A virtual thermometer for ultrahigh-temperature–pressure experiments in a large-volume press

Abstract

Ultrahigh-temperature–pressure experiments are crucial for understanding the physical and chemical properties of matter. The recent development of boron-doped diamond (BDD) heaters has made such melting experiments possible in large-volume presses. However, estimates of temperatures above 2600 K and of the temperature distributions inside BDD heaters are not well constrained, owing to the lack of a suitable thermometer. Here, we establish a three-dimensional finite element model as a virtual thermometer to estimate the temperature and temperature field above 2600 K. The advantage of this virtual thermometer over those proposed in previous studies is that it considers both alternating and direct current heating modes, the actual sizes of cell assemblies after compression, the effects of the electrode, thermocouple and anvil, and the heat dissipation by the pressure-transmitting medium. The virtual thermometer reproduces the power–temperature relationships of ultrahigh-temperature–pressure experiments below 2600 K at press loads of 2.8–7.9 MN (∼19 to 28 GPa) within experimental uncertainties. The temperatures above 2600 K predicted by our virtual thermometer are within the uncertainty of those extrapolated from power–temperature relationships below 2600 K. Furthermore, our model shows that the temperature distribution inside a BDD heater (19–26 K/mm along the radial direction and <83 K/mm along the longitudinal direction) is more homogeneous than those inside conventional heaters such as graphite or LaCrO3 heaters (100–200 K/mm). Our study thus provides a reliable virtual thermometer for ultrahigh-temperature experiments using BDD heaters in Earth and material sciences.