Brillouin zone

About: Brillouin zone is a research topic. Over the lifetime, 13849 publications have been published within this topic receiving 383077 citations.

Phonon instabilities and the ideal strength of aluminum.

Abstract: We have calculated the phonon spectra of aluminum as a function of strain using density functional perturbation theory for $⟨110⟩$, $⟨100⟩$, and $⟨111⟩$ uniaxial tension, as well as relaxed $⟨112⟩{111}$ shear. In all four cases, phonon instabilities occur at points away from the center of the Brillouin zone and intrude before the material becomes unstable according to elastic stability criteria. This is the first time the ideal strength of a metal has been shown to be dictated by instabilities in the acoustic phonon spectra. We go on to describe the crystallography of the unstable modes, all of which are shear in character. This work further suggests that shear failure is an inherent property of aluminum even in an initially dislocation-free perfect crystal.

A fully distributed simultaneous strain and temperature sensor using spontaneous Brillouin backscatter

Abstract: We report here the first simultaneous measurement of strain and temperature using Brillouin backscatter in an optical fiber. A new sensor arrangement is presented which allows the distributed measurement of Brillouin spectra. Simultaneous measurement of spontaneous Brillouin power and Brillouin shift distributions are made from these spectra, and from this information, we obtain fully distributed measurements of strain and temperature. Our sensor achieves a 100-/spl mu//spl epsiv/ strain and 4/spl deg/C temperature resolution, with 40-m spatial resolution, over a sensing length of 1200 m.

Geometrical approach for the study of G band in the Raman spectrum of monolayer graphene, bilayer graphene, and bulk graphite

Abstract: In this paper, a geometrical approach is presented for the study of the double-resonance process, giving rise to the ${G}^{\ensuremath{'}}$ band in monolayer graphene, bilayer graphene, and bulk graphite. It is shown that there are four discrete peaks present in the ${G}^{\ensuremath{'}}$ band spectrum obtained from the stacking of two graphene layers, and these discrete peaks arise from the quantization of the first Brillouin zone caused by its finite size along the $c$ axis. Our analysis includes the study of the selection rules imposed on the electron-radiation and electron-phonon Hamiltonian interactions involving $\ensuremath{\pi}$ electrons near the $K$ point. We show that the anisotropy in the optical absorption (emission) near the $K$ point in the first Brillouin zone of graphite should be taken into account in order to gain an understanding of the selection rules for optical transitions in bilayer graphene. The validity of considering a linear dispersion for $\ensuremath{\pi}$ electrons along the $K\text{\ensuremath{-}}\ensuremath{\Gamma}$ direction is taken into consideration. We present four numerical equations, giving the dependencies of the frequencies of the four peaks composing the ${G}^{\ensuremath{'}}$ feature in the Raman spectrum of bilayer graphene on the laser excitation energy in the visible range. We also show that the two-peak shape of the ${G}^{\ensuremath{'}}$ band in the Raman spectrum of bulk graphite is in fact caused by the convolution of an infinite number of peaks.

Theory of elastic and piezoelectric effects in two-dimensional hexagonal boron nitride

Abstract: Starting from an empirical force constant model of valence interactions and calculating by Ewald's method the ion-ion force constants, we derive the dynamical matrix for a monolayer crystal of hexagonal boron nitride (h-BN). The phonon dispersion relations are calculated. The interplay between valence and Coulomb forces is discussed. It is shown by analytical methods that the longitudinal and the transverse optical (LO and TO) phonon branches for in-plane motion are degenerate at the $\ensuremath{\Gamma}$ point of the Brillouin zone. Away from $\ensuremath{\Gamma}$, the LO branch exhibits pronounced overbending. It is found that the nonanalytic Coulomb contribution to the dynamical matrix causes a linear increase of the LO branch with increasing wave vector starting at $\ensuremath{\Gamma}$. This effect is general for two-dimensional (2D) ionic crystals. Performing a long-wavelength expansion of the dynamical matrix, we use Born's perturbation method to calculate the elastic constants (tension coefficients). Since the crystal is noncentrosymmetric, internal displacements due to relative shifts between the two sublattices (B and N) contribute to the elastic constants. These internal displacements are responsible for piezoelectric and dielectric phenomena. The piezoelectric stress constant and the dielectric susceptibility of 2D h-BN are calculated.

Creation of partial band gaps in anisotropic photonic-band-gap structures

Abstract: The photonic-band-gap (PBG) structure composed of an anisotropic-dielectric sphere in uniform dielectric medium is studied by solving Maxwell's equations using the plane-wave expansion method. In particular, for a uniaxial material with large principal refractive indices and sufficient anisotropy between them, the photonic band structures possess a full band gap in the whole Brillouin zone for a diamond lattice. Furthermore, in the 1/3 partial Brillouin zone where the Bloch wave vector has a dominant component along the extraordinary axis of uniaxial sphere, the photonic band structures are found to exhibit full band gaps for all the other lattices such as face-centered-cubic, body-centered-cubic, and simple-cubic lattices, although a complete band gap does not open in the whole Brillouin zone. The partial band gaps persist at a very low filling fraction of uniaxial sphere. This phenomenon is attributed to the breakdown of the photonic band degeneracy at high-symmetry points of the Brillouin zone by the anisotropy of material dielectricity. The combination of such an anisotropic PBG structure with the self-arrangement technique of colloidal crystal may provide a possible way to fabricate the three-dimensional photonic crystal in visible and infrared regimes. The application of a strong electric field may bring into alignment the extraordinary axis of uniaxial sphere as this configuration of spheres is most favorable thermodynamically.