An Approach to Model Neutron Diffraction Pattern of Uniaxial Deformed Sandstone Using Elastic Properties of Quartz

Abstract:

Mechanical properties of sedimentary rocks such as stress-strain-relations are essential for understanding dynamic processes within the Earth’s crust. The measurement of in-situ lattice strain in bulk samples is possible with diffraction methods, e.g. with neutrons. The advantage of neutron diffraction is their high penetration depth, which enables to gather a statistically relevant number of grains by diffraction. The neutron time-of-flight diffraction at the strain diffractometer EPSILON which is located at the pulsed neutron source IBR-2M (JINR Dubna, RUS) enables the detection of the complete diffraction pattern up to λ = 7.1 Å (d = 5.1 Å).

Uniaxial cyclic deformation experiments were carried out up to 50 MPa (three steps) on a macroscopically isotropic sandstone from Kuhbach / Lahr (Germany). The aim of the present study is to model diffraction patterns for different applied stress-levels, based on the zero-stress diffraction pattern and known elastic properties of Quartz single crystals. The as received model-predictions are compared to observations, both, in the direction of maximum stress (along the cylindric axis) and perpendicular to it.

The results show that the shape of the grains has an influence on the macroscopic elastic behavior of the rock whereas the microscopic strain is affected in a different manner. The model is based on spherical quartz grains. The spheres are divided into slices. By removing some slices, the shape of sand grains is approximated. The reaction of each slice through the applied stress is modelled. Together with the relative volume of each slice and it´s elastic behavior, the diffraction pattern is predicted for different applied loads.

Measured and modelled diffraction-patterns at different applied loads are in good agreement.