# 2NN MEAM Interatomic Potential for the Mg-Sc Binary System

## Overview
This package provides a second-nearest-neighbor modified embedded-atom
method (2NN MEAM) interatomic potential for the Mg-Sc binary system,
together with its constituent Mg and Sc unary descriptions. The potential
was developed to study structural ordering effects on the martensitic
transformation in Mg-Sc shape memory alloys, and is suitable for
atomistic simulations of the bcc (austenite) and martensite phases,
including transformation and mechanical behavior.

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

  H.-H. Ahn, J. Hur, G. Xu, W.-S. Ko,
  "Atomistic insights into structural ordering effects on martensitic
  transformations in Mg-Sc shape memory alloys",
  Acta Materialia 306 (2026) 121929.
  DOI: 10.1016/j.actamat.2026.121929
  https://doi.org/10.1016/j.actamat.2026.121929

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

  J. S. Lee, G. Xu, J. S. Suh, J. H. Bae, B.-C. Suh, Y. M. Kim,
  W.-S. Ko, B.-J. Lee,
  "Atomistic investigation into the formation of axial weak twins during
  the compression of single-crystal Mg nanopillars",
  Acta Materialia 263 (2024) 119512.
  DOI: 10.1016/j.actamat.2023.119512
  https://doi.org/10.1016/j.actamat.2023.119512

## Files
| File           | Description                                          |
|----------------|------------------------------------------------------|
| `library.meam` | Pure-element parameters (Mg, Sc)                     |
| `MgSc.meam`    | Binary parameters for the Mg-Sc system               |

`MgSc.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 `MgSc.meam` are fixed:
- Atom 1 = Mg
- Atom 2 = Sc

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

## Reference Structures
| System | Reference structure   |
|--------|-----------------------|
| Mg     | bcc                   |
| Sc     | bcc                   |
| Mg-Sc  | B2 (CsCl type, MgSc)  |

Note: the reference structure of pure Mg and Sc in this potential is bcc.

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

---

## IMPORTANT NOTES

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

The cutoff in `MgSc.meam` is set to **`rc = 5.0` A**, and this value
should be retained for studies of the Mg-Sc shape memory alloy.

This cutoff is **required to correctly reproduce the martensitic
transformation behavior** of Mg-Sc. It also exceeds the second
nearest-neighbor distances of the constituent elements, ensuring that
2NN interactions are properly captured. Reducing the cutoff below 5.0 A
may degrade or alter the martensitic transformation characteristics and
is not recommended for shape-memory-related simulations.

If you adapt this potential to a different problem, confirm that the
cutoff remains appropriate for the largest 2NN distance among the species
and phases involved. The cutoff is set on the first line of `MgSc.meam`:
```
rc = 5.0     # required for correct martensitic transformation behavior
```

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

The default `delr = 0.1` A follows Baskes' original MEAM convention and
works well for equilibrium and bulk-property simulations.

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

  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

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.

### (3) 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 Mg-Sc (B2) binary block (A = Mg = atom 1, B = Sc = atom 2):

| Paper notation       | Meaning                       | LAMMPS line in `MgSc.meam`   |
|----------------------|-------------------------------|------------------------------|
| C^A-B-A (= 1.20)     | Mg-Mg bond screened by Sc     | `Cmin(1,1,2) = 1.20`         |
| C^B-A-B (= 1.20)     | Sc-Sc bond screened by Mg     | `Cmin(2,2,1) = 1.20`         |
| C^A-A-B (= 0.09)     | Mg-Sc bond screened by Mg     | `Cmin(1,2,1) = 0.09`         |
| C^B-B-A (= 2.00)     | Mg-Sc bond screened by Sc     | `Cmin(1,2,2) = 2.00`         |

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