Measurement of thermal conductivity of sapphire rods II

Takafumi UshibaThe university of Tokyo at Hongo

Tsubono Laboratory

2012/8/8 KAGRA Cryogenic Payload Meeting 1

Contents

• Purpose of the measurement• How to measure• Result• Discussion• Summary

2012/8/8 KAGRA Cryogenic Payload Meeting 2

Purpose of the measurement

• Final goal　　 measure the thermal conductivity of Moltech and INPEX sapphire rods with nail head.• Near goal　　 measure thermal conductivity of polished Photoran’s sapphire rods near peak temperature to confirm the purity of sapphire rods is well or not.

2012/8/8 KAGRA Cryogenic Payload Meeting 3

How to measure

• Sample size　　 diameter : 　　 sample length : 100mm• One dimensional approximation.

:thermal conductivityL :length between two temperature sensors,Q:heat flow,　 A :sample cross section,:difference of values of two temperature sensors

L

temperature sensor

temperature sensor

heater

Q

Heat bath

2012/8/8 KAGRA Cryogenic Payload Meeting 4

How to measure

• Sample size　　 diameter : 　　 sample length : 100mm• One dimensional approximation.

:thermal conductivityL :length between two temperature sensor,Q:heat flow,　 A :sample cross section,:difference of values of two temperature sensor

temperaturesensor

heater

heat bath

2012/8/8 KAGRA Cryogenic Payload Meeting 5

Result

2012/8/8 KAGRA Cryogenic Payload Meeting 6

This time, I take three data near 30K.

Discussion

• Error bars　　 uncertainty of offset voltage of thermometer• Peak’s shape　　 If the offset voltage of thermometer does not depend on temperature, the shape of peak of thermal conductivity is same as the real peak.

2012/8/8 KAGRA Cryogenic Payload Meeting 7

Summary

• I measure thermal conductivity near 30K• The result has too large error bars because of

the offset voltage of the temperature sensor.• In this measurement, I do not confirm the

purity of sapphire rod is well or not.• So, I need to measure thermal conductivity of

sapphire rod again near 30K.

2012/8/8 KAGRA Cryogenic Payload Meeting 8