Thermodynamic measurements of submilligram bulk samples using a membrane-based “calorimeter on a chip”

Abstract

Calorimetry offers a direct measurement of thermodynamic properties of materials, including information on the energetics of phase transitions. Many materials can only be prepared in thin film or small crystal (submilligram) form, negating the use of traditional bulk techniques. The use of micromachined, membrane-based calorimeters for submilligram bulk samples is detailed here. Numerical simulations of the heat flow for this use have been performed. These simulations describe the limits to which this calorimetric technique can be applied to the realm of small crystals ( 1 – 1000 μ g ) . Experimental results confirm the feasibility of this application over a temperature range from 2 to 300 K . Limits on sample thermal conductivity as it relates to the application of the lumped and distributed τ 2 models are explored. For a typical sample size, the simulations yield 2.5% absolute accuracy for the heat capacity of a sample with thermal conductivity as low as 2 × 10 − 5 W ∕ cm K at 20 K , assuming a strong thermal link to the device. Silver paint is used to attach (both thermally and physically) the small samples; its heat capacity and reproducibility are discussed. Measurements taken of a submilligram single crystal of cobalt oxide (CoO) compare favorably to the results of a bulk calorimetric technique on a larger sample.