Relative Amounts of Phases Present

For a random sample, the volume fraction (Vy) of a phase is equal to the cross-sectional area fraction (A, ) of the phase in a random plane through the sample. It is also equal to the linear fraction (Lj) of the phase intersecting 

Experimental measurements on a ceramic sample can be done using a thin section (relative to particle size) of it or a polished plane prepared on it. Following Equation 11.3, the measurements are done by area, lineal, or point analysis. 

For point analysis, point counting is done by randomly distributing a grid of points over the sample in the microscope or on a photomicrograph, or by randomly moving a microscope crosshair and counting the fraction of the total point count that falls in a given phase (Pp). 

Areal analysis is done to determine the relative area of each phase A in the planar section. This is less commonly done, because it is slower than point counting or lineal analysis. Relative areas can be determined by three ways  

By cutting out separate phases from a micrograph and weighing them 

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