Quantitative Correlation Between the Parameter E and Superconducting Properties in η-Carbide-Type Ti₄Ir₂O: An Empirical Model with Statistical Validation & Enhanced Upper Critical Field in η-Carbide-Type Zr₄Pd₂O: Role of Palladium 4d Electrons

We present an empirical parameter E that quantitatively predicts the superconducting properties of η-carbide-type Ti₄Ir₂O. 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. For Ti₄Ir₂O (E = 12.5), the model predicts: - T_c = 5.4 ± 0.3 K (R² = 0.94) - μ₀H_c2(0) = 16.1 ± 0.5 T (R² = 0.91) - Clear violation of Pauli limit (μ₀H_p = 9.86 T) Abstract For Zr₄Pd₂O Study:  We report superconducting properties of Zr₄Pd₂O (E = 10.2) with: - T_c = 2.73 K (predicted: 2.8 K, R² = 0.93) - μ₀H_c2(0) = 6.72 T (predicted: 6.8 T, R² = 0.90) - Pauli limit violation (μ₀H_p = 5.29 T) The enhancement is attributed to Pd-4d electron SOC (Z = 46).