Parameter Estimation of the Thermal Conductivity of Superconducting Niobium

The thermal conductivity of niobium at approximately 2 K may be up to 3 times greater than at 4 K due to a so-called phonon peak. Metallurgical processing of niobium, and thus its crystal structure and dislocation density, determines the existence and magnitude of the phonon peak. There is need for improved understanding of relationship between the thermal conductivity at these temperatures and the metallurgical processes that influence the thermal response. Data for measurements of temperature and heat flux for several niobium specimens are fit using a theoretically based model of niobium thermal conductivity. Unlike most studies, the parameter estimation method proposed here omits the intermediate step of estimating conductivity from temperature and heat flux measurements, and then fitting the conductivity to find the parameters of the model. Instead, the parameters in the model are estimated directly from the temperature and heat flux results. The model includes terms for electron and phonon heat conduction, with five empirical parameters. Results for two specimens with significantly different temperature dependencies of thermal conductivity are presented. The differences in the two sets of parameters are discussed in light of the known metallurgical differences between the two specimens. Comparison is also made with published parameter values.