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

Abstract

We compute the effective dispersion and vibrational density of states (DOS) of two-dimensional subregions of three-dimensional face-centered-cubic crystals using both a direct projection-inversion technique and a Monte Carlo simulation based on a common underlying Hamiltonian. We study both a (111) and (100) plane. We show that for any given direction of wave vector, both (111) and (100) show an anomalous ω(2)∼q regime at low q where ω(2) is the energy associated with the given mode and q is its wave number. The ω(2)∼q scaling should be expected to give rise to an anomalous DOS, D(ω), at low ω: D(ω)∼ω(3) rather than the conventional Debye result: D(ω)∼ω(2). The DOS for (100) looks to be consistent with D(ω)∼ω(3), while (111) shows something closer to the conventional Debye result at the smallest frequencies. In addition to the direct projection-inversion calculation, we perform Monte Carlo simulations to study the effects of finite sampling statistics. We show that finite sampling artifacts act as an effective disorder and bias D(ω), giving a behavior closer to D(ω)∼ω(2) than D(ω)∼ω(3). These results should have an important impact on the interpretation of recent studies of colloidal solids where the two-point displacement correlations can be obtained directly in real-space via microscopy.

Vibrational properties of quasi-two-dimensional colloidal glasses with varying interparticle attraction

“…We calculate vibrational modes of the colloidal samples from particle trajectories [27,28,54]. To this end, we follow the procedure originally suggested with some corrections developed later that improve upon these procedures; all of these techniques and corrections are described in detail in previous work [22,27,28,[54][55][56][57][58][59][60][61][62]. Briefly, we first calculate the timeaveraged covariance matrix <C ij = u i (t)u j (t)> t , where u i (t) are particle displacements from their average positions.…”

Physics in ordered and disordered colloidal matter composed of poly(N-isopropylacrylamide) microgel particles

“…[252,257]. The use of a true 2D monolayer of particles effectively eliminated a whole host of ambiguities that arise when one attempts to draw conclusions about the phonons in a 3D sample using data taken from a 2D slice [253,255,259,260]. In the work of Chen et al [67], a binary mixture of PNIPAM particles with diameter ratio ≈1.4 (to frustrate crystallization) was loaded into the sample cell (i.e.…”