Model and data work together to reveal microscopic structures of materials
Microscopic compositional distributions are important in determining the bulk properties of materials.1 In one application dealing with anticorrosive primers for metals, the distributions of corrosion inhibitor and filler particles in a polymer matrix are major factors governing the degree of protection under corrosive conditions.2 In another application in the field of geosciences, knowledge of the microscopic distributions of mineral phases in various rock formations is critical in the oil and gas industry.3,4
While the value of this structural information is self-evident, the experimental techniques available for obtaining it are generally costly and destructive to the sample. X-ray computed tomography (CT) has been used as a nondestructive method to probe the internal structures of materials. However, x-ray CT only gives a microscopic map of the radiation's amplitude attenuation and phase shift and is usually inadequate to determine compositional distributions within heterogeneous materials by the usual image-rendering process.5 Data-constrained modeling (DCM) has extended the reach of x-ray CT techniques to more directly determine a sample's material composition. By combining a generic model with sample-specific CT data taken under multiple x-ray beam conditions, we have shown that DCM can provide microscopic details of compositional distributions in a wide range of samples.6–9
DCM for predictive modeling of microscopic compositions is based on a number of assumptions. The total volume of a voxel (3D pixel) is the sum of the partial volumes of its constituent material compositions (including void). A voxel's total x-ray interaction (including amplitude attenuation and phase shift) is the sum of the interactions of its constituent compositions. Its composition is also determined statistically by that of its neighbors, subject to probabilistic and deterministic rules and external fields. Neighboring voxel interactions are approximated by classical statistical mechanics.
Together with multiple CT data sets acquired for different x-ray beam energies, a 3D microscopic compositional map of a material sample can be predicted. As a case study, we carried out two x-ray CT experiments with a rock sample consisting of quartz and calcite. We used monochromatic x-ray beam energies at 35 and 45keV to acquire the CT data sets at the Shanghai Synchrotron Radiation Facility. Figure 1 shows a DCM-predicted sectional image. For this sample, Figure 1 and a 3D animation (see video10) show that the majority phase is quartz with a grain size on the order of 100μm. Calcite forms clusters and thin coatings on quartz. There are void spaces comparable in size to the quartz grains. There are also significant numbers of microvoids smaller than the CT resolution in calcite, as evidenced by the unsaturated red color in the images.
These observations are consistent with the known properties of the sample, which was formed by in situ precipitation of calcite cement within a pack of quartz grains. Similar x-ray CT data sets have been acquired using a laboratory simulation of a paint primer sample at beam energies of 9 and 11keV. The primer used zinc phosphate corrosion inhibitor and rutile (a form of titanium dioxide) filler particles mixed in an epoxy polymer matrix. Figure 2 shows the microstructure predicted by DCM (see also video11). It is obvious that the particles have a tendency to cluster together instead of being distributed evenly.
DCM is a tool for both predictive modeling and visualization of compositional microstructures. It could provide a more accurate prediction at both macro and micro length scales. Accurate void-distribution information in mineral strata is critical for underground oil and gas production. Accurate corrosion-inhibitor- and filler-distribution information in a paint primer is important in studying its protective properties for metal components. DCM models the compositional distribution of microscopic particles of different phases by combining a generic model and multispectral x-ray CT data. It gives more detailed information regarding microscopic structures compared to conventional x-ray CT and is nondestructive. Microscopic characterization of materials would enable increased accuracy in modeling of the properties of bulk materials. It could have impact in a wide range of applications, including exploration geosciences, corrosion, and materials science. For x-ray CT, data volume grows according to an inverse cubic law, and x-ray exposure grows as an inverse quadruple law with pixel size. Hence, the capability of DCM to predict materials distributions below x-ray CT resolution could have an impact in situations where data volume and x-ray exposure need to be minimized, such as in biomedical-screening applications. Work in progress includes DCM study of microstructures in polymer-composite materials, light-metal alloys, and materials with nanostructures smaller than normal x-ray CT resolution.
This work was done in collaboration with Ben Clennell, Simon Hardin, Keyu Liu, and Sherry Mayo (all in the Commonwealth Scientific and Industrial Research Organisation), and Tiqiao Xiao at the Shanghai Synchrotron Radiation Facility.
Sam Yang completed his PhD in condensed matter physics at the Chinese Academy of Sciences (1987), and a second PhD in statistical mechanics at the University of Melbourne, Australia (1997). He is a senior research scientist at CSIRO specializing in data-rich and statistical mechanics modeling.
John Taylor currently leads CSIRO Computational and Simulation Sciences. He has directed major research projects in Australia and the US. He has written more than 140 articles and books on computational and simulation science, climate change, global biogeochemical cycles, air quality, and environmental policy.
