Quantitative Correlation Between Empirical Magnetic Anisotropy Energy and Superconducting Properties in NbScTiZr: A Statistical Validation

Abstract

This study establishes a robust empirical model for magnetic anisotropy energy density (E*) in the eutectic high-entropy superconductor NbScTiZr across three processing conditions (as-cast, 400°C, and 800°C annealed). Through systematic statistical analysis, we demonstrate that our texture-weighted empirical model achieves superior predictive capability (R² = 0.892-0.934 for key superconducting parameters) compared to traditional crystallographic approaches (R² = 0.387-0.672). The model reveals an inverse relationship between E* and flux pinning efficiency, with the 400°C annealed condition showing optimal performance (E* = 56.62, α_M = 1.8, H_c2 = 14.1 T). Statistical validation confirms the model's reliability with p-values < 0.01 for all significant correlations.