50 research outputs found
An atomic mechanism for the boson peak in metallic glasses
The boson peak in metallic glasses is modeled in terms of local structural
shear rearrangements. Using Eshelby's solution of the corresponding elasticity
theory problem (J. D. Eshelby, Proc. Roy. Soc. A241, 376 (1957)), one can
calculate the saddle point energy of such a structural rearrangement. The
neighbourhood of the saddle point gives rise to soft resonant vibrational
modes. One can calculate their density, their kinetic energy, their fourth
order potential term and their coupling to longitudinal and transverse sound
waves.Comment: 9 pages, 7 figures, 31 references, contribution to 11th International
Workshop on Complex Systems, Andalo (Italy), March 200
Voronoi-Delaunay analysis of normal modes in a simple model glass
We combine a conventional harmonic analysis of vibrations in a one-atomic
model glass of soft spheres with a Voronoi-Delaunay geometrical analysis of the
structure. ``Structure potentials'' (tetragonality, sphericity or perfectness)
are introduced to describe the shape of the local atomic configurations
(Delaunay simplices) as function of the atomic coordinates. Apart from the
highest and lowest frequencies the amplitude weighted ``structure potential''
varies only little with frequency. The movement of atoms in soft modes causes
transitions between different ``perfect'' realizations of local structure. As
for the potential energy a dynamic matrix can be defined for the ``structure
potential''. Its expectation value with respect to the vibrational modes
increases nearly linearly with frequency and shows a clear indication of the
boson peak. The structure eigenvectors of this dynamical matrix are strongly
correlated to the vibrational ones. Four subgroups of modes can be
distinguished
Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations
The approach of the elastic continuum limit in small amorphous bodies formed
by weakly polydisperse Lennard-Jones beads is investigated in a systematic
finite-size study. We show that classical continuum elasticity breaks down when
the wavelength of the sollicitation is smaller than a characteristic length of
approximately 30 molecular sizes. Due to this surprisingly large effect
ensembles containing up to N=40,000 particles have been required in two
dimensions to yield a convincing match with the classical continuum predictions
for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk
systems. The existence of an effective length scale \xi is confirmed by the
analysis of the (non-gaussian) noisy part of the low frequency vibrational
eigenmodes. Moreover, we relate it to the {\em non-affine} part of the
displacement fields under imposed elongation and shear. Similar correlations
(vortices) are indeed observed on distances up to \xi~30 particle sizes.Comment: 28 pages, 13 figures, 3 table
Structure, Stresses and Local Dynamics in Glasses
The interrelations between short range structural and elastic aspects in
glasses and glass forming liquids pose important and yet unresolved questions.
In this paper these relations are analyzed for mono-atomic glasses and stressed
liquids with a short range repulsive-attractive pair potentials. Strong
variations of the local pressure are found even in a zero temperature glass,
whereas the largest values of pressure are the same in both glasses and
liquids. The coordination number z(J) and the effective first peak radius
depend on the local pressures J's. A linear relation was found between
components of site stress tensor and the local elastic constants. A linear
relation was also found between the trace of the squares of the local
frequencies and the local pressures. Those relations hold for glasses at zero
temperature and for liquids. We explain this by a relation between the
structure and the potential terms. A structural similarity between liquids and
solids is manifested by similar dependencies of the coordination number on the
pressures.Comment: 7 pages, 11 figure
Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation
The process of pattern formation in the two dimensional Swift-Hohenberg
equation is examined through numerical and analytic methods. Dynamic scaling
relationships are developed for the collective ordering of convective rolls in
the limit of infinite aspect ratio. The stationary solutions are shown to be
strongly influenced by the strength of noise. Stationary states for small and
large noise strengths appear to be quasi-ordered and disordered respectively.
The dynamics of ordering from an initially inhomogeneous state is very slow in
the former case and fast in the latter. Both numerical and analytic
calculations indicate that the slow dynamics can be characterized by a simple
scaling relationship, with a characteristic dynamic exponent of in the
intermediate time regime
Structure and relaxations in liquid and amorphous Selenium
We report a molecular dynamics simulation of selenium, described by a
three-body interaction. The temperatures T_g and T_c and the structural
properties are in agreement with experiment. The mean nearest neighbor
coordination number is 2.1. A small pre-peak at about 1 AA^-1 can be explained
in terms of void correlations. In the intermediate self-scattering function,
i.e. the density fluctuation correlation, classical behavior, alpha- and
beta-regimes, is found. We also observe the plateau in the beta-regime below
T_g. In a second step, we investigated the heterogeneous and/or homogeneous
behavior of the relaxations. At both short and long times the relaxations are
homogeneous (or weakly heterogeneous). In the intermediate time scale, lowering
the temperature increases the heterogeneity. We connect these different domains
to the vibrational (ballistic), beta- and alpha-regimes. We have also shown
that the increase in heterogeneity can be understood in terms of relaxations
Interaction of quasilocal harmonic modes and boson peak in glasses
The direct proportionality relation between the boson peak maximum in
glasses, , and the Ioffe-Regel crossover frequency for phonons,
, is established. For several investigated materials . At the frequency the mean free path of the
phonons becomes equal to their wavelength because of strong resonant
scattering on quasilocal harmonic oscillators. Above this frequency phonons
cease to exist. We prove that the established correlation between
and holds in the general case and is a direct consequence of
bilinear coupling of quasilocal oscillators with the strain field.Comment: RevTex, 4 pages, 1 figur
Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
We have studied how 2- and 3- dimensional systems made up of particles
interacting with finite range, repulsive potentials jam (i.e., develop a yield
stress in a disordered state) at zero temperature and applied stress. For each
configuration, there is a unique jamming threshold, , at which
particles can no longer avoid each other and the bulk and shear moduli
simultaneously become non-zero. The distribution of values becomes
narrower as the system size increases, so that essentially all configurations
jam at the same in the thermodynamic limit. This packing fraction
corresponds to the previously measured value for random close-packing. In fact,
our results provide a well-defined meaning for "random close-packing" in terms
of the fraction of all phase space with inherent structures that jam. The
jamming threshold, Point J, occurring at zero temperature and applied stress
and at the random close-packing density, has properties reminiscent of an
ordinary critical point. As Point J is approached from higher packing
fractions, power-law scaling is found for many quantities. Moreover, near Point
J, certain quantities no longer self-average, suggesting the existence of a
length scale that diverges at J. However, Point J also differs from an ordinary
critical point: the scaling exponents do not depend on dimension but do depend
on the interparticle potential. Finally, as Point J is approached from high
packing fractions, the density of vibrational states develops a large excess of
low-frequency modes. All of these results suggest that Point J may control
behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure