Building a setup to measure specific heat

1
Building a set-up to measure specific heat
Michael G. Banks Loughborough University,
Loughborough, UK. Max-Planck-Institute für
Festkörperforschung (Solid State
Research) Stuttgart, Germany.
2
Outline of Talk

• Introduction
• Specific Heat Theory
• Contribution to specific heat
• Calorimetry
• Method of measuring
• and calculating
• Cryostat Bulli
• Apparatus
• Calibration
• Testing

3
Introduction
Why specific heat?
Gives information about Electronic
distribution Energy levels in magnetic
order Order-disorder
Study of low temperatures gives
Rocket fuels to superconductors Quantum effects
Surpassed nature!
4
Specific Heat Theory
5
Contribution to the specific heat
Contributions to the specific heat may come from

• lattice vibrations (phonons)

2) Electronic contribution (conduction electrons)

3) magnetic contribution (spinwaves)
6
Lattice vibrations
Lattice heat capacity contributed by the Lattice
vibrations gt phonons
Einstein came up with the first model
Quantitative features not sufficient with
measurement
Debye proposed a model (assumptions)
Showed good agreement with solids and T3 at low
temperatures was an prediction of the Debye law
7
Electronic contribution
Electronic heat capacity contributed by the
conduction electrons (Sommerfeld term g T )
Sommerfeld applied quantum statistics to the free
electron model exceeds phonon heat capacity
typically below helium temperature (typically
g?10 mJ/molK2) Heavy fermion compounds g?1000
mJ/molK2
Good agreement with experimental data
8
Magnetic Contribution
Magnetic heat capacity contributed by the Spin
waves Magnons Example ferromagnet Bloch T 3/2
law
E.g. at low temperatures for a metallic
ferromagnet
9
Calorimetry
10
Calorimeter
Nernst calorimeter
Apiezon grease as thermal contact
Addenda measured with grease
Sample heat capacity is with addenda measurement
subtracted
11
Example
Example using a sample of 158mg
Heating time of tH of 12.045 s.
Curve fitted in range of t gt 130 s
Gave Cp 6.317 mJ/K
12
How it is calculated
Problem being ?T
Fitted to the post heating and extrapolated to
tH/2
1W.Schnelle, E Gmelin Thermochimica Acta 391
(2002) 4149
13
Correction factors
Advantages of this
Exponential takes into account Thermal loses
Corrective term accounts for Loses in the
heating period
Results in a scatter of 3 to 5 Times lower in Cp1
1W.Schnelle, E Gmelin Thermochimica Acta 391
(2002) 4149
14
Cryostat Bulli
15
Apparatus
Probe
Pressure gauge
Helium Dewar
Pump
Bulli Cryocal 0T
Liquid He4 Dewar - recuperation line
16
Probe
Probe holds the thermometers
3 thermometers -gt CERNOX
Inner shield thermometer
Platform thermometer
Calibrated thermometer
Sample goes on the platform
Inner shield and Platform -gt calibrating
17
Calibration
Calibrated thermometer -gt underneath platform
Obtain Resistances, Rshield, Rplat, Rcal
Use Chebychev polynomial method to obtain
temperature
Where,
18
1st Calibration attempt
Tdiff plot for the regulator and Probe
Band of 40mK seen
Therefore fluctuations too large
Stabilisation time too short
Performed again with a band of 5mK
19
Testing
Testing comprises of relaxation and heat pulse
programs
Fast relaxation, same peak height
?heat leak
Redesigned sample holder
20
Testing
Relaxation time Increased to a Sufficient value
21
Further work
Now with Relaxation time sufficient
Perform Addenda measurements
Measure a standard copper sample
22
Acknowledgements
MPI-FKF Dr R Kremer Mr S Höhn Mr K Graf
Thank you for your attention