Mapping the thermal structure of solid-media pressure assemblies

Abstract

The refractory oxides MgO and Al2O3 are the most commonly used insulator/filler materials in solid-media pressure assemblies. These oxides react with one another at high temperatures and pressures, forming a well-defined layer of spinel (~MgAl2O4) at the contact. The spinel layer widens in proportion to the square root of time at a rate that also depends systematically upon temperature and pressure. On the basis of 44 piston-cylinder runs spanning 1,200–2,000 °C and 1.0–4.0 GPa, we present a general relationship describing the width (ΔX) of the spinel layer as a function of time (t, in s), temperature (T, in K) and pressure (P, in GPa): \(\Delta {\rm X} = \left[ {{\rm 8}{\rm .58} \times {\rm 10}^{{\rm 11}} \cdot \exp \left( { - 48865/{\rm T} - 2.08 \cdot {\rm p}^{1/2} } \right) \cdot {\rm t}} \right]^{1/2}\) . If the pressure and duration of an experiment are known (as is usually the case) this calibration makes it possible to calculate the temperature to within a few degrees at any location in a solid-media assembly where MgO and Al2O3 are in contact (at T above ~1,200 °C) – simply by measuring the width of the spinel layer with an optical microscope. Application of this "reaction-progress" thermometer to the 13- and 19-mm diameter piston-cylinder assemblies used in the RPI lab confirms generally parabolic axial T gradients with acceptably broad hot spots. Three-dimensional maps of the 19-mm assembly reveal a radial component to the thermal field, with somewhat higher temperatures near the graphite heating element (i.e., a saddle-shaped hot region). Two exploratory experiments in a multi-anvil apparatus at 14 GPa (1,700 and 1,975 °C) confirm that the reaction-progress technique will work at pressures well above 4 GPa. The piston-cylinder-based calibration predicts ΔX to within a factor of two in the two multi-anvil runs, and relative changes in T along the assembly can be readily mapped. However, additional high-pressure calibration points will be needed before the thermometer can be used in quantitative multi-anvil applications. The spinel reaction-progress thermometer is easily implemented, and should allow other researchers to map the thermal structures of their own assemblies in a single experiment with one thermocouple.