XRD-NanoSize-Lab

🚀 Conceived, Engineered & Presented by Youssef Attia
🎓 University spin-off competition
📅 Advanced Materials Research & Engineering Initiative | 2025

XRD-NanoSize-Lab was developed as part of a technical competition organized in collaboration with a materials science spin-off, with the objective of designing a robust and reproducible computational tool for quantitative X-ray diffraction (XRD) analysis.

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This project provides a C++ pipeline for analyzing X-ray diffraction (XRD) data of alumina samples. It fits peaks using a pseudo-Voigt profile and calculates crystallite sizes using the Scherrer equation. The Levenberg-Marquardt fitting is implemented using Eigen for accurate and robust optimization.

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Pseudo-Voigt Profile

The pseudo-Voigt function used for peak fitting is:

$$ V(x, A, \mu, \sigma, \gamma) = \eta \cdot G(x, A, \mu, \sigma) + (1 - \eta) \cdot L(x, A, \mu, \gamma) $$

where:

• G(x, A, μ, σ) is the Gaussian component
• L(x, A, μ, γ) is the Lorentzian component
• η is the mixing factor (0 ≤ η ≤ 1)
• A is the amplitude
• μ is the peak center
• σ is the Gaussian width
• γ is the Lorentzian widthth

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Features

• Load XRD data from CSV files
• Preprocess data with smoothing and normalization
• Detect peaks in 2θ space
• Fit Voigt peaks using Levenberg-Marquardt (Eigen)
• Calculate FWHM and crystallite size
• Monte Carlo estimation of FWHM uncertainty
• Compute residuals and statistical anomaly score

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Scientific Highlights

• Fully self-contained nonlinear Voigt fitting implemented from first principles
• Analytical Jacobian construction and LDLT-based Levenberg-Marquardt solver
• Physics-constrained peak parameters for meaningful and reproducible results
• Monte Carlo uncertainty propagation using residual-driven noise injection
• Statistical residual anomaly scoring to detect peak asymmetry, secondary phases, or fitting inadequacy
• Designed for longitudinal and comparative XRD analysis across multiple datasets

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Available databases

• Crystallography Open Database (COD) — open-access
• Inorganic Crystal Structure Database (ICSD) — commercial
• Powder Diffraction File (PDF-4/PDF-2) — commercial

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Dependencies

• C++17 compatible compiler (GCC ≥ 9, Clang ≥ 10, MSVC ≥ 2019)
• Eigen (header-only library, version 3.4+)

No other external libraries are required. All other functionality uses standard C++17 libraries.

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Compilation

g++ -std=c++17 main.cpp xrd_analysis.cpp -I /path/to/eigen -o xrd_analysis