Gamma line calculation via APEX

Introduction

Figure 1. Schematic diagram of Gamma line calculation

The Gamma line (generalized stacking fault energy) function of APEX calculates energy of a series slab structures of specific crystal plane, which displaced in the middle along a slip vector. As illustrated in Figure 2, the slab structrures in APEX are defined by a plane miller index and two orthogonal directions (primary and secondary) on the plane. The slip vector is always along the primary directions with slip length defined by user or default settings. Thus, by indicating plane_miller and the slip_direction (AKA, primary direction), a slip system can be defined.

The parameters related to Gamma line calculation are listed below:

Here is an example:

{
    "type":            "gamma",
    "skip":            false,
    "plane_miller":    [0,0,1],
    "slip_direction":  [1,0,0],
    "hcp": {
          "plane_miller":    [0,1,-1,1],
          "slip_direction":  [-2,1,1,0],
        "slip_length":     [1,0,1],
        "plane_shift": 0.25
      },
    "supercell_size":   [1,1,6],
    "vacuum_size": 10,
    "add_fix": ["true","true","false"],
    "n_steps":         10
  }

It should be noted that for various crystal structures, users can further define slip parameters within the respective nested dictionaries, which will be prioritized for adoption. In the previously mentioned example, the slip system configuration within the "hcp" dictionary will be utilized.

Hands-on example

Install APEX

Download APEX packedge via git clone

APEX can be easily installed via pip, as well as other dependencies such as pydflow.

check if apex is installed

Preperation

Here we take an example of APEX workflow based on molecular dynamic simulation tool: LAMMPS, testing Gamma Line of slip along 1/2<$111$> $\{110\}$ for BCC molybdenum using a DP potential. This process will be running on Bohrium.

Here is a example of local working direction prepared for LAMMPS

global.json contains necessary config for Bohrium (e.g. account infomation; machine type; image address et al.), and should be prepared under current work directory in the first place.

Please replace with your own Borium username, password and program_id via following code:

For most common slip systems in respect to FCC, BCC and HCP crystal structures, slip direction, secondary direction and default fractional slip lengths are already documented and listed below (Users are strongly advised to follow those pre-defined slip system, or may need to double-check the generated slab structure, as unexpected results may occur especially for system like HCP):

• FCC

  Plane miller index	Slip direction	Secondary direction	Default slip length
  $(001)$	$[100]$	$[010]$	$a$
  $(110)$	$[\bar{1}10]$	$[001]$	$\sqrt{2}a$
  $(111)$	$[11\bar{2}]$	$[\bar{1}10]$	$\sqrt{6}a$
  $(111)$	$[\bar{1}\bar{1}2]$	$[1\bar{1}0]$	$\sqrt{6}a$
  $(111)$	$[\bar{1}10]$	$[\bar{1}\bar{1}2]$	$\sqrt{2}a$
  $(111)$	$[1\bar{1}0]$	$[11\bar{2}]$	$\sqrt{2}a$

• BCC

  Plane miller index	Slip direction	Secondary direction	Default slip length
  $(001)$	$[100]$	$[010]$	$a$
  $(111)$	$[\bar{1}10]$	$[\bar{1}\bar{1}2]$	$\frac{\sqrt{2}}{2}a$
  $(110)$	$[\bar{1}11]$	$[00\bar{1}]$	$\frac{\sqrt{3}}{2}a$
  $(110)$	$[1\bar{1}\bar{1}]$	$[001]$	$\frac{\sqrt{3}}{2}a$
  $(112)$	$[11\bar{1}]$	$[\bar{1}10]$	$\frac{\sqrt{3}}{2}a$
  $(112)$	$[\bar{1}\bar{1}1]$	$[1\bar{1}0]$	$\frac{\sqrt{3}}{2}a$
  $(123)$	$[11\bar{1}]$	$[\bar{2}10]$	$\frac{\sqrt{3}}{2}a$
  $(123)$	$[\bar{1}\bar{1}1]$	$[2\bar{1}0]$	$\frac{\sqrt{3}}{2}a$

• HCP (Bravais lattice)

  Plane miller index	Slip direction	Secondary direction	Default slip length
  $(0001)$	$[2\bar{1}\bar{1}0]$	$[01\bar{1}0]$	$a$
  $(0001)$	$[1\bar{1}00]$	$[01\bar{1}0]$	$\sqrt{3}a$
  $(0001)$	$[10\bar{1}0]$	$[01\bar{1}0]$	$\sqrt{3}a$
  $(01\bar{1}0)$	$[\bar{2}110]$	$[000\bar{1}]$	$a$
  $(01\bar{1}0)$	$[0001]$	$[\bar{2}110]$	$c$
  $(01\bar{1}0)$	$[\bar{2}113]$	$[000\bar{1}]$	$\sqrt{a^2+c^2}$
  $(\bar{1}2\bar{1}0)$	$[\bar{1}010]$	$[000\bar{1}]$	$\sqrt{3}a$
  $(\bar{1}2\bar{1}0)$	$[0001]$	$[\bar{1}010]$	$c$
  $(01\bar{1}1)$	$[\bar{2}110]$	$[\bar{1}2\bar{1}\bar{3}]$	$a$
  $(01\bar{1}1)$	$[\bar{1}2\bar{1}\bar{3}]$	$[2\bar{1}\bar{1}0]$	$\sqrt{a^2+c^2}$
  $(01\bar{1}1)$	$[0\bar{1}12]$	$[\bar{1}2\bar{1}\bar{3}]$	$\sqrt{3a^2+4c^2}$
  $(\bar{1}2\bar{1}2)$	$[10\bar{1}0]$	$[1\bar{2}13]$	$\sqrt{3}a$
  $(\bar{1}2\bar{1}2)$	$[1\bar{2}13]$	$[\bar{1}010]$	$\sqrt{a^2+c^2}$

Now let's revise the settings inside param_joint.json to turn on Gamma function:

By this setting, we will be calculating gamma line along $1/2[\bar{1}11]$ on $\{110\}$ plane as $\frac{\sqrt{3}}{2}a$ being default to be slip length. You can also specify it inside json.

Submit a joint workflow (relaxation + property-test)

Now we can submit an overall joint workflow to obtain the stacking fault results by:

It may takes a few minutes to submit to Bohrium depending on one's network connection...

Once submitted, we can monitor this workflow on the workflow link appearing above.

When the workflow completed, the work directory, together with results, will be downloaded automatically to current directory:

We can now plot the Gamma line results: