Characterization of the pressure coefficient of manganin and temperature evolution of pressure in piston-cylinder cells

We report measurements of the temperature- and pressure-dependent resistance, R(T, p), of a manganin manometer in a ⁴He-gas pressure setup from room temperature down to the solidification temperature of ⁴He (T_solid ∼ 50 K at 0.8 GPa) for pressures, p, between 0 GPa and ∼0.8 GPa. The same manganin wire manometer was also measured in a piston-cylinder cell (PCC) from 300 K down to 1.8 K and for pressures between 0 GPa and ∼2 GPa. From these data, we infer the temperature and pressure dependence of the pressure coefficient of manganin, α(T, p), defined by the equation R_p = (1 + αp)R₀, where R₀ and R_p are the resistances of manganin at ambient pressure and finite pressure, respectively. Our results indicate that upon cooling, α first decreases, then goes through a broad minimum at ∼120 K, and increases again toward lower temperatures. In addition, we find that α is almost pressure-independent at T ≳ 60 K up to p ∼ 2 GPa, but shows a pronounced p dependence at T ≲ 60 K. Using this manganin manometer, we demonstrate that p overall decreases with decreasing temperature in the PCC for the full pressure range and that the size of the pressure difference between room temperature and low temperatures (T = 1.8 K), Δp, decreases with increasing pressure. We also compare the pressure values inferred from the manganin manometer with the low-temperature pressure, determined from the superconducting transition temperature of elemental lead (Pb). As a result of these data and analysis, we propose a practical algorithm to infer the evolution of pressure with temperature in a PCC.