On the coarse-grained density and compressibility of non-ideal 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. It also cannot be obtained from the static structure factor measured in a scattering experiment. 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 low-temperature phase diagram.

arXiv comment20 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1206.6183

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Cited by in corpus (12)

• Noether's Theorem in Statistical Mechanics
• Force density functional theory in- and out-of-equilibrium
• Noether-Constrained Correlations in Equilibrium Liquids
• Microscopic approach to the macrodynamics of matter with broken symmetries
• Nonequilibrium statistical mechanics of crystals
• The direct correlation function of a crystalline solid
• Microscopic density-functional approach to nonlinear elasticity theory
• Active crystallization from power functional theory
• On the stress overshoot in cluster crystals under shear
• Continuum mechanics for the elastic properties of crystals: Microscopic approach based on projection-operator formalism
• Elasticity in crystals with high density of local defects : insights from ultra-soft colloids
• On the yielding of a defect-rich model crystal under shear: insights from molecular dynamics simulations