佐久間 美波
238 lines
7.6 KiB
Org Mode
238 lines
7.6 KiB
Org Mode
#+TITLE: PS₄³⁻-Centered I⁻ Geometry Analysis in Li₂S–P₂S₅–LiI Glasses
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#+AUTHOR: Minami Sakuma
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#+OPTIONS: toc:2 num:nil
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* Overview
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This repository contains Python scripts for analyzing the local
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geometrical relationship between I⁻ ions and PS₄³⁻ tetrahedra in
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Li₂S–P₂S₅–LiI glass trajectories.
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For each P atom, nearby I⁻ ions are classified according to the number
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of S atoms from the same PS₄³⁻ tetrahedron located within a specified
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I–S cutoff distance.
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The resulting I⁻ spatial-density distributions are exported as Gaussian
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cube files and visualized as three-dimensional isosurfaces using Mayavi.
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* Analysis Concept
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For a given I⁻ ion and a given PS₄³⁻ tetrahedron, the number of nearby
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S atoms is defined as:
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#+begin_example
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s_count = number of S atoms within 4.7 Å from I⁻
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#+end_example
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The I⁻ configuration is classified as follows:
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| Classification | s_count | Geometrical interpretation |
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|---+---:|---|
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| Zero-type | 0 | I⁻ is not close to any S atom of the reference PS₄³⁻ unit. |
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| Corner-type | 1 | I⁻ is located near one S vertex of the PS₄³⁻ tetrahedron. |
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| Edge-type | 2 | I⁻ is located near two S atoms forming one tetrahedral edge. |
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| Three-type | 3 | I⁻ is located near three S atoms of the same PS₄³⁻ unit. |
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The terms corner-type and edge-type describe geometrical proximity only.
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They do not imply bond sharing or atom sharing between I⁻ and PS₄³⁻
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units.
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* Workflow
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#+begin_example
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LAMMPS trajectory
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v
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dump2cube_edge_corner.py
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+-- PS₄_I_All.cube
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+-- PS₄_I_zero.cube
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+-- PS₄_I_corner.cube
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+-- PS₄_I_edge.cube
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+-- PS₄_I_three.cube
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v
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cube2mayavi_edge_corner.py
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v
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Colored 3D isosurface visualization
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#+end_example
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* Files
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| File | Description |
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|--------------------------------------+------------------------------------------------------------------------------------------------------|
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| =dump2cube_edge_corner.py= | Reads a LAMMPS trajectory, aligns PS₄³⁻ units, classifies nearby I⁻ ions, and generates cube files. |
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| =cube2mayavi_edge_corner.py= | Visualizes multiple classified I⁻ cube files using different colors. |
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| =050Li3PS4-050LiI.lammpstrj= | Example LAMMPS trajectory for a Li₂S–P₂S₅–LiI glass. |
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| =050Li3PS4-050LiI_PS4_I_All.cube= | Spatial density of the four nearest I⁻ ions around each P atom. |
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| =050Li3PS4-050LiI_PS4_I_zero.cube= | Spatial density of zero-type I⁻ configurations. |
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| =050Li3PS4-050LiI_PS4_I_corner.cube= | Spatial density of corner-type I⁻ configurations. |
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| =050Li3PS4-050LiI_PS4_I_edge.cube= | Spatial density of edge-type I⁻ configurations. |
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| =050Li3PS4-050LiI_PS4_I_three.cube= | Spatial density of three-type I⁻ configurations. |
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* Requirements
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** Python packages
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The scripts require Python 3 and the following packages:
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- NumPy
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- Mayavi
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- VTK
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- Traits
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- PyQt5 or PySide6
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Mayavi is generally easiest to install through conda-forge.
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#+begin_src bash
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conda create -n ps4-iodide python=3.10
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conda activate ps4-iodide
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conda install -c conda-forge numpy mayavi pyqt
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#+end_src
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Alternatively, NumPy can be installed with pip:
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#+begin_src bash
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pip install numpy
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#+end_src
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* Input Trajectory Format
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=dump2cube_edge_corner.py= expects a LAMMPS trajectory containing the
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following atom columns:
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#+begin_example
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ITEM: ATOMS id type element xu yu zu mol
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#+end_example
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The trajectory must contain at least the following elements:
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- Li
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- P
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- S
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- I
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The script assumes that P and S atoms belonging to the same PS₄³⁻
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tetrahedron have the same molecule ID (=mol=).
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Periodic boundary conditions are applied when calculating relative
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atomic positions.
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* Analysis Procedure
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For every trajectory frame, the following procedure is performed.
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1. Each P atom is selected as the center of a reference PS₄³⁻ tetrahedron.
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2. The nearest I⁻ ion is used to define the orientation of the PS₄³⁻ unit.
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3. The S atom farthest from the nearest I⁻ ion is aligned with the z axis.
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4. A second S atom is used to fix the rotation around the z axis.
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5. The closest I⁻ ions are rotated into the common PS₄³⁻ reference frame.
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6. I⁻ ions are classified using the number of S atoms within 4.7 Å.
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7. The classified I⁻ coordinates are accumulated over all P atoms and
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trajectory frames.
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8. Three-dimensional histograms are exported as Gaussian cube files.
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* Normalization
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The density fields for zero-type, corner-type, edge-type, and three-type
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I⁻ configurations are normalized by the total number of I⁻ coordinates
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used for the overall I⁻ distribution.
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Therefore, the relative density of each classified field reflects both:
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- the spatial distribution of the configuration, and
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- the relative occurrence of that configuration.
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* Usage
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** Generate Cube Files
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#+begin_src bash
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python dump2cube_edge_corner.py \
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-i 050Li3PS4-050LiI.lammpstrj \
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-m 160 160 160 \
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-cut 8
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#+end_src
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Arguments:
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| Argument | Description |
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|---+---|
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| =-i=, =--trjfile= | Input LAMMPS trajectory file. |
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| =-m=, =--mesh= | Number of grid points along the x, y, and z directions. |
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| =-cut=, =--cutoff= | Spatial cutoff distance around the reference P atom in Å. |
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Expected output files:
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#+begin_example
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050Li3PS4-050LiI_PS4_I_All.cube
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050Li3PS4-050LiI_PS4_I_zero.cube
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050Li3PS4-050LiI_PS4_I_corner.cube
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050Li3PS4-050LiI_PS4_I_edge.cube
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050Li3PS4-050LiI_PS4_I_three.cube
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#+end_example
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** Visualize Classified I⁻ Density Fields
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#+begin_src bash
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python cube2mayavi_edge_corner.py \
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-i 050Li3PS4-050LiI_PS4_I_zero.cube \
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050Li3PS4-050LiI_PS4_I_corner.cube \
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050Li3PS4-050LiI_PS4_I_edge.cube \
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050Li3PS4-050LiI_PS4_I_three.cube \
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-iso 1.2e-09
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#+end_src
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The script assigns colors based on the file name:
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| Classification | Color |
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|----------------+--------|
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| Zero-type | Blue |
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| Corner-type | Green |
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| Edge-type | Red |
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| Three-type | Yellow |
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The reference PS₄³⁻ tetrahedron is shown with:
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| Object | Color |
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|-----------+--------|
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| P atom | Purple |
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| S atoms | Yellow |
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| P–S bonds | Gray |
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* Output
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Each Gaussian cube file contains:
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- A reference PS₄³⁻ tetrahedron
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- P atom at the origin
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- Four S atoms in the aligned coordinate system
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- A three-dimensional spatial-density field of the selected I⁻ category
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The cube files can be visualized using:
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- Mayavi
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- VMD
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- ParaView
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- PyMOL
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- Other software supporting Gaussian cube files
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* Notes and Limitations
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- The I–S cutoff for classification is fixed at 4.7 Å in the script.
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- The cube files represent accumulated spatial-density distributions.
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- The current analysis uses the nearest I⁻ ion to define the orientation
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of each PS₄³⁻ tetrahedron.
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- The script searches the 15 nearest I⁻ ions around each P atom when
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classifying zero-, corner-, edge-, and three-type configurations.
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- The output filename is generated from the input trajectory name.
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The current implementation expects an input filename containing =LiI=.
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- The current trajectory parser is primarily intended for orthorhombic
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simulation cells.
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- The Mayavi visualization requires a GUI-capable Python environment.
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* License
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This repository is intended for academic and research use.
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