On the Increase in Surface Area due to Crystal Faces Developed by Etching

The fact that the surface of an etched crystalline body is made up of crystal faces means that the actual surface is greater than the apparent surface. The ratio of increase in area to apparent area is called the face excess. Given the available crystal faces and the orientation of the crystal, both the criterion for determining those faces which give the least face excess and two methods for calculating the face excess have been worked out. Assuming random crystal orientation and minimum face excess, the face excesses in the cases where (1) cubic and dodecahedral, (2) dodecahedral only, (3) cubic only, and (4) cubic, dodecahedral and octahedral faces are available have been calculated. The face excesses are, respectively, 0.129, 0.225, 0.500, and 0.0882. Certain cases involving preferred orientation are also discussed.