Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (a) Schematic representation of 1D crystal with linear stiffness β and quadratic nonlinearity parameter ε. (b) The potential energy function describing the 1D crystal.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (Left) Band structure of 1D harmonic monoatomic crystal. (Right) SED-frequency plot showing wave vector mode k = π/a.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (Left) Band structure (constant SED contours) for 1D harmonic monoatomic crystal near k = π/10 a. (Right) SED-frequency plots for four MD simulations differing in their initial random configurations.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (Left) Band structure (constant SED contours) for 1D anharmonic monoatomic crystal near k = π/10a. (Right) SED-frequency plots for four MD simulations differing in their initial random configurations.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (Left) Band structure for 1D anharmonic monoatomic crystal. (Right) SED-frequency plot showing wave vector mode k = π/a. ε = 3.0 and initial random displacement does not exceed 10% of a.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (Top, left) SED-frequency plots for wave vector modes k′ and k″, corresponding to Case I. (Bottom, left) SED-frequency plots for wave vector modes k′ and k″, corresponding to Case II. (Right) SED-frequency plot corresponding to k* = π/a. For Cases I and II, wave vectors k′ and k″ satisfy wave vector conservation for mode k*. The frequencies of modes k′ and k″ add (or subtract) to yield near-resonance peaks near ω*(k*).

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: SED-frequency plots for 1D anharmonic monoatomic crystal at k = π/a for MD systems of varying sizes. The parameter characterizing the degree of anharmonicity in the 1D crystal is ε = 3.0.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: Frequency-shift evaluated at k = π/a for 1D anharmonic crystal relative to harmonic case. Symbols represent different magnitudes for the maximum initial random displacement imposed upon the masses in the 1D crystal in terms of percentage of the lattice spacing. Circle, square, and triangle symbols represent small, intermediate, and large initial displacements, respectively.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (Top) Unit cell for diatomic crystal. (Center) Band structure for 1D anharmonic diatomic crystal. (Left) SED-frequency plot at k = π/20a with peaks for harmonic (dashed line) and anharmonic (solid line) cases. (Right) SED-frequency plot at k = π/a with peaks for harmonic (dashed line) and anharmonic (solid line) cases.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (Top) Four-atom unit cell. (Left) Anharmonic band structure corresponding to the four-atom unit cell. (Right) SED-frequency plot at k = π/2a. Dashed line represents the harmonic case, whereas the solid line represents the anharmonic case.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (Top) Eight-atom unit cell. (Left) Anharmonic band structure corresponding to the eight-atom unit cell. (Right) SED-frequency plot at k = π/4a. Dashed line represents the harmonic case, whereas the solid line represents the anharmonic case.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (Top) Sixteen-atom unit cell. (Left) Anharmonic band structure corresponding to the sixteen-atom unit cell. (Right) SED-frequency plot at k = π/8a. Dashed line represents the harmonic case, whereas the solid line represents the anharmonic case.

Date of download: 11/13/2017 Copyright © ASME. All rights reserved. From: Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study J. Vib. Acoust. 2013;135(4):041016-041016-13. doi:10.1115/1.4023824 Figure Legend: (a) (Left to right) 1:1, 2:2, 4:4, and 8:8 SED-frequency plot with peaks respectively corresponding to the superlattice configurations depicted in Figs. 9–12. (b) Lorentzian function fits to the SED-frequency spectra in (a). Lorentzian peaks are labeled with half-width at half-maximum values in units of 10–6 Hz.