measurement of the thermal conductivity of sapphire fibers takafumi ushiba, m2 tsubono lab., the...
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Measurement of the thermal conductivity of sapphire fibers
Takafumi Ushiba, M2Tsubono Lab., The University of Tokyo
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Suspension of KAGRA
Hook the mirror on the sapphire fiber with thick edge
enlarge
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Sapphire Fiber with Thick Edge
Moltech sapphire fibers3
Thin part: about 1.8mm in diameterThick part: 10mm in diameter
These fibers are not polished.
IMPEX is now manufacturing their fibers.
Conceptional drawing of IMPEX fiber
Theory of the Thermal Conductivity
Thermal conductivity
: volumetric specific heat → at low temperature : speed of sound → in sapphire (constant) mean free path of a phonon
Since is constant at low temperature, the thermal conductivity is proportional to at low temperature.
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Previous Measurement
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Physics Letters A 301 (2002) Tomaru et al
Proportional to
sapphire fiber is well fitted by 0.0625.
This result supports that the thermal conductivity is proportional to at low temperature
They use sapphire fibers made by Photoran
Requirement of Thermal Conductivity
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Test mass
Intermediatemass
4 sapphire fibers
For two cryocooler(2W)
Laserabsorption
23K
16K
Thermal resistance of a sapphire fiber
: thermal conductivity length of a sapphire fiber cross-section of a sapphire fiber
If we require , should be larger than
Requirement @ 20K
(
Theory of the Thermal Conductivity
Thermal conductivity
: volumetric specific heat → at low temperature : speed of sound → in sapphire (constant) mean free path of a phonon
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These are inherent in the material
This is the only parameter we can change
We should prepare the sapphire fibers which have the long mean free path of a phonon.
Thermal Conductivity of Sapphire fibers
The side of Moltech and IMPEX sapphire fibers are not polished. → The surface of these sapphire fibers are rough.It makes the thermal conductivity low. (Size effect)
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Highly polished
Sapphire fiber
Not polished
phonon
Completely reflected
Scattering
High thermal conductivity
Low thermal conductivity
Even if the size effect limit the thermal conductivity of sapphire fibers, it is not a matter for KAGRA suspension.
Thermal Conductivity of Sapphire fibers
If the purity of the sapphire fiber is low → The sapphire fibers have defects of phonon and impuritiesIt makes the thermal conductivity low.
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High purity
Sapphire fiber
Low purity
phonon
Nothing disturbs phonon
Scattering
High thermal conductivity
Low thermal conductivity
We should check the thermal conductivity(purity) of sapphire fiber experimentally!
Defects of phonon or impurities
Experimental Setup
One dimensional approximation
heat flux in the sapphire fiber distance between two thermometers cross-section of the sapphire fiber difference of values of two thermometers
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L
thermometer
thermometer
heater
Q
Heat bathheater
First we measure the normal sapphire fiber• Diameter is 1.8mm.• Length is 100mm.• Polished sample.
Sapphire fiber
Result
We could reproduce the result of Tomaru’s work around 80K. 1300 @82K 700 @90K→The method of this measurement might have no serious troubles.
However, our result at low temperature is not proportional to . @12K 1100 @17KWe do not check the reproducibility of this result because of some troubles.
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We should measure the thermal conductivity of sapphire fiber again.
This value might be limited by the impurity
This value is much smaller than we expected.
Summary• Requirement of the thermal conductivity
• To realize the requirement, the purity of the sapphire fiber has to be very high.
• In our result, the thermal conductivity might be limited by the purity of Photoran’s sapphire fiber.
• We should measure the thermal conductivity of Photoran’s fiber again.
• And, we have to measure the thermal conductivity of Moltech and IMPEX sapphire fibers as soon as possible.
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Thank you for your attention.
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