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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