Vibrations of amorphous, nanometric structures: When does continuum theory apply?

Wittmer, J. P.; Tanguy, Anne; Barrat, Jean‐Louis; Lewis, Laurent J.

doi:10.1209/epl/i2002-00471-9

Cited by 105 publications

(179 citation statements)

References 18 publications

Supporting

Mentioning

163

Contrasting

Order By: Relevance

“…In the figure, we have plotted the (normalized) correlation function Interestingly, it can be readily shown that We demonstrate now that the non-affine displacement field in 3D is indeed of predominantly solenoidal nature. This has been anticipated by our previous studies on 2D systems [1] and by the values of the elastic moduli µ and K discussed in Sec. III C. The transverse and longitudinal contributions to the displacement field can be numerically obtained by computing…”

Section: Correlations In the Non-affine Displacement Fieldsupporting

confidence: 76%

“…The second frequency has degeneracy 24, and so on. In our previous analysis of 2D systems [1], we found that this…”

Section: Low Frequency Equilibrium Vibration Modesmentioning

confidence: 60%

“…2, the presented data shows that this coincides with the linear elastic regime where all moments of the non-affine field are similar and the residual plastic field can be neglected. 1 The central point is here that the plateau value of the participation ratio is large (about 25%) indicating that the elastic non-affine displacement involves a substantial fraction of the particles. When the deformation exceeds the plastic threshold ǫ p , however, the participation ratio falls rapidly, indicating that a plastic deformation proceeds via well localized events.…”

Section: B Plastic Displacements and Participation Ratiomentioning

confidence: 83%

“…[1] for the 2D case. In order to make the comparison as direct as possible, the same type of potential was chosen, i.e.…”

Section: Description Of Systems and Simulation Proceduresmentioning

confidence: 99%

“…In a recent series of papers [1,2,3], we investigated the elastic response of zero temperature two dimensional (2D) amorphous systems. Our studies were motivated by the idea that such systems, although they appear perfectly homogeneous when looking at the density field, may be described as heterogeneous from the point of view of the theory of elasticity.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Continuum limit of amorphous elastic bodies. III. Three-dimensional systems

et al. 2005

View full text Add to dashboard Cite

Extending recent numerical studies on two dimensional amorphous bodies, we characterize the approach of elastic continuum limit in three dimensional (weakly polydisperse) Lennard-Jones systems. While performing a systematic finite-size analysis (for two different quench protocols) we investigate the non-affine displacement field under external strain, the linear response to an external delta force and the low-frequency harmonic eigenmodes and their density distribution. Qualitatively similar behavior is found as in two dimensions. We demonstrate that the classical elasticity description breaks down below an intermediate length scale ξ, which in our system is approximately 23 molecular sizes. This length characterizes the correlations of the non-affine displacement field, the self-averaging of external noise with distance from the source and gives the lower wave length bound for the applicability of the classical eigenfrequency calculations. We trace back the "Bosonpeak" of the density of eigenfrequencies (obtained from the velocity auto-correlation function) to the inhomogeneities on wave lengths smaller than ξ.

show abstract

Section: Correlations In the Non-affine Displacement Fieldsupporting

confidence: 76%

“…The second frequency has degeneracy 24, and so on. In our previous analysis of 2D systems [1], we found that this…”

Section: Low Frequency Equilibrium Vibration Modesmentioning

confidence: 60%

Section: B Plastic Displacements and Participation Ratiomentioning

confidence: 83%

“…[1] for the 2D case. In order to make the comparison as direct as possible, the same type of potential was chosen, i.e.…”

Section: Description Of Systems and Simulation Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Continuum limit of amorphous elastic bodies. III. Three-dimensional systems

et al. 2005

View full text Add to dashboard Cite

show abstract

The Microscopic Quantum Theory of Low Temperature Amorphous Solids

Lubchenko¹,

Wolynes²

2007

Advances in Chemical Physics

View full text Add to dashboard Cite

The quantum excitations in glasses have long presented a set of puzzles for condensed matter physicists. A common view is that they are largely disordered analogs of elementary excitations in crystals, supplemented by two level systems which are chemically local entities coming from disorder. A radical revision of this picture argues that the excitations in low temperature glasses are deeply connected to the energy landscape of the glass when it vitrifies: the excitations are not low excited states built on a single ground state but locally defined resonances, high in the energy spectrum of a solid. According to a semiclassical analysis, the two level systems involve resonant collective tunneling motions of around two hundred molecular units which are relics of the mosaic of cooperative motions at the glass transition temperature Tg. The density of states of the TLS is determined by Tg and the mosaic's length scale, which is a weak function of the cooling rate. The universality of phonon scattering in insulating glasses is explained. The Boson Peak and the plateau in thermal conductivity, observed at higher temperatures, are also quantitatively understood within the picture as arising from the same cooperative motions, but now accompanied by thermal activation of the mosaic's vibrational modes. The dynamics of some of the local structural transitions have significant quantum corrections to the semiclassical picture. These corrections lead to a deviation of the heat capacity and conductivity from the standard tunneling model results and explain the anomalous time dependence of the heat capacity. Interaction between tunneling centers contributes to the large and negative value of the Grüneisen parameter often observed in glasses.

show abstract

Raman spectroscopy of nanostructures and nanosized materials

Gouadec

Colomban

2007

J Raman Spectroscopy

View full text Add to dashboard Cite

The interest in micro and tip-enhanced Raman spectroscopy in analyzing nanosized and nanostructured materials, chiefly semiconductors, oxides and pristine or functionalized carbon nanotubes, is reviewed in the light of contributions to this Special Issue. Particular attention is paid to the fact that chemical reactions, size or shape distribution, defects, strain and couplings may add to nanodimensionality in defining the Raman signature.

show abstract

Vibrations of amorphous, nanometric structures: When does continuum theory apply?

Cited by 105 publications

References 18 publications

Continuum limit of amorphous elastic bodies. III. Three-dimensional systems

Continuum limit of amorphous elastic bodies. III. Three-dimensional systems

The Microscopic Quantum Theory of Low Temperature Amorphous Solids

Raman spectroscopy of nanostructures and nanosized materials

Contact Info

Product

Resources

About