Absolute specific heat measurements of a microgram Pb crystal using ac nanocalorimetry

Abstract

Heat capacity measurements using the ac steady state method are often considered difficult to provide absolute accuracy. By adjusting the working frequency to maintain a constant phase and using the phase information to obtain the heat capacity, we have found that it is possible to achieve good absolute accuracy. Here we present a thermodynamic study of a ~ 2.6 {\mu}g Pb superconducting crystal to demonstrate the newly opened capabilities. The sample is measured using a differential membrane-based calorimeter. The custom-made calorimetric cell is a pile of thin film Ti heater, insulation layer and Ge_{1-x}Au_{x} thermometer fabricated in the center of two Si_{3}N_{4} membranes. It has a background heat capacity < 100 nJ/K at 300K, decreasing to 9 pJ/K at 1 K. The sample is characterized at temperatures down to 0.5 K. The zero field transition at Tc = 7.21 K has a width \approx 20 mK and displays no upturn in C. From the heat capacity jump at Tc and the extrapolated Sommerfeld term we find \DeltaC/{\gamma}Tc = 2.68. The latent heat curve obtained from the zero field heat capacity measurement, and the deviations of the thermodynamic critical field from the empirical expression Hc =Hc(0)[1-(T/Tc)^2] are discussed. Both analyses give results in good agreement with literature.