#+TITLE: Nearest P/I Environment Analysis for Li₃PS₄–LiI Glasses
#+AUTHOR: Minami Sakuma
#+OPTIONS: toc:2 num:t

* Overview

This repository contains a Python program for analyzing the local
environments of Li⁺ ions in Li₃PS₄–LiI glass trajectories.

For each Li⁺ ion, the program calculates the distances to the nearest
P atom and I⁻ ion under periodic boundary conditions. It then determines
whether the Li⁺ ion is closer to P or I⁻.

The following two quantities are calculated for each composition:

- The P fraction in the entire system:
  P / (P + I)
- The fraction of Li⁺ ions whose nearest center is P:
  N_{Li-near-P} / N_{Li}

The second quantity is calculated for each molecular-dynamics step and
then averaged over all steps.

* Target System

The target system is Li₃PS₄–LiI glass.

The following compositions are included in this repository:

- 80Li₃PS₄–20LiI
- 70Li₃PS₄–30LiI
- 60Li₃PS₄–40LiI
- 50Li₃PS₄–50LiI

* Analysis Procedure

For each molecular-dynamics step, the program performs the following
operations:

1. Read the coordinates of Li⁺, P, S, and I⁻.
2. Calculate all Li⁺–P distances under periodic boundary conditions.
3. Calculate all Li⁺–I⁻ distances under periodic boundary conditions.
4. Identify the nearest P atom and I⁻ ion for each Li⁺ ion.
5. Classify each Li⁺ ion according to whether P or I⁻ is closer.
6. Calculate the fraction of Li⁺ ions whose nearest center is P.
7. Average the fraction over all simulation steps.

The minimum-image convention is used to calculate distances under
periodic boundary conditions.

* Requirements

- Python 3
- NumPy
- Matplotlib

The required Python packages can be installed using:

#+BEGIN_SRC shell
pip install numpy matplotlib
#+END_SRC

* Repository Contents

#+BEGIN_EXAMPLE
.
├── calc_share.py
├── 050Li3PS4-050LiI_thin100.lammpstrj
├── 060Li3PS4-040LiI_thin100.lammpstrj
├── 070Li3PS4-030LiI_thin100.lammpstrj
├── 080Li3PS4-020LiI_thin100.lammpstrj
├── Readme.org
└── .gitignore
#+END_EXAMPLE

* Usage

Run the program by specifying one or more trajectory files with the
=-i= option:

#+BEGIN_SRC shell
python calc_share.py -i \
  080Li3PS4-020LiI_thin100.lammpstrj \
  070Li3PS4-030LiI_thin100.lammpstrj \
  060Li3PS4-040LiI_thin100.lammpstrj \
  050Li3PS4-050LiI_thin100.lammpstrj
#+END_SRC

A wildcard can also be used:

#+BEGIN_SRC shell
python calc_share.py -i *.lammpstrj
#+END_SRC

* Output

The program generates a plot containing the following quantities:

- Blue line: P / (P + I) in the entire system
- Green line: fraction of Li⁺ ions whose nearest center is P,
  averaged over all simulation steps

The plot is saved as:

#+BEGIN_EXAMPLE
voronoi_count_diff.pdf
#+END_EXAMPLE

* Expected Trajectory Format

The current parser assumes a specific LAMMPS trajectory format:

- Each atom record contains six columns.
- The third column contains the element name:
  Li, P, S, or I.
- The fourth to sixth columns contain the atomic coordinates.
- The simulation cell is orthorhombic.
- The number and order of header fields are fixed for every frame.

If the trajectory format differs from these assumptions, the data-loading
section of =calc_share.py= must be modified.

* Notes

- Li⁺ ions for which the nearest P and I⁻ distances are exactly equal
  are excluded from both counts in the current implementation.
- This analysis is based on nearest-neighbor distances and is not a
  rigorous Voronoi tessellation.
- The local P fraction around Li⁺ should be interpreted by comparison
  with the P / (P + I) fraction in the entire system.
- The current code assumes that both P and I⁻ are present in every
  trajectory.