Density invariant vibrational modes in disordered colloidal crystals

Abstract

We experimentally measure the density of states (DOS) and dynamical structure factor (DSF) arising from the thermal fluctuations in a colloidal crystal composed of thermally sensitive micronsized hydrogel particles at several different particle volume fractions, φ. Particle positions are tracked over long times using optical microscopy and particle tracking algorithms in a single two dimensional (2D) [111] plane of a 3D face-centered-cubic single crystal. The dynamical fluctuations are spatially heterogeneous while the lattice itself is highly ordered. At all φ, the DOS exhibits an excess of low frequency modes, a so-called boson peak (BP), and the DSF exhibits a cross-over from propagating to non-propagating behavior, a so-called Ioffe-Regel (IR) crossover, at a frequency somewhat below the BP for both longitudinal and transverse modes. As we tune φ from 0.64 to 0.56, the Lindemann parameter grows from ∼ 3% to ∼ 8%; however, the shape of the DOS and DSF remain largely unchanged when rescaled by the Debye level. This invariance indicates that the effective degree of disorder remains essentially constant even in the vicinity of melting.

Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids

“…Note that the moduli defined in Eq. (5) are not eigenvalues of the modulus tensor, which is an alternative possibility 45,82 . In that case, however, the corresponding deformations, which are determined by the associated eigenvectors, are not fixed and depend on m.…”

“…In contrast, disordered solids feature vibrational properties anomalous compared to those of the corresponding crystals. (Here, disordered solids include not only topologically amorphous materials as structural glasses 3 , but also disordered crystals 4,5 , which show periodic lattice structures but in the presence of disordered inter-particle potentials, like colloidal crystals with size disorder.) Among these anomalies, the origin of an excess in the low-ω spectrum of the excitations, the boson peak (BP) 6,7 , is still an open issue.…”

Predicting alloy vibrational mode properties using lattice dynamics calculations, molecular dynamics simulations, and the virtual crystal approximation

“…(6) and (7) represents the frequency spectrum required to create a wavepacket with a well-defined wave vector and polarization. 17,36,66 For a perfect lattice, the structure factor peaks are delta functions centered at the mode frequencies, indicating that the modes are pure plane-waves (i.e., phonons). A sampling of the structure factors for the LJ argon alloys are plotted in Fig.…”

Inferring elastic properties of an fcc crystal from displacement correlations: Subspace projection and statistical artifacts

“…(x) is the Heaviside step function, which is equal to 1 when x > 0 and 0 otherwise. S( q,ω), encodes the participation of various plane waves in a normal mode of eigenfrequency ω [21]. Figures 8 and 9 show S( q,ω) plotted in the first BZ for (111) and (100) FCC patches for a set of three values of ω that are typical low, midrange, and high eigenfrequencies of G. We chose these frequencies so that the "high" frequency is roughly near the second van Hove peak in the DOS, while the "mid-" frequency is near the first van Hove peak, and the "low" frequency is lower in the DOS.…”

“…In glassy colloids it has been used to study the density of states (DOS) [9,18], the so-called Boson peak, an excess in the DOS when compared to the Debye theory, [8] and the connection between structural relaxation and low-frequency normal modes [19,20]. For colloidal crystals, the method has been used to characterize the spectrum of normal modes and DOS [7,21]. However, this wealth of information comes at a price and requires good statistical estimates for all entries of G iαjβ .…”