Michael G. Banks
Loughborough University,
Loughborough, UK.
Max-Planck-Institute für Festkörperforschung
(Solid State Research)
Stuttgart, Germany. 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. Building a set-up to measure specific heat
Introduction
Specific Heat Theory
Contribution to specific heat
Calorimetry
Method of measuring
and calculating
Cryostat “Bulli”
Apparatus
Calibration
Testing Outline of Talk
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!
Specific Heat Theory
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‘)
Lattice vibrations Lattice heat capacity contributed by the
Lattice vibrations > 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
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 g10 mJ/molK2)
Heavy fermion compounds g1000 mJ/molK2
Good agreement with experimental data
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:
Calorimetry
Calorimeter Nernst calorimeter Apiezon grease as thermal contact Addenda measured with grease Sample heat capacity is with addenda measurement subtracted
Example Heating time of tH of 12.045 s. Curve fitted in range of t > 130 s Gave Cp = 6.317 mJ/K Example using a sample of 158mg
How it is calculated Problem being ΔT Fitted to the post heating
and extrapolated to tH/2 1W.Schnelle, E Gmelin
Thermochimica Acta 391 (2002)
4149
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
Probe Probe holds the thermometers 3 thermometers -> CERNOX Inner shield thermometer Platform thermometer Calibrated thermometer Inner shield and Platform -> calibrating Sample goes on the platform
Calibration Calibrated thermometer -> underneath platform Obtain Resistances, Rshield, Rplat, Rcal Use Chebychev polynomial method
to obtain temperature Where,
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
Testing Testing comprises of relaxation and heat pulse programs Fast relaxation, same peak
height… heat leak Redesigned sample holder
Testing Relaxation time
Increased to a
Sufficient value
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