# Improvement of Surface Roughness and Cracking Study of Nb\({}_{3}\)Sn SRF Films
## 1 Introduction  
Superconducting radiofrequency (SRF) cavities are widely used in particle accelerators. Traditional niobium cavities have reached outstanding performance levels, which are close to their theoretical limit, in the past half century. Nb\({}_{3}\)Sn is known as a novel and potential material for SRF technology, with a higher critical temperature (18.1 K) and higher predicted superheating field (420 mT) than Nb (9.2 K and 240 mT). Recently, more and more institutes, including Fermilab [1], Cornell University [2], Jefferson Lab [3], IMP [4], KEK [5], PKU [6], SARI [7], etc., have carried out research to improve the performance of Nb\({}_{3}\)Sn cavities by the tin vapor diffusion method. The cavity prepared by this method is expected to be applied in a conduction-cooling cryomodule. Nowadays Nb\({}_{3}\)Sn cavities have been demonstrated in the stable operation of 4.2 K conduction-cooling compact accelerators, showing their great potentials for practical industrial accelerator applications [8]. However, there still remain issues which can lower the acceleration gradients and Q values of cavities, such as large surface roughness, non-stoichiometry in grains and grain boundaries, etc. Furthermore, the preprocessing and postprocessing procedures for Nb\({}_{3}\)Sn cavities are not yet perfect compared with Nb cavities. Surface roughness is one of the limitations of cavity performance, which contributes the residual resistance, enhances the surface magnetic fields and increases the risk of quenches [2]. Typical average roughness value of Nb\({}_{3}\)Sn cavities by tin vapor diffusion method is 200-300 nm for 2-3 \(\upmu\)m thick films and many efforts have been paid on reducing the surface roughness. [PERSON], etc. proposed a rapid ramping in nucleation stage and reduced the film thickness, which generated a \"shiny\" Nb\({}_{3}\)Sn film with mean roughness (R\({}_{\text{a}}\)) of 63 nm and grain size of 0.93 \(\upmu\)m at Fermilab [1]. [PERSON] et al. at Cornell University tried buffered chemical polishing (BCP), electropolishing (EP) and oxipolishing on Nb\({}_{3}\)Sn-coated samples, and the oxipolishing was proved effectively to reduce the surface roughness but with obvious residues in SEM scan results [2]. [PERSON] at Jlab had proposed a pre-electroplating method to fabricate low-roughness and very uniform Nb\({}_{3}\)Sn samples and achieved R\({}_{\text{a}}\) of 54 nm for about 1 \(\upmu\)m Nb\({}_{3}\)Sn film. This method has been demonstrated on cavities and showed improvement in regard to Q values [9]. [PERSON] et al. applied centrifugal barrel polishing (CBP) on Nb\({}_{3}\)Sn films and obtained an RMS roughness lower than 20 nm, but they found that some holes appeared on the surface of polished films, and so a re-coating procedure was necessary [10]. Buffered electropolishing (BEP) is reported to be able to reduce the RMS roughness of Nb to the level of 5 nm and has a potential for reducing film roughness as a preprocess method [11]. To study the influence of surface roughness on the Nb\({}_{3}\)Sn film, we introduce BEP method to treat the Nb substrate before coating Nb\({}_{3}\)Sn, in order to reduce the surface roughness and understand the roughness contribution from substrate aspects. BCP, EP and BEP are adopted to treat the niobium substrate for comparison, which is presented in Section 3. Tuning is one of the necessary procedures to keep accurate working frequency of the cavity. Field flatness adjustments of multi-cell cavities also need to add forces to generate plastic strains on the cavity. Nb\({}_{3}\)Sn is a known brittle and weak grain boundary link [12], but few research studies focus on the performance of Nb\({}_{3}\)Sn films under tuning stress. Cracks and dislocation inside grain or between grains would damage the Nb\({}_{3}\)Sn film on Nb substrate, causing undesirable degradation of RF performance.