rheedium 2025.8.31

Differentiable RHEED simulations and Reconstruction in JAX

Rheedium

High-Performance RHEED Pattern Simulation for Crystal Surface Analysis

A JAX-accelerated Python package for realistic Reflection High-Energy Electron Diffraction (RHEED) pattern simulation using kinematic theory and atomic form factors.

Documentation • Installation • Quick Start • Examples • Contributing

Overview

Rheedium is a modern computational framework for simulating RHEED patterns with scientific rigor and computational efficiency. Built on JAX for automatic differentiation and GPU acceleration, it provides researchers with tools to:

• Simulate realistic RHEED patterns using Ewald sphere construction and kinematic diffraction theory
• Analyze crystal surface structures with atomic-resolution precision
• Handle complex reconstructions including domains, supercells, and surface modifications
• Leverage high-performance computing with JAX's JIT compilation and GPU support

Key Features

• JAX-Accelerated: GPU-ready computations with automatic differentiation
• Physically Accurate: Kirkland atomic potentials and kinematic scattering theory
• Comprehensive Analysis: Support for CIF files, surface reconstructions, and domains
• Visualization Tools: Phosphor screen colormap and interpolation for realistic display
• Research-Ready: Designed for thin-film growth, MBE, and surface science studies

Installation

Prerequisites

• Python 3.8 or higher
• CUDA-compatible GPU (optional, for acceleration)

Install from PyPI

pip install rheedium

Install for Development

git clone https://github.com/your-username/rheedium.git
cd rheedium
pip install -e ".[dev]"

Dependencies

• JAX (with GPU support if available)
• NumPy
• Matplotlib
• SciPy
• Pandas
• Beartype (for runtime type checking)

Quick Start

Basic RHEED Simulation

import rheedium as rh
import jax.numpy as jnp

# Load crystal structure from CIF file
crystal = rh.inout.parse_cif("data/SrTiO3.cif")

# Simulate RHEED pattern
pattern = rh.simul.simulate_rheed_pattern(
    crystal=crystal,
    voltage_kV=10.0,        # Beam energy
    theta_deg=2.0,          # Grazing angle
    detector_distance=1000.0 # Screen distance (mm)
)

# Visualize results
rh.plots.plot_rheed(pattern, interp_type="cubic")

Working with Surface Reconstructions

# Filter atoms within penetration depth
filtered_crystal = rh.ucell.atom_scraper(
    crystal=crystal,
    zone_axis=jnp.array([0, 0, 1]),  # Surface normal
    penetration_depth=5.0            # Angstroms
)

# Simulate pattern for surface layer
surface_pattern = rh.simul.simulate_rheed_pattern(
    crystal=filtered_crystal,
    voltage_kV=15.0,
    theta_deg=1.5
)

Advanced Analysis

# Generate reciprocal lattice points
reciprocal_points = rh.ucell.generate_reciprocal_points(
    crystal=crystal,
    hmax=5, kmax=5, lmax=2
)

# Calculate kinematic intensities
intensities = rh.simul.compute_kinematic_intensities(
    positions=crystal.cart_positions[:, :3],
    G_allowed=reciprocal_points
)

Examples

1. Single Crystal Analysis

import rheedium as rh

# Load SrTiO3 structure
crystal = rh.inout.parse_cif("examples/SrTiO3.cif")

# High-resolution simulation
pattern = rh.simul.simulate_rheed_pattern(
    crystal=crystal,
    voltage_kV=30.0,
    theta_deg=1.0,
    hmax=6, kmax=6, lmax=2,
    tolerance=0.01
)

# Create publication-quality plot
rh.plots.plot_rheed(
    pattern, 
    grid_size=400,
    interp_type="cubic",
    cmap_name="phosphor"
)

2. Surface Reconstruction Study

# Analyze (√13×√13)-R33.7° reconstruction
reconstructed_crystal = rh.ucell.parse_cif_and_scrape(
    cif_path="data/SrTiO3.cif",
    zone_axis=jnp.array([0, 0, 1]),
    thickness_xyz=jnp.array([0, 0, 3.9])  # Single unit cell
)

# Compare patterns at different azimuths
azimuths = [0, 15, 30, 45]
patterns = []

for azimuth in azimuths:
    # Rotate crystal
    rotation_matrix = rh.ucell.build_rotation_matrix(azimuth)
    rotated_crystal = rh.ucell.rotate_crystal(reconstructed_crystal, rotation_matrix)
    
    # Simulate pattern
    pattern = rh.simul.simulate_rheed_pattern(rotated_crystal, theta_deg=2.6)
    patterns.append(pattern)

3. Domain Analysis

# Multi-domain simulation
domains = []
for rotation_angle in [33.7, -33.7]:  # Twin domains
    rotated_crystal = rh.ucell.rotate_crystal(crystal, rotation_angle)
    domain_pattern = rh.simul.simulate_rheed_pattern(rotated_crystal)
    domains.append(domain_pattern)

# Combine domain contributions
combined_pattern = rh.types.combine_rheed_patterns(domains)

Supported File Formats

• CIF files: Crystallographic Information Format with symmetry operations
• CSV data: Kirkland atomic potential parameters
• Image formats: PNG, TIFF, SVG for visualization output

Configuration

Performance Optimization

import jax

# Enable 64-bit precision
jax.config.update("jax_enable_x64", True)

# Use GPU if available
jax.config.update("jax_platform_name", "gpu")

# JIT compilation for speed
@jax.jit
def fast_simulation(crystal, voltage):
    return rh.simul.simulate_rheed_pattern(crystal, voltage_kV=voltage)

Custom Atomic Potentials

# Use custom Kirkland parameters
custom_potential = rh.simul.atomic_potential(
    atom_no=38,  # Strontium
    pixel_size=0.05,
    sampling=32,
    potential_extent=6.0,
    datafile="custom_potentials.csv"
)

Applications

Rheedium is designed for researchers working in:

• Molecular Beam Epitaxy (MBE): Real-time growth monitoring and optimization
• Pulsed Laser Deposition (PLD): Surface quality assessment and phase identification
• Surface Science: Reconstruction analysis and domain characterization
• Materials Engineering: Thin film quality control and defect analysis
• Method Development: New RHEED analysis technique validation

Documentation

Full documentation is available at rheedium.readthedocs.io, including:

• API Reference: Complete function and class documentation
• Tutorials: Step-by-step guides for common workflows
• Theory Guide: Mathematical background and implementation details
• Examples Gallery: Real-world usage scenarios with code

Contributing

We welcome contributions from the community! Please see our Contributing Guide for details on:

• Code style and standards
• Testing requirements
• Documentation guidelines
• Pull request process

Development Setup

git clone https://github.com/your-username/rheedium.git
cd rheedium
pip install -e ".[dev,test,docs]"
pre-commit install

Running Tests

pytest tests/
pytest --cov=rheedium tests/  # With coverage

License

This project is licensed under the MIT License - see the LICENSE file for details.

Citation

If you use Rheedium in your research, please cite:

@software{rheedium2024,
  title={Rheedium: High-Performance RHEED Pattern Simulation},
  author={Mukherjee, Debangshu},
  year={2025},
  url={https://github.com/debangshu-mukherjee/rheedium},
  version={2025.6.16},
  doi={10.5281/zenodo.14757400},
}