Thermal Pressure in the Laser‐Heated Diamond Anvil Cell: A Quantitative Study and Implications for the Density Versus Mineralogy Correlation of the Mantle

Abstract

Thermal pressure is an inevitable thermodynamic consequence of heating a volumetrically constrained sample in the diamond anvil cell. Its possible influences on experimentally determined density-mineralogy correlations are widely appreciated, yet the effect itself has never been experimentally measured. We present here the first quantitative measurements of the spatial distribution of thermal pressure in a laser-heated diamond anvil cell (LHDAC) in both olivine and AgI. The observed thermal pressure is strongly localized and closely follows the distribution of the laser hotspot. The magnitude of the thermal pressure is of the order of the thermodynamic thermal pressure (αK T ΔT) with gradients between 0.5 and 1.0 GPa/10 μm. Remarkably, we measure a steep gradient in thermal pressure even in a sample that is heated close to its melting line. This generates consequences for pressure determinations in pressure-volume-temperature (PVT) equation of state measurements when using an LHDAC. We show that an incomplete account of thermal pressure in PVT experiments can lead to biases in the coveted depth versus mineralogy correlation. However, the ability to spatially resolve thermal pressure in an LHDAC opens avenues to measure difficult-to-constrain thermodynamic derivative properties, which are important for comprehensive thermodynamic descriptions of the interior of planets. Plain Language Summary The primary window into the interior of the Earth below~10-km depth are earthquake waves that give us a three-dimensional elasticity/density image of the planet. In order to translate this into a geological model of the Earth, we need to know the physical and chemical response of rocks with the composition of the Earth's interior at high pressures and temperatures. This is achieved by experiments in which samples are subjected to the high pressures and temperatures of the deep Earth using laser-heated diamond anvil cells. A long-standing problem of such experiments is a hard to quantify pressure term caused by the heating of the sample. This paper, for the first time, experimentally quantifies the spatial distribution of thermal pressure in a typical experiment and explores the effect of its incomplete knowledge on the deduced mineralogical composition of the Earth.

A Comprehensive Review of High-Pressure Laser-Induced Materials Processing, Part I: Laser-Heated Diamond Anvil Cells

“…Inconsistencies in pyrometry measurements pose an ongoing challenge for all LH-DAC temperature measurements [8,166,259]. To obtain accurate temperature measurements over a wide range of temperatures, it is critical to calibrate the pyrometry-system using a black-body source, with a knowledge of the transmission of the systems optics and detector sensitivities.…”

“…Recently, the first quantitative measurements of the thermal pressure distribution across an LH-DAC sample were carried out by a team of researchers from the University of California and the US Advanced Light Source [259] Thermal pressure is a localised pressure that results from a sample being heated in an isochoric (constant volume) chamber (Gay-Lussac's law). Provided the surrounding material remains solid (and retains sufficient shear strength), a pressure gradient is generated within an LH-DAC sample-where the highest pressure is generally at the peak laser-induced temperature.…”

“…Provided the surrounding material remains solid (and retains sufficient shear strength), a pressure gradient is generated within an LH-DAC sample-where the highest pressure is generally at the peak laser-induced temperature. In this experiment, C. E. Yen et al generated a large thermal gradient using a 1090 nm fibre laser, heating silver iodide and olivine using the double-sided illumination method [259]. They subsequently took measurements with a fine X-ray beam at various locations across the 30 µm (FWHM) laser-heated spot and obtained the thermal pressure distribution; this distribution had a similar profile to that of the induced-temperature gradient.…”

Thermal Equations of State of Corundum and Rh2O3 (II)‐Type Al2O3 up to 153 GPa and 3400 K

“…Although the thermal EoS of corundum have been determined up to 65 GPa and 1,500 K by Dubrovinsky et al (1998), experimental pressures at high temperatures were determined from the luminescence of ruby at 300 K by assuming no changes in pressure inside the diamond anvil cells (DACs) during every heating-cooling cycle. This may result in large uncertainties in the obtained thermoelastic parameters (Yen et al, 2020). Furthermore, there are no experimental constraints on the thermoelastic parameters of Rh 2 O 3 (II)-type Al 2 O 3 .…”