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_TDT) with gradients between 0.5 – 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.

Synchrotron X-ray diffraction

Angle-dispersive in situ X-ray powder diffraction patterns at high pressure and high temperature were collected at beamline 12.2.2 at the Advanced Light Source at the Lawrence Berkeley National ­Laboratory using an X-ray wavelength of  λ=0.5166Å (24 keV) and λ=0.4969Å (25 keV) for the silver iodide and San Carlos olivine experiments, respectively. The X-ray energy for the AgI was lowered to 24 keV to be at a safe distance from the Ag-K-a-absorption edge. At each spatial position, X-ray diffraction patterns were taken both before and during the IR laser heating to yield ambient and heated diffraction patterns. The X-ray beam size was 10 mm. Patterns were collected with exposure times of 30 sec on a MAR3450 image plate. The detector distance and orientation were calibrated using a CeO₂ standard at the sample position.

Laser heating and temperature measurement

Laser heating of the LHDAC was conducted using a 1090 nm IR fiber laser system [Kunz et al., 2018], with a beam size of 30μm FWHM in diameter. The silver iodide sample was heated with 0.9-1.0W in both the upstream and downstream directions. The San Carlos olivine sample was heated with powers of 2.5-3.2W upstream and 4.5-5.7W downstream. To probe the sample across the hot spot, the sample had to be moved relative to the stationary X-ray beam, and with it, the laser hot spot which in turn was kept centered on the gasket hole (see Figure 1 in main text). The center of the gasket hole served as the reference for positioning the laser hot spot. As a result, this procedure created an individual hot spot for every diffraction measurement. The laser heating set-up on beamline 12.2.2 [Kunz et al., 2018] allows for quasi real-time temperature mapping of the sample chamber during a heating event. Temperatures were measured using the double sided spectroradiometric pyrometry set up on beamline 12.2.2, which employs a modified peak scaling approach [Kunz et al., 2018; Rainey and Kavner, 2014]. This approach avoids the notorious chromatic aberration artifacts and also produces full absolute temperature maps in real time, thus enabling the spatial mapping of the thermal pressure effects presented here.

The pyrometry setup produces upstream and downstream 74mm x 74mm square temperature maps centered at the peak of the laser hotspot. As a result, radial temperature readings from the center of the sample exist from 0 to 37mm for the full azimuthal range, but disregarding radial completeness, temperature data exist from 0 to 52.3mm from the center. We plotted the upstream and downstream temperatures against radial distance by averaging the temperatures of pixels with the same Euclidian distance (within floating point error) from the center of the 74mm x 74mm temperature maps. The upstream and downstream graphs were averaged to produce an average temperature vs. radial distance plot.

Due to the large thermal conductivity of the diamond anvils, it has been shown that at the diamond/sample interface, the sample has a temperature close to room temperature [Kiefer and Duffy, 2005]. To construct the temperatures between 52.3mm and 80mm (the sample edge), we use a simple linear decrease between the points at (44.5um, avgT_37um,T_52.3um) and (80um, 298K). To construct the first point of the linear decrease, we considered the temperature points between 37mm and 52.3mm because 360-degree azimuthal averaging is only possible between 0 and 37mm. The average distance and temperature of the points between 37mm and 52.3mm gives us the starting point for the linear decrease.

The average beam temperatures of sections centered between 0 and 47.3mm (52.3mm – 5mm) was obtained by averaging the corresponding 10mm section (our beam size) of the average temperature vs. radial distance graphs. Average beam temperatures of sections centered between 52.3mm and 80mm were obtained by taking the average temperature-value of the linear decrease over the corresponding 10mm radial section.

Pressure Determination

Scattering intensity versus 2θ plots were obtained by azimuthal integration of the 2-dimensional powder diffraction patterns using DIOPTAS [Prescher and Prakapenka, 2015]. From the intensity versus 2θ plots for the silver iodide sample, lattice spacings with Miller indices (200), (220), (311), (222), (400), (420), and (422) were used to refine the unit-cell parameters of silver iodide’s cubic crystal structure. From the intensity versus 2θ plots for the San Carlos olivine, lattice spacings with Miller indices (020), (021), (101), (002), (130), (131), (112), and (211) were analyzed using Celref 3 [Laugier and Bochu, 2002] to yield orthorhombic unit-cell parameters.

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Kiefer, B., and T. S. Duffy (2005), Finite element simulations of the laser-heated diamond-anvil cell, Journal of Applied Physics, 97(11), 114902.

Kunz, M., J. Yan, E. Cornell, E. E. Domning, C. E. Yen, A. Doran, C. M. Beavers, A. Treger, Q. Williams, and A. A. MacDowell (2018), Implementation and application of the peak scaling method for temperature measurement in the laser heated diamond anvil cell, Review of Scientific Instruments, 89(8), 083903.

Laugier, J., and B. Bochu (2002), CELREF V3: Cell parameters refinement program from powder diffraction diagram. Laboratoire des Matériaux et du Génie Physique, Institut National Polytechnique de Grenoble, France, edited.

Prescher, C., and V. B. Prakapenka (2015), DIOPTAS: a program for reduction of two-dimensional X-ray diffraction data and data exploration, High Pressure Research, 35(3), 223-230.

Rainey, E., and A. Kavner (2014), Peak scaling method to measure temperatures in the laser‐heated diamond anvil cell and application to the thermal conductivity of MgO, Journal of Geophysical Research: Solid Earth, 119(11), 8154-8170.

Calculations have been performed using the following softwares:

• Eosfit (http://www.rossangel.com/text_eosfit.htm)
• Origin (https://www.originlab.com/)
• Dioptas (http://www.clemensprescher.com/programs/dioptas)
• Microsoft Excel
• a self-written python script for Temperature maps