Correlation of srf performance to oxygen diffusion length of medium temperature heat treated cavities

This comprehensive study, being part of the European XFEL R\&D effort, elucidates the influence of medium temperature (mid-T) heat treatments between 250{\deg}C and 350{\deg}C on the performance of 1.3~GHz superconducting radiofrequency (SRF) niobium cavities. Utilizing a refurbished niobium retort furnace equipped with an inter-vacuum chamber and cryopumps at DESY, we have embarked on an investigation to enhance the state-of-the-art SRF cavity technology. Our research reveals that mid-T heat treatments significantly boost the quality factor ($Q_0$) of the cavities, achieving values between $2\cdot10^{10}$ to $5\cdot10^{10}$ at field strengths around 16~MV/m, while the maximum field strengths are limited to 25-35~MV/m and enhanced sensitivity to trapped magnetic flux is observed. Moreover, we delve into the effects of surface impurity concentration changes, particularly the diffusion of oxygen content, and its impact on performance enhancements. By categorizing treatments based on calculated diffusion lengths using the whole temperature profile, we recognize patterns that suggest an optimal diffusion length conducive to optimizing cavity performance. SIMS results from samples confirm the calculated oxygen diffusion lengths in most instances. Deviations are primarily attributed to grain boundaries in fine-grain materials, necessitating repeated measurements on single-crystal materials to further investigate this phenomenon. Investigations into cooling rates and the resulting spatial temperature gradients across the cavities ranging from 0.04 to 0.2~K/mm reveal no significant correlation with performance following a mid-T heat treatment. However, the increased sensitivity to trapped magnetic flux leads to new challenges in the quest for next-generation accelerator technologies since the requirement for magnetic hygiene gets stricter.