Interpreting In-situ Synchrotron X-ray Diffraction Measurements from Deforming Quartz Using An Elastic Plastic Self Consistent (EPSC) Model

The use of synchrotron x-ray diffraction combined with the recently developed deformation DIA apparatus (D-DIA) has facilitated a new class of deformation experiments in which the state of stress at the grain scale can be observed during controlled deformation experiments. The grain scale nature of the data allows us to examine the distribution of stress across various subpopulations of grains in a polycrystal during deformation, which will ultimately lead to a more sophisticated understanding of polycrystalline deformation in general. A challenge that has come along with these new technological advances is that the data reveal a richer more complex picture of polycrystalline deformation than was anticipated. The grain scale data appear to mirror the heterogeneity of strain commonly observed in naturally and experimentally deformed monomineralic polycrystals, in which heavily deformed grains can be found adjacent to grains that exhibit relatively little deformation. A number of workers have now observed substantial variations in stress levels between grains in deforming monomineralic polycrystalline earth materials. Determining the method to properly interpret the stress data and cast it in terms of macroscopic stresses is important because it is the aggregate properties which are useful for geodynamic calculations. We are exploring the use of elastic plastic self consistent (EPSC) models, developed by metallurgists for describing in-situ neutron diffraction observations of deforming metals, for use in interpreting x- ray diffraction data from deforming silicates. We are conducting deformation experiments on Arkansas novaculite using the D-DIA apparatus on beamline X17b2 at the NSLS. During deformation experiments we are able to observe the behavior of the (100), (101) and (112) lattice reflections of quartz. Strain in our experiments is measured by periodically taking a radiograph of the sample (which is bounded by metal foils) and comparing the length of the sample to a radiograph taken immediately before the start of the deformation experiment. We are able to model the behavior of the (100), (101) and (112) reflections using an EPSC model in which basal and prism <a> slips are activated. An interesting outcome of the EPSC model is the prediction that the macroscopic stress experienced by the sample should be greater than the stress calculated from any of the reflections that we observed. This observation serves as a caution against using reflection stresses as a proxy for the macroscopic stress in in-situ deformation experiments.