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A spatially periodic structure of heterogeneous elastic rods that periodically oscillate along their axes is proposed as a time-modulated phononic crystal. Each rod is a bi-material cylinder, consisting of periodically distributed slices with significantly different elastic properties. The rods are imbedded in an elastic matrix. Using a plane wave expansion, it is shown that the dispersion equation for sound waves is obtained from the solutions of a quadratic eigenvalue problem over the eigenfrequency ω. The coefficients of the corresponding quadratic polynomial are represented by infinite matrices defined in the space spanned by the reciprocal lattice vectors, where elements depend on the velocity of translation motion of the rods and Bloch vector k. The calculated band structure exhibits both ω and k bandgaps. If a frequency gap overlaps with a momentum gap, a mixed gap is formed. Within a mixed gap, ω and k acquire imaginary parts. A method of analysis of the dispersion equation in complex ω−k space is proposed. As a result of the high elastic contrast between the materials in the bi-material rods, a substantial depth of modulation is achieved, leading to a large gap to midgap ratio for the frequency, momentum, and mixed bandgaps. 

Abstract Electrocatalytic nanocarbon (EN) is a class of material receiving intense interest as a potential replacement for expensive, metal-based electrocatalysts for energy conversion and chemical production applications. The further development of EN will require an intricate knowledge of its catalytic behaviors, however, the true nature of their electrocatalytic activity remains elusive. This review highlights work that contributed valuable knowledge in the elucidation of EN catalytic mechanisms. Experimental evidence from spectroscopic studies and well-defined molecular models, along with the survey of computational studies, is summarized to document our current mechanistic understanding of EN-catalyzed oxygen, carbon dioxide and nitrogen electrochemistry. We hope this review will inspire future development of synthetic methods and in situ spectroscopic tools to make and study well-defined EN structures. 

High-performance piezoelectrics benefit transducers and sensors in a variety of electromechanical applications.The materials with the highest piezoelectric chargecoefficients (d33) are relaxor-PbTiO3 crystals, which were discovered two decades ago. We successfully grew Sm-doped Pb(Mg1/3Nb2/3)O3-PbTiO3 (Sm-PMN-PT) single crystals with even higher d33 values ranging from 3400 to 4100 picocoulombs per newton, with variation below 20%over the as-grown crystal boule, exhibiting good property uniformity. We characterized the Sm-PMN-PTon the atomic scale with scanning transmission electron microscopy and made first-principles calculations to determine that the giant piezoelectric properties arise fromthe enhanced local structural heterogeneity introduced by Sm3+ dopants. Rare-earth doping is thus identified as a general strategy for introducing local structural heterogeneity in order to enhance the piezoelectricity of relaxor ferroelectric crystals.