Supercrystallography-Based Decoding of Structure and Driving Force of Nanocrystal Assembly

Nanocrystal (NC) assembly appears as one promising method towards the controllable design and fabrication of advanced materials with desired property and functionality. The achievement of a “materials-by-design” requires not only a primary structural decoding of NC assembled supercrystal at a wide range of length scales, but also an improved understanding of the interactions and changeable roles of various driving forces over the course of nucleation and growth of NC superlattice. The recent invention of a synchrotron-based X-ray supercrystallographic approach makes it feasible to uncover the structural details of NC-assembled supercrystal at unprecedented levels from atomic through nano to mesoscale. Such structural documentations can be used to trace how various driving forces interact in a competitive way and thus change relatively in strength to govern the formation of individual superlattices under certain circumstances. This short review makes use of four single supercrystals typically made up of spherical, truncate, cubic and octahedral NCs, respectively, and provides a comparable description and a reasonable analysis of the use of a synchrotron-based supercrystallographic approach to reveal various degrees of translational and orientational ordering of NCs within various superlattices. In the connection of observed structural aspects with controlled environments of NC assembly, we further address how various driving forces interact each other to develop relatively changeable roles upon variation of the NC shape to respond to the nucleation and growth of various superlattices. With the guidance of such gained insights, we provide additional examples to illustrate how realistic environments are designed into delicate control of NC assembly to achieve particular interactions between NCs towards harvesting superlattice with NC translational symmetry and atomically crystallographic orientation as desired.

Form factor of rounded objects: the sections method

An analytical method, the sections method, is developed to build a close link between the singularities of the surface of a body and the asymptotic behaviour of its amplitude form factor at large scattering vector, q. In contrast with a sphere, for which the asymptotic behaviour is in q −2, surface singularities lead to both narrow regions, for which the amplitude form factor exhibits trailing behaviour, and extended regions, for which it exhibits a rapid decrease. A numerical study of a simple example, the fourfold truncated sphere, illustrates the usefulness of these analytical predictions.

Form factor of any polyhedron: a general compact formula and its singularities

A general and compact formula is established for the form factor of any polyhedron, which involves only the apex coordinates and the apex connections. For large diffusion vectorq, the form factor behaves likeq−3for generic directions, but it exhibitsq−2singularities in the directions perpendicular to the edges andq−1singularities in the directions normal to the faces. General results are established for these singularities. Using a Python implementation, illustrative examples are discussed. The generality of the formula and of its singularities are likely to be important for any discussion of scattering from polyhedral particles.