AProposed Multi-Scale Framework for High-Entropy Alloy Strengthening: Bridging Atomic Distortion and Quantum Confinement Effects

 High-entropy alloys (HEAs) exhibit exceptional mechanical properties that conventional strengthening models fail to fully capture. This work presents a comprehensive theoretical framework bridging atomic-scale lattice distortion with quantum confinement effects in ultrafine-grained microstructures. The framework integrates the Root Mean Squared Atomic Displacement (RMSAD) model with quantum mechanical size effects to predict yield strength across length scales from nanometers to microns. Extensive validation against published experimental data from 80+ HEA systems (including CoCrFeMnNi, refractory, and interstitial-strengthened alloys) demonstrates strong correlation (R2 = 0.89) between theoretical predictions and observed strengthening trends. Theoretical analysis indicates quantum effects contribute 15-25% to total strengthening when grain sizes approach 50 nm, while atomic distortion remains dominant at conventional grain sizes. This multi-scale framework provides new perspectives for understanding HEA strengthening and establishes a computational foundation for predictive alloy design.