Solution
ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2022/paper-2/section-a-iii/18/iv/a/solution
Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge 2022 Paper 2 Section A(iii) 18 iv a Solution by
Codex 0 2026-10-20
With identical A-selective boundaries, stress-free parallel stacks favour approximately integer multiples of . An arbitrary imposed thickness generally cannot preserve both the bulk period and those terminations everywhere.
A small mismatch can be accommodated by compressing or stretching the lamellae. A larger mismatch can favour terraces, islands or holes with locally commensurate heights, separated by steps of roughly . For example, a mean height can be assembled from regions of heights and , with area fraction at the larger height:The cartoon shows this volume-conserving alternative. Which response wins depends on elastic stretching energy, surface energies, lateral constraints, thickness mismatch and equilibration time. If the substrate and processing permit it, dewetting or a different domain orientation can also occur; an arbitrary thickness does not prove that a single specific terrace pattern must form.
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