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Recently, a method for evaluating the fracture toughness of ceramics has been proposed by Fett based on the computed crack‐opening displacements of cracks emanating from Vickers hardness indentations. To verify this method, experiments have been conducted to determine the toughness of a commercial silicon carbide ceramic, Hexoloy SA, by measuring the crack‐opening profiles of such Vickers indentation cracks. Although the obtained toughness value of K o = 2.3 MPa·m 1/2 is within 10% of that measured using conventional fracture toughness testing, the computed crack‐opening profiles corresponding to this toughness display poor agreement with those measured experimentally, raising concerns about the suitability of this method for determining the toughness of ceramics. The effects of subsurface cracking and cracking during loading are considered as possible causes of such discrepancies, with the former based on direct observations of lateral subsurface cracks below the indents.
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The gapped symmetric phase of the Affleck-Kennedy-Lieb-Tasaki model exhibits fractionalized spins at the ends of an open chain. We show that breaking SU(2) symmetry and applying a global spin-lowering dissipator achieves synchronization of these fractionalized spins. Additional local dissipators ensure convergence to the ground state manifold. In order to understand which aspects of this synchronization are robust within the entire Haldane-gap phase, we reduce the biquadratic term, which eliminates the need for an external field but destabilizes synchronization. Within the ground state subspace, stability is regained using only the global lowering dissipator. These results demonstrate that fractionalized degrees of freedom can be synchronized in extended systems with a significant degree of robustness arising from topological protection. A direct consequence is that permutation symmetries are not required for the dynamics to be synchronized, representing a clear advantage of topological synchronization compared to synchronization induced by permutation symmetries.
Linking organic molecules by covalent bonds into extended solids typically generates amorphous, disordered materials. The ability to develop strategies for obtaining crystals of such solids is of interest because it opens the way for precise control of the geometry and functionality of the extended structure, and the stereochemical orientation of its constituents. Covalent organic frameworks (COFs) are a new class of porous covalent organic structures whose backbone is composed entirely of light elements (B, C, N, O, Si) that represent a successful demonstration of how crystalline materials of covalent solids can be achieved. COFs are made by combination of organic building units covalently linked into extended structures to make crystalline materials. The attainment of crystals is done by several techniques in which a balance is struck between the thermodynamic reversibility of the linking reactions and their kinetics. This success has led to the expansion of COF materials to include organic units linked by these strong covalent bonds: B-O, C-N, B-N, and B-O-Si. Since the organic constituents of COFs, when linked, do not undergo significant change in their overall geometry, it has been possible to predict the structures of the resulting COFs, and this advantage has facilitated their characterization using powder X-ray diffraction (PXRD) techniques. It has also allowed for the synthesis of COF structures by design and for their formation with the desired composition, pore size, and aperture. In practice, the modeled PXRD pattern for a given expected COF is compared with the experimental one, and depending on the quality of the match, this is used as a starting point for solving and then refining the crystal structure of the target COF. These characteristics make COFs an attractive class of new porous materials. Accordingly, they have been used as gas storage materials for energy applications, solid supports for catalysis, and optoelectronic devices. A large and growing library of linkers amenable to the synthesis of COFs is now available, and new COFs and topologies made by reticular synthesis are being reported. Much research is also directed toward the development of new methods of linking organic building units to generate other crystalline COFs. These efforts promise not only new COF chemistry and materials, but also the chance to extend the precision of molecular covalent chemistry to extended solids.
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