# 2NN MEAM Interatomic Potential for the Ag-Cu-Sn Ternary System

## Overview
This package provides a 2NN MEAM interatomic potential for the
Ag-Cu-Sn ternary system, developed for atomistic simulations of
lead-free solder materials and related Ag-Cu-Sn alloys. The unary
descriptions of Ag, Cu, and Sn, the related binary subsystems
(Ag-Cu, Ag-Sn, Cu-Sn), and the ternary cross-interactions were
all determined via force-matching to DFT energies and forces.

## References
Please cite the following papers when using this potential:

(1) Ternary potential and related binary/unary descriptions:

    W.-S. Ko, J.S. Lee, D.-H. Kim,
    "Atomistic simulations of Ag-Cu-Sn alloys based on a new
    modified embedded-atom method interatomic potential",
    Journal of Materials Research 37 (2022) 145-161.
    https://doi.org/10.1557/s43578-021-00395-z

(2) The underlying unary description of pure Sn used in (1):

    W.-S. Ko, D.-H. Kim, Y.-J. Kwon, M.H. Lee,
    "Atomistic simulations of pure tin based on a new modified
    embedded-atom method interatomic potential",
    Metals 8 (2018) 900.
    https://doi.org/10.3390/met8110900

## Files
| File              | Description                                          |
|-------------------|------------------------------------------------------|
| `library.meam`    | Pure-element parameters (Ag, Cu, Sn)                 |
| `AgCuSn.meam`     | Ag-Cu-Sn ternary parameters (binaries + cross-terms) |

The ternary file `AgCuSn.meam` 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 = Ag
- Atom 2 = Cu
- Atom 3 = Sn

## LAMMPS Usage Example
```
pair_style    meam
pair_coeff    * * library.meam Ag Cu Sn AgCuSn.meam Ag Cu Sn
```
(adjust element symbols to match your data file's atom types)

---

## IMPORTANT NOTES

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

The radial cutoff (`rc`) is specified in the first line of `AgCuSn.meam`.
The pure-Sn potential of Ref. (2) was developed and validated with
`rc = 5.0 Angstrom`, and the ternary file inherits a consistent value to
ensure correct interatomic interactions across all element pairs in the
Ag-Cu-Sn system. 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` in the ternary file 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.

This potential was not specifically tuned or validated for fracture
phenomena. Users investigating fracture-related behavior in Ag-Cu-Sn
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 Ag-Cu-Sn system (atom 1 = Ag = A, atom 2 = Cu = B,
atom 3 = Sn = C):

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

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

| Paper notation | Meaning                    | LAMMPS line          |
|----------------|----------------------------|----------------------|
| C^A-B-A        | Ag-Ag bond screened by Cu  | `Cmin(1,1,2) = ...`  |
| C^B-A-B        | Cu-Cu bond screened by Ag  | `Cmin(2,2,1) = ...`  |
| C^A-A-B        | Ag-Cu bond screened by Ag  | `Cmin(1,2,1) = ...`  |
| C^B-B-A        | Ag-Cu bond screened by Cu  | `Cmin(1,2,2) = ...`  |

The parameter file distributed here 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]