Uncertainty Quantification and Experimental Design Using a Quantitative Forward Model for Kinematic X-Ray Diffraction
Joel Bernier | 20-ERD-044
X-ray diffraction (XRD) is a cornerstone characterization technique for probing the structure of crystalline materials. It is generally non-destructive and applicable to the study of phenomena spanning an enormous range of length and time scales. Most analysis is undertaken on significantly reduced data, exploiting easily detectable signals (i.e., Bragg peaks) and well-characterized experimental configurations. In these cases, the material parameters of interest are readily extracted. There are many cases, however, where this approach breaks down; these include measurements where the data are noisy, overlapped, incomplete, polluted with concomitant signal, or where independent instrument calibration is not possible. Measurements undertaken at extremes of pressure, strain rate, and temperature (regimes of critical importance to stockpile stewardship science) generally fall into this category. The process of fully recovering the parameters that give rise to an observed diffraction signal is unfortunately an ill-posed inverse problem. It is, however, possible to determine critical material parameters such as density using a sufficiently accurate forward model with appropriate conditioning and constraints. In addition, the ability to reliable quantify uncertainties in parameters measured via XRD is critical to the verification and validation of materials models used in large-scale simulation frameworks.
We developed a general and physically accurate forward model for powder XRD in conjunction with a robust statistical framework for determining the configuration-dependent subsets of identifiable parameters and their associated uncertainties in the form of Bayesian posterior distributions. We demonstrated the accuracy in determining material density from powder XRD data for two fundamental instrument configurations, as well as the TARDIS diagnostic on NIF. Several non-intuitive correlations among instrument parameter that have implications for calibration procedures and required metrology were discovered in each case. The Bayesian framework was also used to study an existing single-crystal XRD model (developed under a previous project, LDRD 10-ERD-053) that is critical to high-precision instrument calibration and the burgeoning field of X-ray microscopy. Beyond providing a robust means for analyzing both legacy data and measurements on established platforms, the software and methods developed under this project provide a generic tool for the design of new XRD platforms, with the possibility of optimization for accuracy of specific parameters of interest.
X-ray diffraction is a cornerstone diagnostic in experimental campaigns that support the mission to maintain and enhance the safety, security, and effectiveness of the U.S. nuclear weapons stockpile. The ability to determine critical material parameters such as structure, density, distortion, and temperature reliably and accurately in specimens subject to extremes of temperature, pressure, and deformation rate is essential to both the validation of materials models and the advancement of world-class discoveries in high energy density (HED) science. The framework we have developed forms a basis for assigning uncertainties to data measured on existing and legacy platforms. This, in conjunction with the ability to optimize the design of next-generation XRD diagnostics, bolsters the status of LLNL as a leader in experimental HED science, and provides an important resource to the broader DOE user facility communities.
Publications, Presentations, and Patents
Bernier, J. V., et al., 2020. "High-Energy X-ray Diffraction Microscopy in Materials Science." Annual Review of Materials Research 50(1): 395-436 (2020). https://doi.org/10.1146/annurev-matsci-070616-124125.
Boyce, D., et al., 2020. "Estimation of Anisotropic Elastic Moduli from High Energy X-ray Data and Finite Element Simulations." Materialia 12: 100795 (2020). https://doi.org/10.1016/j.mtla.2020.100795.
Chandler, B., et al., 2021. "Exploring Microstructures in Lower Mantle Mineral Assemblages with Synchrotron X-rays." Science Advances 7(1): eabd3614 (2021). https://doi.org/10.1126/sciadv.abd3614.
Lim, R. E., et al., 2022. "Grain Reorientation and Stress-State Evolution During Cyclic loading of an α-ti alloy below the elastic limit." International Journal of Fatigue 156: 106614 (2022). https://doi.org/10.1016/j.ijfatigue.2021.106614.
Lim, R. E., et al., 2021. "Grain-Resolved Temperature-Dependent Anisotropy in Hexagonal ti-7al Revealed by Synchrotron X-ray Diffraction." Materials Characterization 174:110943 (2021). https://doi.org/10.1016/j.matchar.2021.110943.
Nygren, K. E., et al., 2020. "An Algorithm for Resolving Intragranular Orientation Fields Using Coupled Far-Field and Near-Field High Energy X-ray Diffraction Microscopy." Materials Characterization 165: 110366 (2020). https://doi.org/10.1016/j.matchar.2020.110366.
Singh, S., et al., 2020. "Discrete Spherical Harmonic Functions for Texture Representation and Analysis." Journal of Applied Crystallography, 53(5):1299-1309, (2020). LLNL-JRNL-796099. https://doi.org/10.1107/s1600576720011097.