Density of dislocations and other defects

To study defects by TEM, the defects must be present in a high enough concentration that there is a good chance of actually finding a defect in 

Ham (1961) and Ham and Sharpe (1961) have discussed the two main methods for determining dislocation densities from electron micrographs of thin foils. In the first method, a set of random lines with a total length L is marked on a given area A of the micrograph, and the number of intersections N that dislocations make with these lines is measured. The dislocation density is then given by 

This method has the advantage of not requiring a knowledge of the foil thickness t, but it becomes very difficult to count surface intersections for dislocation densities higher than about 10 cm . Clearly, measurements of the number-density of small dislocation loops or small inclusions (such as bubbles or voids) requires a knowledge of thickness t. 

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