Size‐Dependent Structural Distortions in One‐Dimensional Nanostructures

Abstract

Nanoscale materials have been intensely studied since the discovery that the optical properties of semiconductor nanoparticles are size dependent. This and subsequent research has demonstrated that a given physical property of a particle exhibits a size dependence when the size becomes comparable to its characteristic length scale. Examples of relevant length scales include the de Broglie wavelength and/or the mean free path of electrons, phonons, and elementary excitations, all of which typically range from one to a few hundred nanometers. The ability to tune a wide variety of properties by controlling the particle size has spurred the development of novel chemistries for preparing nanostructured elements and compounds with goals of precisely controlling size, shape, and ligand shell. As the size of a nanocrystal decreases, the ratio of bulk to surface atoms decreases. This progression increases the relative contribution of the surface free-energy relative to the volume free-energy of the bulk structure, such that distortions from bulk equilibrium structures might be expected as the nanoparticle size decreases. Unfortunately, while researchers have demonstrated the ability to prepare ordered lattices of nanoparticles, the isolation of lattices of nanoparticles with long-range atomic periodicity is rare. Hence detailed atomic structures and, in turn, the size-structure-property relationships of most nanoparticle systems cannot readily be determined. Recently we reported that the intergrown compounds [(MSe)1+y]m(TSe2)n, with M= {Pb, Bi, Ce} and T= {W, Nb, Ta} self-assemble from designed precursors. The values of m and n represent, respectively, the number of MSe and TSe2 structural units of the unit cell of the superstructure and y describes the misfit between these structural units. As reported herein, the long-range structural order along the modulation direction permits us to determine the atomic structure of these precisely defined one-dimensional (1D) nanolaminate structures as a function of m and n using a combination of scanning transmission electron microscopy (STEM) high-angle annular dark-field (HAADF) imaging and X-ray diffraction (XRD) with Rietveld refinement. STEM-HAADF images of the first five [(PbSe)1.00]m(MoSe2)n compounds in the family where m= n are shown in Figure 1 along with aggregate intensity plots used to quantify the PbSe intraand inter-pair distances. All have a regular periodic structure along the modulated axis with well-defined layers of PbSe and MoSe2. The STEM images show ordered domains of PbSe with characteristic dimensions of a single structural unit along the layering direction and tens of nanometers perpendicular to the layering direction, with random in-plane rotational variants both within a layer and between layers. The orientations of the MoSe2 domains are more difficult to discern from the STEM images, but rotational variants have been observed between individual MoSe2 structural units. The STEM-HAADF images reveal a distortion of the PbSe layers, with the atomic planes grouped into pairs rather than being evenly spaced as expected for the equilibrium (bulk) rock salt structure. The distortion is most evident in the structural variant (m, n)= (2, 2) and decreases in magnitude until it can no longer be observed for (5, 5).