Temperature Distribution in a Laser-Heated Diamond-Anvil Cell as Described by Finite Element Analysis

Finite element analysis (FEA) is a powerful tool for numerically solving partial differential equations over complex geometries and is thus useful for analyzing heat transport in laser-heated diamond anvil cell (LHDAC) experiments (e.g., Rainey et al., 2013; Kiefer et al., 2005; Geballe et al., 2020; McWilliams et al., 2015). Our models expand on previously published simulations by calculating the volumetrically-averaged temperatures of both the sample and pressure/insulation media under steady-state heating in order to determine the thermal pressure of the hot sample. Our goal is to produce an accurate relationship between the surface temperature of the absorbing sample and the temperature of the transparent insulating media, which is necessary for determining thermal pressure but susceptible to steep temperature gradients. We find that in doing so, our FEA models of temperature within the pressure/insulation media can differ from simplified estimates of temperature gradients (e.g., Campbell et al., 2009) by more than a factor of 2. We also explore various thermal conductivity models and find that the volumetrically-averaged temperatures differ from simplified models forcing the predicted thermal pressures determined to differ by up to a factor of 1.5 at a temperature of 2000 K. Higher temperatures exacerbate this difference. The FEA models, available in both Python and FlexPDE, are versatile across different geometries, materials, and heat sources. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-825378.