Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2017 / Paper 2 / Section A(i) / 13

A decahedral nanoparticle is a multiply twinned nanoparticle: five fcc-like tetrahedral domains share a common fivefold axis and meet on coherent twin planes. The angle of an ideal fcc tetrahedral wedge is $\arccos (1/3)=70.53^{\circ }$, so five wedges leave about $7.36^{\circ }$ of angular deficit. Elastic distortion and defects accommodate closure. The external shape can be a pentagonal bipyramid or a truncated variant; it is not one unstrained, periodically repeated fcc crystal.

An icosahedral nanoparticle comprises twenty tetrahedral domains arranged around a common centre, with twenty approximately triangular outer facets, twelve vertices and thirty edges. Five domains meet around each radial fivefold direction. Coherent twinning exposes many low-energy close-packed facets, but fivefold symmetry cannot tile ordinary three-dimensional space periodically without strain. The competition between favourable surface/twin energies and volume-dependent elastic strain explains why such morphologies are especially plausible for small particles.

These labels describe the observed domain geometry; cobalt can adopt different crystal phases, so identifying fcc-like twinning also requires diffraction rather than assuming every cobalt particle is bulk fcc.

The Winterbottom construction extends the Wulff construction to a crystal supported on a substrate. It includes the particle-substrate interfacial energy and the substrate surface energy displaced by contact, so the equilibrium Wulff body is truncated by the support plane. The relevant contact contribution is $({\gamma }_{ps}-{\gamma }_s)A_{\mathrm{contact}}$; it determines wetting and contact geometry. The basic unsupported construction accounts only for orientation-dependent free surface energies.^[ref]

In cluster-beam deposition, evaporated or sputtered cobalt atoms cool in an aggregation gas, nucleate clusters and are carried to a substrate. Source temperature, gas pressure, aggregation length and residence time tune the mean size and distribution. A mass selector can narrow the delivered size range, at the cost of transmitted flux; an unfiltered beam does not automatically produce monodisperse particles.

Shape control is less direct. Growth kinetics and cluster temperature can favour particular structures, while multiple morphologies can coexist at one size. Landing energy, substrate interactions and post-deposition annealing can change the delivered shape or cause coalescence. Soft landing helps preserve gas-phase clusters. In solution, ligands, selective facet binding, seed-mediated growth and precursor feeding can give stronger chemical control over shape and size, but introduce ligand/solvent residues and require purification. Neither method guarantees a unique shape merely by selecting particle size.