We establish the formula representing cubic nanocrystals (NCs) as hard cubes taking into account the role of the ligands and describe how these results generalize to any other NC shapes. We derive the conditions under which the hard cube representation breaks down and provide explicit expressions for the effective size. We verify the results from the detailed potential of mean force calculations for two nanocubes in different orientations as well as with spherical nanocrystals. Our results explicitly demonstrate the relevance of certain ligand conformations, i.e., “vortices”, and show that edges and corners provide natural sites for their emergence. We also provide both simulations and experimental results with single component cubic perovskite nanocrystals assembled into simple cubic superlattices, which further corroborate theoretical predictions. In this way, we extend the Orbifold Topological Model (OTM) accounting for the role of ligands beyond spherical nanocrystals and discuss its extension to arbitrary nanocrystal shapes. Our results provide detailed predictions for recent superlattices of perovskite nanocubes and spherical nanocrystals. Problems with existing united atom force fields are discussed.
One of the outstanding questions in planetary science is to determine how the fundamental mechanical and physical properties of materials determine the thermal evolution of asteroids, and which properties have the greatest influence. We investigate the effects of uncertainty in the material properties of asteroid parent bodies on the ability of thermal evolution models to constrain the sizes and formation times of ordinary chondrite parent asteroids. A simple model is formulated for the thermal evolution of the parent body of asteroid 25143 Itokawa. The effects of the uncertainties in the values specified for specific heat capacity, thermal diffusivity, and aluminum abundance are determined. The uncertainties in specific heat capacity and aluminum abundance, or heat production more generally, are found to both have significant and approximately equal effects on these results, substantially widening the range of possible formation times of Itokawa’s parent body. We show that Itokawa’s parent body could have formed between 1.6 and 2.5 million years after the origin of calcium–aluminum inclusions with a radius larger than 19 km, and it could have formed as early as 1.4 millions years, as late as 3.5 million years, or with a radius as small at 17 km if more lenient definitions of uncertainty in aluminum abundance are considered. These results stress the importance of precise data required of the material properties of a suite of LL type 4-6 ordinary chondrite meteorites to place better constraints on the thermal history of Itokawa’s parent body. Graphical Abstract
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