An official website of the United States government
Abstract A single‐crystal X‐ray study of a fullerene‐imidazole adduct at nine temperatures (80 K≤T≤480 K), accompanied by energy calculations, strongly suggested thermal motion of the C60moiety with respect to the imidazolium heterocycle. Analysis of the anisotropic displacement parameters, calculations of frequencies, and the refinement of disorder models for the crystal at four temperatures (230 K≤T≤380 K) lead to the conclusion that the rotator is moving at all temperatures. The rotation barrier is low, with one preferred crystallographic site and several other energy minima.
more »
« less
Geometry and arithmetic of crystallographic sphere packings
We introduce the notion of a “crystallographic sphere packing,” defined to be one whose limit set is that of a geometrically finite hyperbolic reflection group in one higher dimension. We exhibit an infinite family of conformally inequivalent crystallographic packings with all radii being reciprocals of integers. We then prove a result in the opposite direction: the “superintegral” ones exist only in finitely many “commensurability classes,” all in, at most, 20 dimensions.
more »
« less
- Award ID(s):
- 1802119
- PAR ID:
- 10082243
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 116
- Issue:
- 2
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- p. 436-441
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Layered metal-halide perovskites, or two-dimensional perovskites, can be synthesized in solution, and their optical and electronic properties can be tuned by changing their composition. We report a molecular templating method that restricted crystal growth along all crystallographic directions except for [110] and promoted one-dimensional growth. Our approach is widely applicable to synthesize a range of high-quality layered perovskite nanowires with large aspect ratios and tunable organic-inorganic chemical compositions. These nanowires form exceptionally well-defined and flexible cavities that exhibited a wide range of unusual optical properties beyond those of conventional perovskite nanowires. We observed anisotropic emission polarization, low-loss waveguiding (below 3 decibels per millimeter), and efficient low-threshold light amplification (below 20 microjoules per square centimeter).more » « less
-
Significance Self-assembly is one of the central themes in biologically controlled synthesis, and it also plays a pivotal role in fabricating a variety of advanced engineering materials. In particular, evaporation-induced self-assembly of colloidal particles enables versatile fabrication of highly ordered two- or three-dimensional nanostructures for optical, sensing, catalytic, and other applications. While it is well known that this process results in the formation of the face-centered cubic (fcc) lattice with the close-packed {111} plane parallel to the substrate, the crystallographic texture development of colloidal crystals is less understood. In this study, we show that the preferred <110> growth in the fcc colloidal crystals synthesized through evaporation-induced assembly is achieved through a gradual crystallographic rotation facilitated by mechanical stress-induced geometrically necessary dislocations.more » « less
-
We develop the notion of a Kleinian Sphere Packing, a generalization of“crystallographic” (Apollonian-like) sphere packings defined in [A. Kontorovich and K. Nakamura,Geometry and arithmetic of crystallographic sphere packings,Proc. Natl. Acad. Sci. USA 116 2019, 2, 436–441].Unlike crystallographic packings, Kleinian packings exist in all dimensions, as do “superintegral” such.We extend the Arithmeticity Theorem to Kleinian packings, that is, the superintegral ones come from ℚ-arithmetic lattices of simplest type.The same holds for more general objects we call Kleinian Bugs, in which the spheres need not be disjoint but can meet with dihedral angles π/m for finitely many m. We settle two questions from Kontorovich and Nakamura (2019): (i) that the Arithmeticity Theorem is in general false over number fields, and (ii)that integral packings only arise from non-uniform lattices.more » « less
-
Abstract The exploration of quantum materials in which an applied thermo/electrical/magnetic field along one crystallographic direction produces an anisotropic response has led to unique functionalities. Along these lines, KMgBi is a layered, narrow gap semiconductor near a critical state between multiple Dirac phases due to the presence of a flat band near the Fermi level. The valence band is highly anisotropic with minimal cross‐plane dispersion, which, in combination with an isotropic conduction band, enables axis‐dependent conduction polarity. Thermopower and Hall measurements indicate dominant p‐type conduction along the cross‐plane direction, and n‐type conduction along the in‐plane direction, leading to a significant zero‐field transverse thermoelectric response when the heat flux is at an angle to the principal crystallographic directions. Additionally, a large Ordinary Nernst effect (ONE) is observed with an applied field. It arises from the ambipolar term in the Nernst effect, whereby the Lorentz force on electrons and holes makes them drift in opposite directions so that the resulting Nernst voltage becomes a function of the difference between their partial thermopowers, greatly enhancing the ONE. It is proven that axis‐dependent polarity can synergistically enhance the ONE, in addition to leading to a zero‐field transverse thermoelectric performance.more » « less
