# 2NN MEAM Interatomic Potential for the W-H Binary System

## Overview
This package provides a second-nearest-neighbor modified embedded-atom
method (2NN MEAM) interatomic potential for the tungsten-hydrogen (W-H)
binary system, together with its constituent W and H unary descriptions.
The potential was developed to study the effect of hydrogen on the
mechanical response of pure tungsten, including hydrogen-affected
deformation and fracture behavior relevant to plasma-facing materials.

## Reference
Please cite the following paper when using this potential:

  Y. Oh, S. Sung, J. Jang, W.-S. Ko, H. N. Han,
  "Integrated experimental and computational study on the effect of
  hydrogen in mechanical responses of pure tungsten",
  Acta Materialia 280 (2024) 120341.
  DOI: 10.1016/j.actamat.2024.120341
  https://doi.org/10.1016/j.actamat.2024.120341

The pure W unary description is adopted from the earlier W potential.
Users employing the W part should additionally cite:

  Y. Oh, W.-S. Ko, N. Kwak, J. Jang, T. Ohmura, H. N. Han,
  "Small-scale analysis of brittle-to-ductile transition behavior in
  pure tungsten",
  Journal of Materials Science & Technology 105 (2022) 242-258.
  DOI: 10.1016/j.jmst.2021.07.024
  https://doi.org/10.1016/j.jmst.2021.07.024

## Files
| File           | Description                                          |
|----------------|------------------------------------------------------|
| `library.meam` | Pure-element parameters (W, H)                       |
| `WH.meam`      | Binary parameters for the W-H system                 |

`WH.meam` is self-contained for the binary description: it includes the
unary blocks for atoms 1 and 2 and the binary block (1,2).

## Element Ordering (mandatory)
The atom indices in `WH.meam` are fixed:
- Atom 1 = W
- Atom 2 = H

The element ordering in `library.meam` is W, H, matching the index
assignment above. The `pair_coeff` element list must therefore be given
in the order `W H`.

## Reference Structures
| System | Reference structure   |
|--------|-----------------------|
| W      | bcc                   |
| H      | dimer                 |
| W-H    | B1 (NaCl type, WH)    |

Notes:
- The reference structure of pure W is bcc; pure H uses the dimer
  reference. For H, the quantity listed as "B" in the source tables is an
  alpha parameter as defined in the 2NN MEAM model (a bulk modulus is not
  defined for a gaseous element).
- The density-scaling factor ratio is rho0(W):rho0(H) = 1:17.

## LAMMPS Usage Example
```
pair_style    meam
pair_coeff    * * library.meam W H WH.meam W H
```
(adjust the element symbols on the data-file side to match your atom
types; the order on the potential side must remain `W H`)

---

## IMPORTANT NOTES

### (1) Radial cutoff distance (`rc`) and cutoff region (`delr`)

This potential uses **`rc = 4.3` A** and **`delr = 1.0` A** as set on the
first lines of `WH.meam`:
```
rc = 4.3
delr = 1.0
```

These specific values were used in the reference work and **should be
retained to reproduce the published results.**

The enlarged cutoff region `delr = 1.0` A (rather than the conventional
default of 0.1 A) is intentional. Because the W-H study addresses
hydrogen effects on deformation and fracture, the cutoff region was
widened to remove the artificial stress barrier that arises from the
radial-cutoff truncation in fracture-related simulations, following the
guideline of:

  W.-S. Ko and B.-J. Lee, "Origin of unrealistic blunting during
  atomistic fracture simulations based on MEAM potentials",
  Philosophical Magazine 94 (2014) 1745-1753.
  DOI: 10.1080/14786435.2014.895441

If the conventional `delr = 0.1` A were used instead, fracture-related
simulations could exhibit non-physical crack-tip blunting rather than the
correct cleavage/fracture behavior. Users reproducing the published work,
or performing any deformation/fracture study with this potential, should
keep `rc = 4.3` A and `delr = 1.0` A.

If you adapt this potential to a different problem, confirm that `rc` and
`delr` remain appropriate for the species, phases, and phenomena
involved.

### (2) Convention for screening parameters (Cmin/Cmax)

The LAMMPS argument order for `Cmin(I,J,K)` and `Cmax(I,J,K)` differs from
the convention used in the original 2NN MEAM literature and in the paper.
Users editing or extending the parameter file must be aware of this
difference to avoid silently swapping screening atoms.

| Notation                              | Bond formed by | Screening atom |
|---------------------------------------|----------------|----------------|
| Paper / original MEAM:  C^X-Y-Z       | X and Z        | **Y** (middle) |
| LAMMPS:                 Cmin(I, J, K) | I and J        | **K** (last)   |

So in the paper the **middle letter** is the screening atom, whereas in
LAMMPS the **third index** is the screening atom.

Mapping rule:    paper  X-Y-Z   =>   LAMMPS  (X, Z, Y)

Example for the W-H (B1) binary block (atom 1 = W, atom 2 = H):

| Paper notation       | Meaning                       | LAMMPS line in `WH.meam`     |
|----------------------|-------------------------------|------------------------------|
| C^W-H-W (= 0.04)     | W-W bond screened by H         | `Cmin(1,1,2) = 0.04`         |
| C^H-W-H (= 2.52)     | H-H bond screened by W         | `Cmin(2,2,1) = 2.52`         |
| C^W-W-H (= 0.69)     | W-H bond screened by W         | `Cmin(1,2,1) = 0.69`         |
| C^H-H-W (= 0.15)     | W-H bond screened by H         | `Cmin(1,2,2) = 0.15`         |

(the corresponding Cmax values are 1.01, 3.41, 2.91, and 1.10,
respectively)

The distributed parameter file already follows the LAMMPS convention.
This note is provided for users who cross-check the values against the
paper or who construct new parameter files manually.

---

## Contact
Won-Seok Ko
Department of Materials Science and Engineering, Korea University,
Seoul, Republic of Korea
wonsko@korea.ac.kr