Nanoparticles can be beautiful, as in stained glass windows, or they can be ugly as in wear and corrosion debris from implants. We estimate that there will be about 70,000 papers in 2015 with nanoparticles as a keyword, but only one in thirteen uses the nanoparticle shape as an additional keyword and research focus, and only one in two hundred has thermodynamics. Methods for synthesizing nanoparticles have exploded over the last decade, but our understanding of how and why they take their forms has not progressed as fast. This topical review attempts to take a critical snapshot of the current understanding, focusing more on methods to predict than a purely synthetic or descriptive approach. We look at models and themes which are largely independent of the exact synthetic method whether it is deposition, gas-phase condensation, solution based or hydrothermal synthesis. Elements are old dating back to the beginning of the 20th century-some of the pioneering models developed then are still relevant today. Others are newer, a merging of older concepts such as kinetic-Wulff constructions with methods to understand minimum energy shapes for particles with twins. Overall we find that while there are still many unknowns, the broad framework of understanding and predicting the structure of nanoparticles via diverse Wulff constructions, either thermodynamic, local minima or kinetic has been exceedingly successful. However, the field is still developing and there remain many unknowns and new avenues for research, a few of these being suggested towards the end of the review.

Bimetallic nanoparticles are of interest due to their physical and chemical properties, which differ from their monometallic counterparts, and are dependent on size, composition and structure. Their unique chemical and physical properties make them useful in many optical, electronic and catalytic applications. In this perspective article we discuss segregation in bimetallic nanoparticles and highlight a recent analytical model based on minimization of energy. Computational approaches are discussed, along with a few examples and a comparison with the analytical approach. Experimental evidence for surface segregation is described, and finally, future directions are suggested. From this review of theoretical and experimental information it appears that a general consensus is starting to emerge that there are size-dependent variations in segregation in nanoparticles with the experimental data reasonably consistent with the theoretical models.

Experimental results for corner rounding in nanoparticles as a function of size are reported. We find that the rounding is independent of size, which appears to violate the conditions for both the thermodynamic and kinetic Wulff conditions. To understand this, we first verify that continuum concepts such as the weighted mean curvature and preferential nucleation at a twin boundary are valid at the nanoscale using density functional theory calculations. We then explain the rounding as a consequence of a nominal singularity in continuum models for sharp corners, showing that rounded or in some cases slightly truncated corners are a Lyapunov (steadystate) solution. We point out that in almost all cases the corners of materials at the nanoscale will be rounded, and also that the rounding can be exploited to measure the chemical potential during the growth conditions.