Low Temperature Measuring Service

In order to be able to make reliable statements about heat conduction in selected materials in the cryogenic temperature range, a test rig for investigating thermal conductivity was set up at the ILK Dresden. The thermal conductivity \( \lambda \) of a material is defined as the heat flow \( \dot{Q} \) over a defined cross-section \( A \) and a length \( l \) at an externally imposed temperature difference \( \Delta T \). \begin{equation} \lambda = \frac{\dot{Q} \cdot l}{A \cdot \Delta T}\left[ \mathrm{\frac{W}{m\:K}} \right] \end{equation} Thermal conductivity can also be understood as thermal resistance. With the measuring principle used, a heat flow or heating power is specified and the temperature difference across the sample to be tested is measured. It must be ensured that the applied heat flow can only flow over the sample cross-section and not over the surrounding structure or atmosphere. To minimize these lateral influences, a symmetrical measurement setup can be selected, see Figure  1, left. The sample heater is located in the middle between two identical samples. Both samples are surrounded by a thermally conductive structure, the measuring cell. A defined heat output is applied with the heater. The resulting heat flow, yellow arrows, is transferred to the measuring cell via the two samples. The measurements are carried out in a stationary state and in a vacuum. With the aid of the temperature control system, these measurements can be carried out very precisely and fully automatically at different temperatures. For larger sample dimensions, simpler arrangements are also possible, see Figure  1, right.

Like thermal conductivity, the heat capacity is a temperature-dependent physical quantity. The specific heat capacity of a substance measures the ability to store thermal energy and indicates how much energy is required to heat one kilogram of a certain substance by 1  K, for example. The specific heat capacity c can be determined using the heating pulse method. This involves heating a sample equipped with a heater and a temperature sensor for a defined period of time. The integral of the electrical heating power supplied over this period of time gives the amount of energy Q required to heat the sample with a mass m by the measured temperature difference \( \Delta T \). \begin{equation} c = \frac{Q}{m \cdot \Delta T} \left[ \mathrm{\frac{J}{kg\:K}} \right] \end{equation}.

Figure 3 shows the test set-up, with the temperature control system with cryocooler and figure 4 the sample carrier with a sample and sample heater mounted on it on the right.

Starting from a reference temperature \( T_0 \) and a length \( L_0 \) materials change their geometric dimensions when the temperature changes. Most materials expand when heated and shrink when cooled. The physical characteristic value for this behaviour is the temperature-dependent and material-specific coefficient of thermal expansion \( CTE \) or \( \alpha(T) \). \begin{equation} \alpha(T) = \frac{dL(T)}{dT} \cdot \frac{1}{L_0} \left[ \mathrm{K^{-1}} \right]\end{equation} The samples are cooled using a cryocooler. The sample temperature is then changed within a specified range. The temperature is controlled using an electric heater on the sample holder. The change in length of the sample and the temperatures at both ends of the sample are measured discretely over time. The expansion coefficient \( \alpha(T) \) is calculated from these variables for each temperature step.