Coarse-grained density and compressibility of nonideal crystals: General theory and an application to cluster crystals

Abstract

The isothermal compressibility of a general crystal is analyzed within classical density functional theory. Our approach can be used for homogeneous and unstrained crystals containing an arbitrarily high density of local defects. We start by coarse-graining the microscopic particle density and then obtain the long wavelength limits of the correlation functions of elasticity theory and the thermodynamic derivatives. We explicitly show that the long wavelength limit of the microscopic density correlation function differs from the isothermal compressibility. We apply our theory to crystals consisting of soft particles which can multiply occupy lattice sites ('cluster crystals'). The multiple occupancy results in a strong local disorder over an extended range of temperatures. We determine the cluster crystals' isothermal compressibility, the fluctuations of the lattice occupation numbers and their correlation functions, and the dispersion relations. We also discuss their lowtemperature phase diagram.

Chemomechanical equilibrium at the interface between a simple elastic solid and its liquid phase

“…13. Fuchs and coworkers have made significant progress towards this end for the case of crystal hydrodynamics 40,41 . This concerns the problem raised by MPP macroscopic theory mentioned earlier 26,27 .…”

“…Fuchs et al designed a deterministic graining procedure expressing these quantities in terms of instantaneous atom position. The advantage of defining hydrodynamic field variables by a deterministic coarse graining scheme is that these fluctuations of these quantities can be analyzed by the methods of statistical mechanics and related to microscopic correlation functions 41 . The coarse graining scheme of Ref.…”

On the stress overshoot in cluster crystals under shear

“…The bulk modulus of cluster crystals, studied via density functional theory and Monte Carlo simulations was discussed by Mladek et al [32]. In later years, these results for the bulk modulus were compared with the related data obtained from the dispersion relations for cluster crystals by Häring et al [14].…”

“…As expected, the diffusion coefficient exhibits the Arrhenius behaviour confirming that the hoping of particles is an activated process. This particular type of diffusion of particles makes cluster crystals an appropriate model system to study the mechanical response of defect-rich crystals [14], notably the effect of the defect-dynamics on the yielding of crystalline solids, an area which is less explored in the recently developed theories to understand the deformation of crystalline solids [15,16].…”

Self assembling cluster crystals from DNA based dendritic nanostructures

“…In usual crystals, the lattice constant a and the particle concentration c obey the proportionality a ∝ c −1/3 , dictated by the condition that the (conventional) unit cell be populated by a fixed number of particles determined by the lattice geometry. Cluster crystals, a newer concept, are unconventional states of matter whose lattice sites are occupied by clusters of fully or partially overlapping particles rather than single ones 1 – 3 , 6 – 8 , 11 , 12 . In these states, the number of overlapping particles within a cluster, the lattice-site occupancy N occ , is a fluctuating quantity, with its expectation value scaling with concentration as N occ ∝ c and thus resulting in a concentration-independent lattice constant, the latter being the salient structural characteristic of both cluster crystals 1 – 3 and cluster quasicrystals 13 , 14 .…”