An Introduction to Microstructure Mining

Over the last decade the field of materials informatics has emerged in recognition of the potential for systematic approaches to complex problem solving in materials science and engineering¹. If the necessary data rich environments are to be accessible to the widest audience in materials science and engineering materials informatics will require data acquisition and management strategies similar to those previously developed in fields such as bioinformatics.While databases exist for some basic materials information in thermodynamics and crystallography there are no widely used collections for more complex data sets like microstructure. Microstructure Mining, as its name suggests, is the application of data mining concepts², used in many branches of science and engineering, to the analysis of materials microstructure.

At the very core of this approach is the expectation that many problems in microstructure-property analysis are not easily addressed using experimentation involving the characterization of only one simple microstructural lengthscale, such as average grain size. This is especially true for materials that have multiphase microstructures or for material properties that are dominated by relatively rare microstructural events such the nucleation of cracks.In such circumstances the associations between microstructural features (e.g. crystallographic misorientation across grain boundaries) may be just as important as the average lengthscale of the features themselves. Fortunately the continued advances in imaging techniques, digital imaging and data storage are providing the environment were searchable "microstructure banks" become a viable prospect, resulting in the necessary data rich environment in which data mining techniques could be widely applied.

To realize material informatics at the microstructure level it will be necessary to establish standard procedures and formats for acquiring microstructure images to be stored in databanks. The Microstructure Mining methodology is one possible approach that can be broken down into the steps that are illustrated in figure 1.

Figure 1. The steps in the Microstructure Mining process.

The steps are not meant as a strict regiment but a flexible guide to problem solving with each step valued only by its practical utility to the problem in question. It is therefore useful in its own right, independent of any formal system of shared data storage. While the following discussion will be focus on analysis of two dimensional sections there is no reason why it cannot be applied to 3 D images. After preparation of the section the second step in Microstructure Mining method involves a qualitative survey in which the microstructure is observed at increasing magnification from the lowest available for the imaging technique employed. This will result in the identification of all the important microstructural lengthscales bearing in mind that lengthscales can be defined by the association between microstructural features (e.g., aggregate size) as well as the feature size itself.

The decision regarding the choice of the imaging conditions, such as magnification, for the consequent microstructure measurements is thus based on experience and significant understanding of the microstructure variables that affect the property in question. Once the magnification is chosen the quantitative microstructural measurement must be defined and the sampling procedures must be decided upon, the latter is particularly important when considering microstructural features or associations which occur with low frequency. Standard approaches to unbiased sampling have been developed for stereological measurements³.

Once the images are acquired and banked the image processing steps must be assembled to prepare the images for analysis. This is best done with some familiarity concerning the common image processing steps that are widely available in image processing software. The specific procedures in this step depend on the nature of the measurement. For example, simple stereological parameters can be used to determine microstructural averages. If only a single measurement is required for such an average it may be more appropriate to use standard manual counting methods with a minimum of image processing. In other circumstances such as the use of microstructural information for material processing control, more elaborate routines will be necessary to allow information about changes in microstructure populations to be rapidly analyzed. For example, a study, by our group, of the relationship between the powder processing methods and the size of surface flaws in the final ceramic required the use of a new artificial intelligence technique termed "adaptive thresholding" to automate the processing of many images⁴. This allowed the distribution of flaw sizes to be constructed and the consequent use of extreme value analysis to predict the largest flaw size in following image analysis and data mining steps⁵. Future studies will need to combine such techniques with automated specimen preparation techniques to fully implement rapid image acquisition methods that would allow for "machine vision" to be extended down to the microstructural scale.

One example will be used to illustrate the design of a Microstructure Mining parameter to solve a problem in ceramics processing. This parameter addressed the common observation that nanocrystalline ceramic powders often lead to sintering microstructures that consist of dense multigrain aggregates surrounded by pores. An example of such a microstructure is shown in figure 2(a). In this circumstance, the interpore diffusion distance will not correlate with the grains size in the way that is assumed in the kinetic models of sintering.

In fact, the common power-law dependence between measured densification rate and grain size for the zirconia ceramic shown in figure 2(a) gave an exponent of 12, well above the expected value of 3 for volume diffusion in the combined stage sintering model⁶ implemented in the master sintering curve method⁷. Therefore the sintering models will underestimate the average diffusion distance that limit the kinetics of sintering in these aggregated microstructures. Additional consideration leads to the conclusion that diffusion in these aggregated structures will be spatially constrained to "diffusion short-cut" between pores on the aggregate boundaries and will not occur across the dense aggregates illustrated in figure 2(b)

Furthermore, it can also be concluded that the interpore spacing measured using stereological techniques, which assumes random measurements, will overestimate the true diffusion distance because many such intercept lengths will bisect dense aggregates. Therefore measurements of the mean pore spacing will not be appropriate for this problem. Our group used Microstructure Mining involving a simple image processing technique, pore boundary tessellation⁸, to design an effective diffusion distance parameter that would be independent of the state of microstructural aggregation⁹.

The feature boundary tessellation option available on most image processing software effectively dilates the boundary of isolated features on a two dimensional section until the boundaries impinge. Thus boundary tessellation leads to a segmentation of the microstructure into space filling cells, each cell containing all the pixels in the image that are closer to the boundary of feature they contain than the boundary of any other feature. In this case the pore boundaries in the micrographs of the partially sintered ceramic were dilated, resulting in cells, illustrated in figure 3, that each contain a central pore section and the surrounding solid phase that is closest to that pore than any other pore boundary. Therefore all the pixels on the tessellation cell boundaries represent the limiting diffusion distances into the central pore section from the surrounding solid.

Figure 3. The result of pore boundary tessellation for a partially sintered ceramic. Each cell features a central pore section, colored black and an orange cell boundary.

To bias the average diffusion distance for each cell towards the previously illustrated "diffusion shortcuts" on the aggregate boundary, the diffusion distances for each cell were flux weighted and then averaged over thousands of cells taken from several randomly located images. The resulting effective diffusion distance was then tested by using the expected power-law dependence of densification rate on the diffusion distance. This time the exponent was 3, agreeing with that expected for volume diffusion in the sintering models. Therefore the effective diffusion distance correctly approximated the diffusion length for the aggregated microstructures and can be used to replace grain size in the sintering models. This new parameter will allow, independent of the state of aggregation in the microstructure, predictions of sintering time to full density based on microstructural information rather than sintering shrinkage alone. Applications of the parameter could include the prediction of sintering times to full density in a range of circumstances, including the sintering of transparent nanocrystalline ceramics for optical applications where very high densities are crucial.

References

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