Source: Faisal Alamgir, School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA

The imaging of microscopic structures of solid materials, and the analysis of the structural components imaged, is known as materialography. Often, we would like to quantify the internal three-dimensional microstructure of a material using only the structural features evidenced by an exposed two-dimensional surface. While X-ray based tomographical methods can reveal buried microstructure (for example the CT scans we are familiar with in a medical context), access to these techniques is quite limited due to the cost of the associated instrumentation. Optical microscope based materialography provides a much more accessible and routine alternative to X-ray tomography.

In Part 1 of the Materialography series, we covered the basic principles behind sample preparation. In Part 2, we will go over the principles behind image analysis, including the statistical methods that allow us to quantitatively measure microstructural features and translate information from a two-dimensional cross section to the three-dimensional structure of a material sample.

1. Complete all the procedures from Materialography Part 1. It should be reminded that the reproducibility of the following can only be assessed by analyzing multiple images from the same sample.
2. If digital analytical software is available, where the pixels can be categorized based on their brightness and counted accordingly, then it is possible to use Equation [1] to estimate pore volume the based on <A_A>. Otherwise, this analysis can, of course, be done by hand.
3. Now estimate pore volume u

In Figure 1 we see a cross section of a porous material with a grid superimposed on it. The points of intersection can be used to determine <P_p>. The number of intersection points that lie over dark regions (pores) is divided by the total number of intersection points to get P_p an

These are standard methods for analyzing two-dimensional cross sections in materials in order to extract three-dimensional information. We looked specifically at estimating the volume fraction of pores in one material and the average grain size in a second material.

Materialographic sample preparation described here are the necessary first step towards the analysis of internal microstructure of three-dimensional materials using two dimensional information. For example, one might be interested