RESUMEN
The phenomenon of symmetry breaking-in which the order of symmetry of a system is reduced despite manifest higher-order symmetry in the underlying fundamental laws-is pervasive throughout science and nature, playing a critical role in fields ranging from particle physics and quantum theory to cosmology and general relativity. For the growth of crystals, symmetry breaking is the crucial step required to generate a macroscopic shape that has fewer symmetry elements than the unit cell and/or seed crystal from which it grew. Advances in colloid synthesis have enabled a wide variety of nanocrystal morphologies to be achieved, albeit empirically. Of the various nanoparticle morphologies synthesized, gold nanorods have perhaps been the most intensely studied, thanks largely to their unique morphology-dependent optical properties and exciting application potential. However, despite intense research efforts, an understanding of the mechanism by which a single crystal breaks symmetry and grows anisotropically has remained elusive, with many reports presenting seemingly conflicting data and theories. A fundamental understanding of the symmetry breaking process is needed to provide a rational framework upon which future synthetic approaches can be built. Inspired by recent experimental results and drawing upon the wider literature, we present a mechanism for gold nanorod growth from the moments prior to symmetry breaking to the final product. In particular, we describe the steps by which a cuboctahedral seed particle breaks symmetry and undergoes anisotropic growth to form a nanorod. With an emphasis on the evolving crystal structure, we highlight the key geometrical and chemical drivers behind the symmetry breaking process and factors that govern the formation and growth of nanorods, including control over the crystal width, length, and surface faceting. We propose that symmetry breaking is induced by an initial formation of a new surface structure that is stabilized by the deposition of silver, thus preserving this facet in the embryonic nanorod. These new surfaces initially form stochastically as truncations that remove high-energy edge atoms at the intersection of existing {111} facets and represent the beginnings of a {011}-type surface. Crucially, the finely tuned [HAuCl4]:[AgNO3] ratio and reduction potential of the system mean that silver deposition can occur on the more atomically open surface but not on the pre-existing lower-index facets. The stabilized surfaces develop into side facets of the nascent nanorod, while the largely unpassivated {111} facets are the predominant site of Au atom deposition. Growth in the width direction is tightly controlled by a self-sustaining cycle of galvanic replacement and silver deposition. It is the [HAuCl4]:[AgNO3] ratio that directly determines the particle size at which the more open atomic surfaces can be stabilized by silver and the rate of growth in the width direction following symmetry breaking, thus explaining the known aspect ratio control with Ag ion concentration. We describe the evolving surface faceting of the nanorod and the emergence of higher-index facets. Collectively, these observations allow us to identify facet-size and edge-atom effects as a simple fundamental driver of symmetry breaking and the subsequent development of new surfaces in the presence of adsorbates.
RESUMEN
Metal nanocrystals can be grown in a variety of shapes through the modification of surface facet energies via surfactants. However, the surface facets are only a few atoms wide, making it extremely challenging to measure their geometries and energies. Here, we locate and count atoms in Au nanorods at successive time intervals using quantitative scanning transmission electron microscopy. This enables us to determine the atomic-level geometry and the relative stability of the facets and to expound their relationship to the overall three-dimensional nanocrystal shape and size. We reveal coexisting high- and low-index facets with comparable stability and dimensions and find the geometry of the nanorods is remarkably stable, despite significant atom movements. This information provides unique insights into the mechanisms that govern growth kinetics and nanocrystal morphology.
RESUMEN
We determine the three-dimensional shape, to within 1 nm resolution, of single-crystal gold nanorods grown in the presence of silver ions using electron tomography and thickness profile measurements. We find that, contrary to the current literature, the octagonal side-facets are sparsely packed atomic planes all belonging to the same symmetry-equivalent family, {0 5 12}. Furthermore, the rod ends terminate in a pyramid with slightly different facets, and each pyramid is connected to the sides by four small {0 5 12} "bridging" facets.
RESUMEN
We investigate the transformation of single crystal gold nanorod surface morphology over extended growth times. After initial rapid anisotropic growth and disappearance of {111} bridging facets, the aspect ratios converge across AgNO3 concentrations. The surface morphology transitions from faceted to curved. These observations imply the final aspect ratio has little dependence on the AgNO3 concentration, consistent with primary control of the AgNO3 over aspect ratio occurring at the symmetry breaking point.
RESUMEN
Quantitative analysis of lattice resolved images generated by scanning transmission electron microscopy (STEM) requires specification of probe characteristics, such as defocus, aberration and source distribution. In this paper we show that knowledge of such characteristics is unnecessary for quantitative interpretation, if the signal is integrated over a unit cell. Such a condition, whether the result of experimental setup or post-processing of lattice resolved images, reduces the intensity distribution to that of channelling contrast, where the signal for plane wave incidence is averaged over the angular range of the probe, and the result is independent of the probe characteristics. We use a Bloch wave model to show analytically how this applies to all forms of STEM imaging, such as that formed by annular dark field or backscatter detection, as well as characteristic X-ray fluorescence or electron energy loss. As a specific example, we consider how the signal from an annular dark field detector can be used to determine specimen thickness via a transfer curve for the zone axis and scattering geometries employed. This method has advantages over matching lattice images with calculations since these are sensitive to probe coherence and aberration, and saturation of the on-column intensity is approached more rapidly.
RESUMEN
A method to measure the thickness of a single-crystal nanoparticle in the direction parallel to the incident beam from annular dark field scanning transmission electron microscope (ADF-STEM) images is reported, providing a map of thickness versus position across the nanoparticle--a 'thickness profile' image. The method is rapid and hence suitable for surveying large numbers of nanoparticles. The method measures the intensity scattered to a characterised ADF detector and compares this to the incident beam intensity, to obtain a normalized ADF image. The normalised intensity is then converted to thickness via dynamical ADF image simulations. The method is accurate within 10% and the precision is dominated primarily by 'shot noise'. Merits and limitations of this method are discussed. A method to calibrate the response function of the ADF detector without external equipment is also described, which is applicable to the entire range of gain and background settings.