# 2NN MEAM Interatomic Potential for the Cu-Ni-Ti (NiTiCu) Ternary System

## Overview
This package provides a second-nearest-neighbor modified embedded-atom
method (2NN MEAM) interatomic potential for the Cu-Ni-Ti ternary system,
together with its constituent Cu, Ni, Ti unary and Cu-Ni, Cu-Ti, Ni-Ti
binary descriptions. The potential was developed to study phase
transformations in NiTiCu shape memory alloys, and is suitable for
atomistic simulations of Cu-alloyed NiTi, including the martensitic
transformation and related mechanical behavior.

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

  W.-S. Ko, J. Hur, J.-Y. Hwang, Y.-B. Chun,
  "Atomistic investigation of phase transformations in NiTiCu shape
  memory alloys",
  International Journal of Mechanical Sciences 274 (2024) 109256.
  DOI: 10.1016/j.ijmecsci.2024.109256
  https://doi.org/10.1016/j.ijmecsci.2024.109256

The Ni-Ti binary description (and the Ni, Ti unary parameters) is adopted
from the earlier Ni-Ti potential. Users employing the Ni-Ti part should
additionally cite:

  W.-S. Ko, B. Grabowski, J. Neugebauer,
  "Development and application of a Ni-Ti interatomic potential with high
  predictive accuracy of the martensitic phase transition",
  Phys. Rev. B 92 (2015) 134107.
  DOI: 10.1103/PhysRevB.92.134107
  https://doi.org/10.1103/PhysRevB.92.134107

## Files
| File           | Description                                          |
|----------------|------------------------------------------------------|
| `library.meam` | Pure-element parameters (Cu, Ni, Ti)                 |
| `CuNiTi.meam`  | Binary and ternary parameters for the Cu-Ni-Ti system|

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

## Element Ordering (mandatory)
The atom indices in `CuNiTi.meam` are fixed:
- Atom 1 = Cu
- Atom 2 = Ni
- Atom 3 = Ti

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

## Reference Structures
| Binary | Reference structure          | Source            |
|--------|------------------------------|-------------------|
| Cu-Ni  | B2 (CsCl type, NiCu)         | this work         |
| Cu-Ti  | B2 (CsCl type, TiCu)         | this work         |
| Ni-Ti  | B2 (CsCl type, NiTi)         | Ko et al. (2015)  |

The Ni, Ti unary parameters and the Ni-Ti binary parameters are taken from
the Ni-Ti potential of Ko, Grabowski, and Neugebauer, Phys. Rev. B 92
(2015) 134107.

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

---

## IMPORTANT NOTES

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

The cutoff in `CuNiTi.meam` is set to **`rc = 5.0` A**, and this value
should be retained for studies of the NiTi(Cu) shape memory alloy.

This cutoff is **required to correctly reproduce the martensitic
transformation behavior** of NiTi-based alloys. It also exceeds the
second nearest-neighbor distances of all three elements, ensuring that
2NN interactions are properly captured for every species in the system.
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
`CuNiTi.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)

**Note on element order:** In the reference paper, the binary systems are
labeled Ni-Ti, Ni-Cu, and Ti-Cu (i.e., the paper's "A" and "B" do not
follow the atom-index order used in this file). The atom indices here are
fixed as Cu = 1, Ni = 2, Ti = 3. When cross-checking the binary Cmin/Cmax
against Table 2 of the paper, map the paper's A and B to the correct atom
index first. For example, for the paper's "Ni-Cu" system (A = Ni = atom 2,
B = Cu = atom 1):

| Paper notation       | Meaning                       | LAMMPS line in `CuNiTi.meam` |
|----------------------|-------------------------------|------------------------------|
| C^A-B-A (= 0.09)     | Ni-Ni bond screened by Cu     | `Cmin(2,2,1) = 0.09`         |
| C^B-A-B (= 0.09)     | Cu-Cu bond screened by Ni     | `Cmin(1,1,2) = 0.09`         |
| C^A-A-B (= 0.36)     | Ni-Cu bond screened by Ni     | `Cmin(2,1,2) = 0.36`         |
| C^B-B-A (= 0.64)     | Ni-Cu bond screened by Cu     | `Cmin(1,2,1) = 0.64`         |

For the ternary cross-terms (Table 3 of the paper; atom 1 = Cu,
atom 2 = Ni, atom 3 = Ti):

| Paper notation       | Meaning                       | LAMMPS line in `CuNiTi.meam` |
|----------------------|-------------------------------|------------------------------|
| C^Cu-Ti-Ni (= 0.70)  | Cu-Ni bond screened by Ti     | `Cmin(1,2,3) = 0.70`         |
| C^Cu-Ni-Ti (= 0.25)  | Cu-Ti bond screened by Ni     | `Cmin(1,3,2) = 0.25`         |
| C^Ni-Cu-Ti (= 0.16)  | Ni-Ti bond screened by Cu     | `Cmin(2,3,1) = 0.16`         |

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