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Surface Area Measurements
The surface area of contact between different structures is also an important measure in many instances. In section images, the surfaces present in three dimensions appear a boundary lines. In the example, the boundaries of the white phase in the metal are delineated as contour lines. Measuring the length of the contour lines allows the calculation of the surface area per unit volume of the sample, according to the relationship shown in Equation 1. Note that unlike the volume fraction measurement above, which produces a dimensionless number, the surface area per unit volume measurement requires knowing the image magnification. In this case the area of the region in each image is 567 square µm.
As for the volume fraction, using a counting procedure is preferred to a measurement. In this case a grid of lines is drawn on the images. For the case of random section placement and orientation in the structure, any grid of lines can be used and the square grid is convenient. (In the following interactive tutorial, the total length of the grid lines is 114 µm). Counting the number of “hits” that the contour lines make with the grid lines also allows calculation of the surface area per unit volume.
As for the volume fraction measurement, note that variation from one field of view to another is much greater than the differences between the results from the grid count and contour length measurements for each region. This interactive tutorial illustrates the measurement of surface area per unit volume.
The tutorial initializes with one of four randomly selected region images appearing in the Specimen Image window. The Choose A Specimen pull-down menu provides a selection of images of four different regions of the same specimen. For each, the Original button shows the original grayscale image. The Outline button shows the contour lines that define the boundary of the white phase, along with the measured length of the boundary lines. The Grid Overlay button superimposes a line grid on the image and also displays the number of the times that the grid lines “hit” the boundary. The table below summarizes the results for calculated surface area per unit volume (square µm per cubic µm) determined from these measurements.
Contributing Authors
John C. Russ - Materials Science and Engineering Dept., North Carolina State University, Raleigh, North Carolina, 27695.
Matthew Parry-Hill, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.
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