# Presentation: 258107

## Slide 1

## What, Why, How, to improve

**What, Why, How, to improve**

- 2

## Introduction (1)

**Introduction (1)**

**Basics of SRF cavity**

- q = l / (2o2 )RsB2

- 3

- (W/m2)

## Introduction (2)

**Introduction (2)**

**Thermal parameters**

_**Note:**_
*Steady state without internal heat generation or the source term since magnetic field penetration in surface is on the order of nano-meters*

**What to improve?**

- 4

## Introduction (3)

**Introduction (3)**

**Cavity Parameters**

**Thermal-Magnetic interactions (defect free cavities)**

**Improved k & h leads to**
** **higher B and accelerating gradient
-  small temperature rise
- less cryogenic load

**Why to improve?**

- 5

- Here,
- is electrical resistivity

- Rres = 5 nOhms; e = 3 mm; Tb=2 K
- f = 1.3 GHz; RRR = 230

## Introduction (4)

**Introduction (4)**

- Adopted from Padamsee 1998

**Thermal conductivity**

**Below 3 K, not well correlated because of dominant phonon conduction**
** ****Strain / lattice imperfections**
** ****Grain size / grain boundaries**
** ****Impurities****  **

**k=RRR/4 at 4.2 K**

**How to improve?**

- 6

**Plastic deformations, as in deep drawing process during SRF cavity fabrication, may affect its phonon conduction**

**Above 3 K, electrons are the dominant energy carriers**
**k correlated with RRR**

## Introduction (5)

**Introduction (5)**

**Variation in h****k ****data**

- 7

- Experimental data for hk vary over one order of magnitude
- Predictions from theoretical models vary over two orders of magnitudes

- Adapted from Swartz et. al.

**Curve a, b, ....e are R****Bd ****(=1/h****k****) data for Cu by various authors**

**Factors affecting h****k**

- Surface roughness
- Surface impurity density
- Dislocation density
- Surface damage
- Surface stress
- Grain size of the crystals
- Impurities and oxide layers on the surface.

## Introduction (6)

**Introduction (6)**

**Effect of surface roughness**

- 8

**Superfluid He-II is an insulator.**
**Heat transfer via phonons**
**Scattering couple phonons from Nb to He-II**
**Enhanced by surface roughness with dimensions similar to phonon wavelength**
**At 2 K ~2 nm in He-II**

**Larger surface area, containing more nano length scale roughnesses, should result in enhanced phonon transmission**

## Experimental Apparatus (1)

**Experimental Apparatus (1)**

**Dewar assembly**

- Dewar is like a thermal flask.
- Different shields to reduce thermal leakage.
- Dewar lid assembly contains the sample housing attached through vacuum tube
- Liquid helium is filled in the Dewar at its saturation temperature (4.2 K) and pressure (1 atm).
- Pumping is required on the He to lower the temperature down to 2 K and below by reducing the pressure

- 9

## Experimental Apparatus (2)

**Experimental Apparatus (2)**

**Two cylindrical samples**
**Measure h & k**
**Different surface preparations**
**Plastic deformation / strain**
**Heat treatment / titanification**

- 10

## Experimental Apparatus (3)

**Experimental Apparatus (3)**

**Rectangular flat plate sample**
** ****Measure k only **
**Same 3mm thick Nb sheet as SRF cavities**
**Sheet and cylindrical samples have different fabrication processes**
**Effect of heat treatment / titanification**

- 11

## Experimental Results:Thermal conductivity (1)

**Experimental Results:****Thermal conductivity (1)**

**Repeatability**
**Comparison at three different bath temperatures for the same sample S1**

- Nov 2005 sample S1

- 12

## Thermal conductivity (2)

**Thermal conductivity (2)**

**Repeatability**
**Comparison with two independent tests of samples S1 and S2**

- Nov 2005 samples S1 and S2

- 13

- Samples S1 and S2 are from the same stock of Nb with same RRR 232

## Thermal conductivity (3)

**Thermal conductivity (3)**

**Validity**
**Comparison with literature data**

- July 2005 sample S2
- Data adapted from Padamsee et al.

**RRR vs k Check at 4.2 K**

- Nov 2005 data for sample S1 and S2
- Mar 2006 data for sample F1 and F2
- Literature data adapted from Padamsee et. al. and Boucheffa et. al.

- 14

## Thermal conductivity (4)

**Thermal conductivity (4)**

- Absence of phonon peak
- A reduction of almost 80% in k at 2 K

**Effect of plastic deformations**

**Sample S1**

**New trend**

- 15

- SRF cavities are routinely fabricated by inducing plastic deformations through a deep drawing process

## Thermal conductivity (5)

**Thermal conductivity (5)**

**Effect of low temperature heat treatment**

- No significant phonon peak recovery

- Heat treatment at 750 oC for 2 hrs

- 16

**May**: Axially strained sample
**June**: Low temp. heat treated

- Sample S2

## Thermal conductivity (6)

**Thermal conductivity (6)**

**Flat plate sample**
**As received sample**
** ****No phonon peak**

**After heat treatment**
** ****slight increase, only in phonon conduction region**

**Mar**-As received
**July**- Low temperature heat treatment at 750 oC for 2 hrs

- 17

**Effect of low temperature heat treatment (Cont’d)**

- Sample F2

## Thermal conductivity (7)

**Thermal conductivity (7)**

**Titanification**

- A purification process through Ti vapor deposition at moderate temperatures (~1300 to 1400 oC) in a high vacuum oven.
- Interstial impurities like O, N and C have greater affinity towards Ti than Nb. Impurities diffuse out near the surface.
- Outer titanium oxide layer (~50 m) removal through buffer chemical polish (BCP) etch. BCP 1:1:2 (HF:HNO3:H3PO4) is usually done to remove surface impurities from the cavities.
- High temperature purification leads to high RRR (and high k above 3 K) _**and annealing**_ of the bulk Nb.
- Samples S1 and S2 titanified at 1300 oC for 2 hrs and at 1200 oC for 4 hrs.

- 18

## Thermal conductivity (8)

**Thermal conductivity (8)**

- Phonon peak recovered due to annealing.
- Diffusion time of O2 is ~ 1mm/hr and the titanification system used is optimized for thin sheet (~ 2-4 mm) cavities.
- No improvement above 3 K.

**Effect of titanification**

- 19

## Kapitza Conductance (1)

**Kapitza Conductance (1)**

-  Reasonable agreement with literature data of Bousson et. al.
- BCP etched sample S1 has higher hk than S2.
- The data is on the low end of that available in the literature (~1 order of magnitude difference within the literature values even for the same material)

**S1**: machine cut & BCP etched
**S2**: machine cut surface

**Nov 05**

- 20

** ****Comparison with literature data**

## Kapitza Conductance (2)

**Kapitza Conductance (2)**

**S1 May 05**: Mech. polish + light BCP etch
**S1 June 06**: 3 % strained (L/L) + mech. polish + light BCP etch
**S1  Oct 06**: Titanification (1300 oC/2 hrs;1200 oC/4 hrs) + BCP etch 50 m

**After titanification, h****k**** increased (125% at 2.1 K) as compared with its June test.**

**Sample S1**

- 21

- Sample S1

**Repeatability**
**Same surface treatment before and after deformations**
**No significant change in h****k**

**Titanification**

## Kapitza Conductance (3)

**Kapitza Conductance (3)**

- In June test, hk increased (~ 100%) after annealing as compared with its May value

- Increase in hk for S2 (68% at 2.1 K from Nov to May).
- hk got closer to the literature data by Bousson.

-  **Large surface index (SI > 3)**

- 22

- S2  June 06: rough ~1-2 mm + BCP etch + annealing at 750 oC /2 hrs

**Low temperature annealing**

**Sample 2 tests**

- S2 Nov 05: machine cut surface
- S2 May 06: rough ~1-2 mm + light BCP etch

## Kapitza Conductance (4)

**Kapitza Conductance (4)**

**S2 Nov 05**: machine cut
**S2 May 06**: rough ~1-2 mm + light BCP etch
**S2  June 06**: rough ~1-2 mm + BCP etch + annealing at 750 oC /2 hrs
**S2  Oct 06**: Titanification (1300 oC/2 hrs;1200 oC/4 hrs) + BCP etch 50 m

**Titanification on S2**

- 23

- As expected hk for S2 also increased (30% at 2.1 K) after titanification as compared with its June test.
- Total change in hk from Nov 05 to Oct 06 is ~300% at 2.1 K

## Kapitza Conductance (5)

**Kapitza Conductance (5)**

- Comparison of samples S1 and S2

- S1 has a smooth surface whereas S2 has a rough surface leading to SI > 3

- 24

- After titanification, the hk for the two samples is quite close to each other within experimental error.
-  Possibly, crystal orientation on the surface or the phonon wavelength within the solid has more influence on hk than simply from area increase.
- Further investigation is needed

## Discussion

**Discussion**

- Plastic deformations in Nb reduced the thermal conductivity by almost 80% at 2 K causing absence of the phonon peak.

- Effect of surface roughness / surface area on Kapitza conductance remains inconclusive.

- Moderate temperature annealing (~ 1200-1300 oC for 6 hrs) during the titanification process recovered the lost phonon peak.

- Low temperature annealing (~ 750 oC for 2 hrs) found to be insufficient to recover the lost phonon peak in the Nb samples.

- 25

- Improvements of ~ 300% in hk were observed due primarily to annealing.

## Conclusion

**Conclusion**

- 26

**For high frequency defect free cavities operating at 2 K, ~ 50% improvement in magnetic fields is realizable through a single step of annealing.**
**Annealing is more important than improved RRR during titanification**
**Both phonon peak and Kapitza conductance are enhanced**

**High frequency cavities**

## Future Work

**Future Work**

- Testing of flat plate samples (F1 and F2) after titanification.
- Confirm improved RRR and recovery of phonon peak
- Higher phonon peak in polycrystalline Nb is realizable through annealing either at elevated temperatures or for longer durations.
- Need high temperature oven for annealing and purification
- Unstrained large grain or single crystal Nb is also a promising material for higher phonon peak.
- Future work to further improve upon Kapitza conductance is needed especially through the effect of surface strains or through the distribution of crystal orientations on the surface.

- 27