Conspectus
For almost a decade now, lead
halide perovskite
nanocrystals have
been the subject of a steadily growing number of publications, most
of them regarding CsPbBr3 nanocubes. Many of these works
report X-ray diffraction patterns where the first Bragg peak has an
unusual shape, as if it was composed of two or more overlapping peaks.
However, these peaks are too narrow to stem from a nanoparticle, and
the perovskite crystal structure does not account for their formation.
What is the origin of such an unusual profile, and why has it been
overlooked so far? Our attempts to answer these questions led us to
revisit an intriguing collective diffraction phenomenon, known for
multilayer epitaxial thin films but not reported for colloidal nanocrystals
before. By analogy, we call it the multilayer diffraction effect.
Multilayer diffraction can be observed when a diffraction experiment
is performed on nanocrystals packed with a periodic arrangement. Owing
to the periodicity of the packing, the X-rays scattered by each particle
interfere with those diffracted by its neighbors, creating fringes
of constructive interference. Since the interfering radiation comes
from nanoparticles, fringes are visible only where the particles themselves
produce a signal in their diffraction pattern: for nanocrystals, this
means at their Bragg peaks. Being a collective interference phenomenon,
multilayer diffraction is strongly affected by the degree of order
in the nanocrystal aggregate. For it to be observed, the majority
of nanocrystals within the sample must abide to the stacking periodicity
with minimal misplacements, a condition that is typically satisfied
in self-assembled nanocrystal superlattices or stacks of colloidal
nanoplatelets.
A qualitative understanding of multilayer diffraction
might explain
why the first Bragg peak of CsPbBr3 nanocubes sometimes
appears split, but leaves many other questions unanswered. For example,
why is the split observed only at the first Bragg peak but not at
the second? Why is it observed routinely in a variety of CsPbBr3 nanocrystals samples and not just in highly ordered superlattices?
How does the morphology of particles (i.e., nanocrystals vs nanoplatelets)
affect the appearance of multilayer diffraction effects? Finally,
why is multilayer diffraction not observed in other popular nanocrystals
such as Au and CdSe, despite the extensive investigations of their
superlattices?
Answering these questions requires a deeper understanding
of multilayer
diffraction. In what follows, we summarize our progress in rationalizing
the origin of this phenomenon, at first through empirical observation
and then by adapting the diffraction theory developed in the past
for multilayer thin films, until we achieved a quantitative fitting
of experimental diffraction patterns over extended angular ranges.
By introducing the reader to the key advancements in our research,
we provide answers to the questions above, we discuss what information
can be extracted from patterns exhibiting collective interference
effects, an...
