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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2022/paper-2/section-a-iii/18/ii/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 2 / Section A(iii) / 18 / ii / Solution by

Codex  0 2026-10-20

Symmetric wetting and an A-preferring substrate imply an A-preferring free surface as well. Parallel lamellae satisfy both preferences. For equal-width A and B domains, a thickness

2 L_{0}

contains two repeats, with terminal A half-domains:

A_{L_{0} /4} ∣ B_{L_{0} /2} ∣ A_{L_{0} /2} ∣ B_{L_{0} /2} ∣ A_{L_{0} /4} .

(1)

The sequence is written from substrate to atmosphere. Its total thickness is

2 L_{0}

, the total A and B thicknesses are each

L_{0}

, and both interfaces contact A. A diagram using five full half-period domains would instead give

2.5 L_{0}

and would not match the stated thickness.

The quarter-period end domains place an A-domain centre at each boundary in this ideal symmetric-lamella model. Real surface reconstruction and non-equal block fractions can change their detailed widths without changing the key requirement of identical terminations.

Figure 1.
Lamellar terminations, thickness terraces and a single neutral boundary
. Original idealized equal-block diagrams. The neutral-top panel is one admissible mixed arrangement, not a unique prediction; the bottom surface still prefers A. **Details**.

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