above and run simulations on the other nine planes in Ag. In each simulation, use the data file data.AgCu_type1_Ag_5nm_x, where x varies from 2 to 10. Remember to make those three changes in lmp.in.

Once all simulations are done, plot the ten stress-strain curves in two figures. The first figure is for planes 1 to 5, while the second is for planes 6 to 10.

Planes in Cu

Follow the steps above. Note that the data files are now data.AgCu_type1_Cu_5nm_x, where x varies from 1 to 10. In line 28 of the input file, change the last directory name to AgCu_type1_Cu_x, where x varies from 1 to 10.

Ag/Cu Nanolaminate - type 2

The crystallographic orientations are the same for both Ag and Cu, i.e., [1-10]-[11-2]-[111]. This is the cube-on-cube orientation. Thus, the interface is also known as the Ag/Cu cube interface. Its interfacial energy is 474.74 mJ/m².

Follow the steps in the previous section Ag/Cu Nanolaminate - type 1. The data file here is either data.AgCu_type2_Ag_5nm_x or data.AgCu_type2_Cu_5nm_x, where x varies from 1 to 10. Also, in line 28 of the input file, change the last directory name to AgCu_type2_Ag_x or AgCu_type2_Cu_x, where x varies from 1 to 10.

Here, we will eventually obtain 20 stress-strain curves.

Single crystalline pure metals

There are two pure metals, Cu and Ag. We can simulate the dislocation glide in their single crystals, and compare results with those in nanolaminates.

The dislocation glide in a Cu single crystal has been modeled in this paper using the same Cu potential used here, with the stress-strain curves shown in Figure 2 (labels: SC-Cu and FC-Cu). SC is when periodic boundary conditions are applied along the dislocation line; FC is when traction-free boundary conditions are applied along the dislocation line. The same paper also calculated the {112} free surface energy in Cu, 1432 mJ/m².

Here, we will simulate the dislocation dynamics in an Ag single crystal.

To build an Ag single crystal containing an unrelaxed edge dislocation, we use Atomsk to process the atomsk_Ag.sh file which can be found in the SC-Ag directory in this GitHub repository, i.e.,

sh atomsk_Ag.sh

which will create a file data.Ag.

Periodic boundary conditions

The two input files to be used can be found in the SC-Ag directory in this GitHub repository.

First, we apply energy minimization to create an Ag single crystal containing a relaxed, infinitely long edge dislocation. To this purpose, create a new directory, and run a LAMMPS simulation using files lmp_minSCAg.in, data.Ag, AgCu.eam.alloy, and lmp.batch. Remember to modify the input file name in the last file. Dump files will be written to this directory, but that is fine because there aren't many.

Once the simulation is finished, we will find a file data.minSCAg.

Second, create a new directory and run a LAMMPS simulation to model the dislocation glide with files lmp_SCAg.in, data.minSCAg, AgCu.eam.alloy, and lmp.batch. Again, remember to modify the input file name in the last file.

All dumpe files can be found in /ourdisk/hpc/cm3atou/dont_archive/mahshad1994/Ag-SC. Record the stress-strain curve and plot it together with the three curves for the nanolaminated Ag.

Traction-free boundary conditions

The two input files to be used can be found in the FS-Ag directory in this GitHub repository.

First, we apply energy minimization to create an Ag single crystal containing a relaxed edge dislocation pinned between two {112} free surfaces. To this purpose, create a new directory, and run a LAMMPS simulation using files lmp_minFSAg.in, data.Ag, AgCu.eam.alloy, and lmp.batch. Remember to modify the input file name in the last file. Dump files will be written to this directory, but that is fine because there aren't many.

Once the simulation is finished, we will find a file data.minFSAg.

Second, create a new directory and run a LAMMPS simulation to model the dislocation glide with files lmp_FSAg.in, data.minFSAg, AgCu.eam.alloy, and lmp.batch. Again, remember to modify the input file name in the last file.

All dumpe files can be found in /ourdisk/hpc/cm3atou/dont_archive/mahshad1994/Ag-FS. Record the stress-strain curve and plot it together with the three curves for the nanolaminated Ag.

Third, we calculate the {112} free surface energy in Ag. To this purpose, create a new directory, and run a LAMMPS simulation using lmp_minFSEAg.in, AgCu.eam.alloy, and lmp.batch. Again, remember to modify the input file name in the last file. Dump files will be written to this directory, but that is fine because there aren't many.

Once the simulation is finished, we will find a file FSE, which contains the free surface energy, in units of mJ/m².

Note: Density functional theory-based {112} free surface energies in Ag and Cu, are 868 mJ/m² and 1626 mJ/m², respectively, according to this paper.

Reference

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

• Mahshad Fani, Wu-Rong Jian, Yanqing Su, Shuozhi Xu, Confined layer slip process in nanolaminated Ag and two Ag/Cu nanolaminates, Materials 17 (2024) 501