0. Measurement of Nb3Sn conductor dimension changes during heat treatment
D. Bocian, G. Ambrosio, M. Whitson
Fermi National Accelerator Laboratory,
P.O. Box 500, Batavia, IL , USA
The main author would like to thank E. Barzi, T. Beale, R. Bossert, D. R. Dietderich, M.Field, A. Ghosh, A. Nobrega, A. McInturff, D. Turrioni for their help and support during the course of this work.

1. OUTLINE
Motivation
Simulation plans
Experimental setup
Results
Conclusions and future plans

2. MOTIVATION
Nb3Sn demonstrate better performance than NbTi  possible use for LHC upgrade
Nb3Sn is a brittle material  sensitive for strain state of the conductor
During the reaction of LARP Long Nb3Sn Quadrupole coil some issues were found
the inner layer had ~5.3 kN of longitudinal tension,
the total length of the outer and inner layers pole parts changed by different amounts
Experimental data needed to model and understand this problem
Material properties E, ρ, CTE are required
Strand Model
Strand Subelement Model
Nb barier Sn
Nb+Cu Cu

3. HEAT TREATMENT SIMULATION
Temperature 400 → 640°C
Nb3Sn formation start
(Sn diffusion into Nb)
Need Nb3Sn properties
→ tuning of the model
Temperature 210 → 400°C
Continuation of Sn diffusion to Cu
(Sn melts at 238°C)
Temperature 20 → 210°C
Linear/non-linear elongation
Temperature 640 → 20°C
→ strand/cable shrinks I II
III IV V VI
VII
VIII
T [°C]
48 h
Preload on Nb (z-axis)
(Nb under tension,
Cu under compression)
640
50°C/h
48 h
400
25°C/h
~48 h
72 h
Strand/cable annealing
( 2 h at 200 °C)
Linear elongation,
Plastic deformation.
210
25°C/h
Cu6Sn5
Cu3Sn
Nb3Sn 20
7h36’
79h36’
87h12’
135h12’
140h
188h
Ch. Scheuerlein et al.,
IEEE Trans. Appl. Supercond.
VOL.18, NO. 4, 2008,
Temperature=210°C
Sn diffusion to Cu
→ Cu6Sn5 formation
Strand/cable shrinkage
Need Cu6Sn5 properties
→ tuning of the model
Temperature=400°C
Further Sn diffusion to Cu
→ Cu3Sn formation,
→ strand/cable shrinks,
→ all Sn reacted
Need Cu3Sn properties
→ tuning of the model
Temperature = 640°C
→ Strand/cable expand,
→ Plastic deformation?
→ Larger strand cross-section?
E, ρ and CTE needed for each step

4. WORK PLAN Bibliography study and discussion with experts
Collection of the data and material properties for simulation (limited data available, poor statistics )
Experimental data collection
strand/cable sample measurement before/after heat treatment
dilatometer measurement  material properties estimation
FEM simulation of the strand/cable/coil behavior during reaction
parameter tuning based on dilatometer measurement results
Feedback to the coil fabrication technology
Strand Model
Strand Subelement Model
Nb barier Sn
Nb+Cu Cu

5. EXPERIMENTAL DATA COLLECTION
reference data from off-line strand measurements
prepare samples for dilatometer measurements basing on off-line measurements
perform strand dilatometer measurements with dilatometer
Dilatometer sample preparation:
Sample length < 50 mm.
sample ends fused and filled
Linear Variable Differential Transformers (LVDT)
Continous ΔL/L measurement during Heat Treatment
measurement tip
furnace
measured
sample
reference
material
sample
holder
D. R. Dietderich et al., “Dimensional changes of Nb 3Sn, Nb3Al, and Bi2Sr2CaCu2O8 conductors
during heat treatment and their implication for coil design.” Adv. Cryo. Eng., vol. 44b, 1013–1020,

6. EXPERIMENTAL SETUP Strand samples ends fused  avoid Sn leak
Strand samples filled  measurements precision, dilatometer
Strand sample inserted into quarts tube  keep straight, reduce environment impact
Measured samples
OST RRP 54/61 and 108/128, diameter 0.7 mm and 0.8 mm
Strand samples twisted and non-twisted
Sample length: 50, 100, 200, 300, 560 and 1000 mm
Different sample ends preparation: crimped, fused, as cut
Samples painted along with temperature resistant marker
Measurements tools
Video Measuring System (5 μm precision) – sample length
Micrometer – sample diameter (5 μm precision)
Twist-meter – a dedicated tool build to measure twist change

7. First measurements results
After a few first measurements, following questions needed to be answered:
Why strand sample elongate?
in literature strand shrinks! (heat treatment duration?)
strand twist change contribution?
Why ΔL/L depend on sample length?
is there end effect?
Does ΔD/D depends on sample length?
Any other effects?
conductor type, Cu content?
Before dilatometer measurements (lsample<50 mm):
short sample behavior during heat treatment
single strand vs. bunch of strands
STRANDS ENDS: C – crimp, F – fused, NF – not fused (as cut)

8. Strands diameter change measurement
ΔD/D remains constant with sample length.
Show conformance with previous measurements (Andreev N.et al., Adv. in Cryogenic Eng.,  vol. 48B,  p.941 , 2001)
STRANDS ENDS: C – crimp, F – fused, NF – not fused (as cut)

9. Strands length change measurement summary
The length changes were measured from scratch to scratch starting from centre strand
In the ends ΔL/L „end effect” observed.
STRANDS ENDS: C – crimp, F – fused, NF – not fused (as cut)

10. End preparation impact on ΔL/L
The length changes were measured from scratch to scratch
ΔL/L remains constant in the straight part of strands
In the ends ΔL/L show large end effect.

11. Strands twist change measurement

12. Twist change impact on ΔL/L
OST RRP 108/127 strand (#12521)
Twisted samples elongate during the heat treatment
nt- non twisted
tw - twisted

13. STRAND measurement summary
4/13/2018
Measured strand samples:
Strand OST RRP 54/61 and OST RRP 108/127
strand diameter 0.7 mm – twisted and 0.84 mm – „non-twisted”,
Sample length: mm, sample ends: fused
Measured strand samples demonstrate:
OBSERVATIONS:
Twisted strands are longer after reaction because they „untwist”
Correlation strand diameter change and Cu/sc ratio (54/61 – 0.85, 108/ )
SAMPLE
Length change
Diameter change
Twist change
Strand 108/127 - twisted
Strand 108/127 - „non-twisted”
Strand 54/61 – twisted
Cable 54/61 – not constrained -

14. Some conclusions Dilatometer measurements - on going
Strand dimension changes before/after reaction completed
ΔL/L and twist change dependence confirmed by testing „non-twisted” strands
Strand ends can introduce „noise” in measurements
Important for measurements of short sample (< 50 mm) with dilatometer
Welded and filed samples are currently the best solution
„non-twisted” strands length change is the same order as measured cable length change
BUT comparison done with „54/61” cables
It should be compare with „108/127” cable measurements (on going)
„non-twisted” strands are preferred in dilatometer measurements
twist change effect eliminated
very likely behaves as confined strand in cable
Dilatometer measurements - on going

15. FUTURE PLANS PENDING NEEDED (for all HT phases) IN FUTURE?
Dilatometer strand measurement
NEEDED (for all HT phases)
Young modulus
Material density
CTE (coefficient of thermal expansion)
IN FUTURE?
Full image of strand/cable/coil behavior during HT
FEM modeling of strand/cable/coil behavior during reaction
Feedback to the coil fabrication technology
← Data for simulations,
(possible estimations from
dilatometer measurements)
Dariusz Bocian 15