Superconducting radio frequency (SRF) cavities fabricated from bulk high purity niobium (Nb) are increasingly used for particle accelerators to achieve continuous operation. Even in the superconducting regime, residual resistance and small imperfections on the RF surface can dissipate energy and cause local heating that leads to cavity quench. Large values of thermal conductivity can mitigate local temperature excursions and prevent cavity quench, thus improving cavity performance. Understanding thermal transport in bulk and thin film superconducting Nb may guide thermal design of current and next generation SRF cavities.The thermal conductivity of metals is composed of electronic and lattice (phonon) components. In normal conductors, the electronic component dominates, and in superconducting metals, as the temperature drops below the critical temperature, phonons become increasingly important carriers of thermal energy. A widely used model of thermal conductivity in superconductors omits explicit accounting of the effect of dislocations, which result from deformation. Here, this model is extended by accounting for the effects of phonons scattered by dislocations independent from boundary scattering. This extended model agrees better with measurements of thermal conductivity in deformed Nb samples, especially at temperatures T less than 3 K. An apparent threshold of dislocation density Nd is found to be Nd = O(1012) m-2 for Nb and when applied to tantalum (Ta), it is Nd = O(1011) m-2. There is little contribution to the thermal conductivity when the dislocation density is less than this threshold. This model can also be used to estimatethe dislocation density by fitting measured values of thermal conductivity.Examination of thermal conductivity data for superconducting Nb shows that there is often a local maximum, a so-called phonon peak, kpp. The temperature at which this kpp occurs Tpp is between 1.72 K and 2.35 K and shifts for samples after deformation. It is well known that the magnitude of kpp decreases as the material is deformed, and hence with increasing Nd. Less cited is that Tpp increases with increasing Nd. This may affect the operating temperature of an SRF cavity. At a certain level deformation (i.e., 4.7% deformation for a residual resistivity ratio RRR = 185), the phonon peak disappears. More deformation is needed for higher RRR, (i.e., greater purity).The models discussed above require estimating several parameters from thermal conductivity measurements and may be best suited to explaining the relative importance of the several scattering mechanisms. For predicting thermal conductivity from basic material variables, the Boltzmann transport equation (BTE) is solved by two methods to predict the lattice component of thermal conductivity. One method uses a substitution of variables from frequency to wavevector in the Callaway model to include the nonlinear phonon dispersion relationship for the longitudinal acoustic (LA) and transverse acoustic (TA) phonon polarizations. This model incorporates a relaxation time approximation using Matthiessen's rule to consider phonon scattering by electrons, boundaries, and dislocations. Another method to predict the lattice thermal conductivity uses an energy-based, variance-reduced Monte Carlo (MC) solution to the BTE for phonons. The MC solution allows more general consideration of the individual scattering mechanisms. It may also be generalized for more complex geometries. The MC solution technique was first verified by comparing the predicted thermal conductivity in bulk Si and Si nanowires with experimental results. Both solutions of the BTE for the lattice thermal conductivity of undeformed and deformed superconducting Nb agreed well with experimental values. The MC model was also used to demonstrate that interstitial impurities must be near saturation to change the lattice thermal conductivity of Nb. The MC solution was also effective in predicting the lattice thermal conductivity of superconducting Ta, with the appropriate change in dispersion relation and other material parameters.
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