Abstract

The interplay between alloying and superconductivity remains a central topic in condensed matter physics, particularly in low-temperature superconductors where electron–phonon interactions dominate. In this study, we investigate how alloying influences the superconducting transition temperature (TcT_cTc ) within the BCS–McMillan theoretical framework. By introducing phenomenological concentration-dependent modifications to the Debye temperature (ΘD\Theta_ DΘD ) and electron–phonon coupling constant (λ\lambdaλ), we model the non monotonic behavior of TcT_cTc in representative Nb–Sn alloy systems. Our results reveal that moderate alloying enhances superconductivity by increasing the density of states at the Fermi level and strengthening electron–phonon coupling, while excessive substitution suppresses TcT_cTc due to disorder and phonon softening. Comparison with experimental data for Nb–Sn and emerging high-entropy alloys confirms that alloying acts as a tuning parameter for superconducting properties, albeit limited by disorder-induced suppression. This framework provides both a pedagogical and predictive model for exploring superconductivity in complex alloy systems. Background: The relationship between alloying and superconductivity remains a critical focus in condensed matter physics, particularly in low-temperature superconductors (LTS) where the electron–phonon mechanism dominates. Aim: To model and interpret how alloying influences the superconducting critical temperature (Tc) within the BCS–McMillan theoretical framework. Objectives: Journal of Biochemistry and Biophysics 1. To establish a phenomenological relationship between alloy concentration and Tc. 2. To identify competing mechanisms enhancement from increased electron phonon coupling versus suppression due to disorder. 3. To validate theoretical predictions against Nb–Sn experimental data. 4. To extend the model’s applicability to emerging high-entropy superconductors. Material: Theoretical modeling based on McMillan’s extension of BCS theory. The alloying dependence of Debye temperature (ΘD) and electron–phonon coupling constant (λ) were parameterized as concentration-dependent functions. Result: The model predicts a non-monotonic dependence of Tc on alloying concentration. Moderate alloying enhances Tc by increasing λ and density of states at the Fermi level, whereas excessive substitution suppresses superconductivity through phonon softening and disorder scattering. Conclusion: Alloying serves as a tuning mechanism for superconductivity. The BCS–McMillan framework successfully reproduces experimental trends in Nb–Sn and provides insights applicable to high-entropy alloys.

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