Quantitative Correlation Between Parameter E and Superconducting Properties in η-Carbide-Type Zr₄Rh₂O

We present an empirical parameter E that quantitatively predicts the superconducting properties of η-carbide-type oxides, focusing on Zr₄Rh₂O. The parameter combines elemental composition weights and spin-orbit coupling effects through the relation: E = 0.355A + (0.163 - 0.031A)·wt% - 1.898 where A is the weighted average of superconducting elements. Statistical analysis reveals strong correlations between E and: - Critical temperature T_c (R² = 0.92) - Upper critical field μ₀H_c2(0) (R² = 0.89) - Pauli limit violation threshold (R² = 0.85) For Zr₄Rh₂O (E = 9.41), the model predicts T_c = 3.3 ± 0.2 K and μ₀H_c2(0) = 6.2 ± 0.3 T, matching experimental values within 10% error.