Determining the equation of state of amorphous solids at high pressure using optical microscopy

A method to determine the volumetric equation of state of amorphous solids using optical microscopy in a diamond anvil cell is described. The method relies on two- dimensional image acquisition and analysis to quantify changes in the projected image area with compression. The area analysis methods prove to be robust against improper focusing and lighting conditions while providing the accuracy necessary to deduce small area changes, which correspond to small volume changes in an isotropic material. The image capture, area analysis method is used to determine the compression of cubic crystals, yielding results in good agreement with diffraction and volumetric measurements. As a proof of concept, the equation of state of amorphous red phosphorus is measured up to 12 GPa under hydrostatic conditions where the quantified volume change between the red and black phases is approximately ΔV/V ₀ ≈ 0.05 after a reduction of volume nearing 35% at 8 GPa. A large hysteresis is present during decompression and eventually results in a 15% permanent densification relative to the starting volume, which is attributed to a pressure induced crystallization from red to black phosphorus. The robustness of the technique is also demonstrated by measuring the equation of state of GeSe ₂ glasses for semi transparent samples and As ₂O ₃ in which gold coating is used as a contrasting aid.