C. Higher resolution in stress measurement

We use x-ray diffraction to measure the state of stress in a sample by measuring the state of (elastic) strain and multiplying by the appropriate elastic moduli (SINGH et al., 1998). We adapted this technique to the high T – high P multianvil apparatus many years ago and have continued to refine it under RGC phase I (LI et al., 2004a). We use both white x-ray and monochromatic techniques. For the white beam studies, we use a four-element (at azimuths 0°, 90°, 180°, and 270° around the x-ray beam) solid-state detector that was designed for EXAFS studies. A conical slit system was designed and built to fit the detector. Because of the small diameter of detector, we could not build a slit system that optimized the optics such as the acceptance angle and spatial resolution. Nevertheless, we obtain precision of 100 MPa. The number of detectors in our current system precludes defining the orientation of the principal stress axes projected on the plane of the detectors (so they must be known a priori), and the dimension of the slits limits the x-ray resolution. This is particularly critical for the RDA system where the orientation of the stress is not known a priori. The monochromatic system yields about the same precision, with a greater ability to define the axis of the stress field because a 2-D detector is used. However, the monochromatic system cannot readily collimate the diffracted x-ray beam, so the background due to diffraction from the pressure medium and parts of the sample assembly can easily hide diffraction from the sample, which limits our choices of building materials. Amorphous boron window inserts have been used to minimize these unwanted effects. Our strategy for reaching 10 MPa resolution for energy dispersive measurements is to (a) increase the number of detectors from 4 to 10,(b) locate the detectors to allow measurement of the orientations of principal strains in the plane normal to the x-ray beam and thereby define the orientation of the stress field,(c) improve collimation to narrow acceptance angle and decrease the scattering volume. To improve resolution of d we propose to procure an array of energy-dispersive detectors arranged in a circle, with a conical slit to capture diffracted data as a function of azimuth around the direct x-ray beam. It uses 4 detectors at a radius of 25 mm, located at ? = 0, 90, 180, and 270°. The new system will host 10 detectors with 9 of them separated by 22.5 degrees in a semicircle and the other detector at 90 degrees from the array to provide input for alignment. The radius of the new detector ring will be 76 mm. This larger-radius detector will allow conical slits with diffraction angles up to 10°, while the current system is limited to 6.5o. We will fabricate a new conical slit at 7.5 o as described below. These improvements will impact resolution in four ways: (1) Better counting statistics. Quantitative measures of peak positions are generally governed by counting statistics. Errors generally decrease with the square root of the number of counts. Because the count rate of any detector is limited by the electronics, increased count rates come with more detectors. By increasing the number of in redundant detectors. We therefore expect a gain of at least a factor of two in precision of the strain measurement from the increase in number of detectors. (2) Detection of lower symmetry d(x). With 10 detectors, we are in a better position to define the stress geometry. Others, such as the DDIA, set the stress orientation by virtue of the driving pistons. Many experiments, including the RDA system, do not uniquely define the stress orientation a priori, so the 10 elements can be used to determine the principal stress axes. In the RDA, the stress state is a mixture of uniaxial compression and simple shear, and the stress state varies from one place to another in a single sample. (3) Improved scattering geometry. The slit system defines the 2 ? acceptance angle and the scattering volume. The range of the acceptance angle defines the energy band that is present in a diffraction peak. It also affects the length of the sample along the x-ray beam that contributes scattering to the detector. The dimensions of the current conical slit system are 100 mm length, the tip an additional 100 mm from the scattering volume, a gap of 100 µm, and a scattering angle of 6.5° (we actually use a gap of 50 µm for most of the studies). We compare these values with those for the proposed system (Table 1), designed to match the detector array with a 2 ? of 7.5° and a gap of 10 µm, still with the front end 100 mm from the sample, but now with the slit system about 500 mm long. The current system has an acceptance angle of + 0.057°, while the new systems accept + 0.001°. The acceptance angle increases the length of the x-ray path that will be seen by the detector by + 1.3 mm for the old system and by + 0.05 mm for the new system. The energy half width caused by the acceptance angle is 400 eV for the current system and 8 eV for the proposed system. The combined reduction of the slit size, increased length of the conical slit system afforded by the large diameter of the detector array, and increased 2 ? thus increase resolution of scattering angle and scattering volume by a factor of 50. The new detector system will be the responsibility of Weidner.