Bayesian Parameter Estimation for Temperature-Dependent Young's Modulus in Aluminum

Building on: Rahemi, R., & Li, D. (2015). Variation in electron work function with temperature and its effect on the Young’s modulus of metals. Scripta Materialia, 99, 41–44.
DOI | arXiv

This Jupyter notebook implements MCMC-based Bayesian inference to quantify uncertainty in model parameters for the temperature dependence of Young's modulus in aluminum (FCC structure). It extends the 2015 theoretical framework — where temperature reduces the electron work function φ(T) = φ₀ − γ (k_B T)² / φ₀, leading to softening of elastic stiffness (E ∝ φ⁶) — by fitting to experimental data with full posterior distributions, credible intervals, and diagnostics.

Key features:

• Markov Chain Monte Carlo sampling for parameter estimation and uncertainty propagation
• Application to aluminum: modeling thermal effects on interatomic bonding via work function
• Visualizations: posterior distributions, trace plots, pair plots, model fits vs. data
• Improves predictive capability for materials behavior at elevated temperatures