Erratum: Low Frequency Raman Scattering from Acoustic Phonons Confined in ZnO Nanoparticles [Phys. Rev. Lett.<b>97</b>, 085502 (2006)]

Yadav, Harish Kumar; Gupta, Vinay; Sreenivas, K.; Singh, Surinder P.; Sundarakannan, B.; Katiyar, Ram S.

doi:10.1103/physrevlett.98.029902

Cited by 25 publications

(45 citation statements)

References 4 publications

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“…Acoustic modes are generally not observed in bulk crystals because of inverse particle size dependence of their frequency. [10] The optical branch consist of an A 1 mode, a doubly degenerate E 1 mode, two doubly degenerate E 2 modes, and two B 1 modes, and are mathematically represented by, [11] = A 1 (z, z 2 , x 2 + y 2 ) + 2B 1 + E 1 (x, y, xz, yz) + 2E 2 (x 2 − y 2 , xy) A 1 and E 1 branches are both Raman and infrared active; E 2 branches are only Raman active, whereas B 1 branches are both Raman and infrared inactive (silent modes). [12] Since ZnO is ionic (ionicity = 0.616 at Phillips ionicity scale) the strong electrostatic or Coulombic forces split the A 1 and E 1 branches into longitudinal optical (LO) and transverse optical (TO) modes.…”

Section: Resultsmentioning

confidence: 99%

Structural studies and Raman spectroscopy of forbidden zone boundary phonons in Ni‐doped ZnO ceramics

Yadav

Sreenivas

Gupta

et al. 2008

J Raman Spectroscopy

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We present X-ray diffraction and Raman spectroscopy studies of Ni-doped ZnO (Zn 1−x Ni x O, x = 0.0, 0.03, 0.06, and 0.10) ceramics prepared by solid-state reaction technique. The presence of the secondary phase along with the wurtzite phase is observed in Ni-doped ZnO samples. The E 2 (low) optical phonon mode is seen to be shifted to a lower wavenumber with Ni incorporation in ZnO and is explained on the basis of force-constant variation of ZnO bond with Ni incorporation. A zone boundary phonon is observed in Ni-doped samples at ∼130 cm −1 which is normally forbidden in the first-order Raman scattering of ZnO. Antiferromagnetic ordering between Ni atoms via spin-orbit mechanism at low temperatures (100 K) is held responsible for the observed zone boundary phonon.

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Section: Resultsmentioning

confidence: 99%

Structural studies and Raman spectroscopy of forbidden zone boundary phonons in Ni‐doped ZnO ceramics

Yadav

Sreenivas

Gupta

et al. 2008

J Raman Spectroscopy

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“…Acoustic vibration modes frequencies of NP measured by Raman scattering or pump-probe experiments are fairly well reproduced by linear elastic-theory calculations even for NPs with sizes of a few nanometers. [6][7][8][9] The present work is concerned with the validity of elasticity within the vibration properties computed for systems whose sizes are smaller than the ones currently and experimentally explored. To achieve this goal, we compare the vibration modes calculated by linear elasticity and atomistic semiempirical potential calculations in the case of metallic NP of diameter ranging from 1.4 to about 4 nm.…”

Section: Introductionmentioning

confidence: 99%

Acoustic modes in metallic nanoparticles: Atomistic versus elasticity modeling

Combe

Saviot

2009

Phys. Rev. B

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The validity of the linear elasticity theory is examined at the nanometer scale by investigating the vibrational properties of silver and gold nanoparticles whose diameters range from about 1.5-4 nm. Comparing the vibration modes calculated by elasticity theory and atomistic simulation based on the embedded-atom method, we first show that the anisotropy of the stiffness tensor in elastic calculation is essential to ensure a good agreement between elastic and atomistic models. Second, we illustrate the reduction in the number of vibration modes due to the diminution of the number of atoms when reducing the nanoparticles size. Finally, we exhibit a breakdown of the frequency-spectra scaling of the vibration modes and attribute it to surface effects. Some critical sizes under which such effects are expected, depending on the material and the considered vibration modes, are given.

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“…For weak vibration coupling between a continuum of homogeneous elastically isotropic NCs and their matrix, Lamb's theory 5 is suitable for identifying the acoustic modes of free or embedded NCs. 6,7,9 For strong coupling, theories proposed recently point out that the vibration eigenvector should incorporate coupling to the matrix that causes thermal fluctuations in both the amplitude and phase of the lattice vibration within the NCs. 3,12 In this case, a complex-frequency ͑CF͒ model which takes into account the action of an infinite matrix may predict the dominant frequencies of the acoustic vibration modes.…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11] A difficult task is the assignment of the low-frequency modes because of the complexity of the environment around the NCs. For weak vibration coupling between a continuum of homogeneous elastically isotropic NCs and their matrix, Lamb's theory 5 is suitable for identifying the acoustic modes of free or embedded NCs.…”

Section: Introductionmentioning

confidence: 99%

Nanocrystal-induced line narrowing of surface acoustic phonons in the Raman spectra of embeddedGexSi1−xalloy nanocrystals

Xiong

Yang

et al. 2008

Phys. Rev. B

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Raman scattering was performed on Ge x Si 1−x ͑x = 0.54 or 0.28͒ alloy nanocrystals embedded in amorphous Si oxide. An asymmetric, depolarized, and size-dependent low-frequency Raman peak was observed and identified as the superposition of two surface acoustic vibration modes of the alloy nanocrystals. The current theoretical models can be used to explain the mode frequencies but not the dampings observed experimentally. Based on energy-dispersive x-ray microanalysis and density-functional-theory total energy optimization of structures, a modified core-shell-matrix model in which the effects of neighboring nanocrystals in the matrix are taken into account is in good agreement with experiments. This work provides good insight into the frequencies and dampings of acoustic vibrations of the nanocrystals embedded in the matrix.

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Erratum: Low Frequency Raman Scattering from Acoustic Phonons Confined in ZnO Nanoparticles [Phys. Rev. Lett.97, 085502 (2006)]

Cited by 25 publications

References 4 publications

Structural studies and Raman spectroscopy of forbidden zone boundary phonons in Ni‐doped ZnO ceramics

Structural studies and Raman spectroscopy of forbidden zone boundary phonons in Ni‐doped ZnO ceramics

Acoustic modes in metallic nanoparticles: Atomistic versus elasticity modeling

Nanocrystal-induced line narrowing of surface acoustic phonons in the Raman spectra of embeddedGexSi1−xalloy nanocrystals

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