Temperature gradients and evaluation of thermoelastic properties in the synchrotron-based laser-heated diamond cell

Abstract

Reliable determinations of thermoelastic properties inside the laser-heated diamond cell depend critically on accurate measurement of temperature, temperature gradients, and the relationship between the hotspot and the X-ray beam. Here we examine these issues and their relative importance in interpreting data from synchrotron-based studies of materials at high pressures and temperatures. When combining laser heating and X-ray diffraction, temperature gradients must be measured and compared with the size of the X-ray beam in synchrotron-based laser-heated diamond anvil cell experiments in order to avoid systematically overestimating the actual average temperature of the X-rayed volume. For a laser-heated sample with a hotspot that drops to 75% of its value at the edge of the X-ray beam, the temperature measured at the hotspot center overestimates the actual average temperature by 17%, leading to up to a 20% underestimate of thermal expansion. As temperature gradients become steeper with increasing pressure, the temperature measured at the hotspot center increasingly overestimates the average temperature of the X-rayed volume, which further distorts measurements of higher order thermoelastic parameters. This can help to explain a wide variety of anomalous experimental results, including low thermal expansion values, and a higher than expected decrease of thermal expansion with increasing pressure without necessarily calling upon constant volume conditions in the cell. To help address these issues, we present four semi-independent methods to calculate temperature gradients inside the laser-heated diamond cell by taking advantage of the Planck’s law relationships between spectral intensity, integrated intensity, and temperature. Together, these methods yield a precise determination of the radial temperature gradient and provide an internal consistency check on the accuracy of the absolute temperature measurement. We show how these methods can be used to recover precise measurements of temperature gradients even in the presence of optical chromatic aberrations.