Equation of state and refractive index of argon at high pressure by confocal microscopy

The response of matter to extreme pressures is of fundamental interest to condensed matter physics, geology, and planetary science. Diamond anvil cells DACs have been used with great success in high-pressure investigations.1 However, it is difficult to measure the volume of a sample contained in a DAC. While the area of the sample is easily observed through the diamond anvils, the metal gasket which contains the sample is not transparent, making thickness measurements challenging. While x-ray and neutrondiffraction techniques can measure the lattice volume of a solid sample to high precision, they do not measure the absolute volume and they cannot measure the molar volume of fluids. These experimental limitations have prevented researchers from obtaining accurate equation of state data for a range of fluids and amorphous solids.2,3 In the present work, we overcame the difficulties associated with measuring compressed fluids by using confocal microscopy. A confocal microscope illuminates the sample by a laser focused through the objective lens onto the point to be imaged.4 Light originating from the focal point of the objective passes through the microscope to a pinhole located at the focus of the tube lens. The pinhole screens light originating from points other than the focus of the objective lens. This screening results in a significantly higher resolution than a conventional microscope,5 by imaging one point at a time. The microscope scans the volume of the sample and assembles a three-dimensional 3D image. Typically the scanning in the x and y directions is done by mirrors, keeping the z coordinate which corresponds to the position of the objective lens fixed. Thus the 3D image consists of a series of cross sections of the sample, each collected at a different position of the objective lens. When scanning a DAC, light is reflected from the surfaces of the diamond anvils back through the pinhole. The reflected intensity varies as a function of focus position and is maximized when the objective is focused at a surface Fig. 1 . If the sample is optically homogeneous, there will be four peaks in the reflected intensity profile. The distance between the second and third peaks gives the thickness d of the sample divided by its refractive index n.6,7 The refractive index can be determined from the ratio of the amplitudes of the first and second peaks.8 Finally, the area is determined from the high-resolution image of the sample cross section. A major advantage of this technique is that volume, refractive index, and pressure are determined in a single experiment. It should be noted that this technique was developed using thick samples about 100 m under relatively low pressures less than 10 GPa . Under these conditions the diamonds do not distort significantly. The technique is predicated on plane surfaces perpendicular to the optical axis and its effectiveness for less ideal conditions has not been evaluated. In this work we measured the equation of state and refractive index of argon at 300 K. Argon is a model system that has been the subject of numerous experimental and theoretical investigations.9–18 For weakly interacting systems, the dependence of refractive index on density is described by the Clausius-Mossotti relation