# Development of a relaxation calorimeter for temperatures between 0.05 and 4 K

## TL;DR

This paper presents a simple, inexpensive isoperibol calorimeter for measuring heat capacity of small samples between 0.05 and 4 K, using a thermal-relaxation method with adjustable thermal link for rapid measurements.

## Contribution

The design employs a sapphire substrate platform and a lock-in amplifier, enabling easy construction and adjustable thermal conductance for efficient low-temperature heat capacity measurements.

## Key findings

- Thermal conductance $k(T)/T$ is nearly constant down to 1 K.
- No significant difference in $k(T)/T$ between sapphire and silver platforms.
- Calorimeter can be optimized for fast measurements in limited time environments.

## Abstract

A detailed description of an isoperibol calorimeter for temperatures between 0.05 and 4 K is presented. The proposed setup can provide absolute values of the heat capacity $C$ of small samples (typically 1 mg). The extremely simple design of the sample platform, based on a sapphire substrate, and the experimental setup, which makes use only of a lock-in amplifier and a temperature controller, make the construction of such a calorimeter easy and inexpensive. The thermal-relaxation method is employed, which utilizes a permanent thermal link $k$ between the sample platform and the low-temperature bath. The temperature dependence of $k(T)$ is shown for several platforms throughout the entire temperature range: $k(T)/T$ is nearly constant down to 1 K, where it starts to decrease smoothly. The observed behavior is thoroughly explained by considering the thermal resistances of the platform constituents. A comparison between the values of $k(T)/T$ for platforms based on sapphire and on silver is presented where no significant difference has been observed. Each platform can be assembled to have a particular value of $k/T$ at 1 K. Since the sample relaxation time $\tau \sim C/k$, $k(T)$ can be adjusted to $C(T)$ to give a reasonably fast measuring time: Here, it is demonstrated how this calorimeter can be used in so-called single-shot refrigerators ($^{3}$He or demagnetization cryostats), where the time for a single measurement is limited. In addition, it can be used in moderate magnetic fields $B \leq 10$ T, because the platform constituents are weakly field dependent.