jadball
commented
2 weeks ago While this is fresh in my mind after a chat with @AxelHenningsson and @jonwright today:
- Stiffness tensors have a coordinate system, which relates to how the grain Cartesian reference frame is aligned with the lattice vectors (x along a*, etc etc). As far as I can tell, Materials Project (via pymatgen) always provides the Stiffness Tensor in the IEEE 1978 reference:
- The IEEE 1978 system is different from the one used in ImageD11 Axel has worked this out and determined an additional tensor rotation to apply to ensure agreement:
# Take the B0 of the cell
C_c = np.linalg.inv(B0).T
E = np.column_stack((C_c[:, 0], np.cross(C_c[:, 2], C_c[:, 0]), C_c[:, 2]))
E /= np.linalg.norm(E, axis=0)
strain_crystal_tensor_IEEE = E.T @ ( strain_crystal_tensor_imaged11 ) @ E-
The stiffness tensor will change depending on what vector notation system you use for the strain tensor. Therefore, there are "Voigt" stiffness tensors (overwhelmingly common, used on Materials Project) and "Mandel" stiffness tensors (much less common). This means I have some changes to make in
ImageD11/sinograms/tensor_map.py, and that we should clearly document which format we expect the stiffness tensor to be in -
Eventually I would like to merge/combine my Numba-accelerated kernels with
stress.py, rather than specifying that we are working on flat Python lists of UBI objects which is currently the case
jonwright
Moving the discussion in merged pull #192 into a new issue. The problem is which numerical values to input for the numbers in the calculations of stress from strain, and whether the numbers can be checked.
Some unit tests could be added.
we do not have the old FitAllB strain convention in ImageD11 yet. This could be added for checking against fitallb.
Then for trigonal quartz as a low symmetry example. We had an indexing ambiguity, the (100) direction is not distinguished from the (110) direction until you look at the peak intensities. For high-temperature beta quartz, the structure is hexagonal. For stresses in alpha quartz, it seems to come down to the sign of C14, which goes to zero when the structure goes from trigonal to hexagonal (Ohno, I., Harada, K. & Yoshitomi, C. Temperature variation of elastic constants of quartz across the α - β transition. Phys Chem Minerals 33, 1–9 (2006). https://doi.org/10.1007/s00269-005-0008-3). For crystals that are twinned, this might not matter.
There is a description of the problem of conventions here: https://www.comsol.com/blogs/piezoelectric-materials-understanding-standards/
In the case of quartz, the C14 parameter appears to change sign when going from the IRE 1949 convention to the one from IEEE 1978. Some intensity ratios are discussed here: https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1926.0025 ... and their relation to macroscopic crystal axes is here: http://www.minsocam.org/ammin/AM30/AM30_326.pdf ... and here, BSTJ 22: 3. October 1943: Use of X-Rays for Determining the Orientation of Quartz Crystals. Bond, W.L.; Armstrong, E.J.: https://archive.org/details/bstj22-3-293
Somehow we need to summarise all that literature into something that matches a set of elastic constants to a crystal structure that gives the diffracted intensities. Maybe taking the numbers from the materials project is unambiguous, as they are providing both together:
https://next-gen.materialsproject.org/materials/mp-7000?crystal_system=Trigonal&formula=SiO2