Interplay Between Energy Density and Superconducting Properties in Negative Thermal Expansion Superconductor IrZr₃

We establish a unified theoretical framework connecting the empirical energy density (E) of tetragonal IrZr₃ with its superconducting properties. Through derived mathematical relationships, we demonstrate how texture (A) and composition (wt%) control: (i) Critical temperature enhancement ΔT_c ~ 0.12E² (ii) Critical current modulation J_c = J_c0(1+0.15E) (iii) Flux pinning optimization F_p ∝ (1+0.2E) The model explains the unusual -1.898 kJ/m³ baseline energy through negative thermal expansion (NTE) effects, providing design principles for strain-engineered superconductors. Detailed Description:This study establishes a predictive model connecting the empirical energy density (E) of tetragonal IrZr₃ to its superconducting properties. By deriving explicit relationships between texture (A), composition (wt%), and key metrics (T_c, J_c, F_p), we reveal how the unique -1.898 kJ/m³ baseline energy—rooted in uniaxial negative thermal expansion (α_c = -4×10⁻⁶ K⁻¹)—enhances electron-phonon coupling and flux pinning. Experimental validation shows <3.5% error in predicting T_c (2.34 K vs. 2.31 K measured) and B_c2 (12.3 T vs. 12.7 T).