# 2NN MEAM Interatomic Potentials for Fe-Cu-X Ternary Systems
## (X = Sn, Sb, As, Pb, Bi)

## Overview
This package provides 2NN MEAM interatomic potentials for five ternary
alloy systems based on Fe-Cu, developed for atomistic simulations of
liquid metal penetration and embrittlement in Fe-Cu-X (X = Sn, Sb, As,
Pb, Bi) systems under hot-rolling conditions.

## Reference
Please cite the following paper when using these potentials:

  J.-H. Park, H.-J. Jo, H.-H. Ahn, D.-H. Kim, M. Kang, Y. Kim, W.-S. Ko,
  "Atomistic simulation study of tramp element effects on liquid metal
  penetration in Fe-Cu-X systems",
  Acta Materialia 313 (2026) 122296.
  https://doi.org/10.1016/j.actamat.2026.122296

## Files
| File              | Description                                          |
|-------------------|------------------------------------------------------|
| `library.meam`    | Pure-element parameters (Fe, Cu, Sn, Sb, As, Pb, Bi) |
| `FeCuSn.meam`     | Fe-Cu-Sn ternary parameters                          |
| `FeCuSb.meam`     | Fe-Cu-Sb ternary parameters                          |
| `FeCuAs.meam`     | Fe-Cu-As ternary parameters                          |
| `FeCuPb.meam`     | Fe-Cu-Pb ternary parameters                          |
| `FeCuBi.meam`     | Fe-Cu-Bi ternary parameters                          |

Each ternary file is self-contained: it includes the unary blocks for
atoms 1, 2, 3 and the binary blocks (1,2), (1,3), (2,3) plus the
ternary cross-terms.

## Element Ordering (mandatory)
The atom indices in the parameter files are fixed:
- Atom 1 = Fe
- Atom 2 = Cu
- Atom 3 = X (Sn, Sb, As, Pb, or Bi, depending on the file)

## LAMMPS Usage Example
```
pair_style    meam
pair_coeff    * * library.meam Fe Cu Sn FeCuSn.meam Fe Cu Sn
```
(adjust element symbols to match your data file's atom types and the
selected ternary file)

---

## IMPORTANT NOTES

### (1) Radial cutoff distance (`rc`)

The default cutoff in each ternary `.meam` file is **`rc = 4.0` Angstrom**.

This is the cutoff used in the paper for:
- Grain boundary penetration simulations
- Liquid-phase mixing enthalpy calculations (Supplementary Note S5)
- Diffusion and viscosity calculations (Supplementary Notes S6-S7)
- Related extended MD analyses (Supplementary Notes S8-S10)

It was selected for computational efficiency in extended MD simulations
and adequately captures interatomic interactions in fcc Fe.

For **physical property validation** (cohesive energy, lattice parameter,
elastic constants, thermal expansion, etc., as presented in
Supplementary Notes S2-S4), the paper used **`rc = 5.1` Angstrom**, which
exceeds the second nearest-neighbor distance of fcc Pb -- the largest
atom considered -- to ensure conservative validation across all elemental
systems.

To switch the cutoff, edit the first line of the ternary `.meam` file:
```
rc = 5.1     # for Supplementary Notes S2-S4 reproduction
rc = 4.0     # for Supplementary Notes S5-S10 (default in this distribution)
```

Users running new simulations should choose `rc` based on the largest
2NN distance among the species and phases involved in their study.

### (2) Cutoff region (`delr`) for fracture-related simulations

The default `delr = 0.1` Angstrom in the ternary files follows Baskes'
original MEAM convention and works well for equilibrium and bulk-property
simulations.

**However, for any simulation involving fracture, crack propagation,
cleavage, free-surface creation, or other processes where atoms separate
across the radial cutoff without intervening neighbors (where MEAM
many-body screening no longer suppresses interactions), both `rc` and
`delr` should be increased** to remove the artificial stress barrier
caused by the cutoff truncation. Following the guideline in:

  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.
  https://doi.org/10.1080/14786435.2014.895441

representative settings such as `rc ~ 5.4 Angstrom, delr ~ 2.5 Angstrom`
(for bcc-W-like systems) or larger have been shown to remove the
unrealistic blunting and recover correct cleavage fracture behavior.
Without this adjustment, fracture simulations may exhibit non-physical
crack-tip blunting instead of brittle cleavage.

These potentials were not specifically tuned or validated for fracture
phenomena. Users investigating fracture-related behavior in Fe-Cu-X
systems should (i) follow the cutoff guideline above and (ii) verify
the appropriateness of the resulting energy-distance and stress-distance
responses through uniaxial tensile tests across the relevant cleavage
planes before drawing conclusions.

### (3) Convention for ternary 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
companion paper. Users editing or extending these parameter files 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 Fe-Cu-Sn system (atom 1 = Fe = A, atom 2 = Cu = B,
atom 3 = Sn = C):

| Paper notation    | Meaning                       | LAMMPS line in `FeCuSn.meam` |
|-------------------|-------------------------------|------------------------------|
| C^A-C-B (= 0.09)  | Fe-Cu bond screened by Sn     | `Cmin(1,2,3) = 0.09`         |
| C^A-B-C (= 1.44)  | Fe-Sn bond screened by Cu     | `Cmin(1,3,2) = 1.44`         |
| C^B-A-C (= 1.69)  | Cu-Sn bond screened by Fe     | `Cmin(2,3,1) = 1.69`         |

The same convention applies inside each binary (B2) block. For
example, in the Fe-Cu block:

| Paper notation    | Meaning                       | LAMMPS line                  |
|-------------------|-------------------------------|------------------------------|
| C^A-B-A (= 1.20)  | Fe-Fe bond screened by Cu     | `Cmin(1,1,2) = 1.20`         |
| C^B-A-B (= 0.90)  | Cu-Cu bond screened by Fe     | `Cmin(2,2,1) = 0.90`         |
| C^A-A-B (= 0.09)  | Fe-Cu bond screened by Fe     | `Cmin(1,2,1) = 0.09`         |
| C^B-B-A (= 0.36)  | Fe-Cu bond screened by Cu     | `Cmin(1,2,2) = 0.36`         |

The parameter files distributed here already follow 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]