High field Q slope and the baking effect: Review of recent experimental results and new data on Nb heat treatments

Here, the performance of superconducting radio-frequency (SRF) cavities made of bulk Nb at high fields (peak surface magnetic field greater than about 90 mT) is characterized by exponentially increasing rf losses (high-field Q-slope), in the absence of field emission, which are often mitigated by low temperature (100-140 °C, 12-48 h) baking. In this contribution, recent experimental results and phenomenological models to explain this effect will be briefly reviewed. New experimental results on the high-field Q-slope will be presented for cavities that had been heat treated in a vacuum furnace at high temperature without subsequent chemical etching. These studies are aimed at understanding the role of hydrogen on the high-field Q-slope and at the passivation of the Nb surface during heat treatment. Improvement of the cavity performances, particularly of the cavities’ quality factor, have been obtained following the high temperature heat-treatments, while SIMS surface analysis measurements on Nb samples treated with the cavities revealed significantly lower hydrogen concentration than for samples that followed standard cavity treatments.


I. INTRODUCTION
The use of superconducting rf (gigahertz range) cavities made of high purity (residual resistivity ratio > 200) bulk niobium has been increasing steadily over the last decade, as these cavities are being employed in a growing number of accelerator facilities all over the world for applications that range from basic energy science to high energy physics. This demand requires continuous improvement of the cavity performance, both in terms of higher quality factors (to reduce cryogenic losses) and higher accelerating gradients (to reduce the real-estate gradient of high-energy accelerators).
The most outstanding issue related to the basic understanding of the superconductivity of high-purity, bulk Nb in strong rf fields is the occurrence of a sharp increase of the RF losses when the peak magnetic field, B p , reaches about 90 mT; consequently limiting the operational accelerating gradient of SRF Nb cavities for particle accelerators to about 25 MV/m. This phenomenon was discovered in 1997 [1,2], after the development of improved surface cleaning techniques allowed the preparation of cavities which achieved high surface fields, without being limited by "extrinsic" losses, such as those caused by field emission.
Experiments showed that the onset of the newly discovered "anomalous" losses, which are commonly referred to as "high field Q-slope" or "Q-drop", range between 80 -110 mT (it has been established that the Q-drop is a magnetic field phenomenon), depending on the particular material-processing combination. Lower onset of the Q-drop is typically associated with "rougher" surfaces.
Currently, two types of high-purity (residual resistivity ratio greater than 200) Nb material are used for cavity fabrication: fine grain (ASTM 5), and large (cm 2 size) grain or even single crystal. The two techniques currently used for the final surface polishing of Nb cavities are Buffered Chemical Polishing (BCP) and Electropolishing (EP).
An empirical "cure" for the Q-drop had already been discovered in 1998 and consisted of a low-temperature (100-140 °C, 48 h) baking of the cavities in ultra-high vacuum [3,4]. Later experiments showed that the benefit of baking and the baking parameters (time and temperature) depend significantly on the cavity material-processing combination. These findings are summarized in [5].
A model which describes all the experimental results related to the Q-drop and the baking effect has yet to be found. The solution to this problem will help devise new, possibly cheaper, ways of improving the overall performance of Nb cavities. In addition, it will give important clues to the understanding of loss mechanisms in high-temperature superconductors, comparatively more difficult to understand than Nb, which are being investigated for future SRF applications.
Several models to explain the Q-drop and the baking effect had been proposed over the last decade, but strong contradictions between each one of them and experimental results were found, as more experiments to test their assumptions had been carried-out over the past years. Reviews of such models and experimental results can be found in Ref. [5,6].
Temperature mapping of the cavity surface during high-power RF tests at 2 K consistently show strong, non-uniform heating occurring in the high-magnetic field area of the cavity ("equator" area), causing the Q-drop [5,6]. The regions of the cavity where the strong heating occurs are referred to as "hot-spots". In one occasion, hot-spots corresponding to a Q-drop occurring at much lower field (B p ∼ 30 mT) were measured closer to the iris of a single-cell cavity made by spinning, an alternative cavity fabrication technique [7]. The hot-spots moved closer to the equator as the Q-drop onset increased with additional BCP. In this particular case, roughness may play a major role, as cavities made by spinning showed very rough surfaces, with macroscopic cracks visible near the iris region as a consequence of the large material deformation.
In this contribution we will briefly review theoretical and experimental results on the high-field Q-slope published in the last two years. Earlier models and experimental results have been already discussed in previous reviews [5,6]. In particular, we will review two models which give a good description of the observed Q 0 (B p ) dependency, and a phenomenological model (so called "oxygen pollution model") along with results which contradict some of its hypotheses. We will then review recent theoretical and experimental results indicating a connection between the Q-drop and magnetic vortices pinned or entering the Nb surface. Results on niobium samples related to the Q-drop will also be discussed. All these are the subject of Sec. II of this article. Section III is a discussion on the possible role of hydrogen as a cause for the Q-drop, while Sec. IV shows new cavity test results after low temperature baking in hydrogen atmosphere.
Section V presents new cavity test results and sample analysis by Secondary Ion Mass Spectrometry (SIMS) after high temperature heat treatment followed by an attempt to passivate the Nb surface by growing a thin layer of niobium nitride by thermal diffusion.
A discussion of the new experimental results is given in Sec. VI, while conclusions are given in Sec. VII.

RESULTS RELATED TO THE HIGH-FIELD Q-SLOPE
A. Models that describe the Q 0 (B p ) curves One model which provides a good description of the Q 0 (B p ) curves was proposed by Gurevich [8] and it is based on an analytical solution of the 2D thermal diffusion equation which includes the extra power localized in a small defect region. Losses are caused by Joule heating of regions with higher surface resistance than the surrounding Nb. The results show that a hot-spot of radius much larger than the defect size is produced. The sum of N non-overlapping hot-spots yield an expression for the global surface resistance of the cavity, which is then used in the heat balance equation for the temperature of the cavity surface exposed to rf field. The solution of such equation is expressed in the following parametric dependence Q 0 (B p ): where g, Q 0 (0) and B b0 are fit parameters. g is a parameter which is related to the number and intensity of hot-spots, Q 0 (0) is the Q 0 -value at low field and B b0 is the thermal breakdown field in absence of defects.
A recent model proposed by Weingarten [9] gives an expression for a fielddependent surface resistance obtained assuming that defects of density n s0 with smaller values of the lower critical field (B 0 ) than Nb are present on the surface and that the size of the normal conducting regions increases with increasing magnetic field, above B 0 .
Increase of the surface resistance is due to the increase of the condensation energy density due to the loss of Cooper pairs by loss of volume. The field-dependent surface resistance given in [9] is an infinite product expansion: where the first term in the sum describes the low-field Q-increase while the second term describes the medium and high-field Q-slopes. λ is the penetration depth, B c is the thermodynamic critical field at the He bath temperature, f is the resonant frequency and κ is the Ginzburg-Landau parameter. The expression in Eq. (2) is added to the BCS and residual resistance to determine the total surface resistance, R s (B p ). The cavity quality factor is then calculated through the usual relation Q 0 = G/R s . κ , n s0 , B 0 and the residual resistance, R res , are used as fit parameters. Figure 1 shows, as an example, the Q 0 (B p ) data at 1.4 K for a typical bulk Nb cavity affected by the Q-drop and the curve fits using the two models mentioned above.
The data are taken from [10]. The fit parameters of the two models and the fit correlation factor, r 2 , are reported in Table I. Both models provide a good description of the data with reasonable values of the fit parameters. It should be mentioned that 25 terms of the product expansion in Eq. (2) were needed for a good fit using Weingarten model [11].
Although both models mentioned in this Section give a good description of the   [12]. Oxygen is the impurity whose diffusion length in Nb is comparable to the rf penetration depth, for the typical baking parameters. Oxygen concentrations high enough to change the superconducting properties of Nb had been measured at the Nb/oxide interface by surface analytical methods. A refinement of the model includes the effects of both oxygen diffusion and oxide decomposition in determining the oxygen concentration at the metal/oxide interface, after the lowtemperature baking [13]. The calculation shows a minimum of the oxygen concentration in the temperature range 120°-150°C for a 48 h long bake-out, in good agreement with the baking parameters which give the highest improvement of the cavity performance.
The diffusion mechanism is also consistent with the following experimental results:  [15].
(ii) The Q-drop did not improve after baking a cavity "in-situ" at 400 °C/2 h, although the interstitial oxygen should have diffused deeper into the bulk by baking at such high temperature [16].
(iii) Measurements of the sub-surface oxygen profile by diffuse X-ray scattering on a single-crystal Nb sample revealed a diffusion length of only about 2 nm after baking at 145 °C/5 h, in spite of the 40 nm diffusion length as calculated using the diffusion equation [17]. This result, shown in Fig. 2, is explained as oxygen segregation towards the surface during cool-down to room temperature balances the diffusion at 145 °C. Nevertheless, diffusion can occur at much higher rate along grain boundaries than within a single grain.
While the role of oxygen as the impurity leading to the Q-drop is significantly diminished by the experimental results mentioned above, recent theoretical and experimental work [18,19] still support the idea that the hot-spots are caused by magnetic vortices oscillating at the Nb surface under the action of the rf field. These findings will be discussed briefly in what follows. the oxide layer, measured using X-ray diffuse scattering on a single-crystal Nb sample before and after baking. The figure is taken from Ref. [17].

C. Hot spots due to magnetic vortices
Theoretical calculations show that rf losses due to the motion of vortices at the Nb surface can certainly generate hot-spots at high field, which cause the cavity quality factor to drop [18]. There are two possible ways in which vortices can cause losses at the Nb surface: Vortices with segments pinned near the surface oscillate under the Lorentz force given by the rf field, causing losses.
(ii) Vortices can be pushed into the surface when the amplitude of the rf field exceeds the local surface barrier. The periodic motion of such vortices produces losses.
These phenomena will be discussed more in details in what follows.

Losses due to pinned vortices
Because of the incomplete Meissner effect in technical Nb, trapped vortices are always present upon cooling a Nb cavity below T c , in the presence of a residual DC magnetic field. The resulting distribution of pinned vortices can be highly inhomogeneous and the pinning efficiency depends on the treatments applied to the Nb.
where J c = 1 kA/cm 2 is the critical de-pinning current density, B c1 = 170 mT is the lower critical field at 2 K, T c = 9.25 K is the critical temperature and T = 2 K is the He bath temperature.
The hypothesis of hot-spots being caused by pinned vortices can therefore be tested by application of a thermal gradient of the order of the value calculated with Eq.
(3) across the 3 mm thick walls of a Nb SRF cavity and then a check for changes in the thermal maps of the cavity, before and after application of the thermal gradient.
Experiments of this type were done recently at JLab [19] and clearly showed changes in the intensity of the hot-spots, after a thermal gradient of about 0.5 K/mm was applied by heaters glued to the outer surface of a large-grain cavity. Although a proof of principle for pinned vortices as being one of the causes for the hot-spots was achieved, the applied thermal gradient was not high enough to really push vortices away from the rf surface.
Most likely, what happened was a re-distribution of the pinned vortices over a larger area.
In order to fully test the hypothesis of pinned vortices generating hot-spots and the possibility of improvement of the cavity performance by application of a high enough thermal gradient, a series of experiments are planned at JLab where a scanning laser light, directed on the inside surface of a Nb cavity, will act as a "thermal broom" to push trapped vortices deeper into the bulk.

Losses due to vortex penetration
At high peak surface magnetic fields, approaching the lower critical field of Nb, vortices overcome the surface barrier, locally depressed in some areas, and enter the Nb surface. The simplest way to describe this is to solve the equation of motion of a vortex subjected to the Lorentz force generated by the rf field, the image force, attracting the vortex to the surface, and the viscous drag force, opposing the motion [18]. The solution of such an equation is shown, as an example, in Fig. 4: a single vortex enters the surface when B p exceeds the local penetration field, B v . As the rf field changes sign, the vortex is pulled toward the surface, while an anti-vortex is pushed in, when -B p = -B v , and annihilates with the vortex already inside the surface. This phenomenon repeats for each rf period. It is important to notice that the calculation shows that the characteristic time, τ, it takes for the vortex to travel a distance of the order of the penetration depth is much smaller than the rf period. The maximum power, P 0 , dissipated by this mechanism is twice the work done by the Lorentz force to bring a vortex from the surface deeper into the bulk: The figure is taken from Ref. [18].

High field losses due to vortices
Theoretical calculations show that the local dissipation due to pinned vortices produces a long-range temperature distribution, which spreads out on the scale ∼ 2d/π (d is the cavity wall thickness). Even if these temperature variations are weak, they can nevertheless produce strong variations in the surface resistance R s of the surrounding areas, because of the exponential dependence of R BCS on temperature [18]. This nonlinear R s can be estimated as follows: where P 0 is the dissipated power at the local heat source of size r 0 , κ is the thermal conductivity, Δ is the energy gap and T 0 is the He bath temperature.

D. Results on Nb sample measurements
While experiments and calculations highlight the contribution of magnetic vortices to high-field losses, what impurities or defects on the Nb surface are involved in this process and how the low-temperature baking affects them is still unclear. Niobium samples had been cut from the "hot" and "cold" spots of a single-cell cavity and have been analyzed at Cornell using a variety of surface analytical tools [22]. The results showed no difference in terms of surface roughness, oxide structure or crystalline orientation between the two types of samples. What was found is that "hot" samples had a larger local misorientation angle than "cold" ones, as measured by Electron BackScatter Diffraction (EBSD). The local misorientation angle is related to the density of lattice defects (vacancies and/or dislocations) near the surface. In addition, it was found that the local misorientation angle in "hot" samples is reduced by the low-temperature baking (120 °C/ 40 h). On the other hand, preliminary results on single-crystal samples measured by Positron Annihilation Spectroscopy (PAS) show an increase of vacancy density within the rf penetration depth after low-temperature baking [23]. These results, which are somewhat in contradiction with the Cornell results, were interpreted as due to the dissociation of vacancy-hydrogen complexes during baking.

Sample characterization by Point-Contact Tunneling (PCT), has been done at
Argonne on Nb samples prepared by EP, before and after baking [24]. The results show that unbaked samples have a high zero-bias conductance value, indicating the presence of quasiparticle states inside the superconducting energy gap, as shown in Fig. 5. The zerobias conductance value is significantly reduced by the low-temperature baking and correlates well with the reduction of the BCS surface resistance observed on Nb cavity tests. These results are also consistent with a correlation between the amplitude of the energy gap and the Q-drop onset/quench field after baking inferred from cavity test results [15]. The reduction of the zero-bias conductance value was explained by reduced scattering by magnetic impurities near the surface. Oxygen vacancies in the nonstoichiometric niobium pentoxide were proposed as the source of magnetic impurities.

This interpretation somehow contradicts experimental results showing that the Q-drop
does not re-occur in a baked cavity after the oxide is removed with hydrofluoric acid and a new one is grown by water rinses [14]. In addition, measurements of the magnetic susceptibility in Nb samples done at DESY showed an increase of the Curie constant after baking. This was interpreted as an increase of the concentration of localized magnetic moments near the surface [25]. Corresponding Shiba density of states. The figure is taken from Ref. [24].

A. How hydrogen enters niobium
Niobium is an active metal that will spontaneously react with water, or water vapor, to produce hydrogen at high partial pressures. The passivating (continuous) surface niobium oxide film seals the active Nb metal from exposure to water preventing this reaction, but conditions that attack, break, or remove this film in the presence of water will result in H uptake as the water is reduced on the surface of the metal according to reactions of the form where the values of the variables x and y depend on the stochiometry of the oxide produced by the reaction. These reactions can produce hydrogen at fugacities as large as 2.13×10 25 Pa (2.1×10 20 atm) at room temperature [26]. Therefore, processing steps such as grinding, welding, chemical and electro-polishing that remove the protective oxide in the presence of water or water vapor will result in the spontaneous reduction of water molecules to form adsorbed H atoms on the surface of Nb metal.
The equilibrium fugacity or activity of the H 2 produced by these reactions exceeds the solubility limit for H in Nb. This could result in the formation of H 2 blisters or Nb-H phases. It also exceeds that of the processing environments, and H 2 gas evolution should prevent the actual H activity on the surface from reaching these high theoretical equilibrium values. The relatively slow kinetics of recombination and H 2 bubble nucleation compared with the reduction of water molecules will still result in significant hydrogen activities and absoprtion. Fortunately, these reactions also produce Nb oxides that can cover the surface and seal the undelying metal from water, but these oxides will also retard or block H outgassing. The extent of H absorption will depend on the relative kinetics of these processes and the stability of the repassivating oxide in the processing environment.
The application of an anodic current, such as during the EP process, can suppress, at least theoretically, hydrogen evolution at the Nb surface [26]. However, natural perturbations to the current distribution or local shielding from the polarizing current could still result in the establishment of conditions where hydrogen evolution is favorable. This is in agreement with experimental results by Hydrogen Forward Scattering technique on Nb samples, showing low H contamination during EP as long as the polarizing current was applied [27].
The diffusion coefficient of hydrogen in niobium at room temperature (∼5×10 -6 cm 2 /s) is more than ten orders of magnitude greater than that of other impurities, such as N, C, or O, therefore hydrogen produced by the reduction of water on the Nb surface will rapidly diffuse into the bulk even at room temperature. Hydrogen occupies octahedral and tetrahedral interstitial sites of the niobium's body-centered cubic lattice. In spite of the large diffusion coefficient, there are a few factors which may lead to nonhomogenous hydrogen distribution: (i) Higher hydrogen concentrations are found at locations of higher tensile stress, due to the hydrogen interaction with lattice defects, such as dislocations and vacancies.
(ii) Impurities such as nitrogen, oxygen and tantalum in niobium constitute hydrogen "trapping" sites.
Heat treatments will also influence the amount of hydrogen absorbed or desorbed from niobium. Heating at temperatures greater than about 250 °C will cause the dissociation and reduction of the natural  This type of heat treatment is commonly used to lower the bulk hydrogen concentration in niobium cavities after fabrication and heavy chemical etching.
Nevertheless, a fraction of the residual hydrogen in the furnace is re-absorbed into Nb during cool-down and this is a well-known problem [30]. Thermal desorption spectroscopy (TDS) on high-purity Nb samples used for cavity fabrication showed [31]: (i) a hydrogen bulk desorption peak, at about 530 -590 °C depending on the amount of chemical etching by BCP done to the samples.
(ii) The presence of a second desorption peak at higher temperature (about 700 °C), possibly caused by the presence of high energy trapping sites (iii) the main desorption peak shifts to higher temperatures after annealing at temperatures ≥ 600 °C for a duration ≥ 6 h. Figure 6 illustrates some of the findings summarized above. The heat treatment parameters used at DESY for hydrogen degassing are 800 °C/2 h, while 600 °C/10 h was developed at JLab because a reduced yield strength, due to non-uniform grain growth occurring after the heat treatment at 800 °C, was measured on some batches of fine-grain Nb used for the fabrication of SRF cavities for the Spallation Neutron Source project [32]. In what follows, we indicate several observations found in the literature which may link hydrogen to the baking effect and the sample measurement results described in Sec. II-D: (i) Thermal desorption studies on Nb foils, where the natural oxide layer was removed by cycles of thermal treatments and Ar ion sputtering, showed hydrogen desorption peaks at 130 °C and 198 °C, interpreted as hydrogen desorption from surface and subsurface sites [34]. Several experimental [35] and theoretical studies [36] have concluded that Nb surfaces exhibit a strongly bound subsurface state of hydrogen.
(ii) Measurements by Positron Annihilation Spectroscopy (PAS) show that the defect density (vacancies) increases with hydrogen concentration in Nb samples [37].
Hydrogen entering Nb during chemical etching or mechanical polishing could actually be the source of the high defect density in the "hot-spot" samples measured by EBSD.
(iii) Hydrogen affects the magnetic behavior of Nb by lowering the magnetic susceptibility for increasing H concentration [38]. It is possible that hydrogen is the "magnetic impurity" invoked by the PCT results.
While these findings may suggest a link between hydrogen and the Q-drop and the baking effect which requires deeper investigation, a more complete model of the Nb surface before and after baking would most likely involve both oxygen and hydrogen, both present in large quantities at the metal/oxide interface, and the interactions between them and with the Nb metal.

C. Q-disease
Hydrogen received a lot of attention from the SRF community in the 1990s because of the so-called "Q-disease" (see the review [39] and references therein). This phenomenon was characterized by the reduction of the cavities' quality factor by more than one order of magnitude, when the cavity was maintained in the temperature range 90

IV. CAVITY TEST RESULTS AFTER BAKING IN HYDROGEN ATMOSPHERE AND 600°C/10h HEAT TREATMENT
The single-cell cavity used for the experiments described in this Section was made of large-grain niobium from OTIC, Ningxia, China and it has the same cell shape as the one used in the CEBAF accelerator. The resonant frequency of the TM 010 mode is 1.47 GHz. The same cavity was used for a study reported in [15] and the baseline rf performance at 1.7 K, after post-purification at 1250 °C, buffered chemical polishing (BCP), and UHV baking at 120 °C, is shown in Fig. 8. The Q 0 at low field was 2.28×10 10 and the cavity quenched at B p = 169 mT, without field emission or Q-drop. It was reported in [40] that an increase of the residual resistance was observed after exposure of a low residual resistivity ratio (RRR) niobium cavity to 1/7 atm of pure H 2 gas for 1 h.
We performed a similar experiment with our high-purity large-grain Nb cavity, which was evacuated to ∼ 10 -7 mbar and backfilled with scientific grade H 2 up to 1 atm, after the cavity had been stored in air for about 4 months after the baseline test. Hydrogen was left in the cavity for ∼ 11 h at room temperature. The cavity was then high-pressure rinsed, dried in a class 10 clean room, assembled on a vertical stand with a temperature mapping system 1 and inserted in the cryostat. The rf performance at 1.7 K showed a reduction of residual resistance by about 4 nΩ and ∼ 7% improvement in the quench field, as shown in Fig. 1. Moderate heating is visible in the equator region (Fig. 9a).
In order to accentuate hydrogen diffusion through the oxide into Nb, we evacuated the cavity to ∼ 4×10 -7 mbar and backfilled it with scientific grade H 2 up to 1 atm. The cavity was baked in the hydrogen atmosphere at 120 °C for 12 h, followed by high-pressure rinsing and assembly. The rf test at 1.7 K showed an increase of the residual resistance by about a factor of two while the quench field was reduced to about 162 mT. We repeated the same baking procedure in 1 atm of H 2 and the subsequent rf test results at 1.7 K (shown in Fig. 8) did not show any significant change from the previous test after the first baking.
The next treatment consisted in degassing in the furnace at 600 °C for 10 h, which is done at JLab to reduce the bulk hydrogen content. Hydrogen was the gas with the highest partial pressure in the furnace, at approximately 2.5×10 -6 mbar after the temperature ramp-up to 600 °C and at approximately 8×10 -8 mbar before cooldown. The partial pressures of the main residual gases in the furnace and the temperature profile during the heat treatment are shown in Fig. 10. After the heat treatment, the cavity was degreased in a tank with ultrasonic agitation and high-pressure rinsed. No chemical etching, typically done after heat treatments, was done on the cavity surface. The results of the rf test at 1.7 K, shown in Fig. 8, are characterized by an increase of the residual resistance by ∼ 6.5 nΩ and, most noticeably, by the reoccurrence of the high-field Qdrop. Temperature maps show strong hot-spots in the equatorial region of the cavity (Fig.   9c), in the same areas where they occurred before the baking for the baseline test. After the cavity was baked "in situ", on the vertical test stand, in UHV conditions at 120 °C for 8) and the temperature maps show much lower heating (Fig. 9d). The quench location was, for all tests, in the region at the angles 20°-30°, sensors No. [8][9].
The values of the residual resistance, R res and energy gap, Δ, at 0 K divided by the product of the Boltzmann constant, k B , and the critical temperature, T c , obtained from a fit of R s (T, 10 mT) between 4.3 K and 1.7 K are shown in Table II  There was no field emission in any of the tests.

A. Cavity test results
As it was discussed in Sec. II, it is clear that a significant improvement of the cavity performance, both in terms of quality factor and maximum accelerating gradient, should be achieved by reducing the amount of impurities and defects within a few hundred nanometers from the Nb surface. One way to accomplish this is to heat treat the Torr at 400 °C for 15 min.

Large-grain CEBAF single-cell cavity
We attempted this process first on the large-grain single cell cavity used for the experiments described in Sec. IV. The cavity was heat treated at 800 °C/3 h, then cooled to 400 °C at which point a nitrogen partial pressure of about 1×10 -5 mbar was maintained in the furnace for about 15 min. Then the furnace was cooled to room temperature.
Hydrogen was the gas with the highest partial pressure in the furnace, at approximately The average value of R s between 9.5 K and 10 K was about 9 ± 7 mΩ, corresponding to a surface RRR of only 10 +135 -7. There was no other transition between 9.5 K and 20 K 2 .
The cavity was then baked "in situ" at 120 °C for 12 h and tested again at 1.7 K. The results, shown in Fig. 12, indicate an improvement of the Q 0 at high field. A small amount of field emission (radiation level < 4 mR/h) was detected above B p = 115 mT (E p = 46 MV/m). Temperature maps were measured during each of the three rf tests and showed a major hot-spot over the area between angles 150°-180° and sensors 6-9 (similar to a hot-spot shown in Fig. 9c) during the baseline test. The area and intensity of this hotspot was reduced by the high-temperature heat-treatment, while more uniform heating over the cavity surface was observed after the additional "in-situ" baking. 2×10 -8 mbar, the pressure of N 2 was 6.7×10 -9 mbar and that of CO 2 was 4×10 -9 mbar.
After the heat treatment the cavity was degreased for 1 h, followed by HPR for 1 h. The rf test results at 2 K are shown in Fig. 14 (labelled "Heat treatment 2"): the low-field Q 0 improved by aboout 26% while no Q-drop was found up to a quench field of 118 mT.
Temperature maps measured during the baseline test showed some hot-spots in the equator region similar to the ones observed in the previous tests. These hot-spots were significantly reduced after the heat treatment and the quench location was at location 20°, sensor 11. Temperature maps at the highest field achieved during the baseline and after the heat treatment tests are shown in Fig. 15.
As will be discussed more in the next Section, niobium samples which were heat

Rolled single-crystal ILC single-cell cavity
The heat treatment with N 2 injection described in the previous Section was applied to a 1.3 GHz single-cell cavity of the same shape as that of the center cell of the 9-cell cavity for the proposed International Linear Collider (ILC) project [42]. The single-crystal Nb discs from Heraeus, Germany, were prepared at DESY by few cycles of rolling and annealing to enlarge their diameter while maintaning a single crystal structure [43]. The best rf performance of the cavity at 2 K can be found in [44] Fig. 16: the low-field Q 0 improved by about 35% but the Q-drop was still present at about 10% higher onset field. The cavity was then baked "in situ" at 120 °C for improve after the additional baking, consistent with earlier measurements reported in [44].
FIG. 16. Q 0 vs. B p measured at 2.0 K on a "rolled" single-crystal ILC single-cell cavity after the baseline test (squares) and after the heat treatment (triangles) at 800 °C/3 h, 400 °C/20 min with 1×10 -5 mbar N 2 injection, 120 °C/6 h. The round symbols are the data after additional "in situ" baking at 120 °C for 48 h.

Fine-grain ILC single-cell cavity
The process of high temperature heat treatment without subsequent chemical etching was tried also on a 1.  Fig. 17: the low-field Q 0 improved by about 30% while the Q-drop, although still present, shifted to about 8% higher field. No field emission was detected. The cavity was subsequently "insitu" baked at 120 °C for 24 h and the following rf test at 2.0 K (also shown in Fig. 17 °C/20 min. The round symbols are the data after additional "in situ" baking at 120 °C for 24 h.

Large-grain ILC single-cell cavity
Another single-cell used for this study was a 1.3 GHz cavity of the ILC shape built at JLab from large-grain Nb from Tokyo-Denkai, Japan. Earlier rf tests showed a quench field of about 136 mT, after the low-temperature baking at 120 °C [46]. A new baseline was established by removing about 1 μm from the inner surface by BCP 1:1:2 and the rf test results at 2.0 K showed the Q-drop starting at B p = 106 mT (Fig. 18). The heat treatment procedure was modified to eliminate the holding at 400 °C for 20 min but to include the low-temperature baking by holding at 120 °C for 12 h before the cooldown to room temperature. Hydrogen was the residual gas with the highest partial pressure (∼ 1.2×10 -5 mbar upon reaching 800 °C and ∼ 3.4×10 -7 mbar before cool-down to 120 °C). After the heat treatment, the cavity was degreased for 1 h followed by 1 h of HPR. The rf test results at 2.0 K (Fig. 18) showed an improvement of the low-field Q 0 by about 74% while there was no Q-drop up to a quench field of about 128 mT. Some multipacting activity was detected before and after the heat treatment at E p = 37 MV/m (B p = 86 mT), but there was no field emission in either test.

Summary of cavity rf test results
In Table III we  The data reported in Table III indicate that the improvement of the Q 0 -value at B p = 100 mT is the result of a reduction of the BCS surface resistance while the R res remained mostly unchanged by the heat treatment, without 120 °C baking. The reduction of R BCS is mainly described by an increase of the gap parameter in the data fit with the theoretical calculation of the BCS surface resistance. An increase of R res , which is commonly observed after the low temperature baking, compensates the further reduction of R BCS after 120 °C baking. The Q-drop was still present after heat treatment, unless the 120 °C baking was included, and the high field performance of the cavities was limited by quenches at ∼ 135 mT, most likely due to defects, and only on the fine-grain ILC cavity a significant improvement of B p,max was obtained.

Samples
Samples made of high purity (RRR > 200) large-grain Nb from CBMM, Brazil (Ingot "D") and fine-grain Nb from Wah Chang, USA, with area 5 mm × 7.5 mm, 3.125 mm thick were cut by wire electro-discharge machining from larger discs. After cutting to dimensions, the samples were subjected to the following treatments:  The samples were heat treated with the cavities as indicated in Table IV. "Control" samples were not heat treated but were analyzed by SIMS in the same experimental conditions in which the heat treated samples were analyzed. The letter "F" in the sample code refers to fine-grain Nb, while the letter "L" refers to large-grain Nb. and Cs + primary beams indicated apparent high levels of hydrogen and also showed the presence at high intensity of unusual species, NbH x -, where x = 1 to 5, for Cs + bombardment [47]. However, depth resolution and detailed interpretation were limited because of sample surface roughness.
A nanopolish procedure developed by Wah Chang (proprietary method) was able to provide niobium surfaces with mirror quality smoothness. With a large grain sample prepared in this manner, it was possible to make a SIMS standard for C, O, and N in niobium. SIMS standards are typically made by ion implantation of the element of interest into a sample with matrix the same as the matrix to be analyzed [48]. In order to check the implant doses, a piece of (100) Si was implanted with C, N, O at the same time.
Because hydrogen was known to be at a high intensity in niobium from the earlier study, deuterium (D) was also implanted instead of hydrogen. The implanted samples showed typical Gaussian shaped curves for all four elements in silicon, but only for C, N, and O in niobium. The D profile in niobium showed no implant peak, indicating that the D is very mobile and can diffuse through the metal either without assistance or with the influence of the charged analysis beam [49]. Analysis of the SIMS standard provided relative sensitivity factors (RSFs) from which quantitative results for C, O, and N could be obtained. The niobium samples listed in Table IV  profiles and mass spectra. It was necessary to monitor a molecular species, NbN -, to detect N in niobium because the secondary ion yield for Nis effectively zero. Depth determination of each crater was made using a Tencor P-10 stylus profilometer and these measurements were used to calibrate the depth axis. A uniform sputtering rate is assumed for the depth profiles.
Depth resolution for SIMS is typically improved by analysis at lower impact energy. Some of the initial analyses were made at Cs + impact energy of 6 keV and show improved depth resolution at the surface compared with 14.5 keV bombardment [49].
This condition was primarily used as a check for N at the surface after the initial nitrogen exposure experiments. However, most of the data reported here were obtained at Cs + impact energy of 14.5 keV as this operating condition provided improved count rates, which is important for species such as D -, and the Hand Dprofiles have typically shown constant levels which do not require improved depth resolution.
For each sample, a series of analyses were made. Because the SIMS analysis area is relatively small, at least two depth profiles were obtained from each sample. If there was a difference in intensity levels for these two profiles, then at least one more profile was obtained. For most samples, an additional profile using raster reduction was made.
The raster reduction method consists of a depth profile where, after constant intensities have been achieved for the species of interest, the raster is reduced by approximately 50% in x and y, but the sputtering current is maintained. This increases the ion current density by approximately a factor of four. If the intensity of a species increases by a similar factor after raster reduction, then one can conclude that that species is present in the sample at the concentration measured. If the intensity does not change, then the intensity observed is background. Changes between zero and approximately a factor of four increase indicate that the intensity is near background [48,50]. This raster reduction measurement is important because the species of interest in this study are residual gas species which are always present to some degree in the vacuum system. For some of the samples, especially the control samples, multiple sets of measurements were made. Mass spectra were also obtained on all the samples in order to check for Nb x H y species and for contaminants.

Results on Samples
Analysis was first made on samples L18 (after 800ºC heat treatment and 400ºC exposure to N 2 ) and L19 (control sample), and the implant standard. Samples L18 and L19 were not nanopolished and it was very difficult to make crater depth measurements.
These analyses were made using low energy Cs + impact energy (6 keV) in order to check for the nitride layer. No nitride layer was detected. It was observed that the Hcount rate was approximately two orders of magnitude higher in the implant standard (which should be similar to a control sample) compared with sample L18. Sample L19 showed H intensity between L18 and the standard.
Because N was not detected in the first experiment, samples were analyzed from a similar experiment, but with an additional baking and with nanopolished samples.
Sample L16 had 800ºC/400ºC N 2 exposure/120ºC and L14 was a control sample. L14 was used as reference sample for subsequent experiments. Once again the analysis was conducted at low Cs + impact energy and N was not detected. Both L14 and the control sample showed as much as two orders of magnitude more H than the heat treated sample.
Results on these two samples were then repeated at higher Cs + impact energy (14.5 keV).   Table IV). Samples were then prepared without nitrogen exposure during heat treatment.
Sample L10 was analyzed using SIMS and the result is shown in Fig. 21. This profile is very similar to that for sample L16 which was exposed to N during 400ºC heating and baked at 120 °C.  Table IV).
Mass spectra were obtained on L10 and on the control sample L14. Figure 22 shows that the heat treated sample as received showed NbH x species up to NbH 2 -. Other samples after heat treatment showed a similar spectrum. Figure 23 on the control sample shows high intensity species up to NbH 5 were detected. The broad peak underlying the Nb peaks is thought to be a metastable species. Sample L8 had been heat treated at 800 °C and baked at 120 °C during the same furnace run and the SIMS analysis (Fig. 24) showed similar H content to other largegrain samples heat treated at 800 °C. NbH 5 -(mass 98) was also monitored in this profile and shows a constant value through the depth analyzed. Fine-grain samples F2 and F3 were heat treated with the same parameters as sample L10 and the reduced data SIMS depth profile of sample F3 is shown in Fig. 25: the hydrogen concentration is about a factor of 30 lower than the control sample (F5). Sample F2 was subsequently baked in UHV for an additional heat treatment at 120 °C for 48 h and the SIMS analyses showed similar H content as sample F3. The H content of the fine-grain samples is higher than that of the large-grain sample for the same chemical and heat treatments.
Samples which were heat treated to 600 ºC instead of 800 ºC were also analyzed. Figure 26 shows the reduced SIMS depth profile for sample L5, which indicates a similar but slightly higher H concentration than sample L10, which was heat treated at 800 °C.
Sample L7 (identical to L5) was then baked in UHV at 120 °C for 48 h and the new SIMS analysis (Fig. 27) showed reduced H concentration by baking but still higher than sample L8, heat treated at 800 °C and baked at 120ºC for 12 h. Note that in this profile  Table IV).  Table IV.

VI. DISCUSSION OF EXPERIMENTAL RESULTS
Experimental results on the surface analytical investigation of the native oxide layer on low purity (RRR < 100) polycrystalline Nb had shown that the thickness of the oxide layer is non-uniform and oxidation along grain boundaries may proceed down to about 1 μm below the surface [51]. Cracks through the oxide may favor hydrogen absorption from the atmosphere and this explained results on Nb cavities of similar low purity for which the Q 0 degraded by long time exposure to air or exposure to hydrogen atmosphere for few hours [40]. This does not seem to be the case for high RRR Nb: images of the oxide layer by transmission electron microscopy (TEM) on both single crystal [47] and fine-grain [15] Nb samples showed a very uniform oxide layer with thickness ranging from 5 to about 8 nm and no significant sub-oxide region. This was also confirmed by Atom Probe Tomography (APT) [52]. Surface included hydrogen perturbs the electronic structure of the host metal, with the 1s-electron that accompanies the hydrogen nucleus entering the s-and d-bands of the host metal, changing the density of states at the Fermi surface and causing shifts of the energy bands [54]. This may of course alter the superconducting properties of Nb and may be related to the anomalous zero-bias conductance observed in PCT experiments mentioned in Sec. II. The reduction of the BCS surface resistance after the high temperature heat treatment may in fact be related to the reduction of this zero-bias conductance value, as observed for the 120 °C baking. Since this phenomenon is not included in the theoretical calculations of the surface impedance based on the BCS theory, the reduction of R BCS is fitted by an increased value of the gap parameter (see Table III).
The possibility of hydrogen generating vacancy clusters in Nb, due to lattice expansion, may also explain the presence of a higher defect density of chemically polished Nb surfaces shown by the EBSD data mentioned in Sec. II. While SIMS and NRA data indicate a reduction of hydrogen concentration after the 120 °C baking, it is not clear in which direction it moves: it could either be de-trapped from the surface, because of movement of interstitial oxygen and vacancies, and distribute uniformly within the bulk, or it may desorb from the surface through channels in the oxide during the partial decomposition of the Nb 2 O 5 layer at the metal/oxide interface.
The SIMS analyses of fine-grain and large-grain samples treated by BCP and EP, before and after heat-treatments, summarized in Tables V and VI, do not show significant differences in terms of C, N and O concentration. There is an increase in C measured after heat treatment, but all of the concentrations of these elements measured below the oxide are less than 0.1% atomic. However, the SIMS measurements do show a trend with respect to H concentration, and this trend seems to correlate well with general cavity performance: (i) the H content is lower in BCP-treated large-grain Nb than in fine-grain Nb for the same heat treatment parameters.
(ii) Baking at 120 °C further reduces the H concentration in Nb previously heat treated at 600 ºC.
(iii) Fine-grain samples treated by EP have much lower H content than finegrain samples treated by BCP.
Because of the sputtering technique used in SIMS measurements, H may readily diffuse through the crater from different directions, due to its high mobility, and is therefore difficult to observe the H peak at the metal/oxide interface, as detected with the NRA technique.
The passivation of the Nb surface by depositing a thin nitride layer by thermal diffusion of nitrogen introduced at low partial pressure at 400 °C was not successful.
Nitridation of niobium at 800 °C with a nitrogen partial pressure of 10 -2 mbar for 5 min or at 600 °C for longer time, followed by rapid quenching of the furnace from the nitridation temperature to room temperature has been reported in the past [55]. The furnace available for the experiments described in this article is interlocked to prevent operation at high temperature if the pressure inside the chamber is greater than 10 -4 mbar.
Because a nitride layer of only few nanometers thick would be required for the passivation of the niobium surface, nitridation should be done at relatively low temperature to reduce nitrogen diffusion into the bulk. Therefore it may be necessary to increase the nitrogen partial pressure or to react Nb with dissociated nitrogen from a plasma. A more versatile furnace to try such experiments is planned to be installed at JLab.

VII. CONCLUSIONS
The understanding of the origin of anomalous rf losses ("Q-drop") in SRF Nb