Modulation calorimetry in diamond anvil cells. II. Joule-heating design and prototypes

Abstract

Part I shows that quantitative measurements of heat capacity are theoretically possible inside diamond anvil cells via high-frequency Joule heating (100 kHz–10 MHz), opening up the possibility of new methods to detect and characterize transformations at high-pressure such as the glass transitions, melting, magnetic orderings, and the onset of superconductivity. Here, we test the possibility outlined in Part I, using prototypes and detailed numerical models. First, a coupled electrical-thermal numerical model shows that specific heat of metals inside diamond cells can be measured directly using ∼1 MHz frequency, with <10% accuracy. Second, we test physical models of high-pressure experiments, i.e., diamond-cell mock-ups. Metal foils of 2–6 μm-thickness are clamped between glass insulation inside diamond anvil cells. Fitting data from 10 Hz to ∼30 kHz, we infer the specific heat capacities of Fe, Pt, and Ni with ±20%–30% accuracy. The electrical test equipment generates −80 dBc spurious harmonics, which overwhelm the thermally induced harmonics at higher frequencies, disallowing the high precision expected from numerical models. An alternative Joule-heating calorimetry experiment, on the other hand, does allow absolute measurements with <10% accuracy, despite the −80 dBc spurious harmonics: the measurement of thermal effusivity, ρck (ρ, c, and k being density, specific heat, and thermal conductivity), of the insulation surrounding a thin-film heater. Using a ∼50 nm-thick Pt heater surrounded by glass and 10 Hz–300 kHz frequency, we measure thermal effusivity with ±6% accuracy inside the sample chamber of a diamond anvil cell.