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Heat capacity measurements in high magnetic fields
Scott C. Riggs, J. B. Betts, A. Migliori, F.F.Balakirev National High Magnetic Field laboratory @ Tallahassee & Los Alamos National Laboratory
C (H=0) = γ T + βT3
Specific heat – why?
Most fundamental thermodynamic quantity.
Gives the density of states:
Electronic component:
In a metal:
Outline
• Heat capacity measurement methods • Cryogenics and probes • Making a measurement/taking the data • High magnetic field issues • Some results • Future work
Methods we use to measure heat capacity. • Classic Relaxation Calorimetry • Dual Slope relaxation Calorimetery • AC Calorimetry • Differential Scanning Calorimetry
The same calorimeter setup can be used for 3 methods
Heater
Thermometer
Weak thermal link Temperature controlled block
Sample platform
With integral heater and thermometer
Sample Thermometer (Cernox) NiCr Heater
NiCr leads Silver epoxy contacts
Sapphire platform
1. Measure platform temperature with zero heat applied.
2. Turn on platform heater.
3. Allow platform temperature to relax exponentially to new stable temperature.
4. Turn off platform heater
5. Allow platform temperature to relax exponentially to initial stable temperature.
Cp = κ * τ = P/ΔT * τ = IV/ΔT * τ
Classic relaxation method
Cons. • High temperature stability of block required • Needs exponential fit • Stable magnetic field during measurement • Long time to take measurement
Pros. • Simple method • Real units of heat capacity • Easy to implement
Classic relaxation method – tau 2 issues
Heater
Thermometer
Weak thermal link Temperature controlled block
Sample platform
With integral heater and thermometer
Sample
Strong or comparable thermal link
1. Measure platform temperature with zero heat applied.
2. Turn on platform heater.
3. Allow platform temperature to relax exponentially to new temperature.
4. Turn off platform heater
5. Allow platform temperature to relax exponentially to initial temperature.
Cp = Heater Power/(slope(W) – slope(C))
Pros. • Simple fitting routines to determine slopes • Excellent results • Relatively fast measurement • No need to wait for temperature stabilization • External influences cancel at slope(W) = slope(C)
Dual slope relaxation method
Cons. • High temperature stability of block required • Stable magnetic field during measurement • Both warming & cooling curves needed
Cryogenics
• To measure heat capacity with small errors using any methods requires excellent block temperature stability.
• Great care must be taken with wiring and grounding of all measurement leads
• Sample is in a vacuum • Good heat sinking of leads is required to
reach lowest temperatures • 100K – 300mk temperature range • Materials selected for maximum thermal
conductivity and minimum eddy current heating
Temperature control & taking the data
• Conventional hardware temperature control.
• LabView software temperature control
Current resistor
Platform
Thermometer Transformer
Platform
Heater
I
V
Heat capacity platform
Lockin Amplifier
+
- 1KHz – 5KHz
• Lockin limited to 512Hz measurement • Internal time constants cause problems with fitting data • Noise from large GPIB data transfers
Taking the data with the digital lockin
The hardware
• Three independent synchronously locked outputs
• Variable voltage sine wave • fixed voltage sine wave • Clock • Frequency of all three outputs can be
varied in multiples of each other. • Onboard USB digitizer 8 channels • Data streams to computer continuously • Onboard Preamplifier with configurable
settings
Real experimental set-up – with experimenter
In Cell 12 – 36T Resistive magnet
In Office – Second Floor
Taking the data with the digital lockin
The software • Raw sine wave data streamed to computer • Raw data can be saved and operated on later • No fixed time constants • “On the fly” lockin processing implemented in LabView (2.5KHz max data rate 2 channels) • Labview modules can be used to meet individual circumstances.
Addenda Measurements.
0 10 20 30 40 500
50
100
150
200
250
300
350
400
450
500
C (µ
J/K)
Temperature (K)
Addenda Comparison between PPMS and NHMFL Calorimeter
PPMS
NHMFL
• Area of NHMFL platform is 4 times larger than PPMS
• Large-area, insulating nano material samples easily mounted
• At 50K addenda are < ½ of a typical PPMS setup
• Only useful up to 50K because of small thermometer dR/dT
Heat capacity in high magnetic fields.
• Calorimeter Design • Calibration • Cryogenics • Electronics and software • Calorimeter Comparisons
• Sapphire platform • Cernox™ Thermometer
evaporated directly onto the platform
• NiCr Heater evaporated directly onto the platform
• Manganin leads used also for thermal contact to the block
2nd generation design of the calorimeter.
High magnetic field issues
• Vibration of the platform in the magnetic field causes heating. • Open loop area of platform leads causes Bdot pickup on the measuring circuit.
8 small Manganin leads, large open loop area Good vibrational stability
4 small NiCr leads smaller open loop area Very good vibrational stability
• Sapphire platform cut down to reduce addenda
• Cernox™ Thermometer contact traces changed to reduce loop area
• Twisted pair leads used to reduce loop area
2nd generation design of the calorimeter.
Magnetic Field Calibrations
0 10 20 30 40 50
-0.20
-0.15
-0.10
-0.05
0.00
∆R/R
Magnetic Field (T)
Magnetoresistance of platform thermometer
500mK
4K
17K Magnetoresistance of the platform thermometer was measured in a 50T pulsed magnet at the NHMFL Los Alamos.
Pulsing the magnet
Process • Get data at fixed
temperature
• Build a temperature array
• That’s it.
0 10 20 30 40 50150
200
250
300
350
400
450
500
550
600
650
R (O
hms)
Field (T)
20K
7.5K
4K5K
3.2K
1K0.7K
*Important* - Know your temperature ranges
• Log-log scale
• Polynomial fit
o More weight on low temp data
1 10 100
100
1000
10000
B=20T 4th order fit
R (Ω
)
Temp (K)
What we’ve been able to achieve
• New calorimeter design – low addenda, good thermal contact
• Properly calibrate for high magnetic fields • Cryogenics • Grounding • Vibration isolation • New electronics
0 1 2 3 4
Tem
pera
ture
Time (s)
6T (SC magnet Hmax=16 T) 45T (Hybrid magnet)
YBCO x=6.55
28 30 32 34 36 38 40 42 44 4616
18
20
22
24
26
28
30
Magnet sweep up (T=1K) Magnet sweep down
C (m
J m
ol-1
K-1)
Magnetic Field (tesla)
Each point in the field sweeps below is determined over one cycle
High Magnetic Fields - YBCO
Future work and conclusions
• Heat capacity can be measured with good accuracy and repeatability in very high magnetic fields, but great care is needed with the initial setup to avoid large scatter in the measurements.
• Dual slope method is faster and has less scatter than the classic exponential fit relaxation method
• Digital lock-in techniques greatly enhance the capability.
• The development of the next generation thermometers with little or no magnetic
field dependence will greatly improve our ability to measure heat capacity especially in sweeping magnetic fields.
• Development of top loading sorbtion pumped cryogenics will allow faster sample turn around and lower base temperatures.