On the elastic softening due to a vacancy in Si

The Raman spectra of numerous dodecaborides have been measured on high-quality single crystals at ambient conditions with high spectral resolution and signal-to-noise ratio. Besides the strong Raman-active modes, numerous Raman-inactive modes occur in the spectra, indicating distortions of the structures. Ab initio calculation of the phonon spectra on ZrB(12) excellently agrees with the experimental results. Force constants are theoretically calculated and force parameters are estimated from the Raman frequencies. The influence of the surface range on the Raman spectra is evident. The different isotopic effects (virtual crystal approximation, the polarization effect and the effect of isotopic disorder) on the phonon frequencies are determined, separated and discussed.

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“…In effect, the frequency is increased. A related subject has been investigated in the vacancy problem of Si [78].…”

Section: Anharmonicitymentioning

confidence: 99%

Raman scattering and isotopic phonon effects in dodecaborides

Werheit

Филипов

Shirai

et al. 2011

J. Phys.: Condens. Matter

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“…A recent molecular dynamics simulation combined with a first-principle calculation revealed that such a high symmetric vacancy state is realized at a finite temperature. 15) The explicit calculation of the quadrupole susceptibility including the effect of the lattice relaxation is an important future problem. In addition, the explicit estimation of the quadrupole-strain coupling g Γ is also important to determine the absolute value of the elastic softening.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…14) More recently, the elastic properties in a Si vacancy have also been discussed by using the first-principle calculations. 15,16) In the EPR experiments, 3) the vacancies were intentionally created by electron-beam and γ-ray irradiations, and then, the observed local distortions in the EPR are considered to be caused by the cooperative Jahn-Teller effect among the highly irradiated vacancies being strongly coupled each other. 1) Such vacancies are well described by the first-principle calculations with supercells where the vacancy concentration is ∼ 1/1000.…”

Section: Introductionmentioning

confidence: 99%

Quadrupole Susceptibility and Elastic Softening due to a Vacancy in Silicon Crystal

2009

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We investigate the electronic states around a single vacancy in silicon crystal by using the Green's function approach. The triply degenerate vacancy states within the band gap are found to be extended over a large distance ∼ 20Å from the vacancy site and contribute to the reciprocal temperature dependence of the quadrupole susceptibility resulting in the elastic softening at low temperture. The Curie constant of the quadrupole susceptibility for the trigonal mode (Oyz, Ozx, Oxy) is largely enhanced as compared to that for the tetragonal mode (O 0 2 , O 2 2 ). The obtained results are consistent with the recent ultrasonic experiments in silicon crystal down to 20 mK. We also calculate the dipole and octupole susceptibilities and find that the octupole susceptibilities are extremely enhannced for a specific mode.

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On the elastic softening due to a vacancy in Si

Cited by 2 publications

References 9 publications

Raman scattering and isotopic phonon effects in dodecaborides

Raman scattering and isotopic phonon effects in dodecaborides

Quadrupole Susceptibility and Elastic Softening due to a Vacancy in Silicon Crystal

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