Modified Wulff constructions for twinned particles

L. D. Marks*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

150 Scopus citations


This paper reports the application of a modified form of the Wulff construction to derive theoretical shapes and total surface energies for twinned particles. It is proposed that the incorporation of twin boundaries in faceted particles leads to a number of constrained local minimum in the total surface energy (at constant volume), in addition to the minimum of a single crystal Wulff polyhedron. A procedure for generating these constrained local minima is described. The model is then applied to determine the structures of twinned particles in face-centred materials. Two possible configurations are examined, an arrangement where the crystals are symmetric about the twin boundaries, and an asymmetric configuration. Shapes and total surface energies for a large number of twinned structures are given using a simple model which includes only (111) and (100) surface facets. Excellent agreement is obtained between the theoretical model and experimental results.

Original languageEnglish (US)
Pages (from-to)556-566
Number of pages11
JournalJournal of Crystal Growth
Issue number3
StatePublished - 1983

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Inorganic Chemistry
  • Materials Chemistry


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