Past exam of the materials science course of the University of Cambridge / 2018 / Paper 1 / 4 / d / Solution

The danger is identifying an etched height interval with the original planar phase intersection. Preferential ferrite dissolution exposes inclined cementite faces and can produce overhangs. A conventional AFM tip cannot follow a reentrant underside; its finite size also broadens ridge tops and may not enter the intervening troughs. A thresholded height width can consequently differ from both the true plate thickness and its original surface intersection.

A uniform inclination at an ideal flat cut does not itself invalidate a line-fraction estimate: both phases acquire the same geometrical width factor, which cancels in their ratio. The problem is differential relief and probe accessibility after etching, together with uncertain local angles and limited sampling. Using only the apparent ridge occupancy can overestimate cementite. An independently polished section, calibrated probe geometry, several directions and colonies, or another phase-sensitive method is needed to test the inference.