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Calorimetry / Dilatometry

Heat capacity and thermal expansion

Heat capacity

Contact: Dr. Manuel Brando Dr. Thomas Luehmann


The heat capacity of small solid samples (typically 1 mg) at low temperatures and in high magnetic field is measured by means of two similar techniques: the thermal relaxation (TR) method [1] and the compensated heat-pulse (CHP) method [2]. In both techniques, the sample is attached to a platform connected through a permanent thermal link to the low-temperature stage of the cryostat. The principle of operation is based on the one-dimensional heat-flow model illustrated in the figure above where
Cp = sample heat capacity
Ca = platform heat capacity
k1 = thermal conductance between platform and bath
k2 = thermal conductance between sample and platform
P0 = power applied to the system.

In the RT method, a heat pulse is applied to the platform until a steady state is reached at a temperature T1. The heat capacity can be derive from the following equation

$C_{p}=k_{1}\tau_{1}\left (1-\frac{k_{1}\tau_{2}}{C_{a}}\right ) +k_{1}\tau_{2}-C_{a}$\\
$k_{1}=P_{0}/(T_{1}-T_{0})=P_{0}/\Delta T$

To decrease the measuring time, the CHP method applies the heat pulse only for a short time period dt and compensate the thermal losses through a background heating. The heat capacity is then

$k_{1}\tau_{1}=(C_{p} + C_{a})\left (1 + \frac{k_{1}}{k_{2}}\frac{C_{p}}{C_{p} + C_{a}} \right )$\\

- Typical masses of the samples: 1-10 mg
- Temperature range: 0.03 < T < 5 K
- Magnetic field range: 0 < B < 14T

Figure 1. Figure 1. Schematic view of the measuring platform: P, silver platform; N, nylon thread, S, sample; T, RuO2-chip temperature sensor; H, heater.

[1] M. Brando, Rev. Sci. Instr. 80, 095112 (2009)
[2] H. Wilhelm, T. Luehmann, T. Rus and F. Steglich, Rev. Sci. Instr. 75, 2700 (2004)

Thermal expansion and magnetostriction

Contact: Dr. Manuel Brando Dr. Thomas Luehmann


The thermal expansion at low temperatures is determined by means of a capacitive method. By varying the temperature (thermal expansion) or the magnetic field (magnetostriction) the sample length change yields a differing distance between the capacitor plates which is detected. [ * b r * ] The thermal expansion is given by the derivative of the sample length with respect to the temperature. It is very sensitive to phase transitions, structural or electronic and allows for differentiating between 1st order and 2nd phase transitions. Furthermore, it is well suitable to study quantum phase transitions since there it is expected for the thermal expansion to exhibit a stronger divergence than the specific heat. This means that the Grueneisenparameter which is defined as [ * b r * ] diverges upon lowering the temperature. [ * b r * ] The resolution of the sample holders in use is better than 1/1000A. A silver cell is used for the thermal expansion at temperatures between 20mK and 4K, a cell out of CuBe was constructed for magnetostriction measurements up to 18T. A variety of different thermal expansion cells allows for measurements with perpendicular magnetic field.

Last modified on April 7, 2011 Print version         Top
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