Yukawa Crystals Research Articles

Strong Impact of Particle Size Polydispersity on the Thermal Conductivity of Yukawa Crystals

Control of thermal transport in colloidal crystals plays an important role in modern technologies. A deeper understanding of the governing heat transport processes in various systems, such as polydisperse colloidal crystals, is required. This study shows how strongly the particle size polydispersity of a model colloidal crystal influences the thermal conductivity. The thermal conductivity of model colloidal crystals has been calculated using molecular dynamics simulations. The model crystals created by particles interacting through Yukawa (screened-Coulomb) interaction are assumed to have a face-centered cubic structure. The influence of the Debye screening length, contact potential, and particle size polydispersity on the thermal conductivity of Yukawa crystals was investigated. It was found that an increase in particle size polydispersity causes a strong—almost fivefold—decrease in the thermal conductivity of Yukawa crystals. In addition, the obtained results showed that the effect of the particle size polydispersity on reducing the thermal conductivity of Yukawa crystals is stronger than changes in values of the Debye screening length or the contact potential.

Auxeticity modifications and unit cell doubling in Yukawa fcc crystals with [001]-nanochannels filled by hard spheres

In recent years, the investigation of auxetic materials is receiving more and more attention due to their wide range of applications which follow enhancing indentation resistance, toughness, shear resistance, and other advantages of such materials. This work reports results of studies of models of auxetic metamaterials with nanoinclusions. Yukawa crystals with nanoinclusions in the form of nanochannels (NCs) in the [001] crystallographic direction, filled by hard spheres, were simulated by Monte Carlo in a wide range of pressures to determine their elastic properties. Particular attention has been devoted to the Poisson’s ratio (PR). It has been found that depending on the NCs’ type and pressure, the value of PR can vary from −0.302(12) to 1.083(14). The microscopic structures of the crystals were also examined in detail. A solid-solid phase transition in a host-guest system (the Yukawa crystal with hard spheres) was observed. Interestingly, this phase transition generates a unit cell doubling along the NCs. To localize this phase transition, apart from studies of the structure, the PR as a sensitive indicator of the phase transition was applied. In addition, it was found that the studied Yukawa systems with nanoinclusions for certain pressure values are completely non-auxetic, despite both the Yukawa and hard sphere crystals without inclusions are partially auxetic at the same conditions. This indicates that the presence of [001] NCs in the system not only can enhance auxeticity in comparison to the system without NCs but also, at some thermodynamic conditions, can lead to a completely non-auxetic behavior of the system which is partially auxetic without the NCs. Hence, one can use NCs to tune auxetic properties of crystals.

Parametric decay induced first-order phase transition in two-dimensional Yukawa crystals

The melting process of two-dimensional (2D) Yukawa crystals for dusty plasma medium induced by external perturbations has been explored using molecular dynamics simulations. A 2D monolayer of particles interacting via Yukawa pair potential is formed in the presence of an external confinement potential. The confinement potential is a combined effect of the gravitational force and an externally applied electric force, which mimics the sheath electric field in dusty plasma experiments. The response of the 2D crystalline layer to an external perturbation is investigated. It is shown that transverse surface waves are generated below a particular threshold value of initial perturbation, but the crystalline order remains. However, above a threshold value of initial disturbance, the crystalline order structure of the 2D layer breaks, and it melts. The melting process is shown to be a first-order phase transition. We have demonstrated that the nonlinear amplitude modulation of initial disturbance through the parametric decay instability is responsible for the melting. Our proposed mechanism of first-order phase transition in the context of 2D dusty plasma crystal is distinctly different from the existing theoretical models. This research can provide a deeper understanding of the experimental observations in the context of plasma crystal.

Elastic–plastic transition of compressional shocks in a perfect 2D Yukawa crystal

Molecular dynamical simulations are performed to systematically investigate the elastic–plastic transition of compressional shocks in a perfect two-dimensional Yukawa crystal. Following the tradition in the theory of elasticity, a stress tensor is used to characterize the state of stress of the simulated systems, and then the variation of the maximum shear stress in the postshock region is precisely obtained. It is found that, as the compression level gradually increases in the 2D Yukawa crystal, the maximum shear stress first increases linearly with the compressional speed until it reaches its extreme value, then decreases drastically to a much lower level. This obtained extreme value of the maximum shear stress is just at the elastic–plastic transition point, corresponding to one-half of the yield stress, which represents the ability to resist the maximum applied shear for the simulated Yukawa crystal. Our calculated Voronoi diagrams and pair correlation functions in the direction perpendicular to the shock compression further confirm this elastic–plastic transition point. It is also found that the critical compressional speed of the elastic–plastic transition point increases with the coupling parameter and decreases with the screening parameter of the 2D Yukawa crystal.

Elastic properties of Yukawa crystals

We study elastic properties of solid Yukawa systems. Elastic moduli and effective shear modulus of body-centered cubic and face-centered cubic lattices are obtained from electrostatic energies of deformed crystals. For the bcc lattice, our results are well consistent with previous calculations and improve them, while results for the fcc lattice are mostly new. We have also obtained an analytical expression of the elastic moduli for the weak polarization and constructed a convenient approximation for the higher polarization.

Phase coexistence of Yukawa liquid and bcc crystal by the Kofke integration method and a two phase approach

The present work is devoted to the investigation of the melting line of the body centered cubic Yukawa crystal. Two different methods were applied: numerical integration of the Clapeyron–Clausius equation by Kofke algorithm and study of a equilibrium two-phase system, containing the both liquid and crystal phases. The values of the widely used in practice empirical phase transition criteria were calculated on the melting line. During the melting and crystallization the density of the Yukawa ensemble changes abruptly, which makes it impossible to obtain the self-similar solution of the equations of motion of the particles. As a result, using of a couple of dimensionless parameters lead to errors when calculating the melting line. However results of this paper show that these errors are comparable with the density change, which is less than 3% in the selected range of parameters.

Absence of diagonal force constants in cubic Coulomb crystals.

The quasi-harmonic model proposes that a crystal can be modelled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss’s law shows that the ion–ion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modelled by springs. We investigate the repercussions of this observation by examining three illustrative regimes: the bare ionic, density tight-binding and density nearly-free electron models. For the bare ionic model, we demonstrate the zero elements in the force constants matrix and explain this phenomenon as a natural consequence of Poisson’s law. In the density tight-binding model, we confirm that the inclusion of localized electrons stabilizes all major crystal structures at harmonic order and we construct a phase diagram of preferred structures with respect to core and valence electron radii. In the density nearly-free electron model, we verify that the inclusion of delocalized electrons, in the form of a background jellium, is enough to counterbalance the diagonal force constants matrix from the ion–ion potential in all cases and we show that a first-order perturbation to the jellium does not have a destabilizing effect. We discuss our results in connection to Wigner crystals in condensed matter, Yukawa crystals in plasma physics, as well as the elemental solids.

A Hybrid Optimization from Two Virtual Physical Force Algorithms for Dynamic Node Deployment in WSN Applications.

With the rapid development of unmanned aerial vehicle in space exploration and national defense, large-scale wireless sensor network (WSN) became an important and effective technology. It may require highly accurate locating for the nodes in some real applications. The dynamic node topology control of a large-scale WSN in an unmanned region becomes a hot research topic recently, which helps improve the system connectivity and coverage. In this paper, a hybrid optimization based on two different virtual force algorithms inspired by the interactions among physical sensor nodes is proposed to address the self-consistent node deployment in a large-scale WSN. At the early stage, the deployment algorithm was to deploy the sensor nodes by leveraging the particle motions in dusty plasma to achieve the hexagonal topology of the so-called “Yukawa crystal”. After that, another virtual exchange force model was combined to present a hybrid optimization, which could yield perfect hexagonal topology, better network uniformity, higher coverage rate, and faster convergence speed. The influence of node position, velocity, and acceleration during the node deployment stage on the final network topology are carefully discussed for this scheme. It can aid engineers to control the network topology for a large number of wireless sensors with affordable system cost by choosing suitable parameters based on physical environments or application scenarios in the near future.

On virtual-force algorithms for coverage-optimal node deployment in mobile sensor networks via the two-dimensional Yukawa crystal

As theoretical proof has shown that a hexagonal topology can obtain maximal coverage with a fixed number of sensor nodes, node deployment for mobile sensor networks has the objective of forming a hexagonal network topology while consuming minimum energy. Using virtual-force algorithms to move initially randomly distributed nodes into a target topology is one of the widely studied methods for achieving this goal. In this work, a novel virtual-force algorithm based on physical laws in a dusty plasma system (i.e. VFA-DP) was applied within a mobile sensor network deployment scenario. The VFA-DP force has a central attracting force which can provide a screening effect via exponential decay. Here, to evaluate how perfect the final grids become from virtual-force algorithms, we introduce a performance metric based on the pair correlation function in a crystalline structure. Via simulation studies, we determined that the topology resulting from the VFA-DP is much closer to a hexagon. The analysis also indicated that the VFA-DP converges faster than another virtual-force algorithm based on the Lennard-Jones potential (VFA-LJ), resulting in lower communication-related energy costs in real deployment scenarios. The method developed in this article is derived from studies of crystalline structure from condensed matter physics and shows clear evidence of when the regular lattice is ready. It will provide some guidance for engineering by aiding deployment in complex geometric areas or those recovering from disaster.

Properties of Yukawa Crystals and Liquid under Phase Equilibrium Conditions

The equilibrium properties of a system of particles whose interaction is described by the Yukawa potential are studied. Liquids and crystals with bcc and fcc lattices near the melting line are considered. The latent heat of melting for crystals and the density change during the phase transition are calculated. We analyze the temperature dependences of the thermodynamic quantities near the melting line and calculate the thermal expansion coefficient and the heat capacity at constant pressure. We show that the state of a Yukawa system cannot be uniquely defined by a pair of dimensionless quantities, the temperature and the pressure, which use the interaction potential parameters (the product of the charges and the screening length) as scales. In particular, the position of the melting line is ambiguously determined on a two-parameter phase diagram constructed in dimensionless quantities.

Inhomogeneity of a harmonically confined Yukawa system

A crystalline system of strongly screened Yukawa particles in a harmonic trap is under consideration. We show that structural and dynamic properties of confined Yukawa crystals are fundamentally nonuniform. The average interparticle distance, thermal oscillation amplitude, and Lindemann and inverse coupling parameters are found to increase with the radial distance from the center of a structure. We verify the inhomogeneity of these parameters by molecular dynamics simulations and the analytical approach. Analytical formulas are in good agreement with a dusty plasma experiment. The obtained results might be important for the theory of crystal formation and phase transitions in dusty plasmas, colloidal suspensions, and Coulomb crystals.

Shear modulus of two-dimensional Yukawa or dusty-plasma solids obtained from the viscoelasticity in the liquid state.

Langevin dynamical simulations of two-dimensional (2D) Yukawa liquids are performed to investigate the shear modulus of 2D solid dusty plasmas. Using the known transverse sound speeds, we obtain a theoretical expression of the shear modulus of 2D Yukawa crystals as a function of the screening parameter κ, which can be used as the candidate of their shear modulus. The shear relaxation modulus G(t) of 2D Yukawa liquids is calculated from the shear stress autocorrelation function, consisting of the kinetic, potential, and cross portions. Due to their viscoelasticity, 2D Yukawa liquids exhibit the typical elastic property when the time duration is much less than the Maxwell relaxation time. As a result, the infinite frequency shear modulus G_{∞}, i.e., the shear relaxation modulus G(t) when t=0, of a 2D Yukawa liquid should be related to the shear modulus of the corresponding quenched 2D Yukawa solid (with the same κ value), with all particles suddenly frozen at their locations of the liquid state. It is found that the potential portion of the infinite frequency shear modulus for 2D Yukawa liquids at any temperature well agrees with the shear modulus of 2D Yukawa crystals with the same κ obtained from the transverse sound speeds. Thus, we find that the shear modulus of 2D Yukawa solids can be obtained from the motion of individual particles of the corresponding Yukawa liquids using their viscoelastic property.

Electrostatic energy and phonon properties of Yukawa crystals

We study electrostatic and phonon properties of Yukawa crystals. It is shown that in the harmonic approximation these systems which are used in the theory of dusty plasma can be described analytically by the model from the theory of neutron stars and white dwarfs. Using this approximation, we consider properties of body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal-close-packed (hcp), and ${\mathrm{MgB}}_{2}$ lattices. Studies of ${\mathrm{MgB}}_{2}$ and hcp lattices in the context of Yukawa systems are lacking. It is shown that they never possess the smallest potential energy and the phase diagram of stable Yukawa crystals contains bcc and fcc lattices only. However, corrections to the charge density proportional to ${(\ensuremath{\kappa}a)}^{4}$ can noticeably change the structural diagram of Yukawa systems. The analytical model developed also allows us to describe low-temperature effects where numerical simulations are difficult.

Selective enhancement of auxeticity through changing a diameter of nanochannels in Yukawa systems

A new effect of selective enhancement of auxeticity through the changes of nanochannels’ diameter in Yukawa systems is reported. Elastic properties of the model of Yukawa crystals with narrow nanochannels in the [001] crystallographic direction have been studied by Monte Carlo simulations in the isobaric–isothermal ensemble. It has been found that the choice of nanochannels’ diameter allows one to decrease the Poissons ratio value of the system in one of two selected crystallographic directions. The value of Poisson’s ratio in those directions can be changed in a wide range, e.g. from −0.061(9) to −0.625(44) in the -direction, depending on the nanochannels’ type and the Debye screening length.

Auxeticity of Yukawa Systems with Nanolayers in the (111) Crystallographic Plane.

Elastic properties of model crystalline systems, in which the particles interact via the hard potential (infinite when any particles overlap and zero otherwise) and the hard-core repulsive Yukawa interaction, were determined by Monte Carlo simulations. The influence of structural modifications, in the form of periodic nanolayers being perpendicular to the crystallographic axis [111], on auxetic properties of the crystal was investigated. It has been shown that the hard sphere nanolayers introduced into Yukawa crystals allow one to control the elastic properties of the system. It has been also found that the introduction of the Yukawa monolayers to the hard sphere crystal induces auxeticity in the -direction, while maintaining the negative Poisson’s ratio in the -direction, thus expanding the partial auxeticity of the system to an additional important crystallographic direction.

Auxeticity enhancement due to size polydispersity in fcc crystals of hard-core repulsive Yukawa particles.

The Poisson's ratio of the fcc hard-core repulsive Yukawa crystals with size polydispersity was determined by Monte Carlo simulations in the isothermal-isobaric ensemble. The effect of size polydispersity on the auxetic properties of Yukawa crystals has been studied. It has been found that an increase of particle size polydispersity causes a decrease of the Poisson's ratio in auxetic directions as well as appearance of a negative Poisson's ratio in formerly non-auxetic directions. A measure of auxeticity was introduced to estimate quantitatively an enhancement of auxetic properties in polydisperse Yukawa crystals. The proposed measure of auxeticity can be applied to appraise the auxeticity of any studied system.

Partial auxeticity induced by nanoslits in the Yukawa crystal

Monte Carlo simulations in the isobaric–isothermal ensemble with variable shape of the periodic box were used to investigate Poisson's ratios of the hard‐core repulsive Yukawa crystals with periodically distributed nanoslits. Each nanoslit, oriented perpendicularly to the crystallographic direction [010], was filled by a monolayer of hard spheres. It is shown that presence of the nanoslits leads to negative Poisson's ratio, as low as –0.57(2), in the [100][001]‐direction. This direction is not auxetic in the pure Yukawa crystal, i.e. shows positive Poisson's ratio, equal to 0.43(1).

Enhanced auxeticity in Yukawa systems due to introduction of nanochannels in -direction

A new approach to search for materials with auxetic properties by modifying structures of solids at molecular level has been proposed. The analysis of elastic properties of the face-centered cubic Yukawa crystals with very narrow nanochannels in the [001] crystallographic direction using Monte Carlo simulations in the isothermal–isobaric ensemble has been done. An influence of the size of nanochannels on the value of Poisson’s ratio in main crystallographic directions has been studied. It has been shown that the insertion of nanochannels in the system causes a decrease of the Poisson’s ratio in the direction from –0.15(2) to –0.29(3). That means an amplification of auxetity in the studied system twice as compared to the system without nanochannels.

Pair correlations in classical crystals: The shortest-graph method.

The shortest-graph method is applied to calculate the pair correlation functions of crystals. The method is based on the representation of individual correlation peaks by the Gaussian functions, summed along the shortest graph connecting the two given points. The analytical expressions for the Gaussian parameters are derived for two- and three-dimensional crystals. The obtained results are compared with the pair correlation functions deduced from the molecular dynamics simulations of Yukawa, inverse-power law, Weeks-Chandler-Andersen, and Lennard-Jones crystals. By calculating the Helmholtz free energy, it is shown that the method is particularly accurate for soft interparticle interactions and for low temperatures, i.e., when the anharmonicity effects are insignificant. The accuracy of the method is further demonstrated by deriving the solid-solid transition line for Yukawa crystals, and the compressibility for inverse-power law crystals.

Ion-wake-induced anomaly of dust lattice mode in the presence of an external magnetic field

We report a theoretical investigation of the dust lattice (DL) mode in two-dimensional Yukawa crystals in the presence of asymmetric ion flow and an external magnetic field perpendicular to the crystal plane. Two mutually perpendicular modes are found to be coupled due to Lorentz force. Interaction among the dust grains along the vertical direction of ion flow is strongly affected due to the formation of an ion wake. This causes anisotropy in interaction strength along two mutually perpendicular directions. Both hybrid modes are studied as characteristics of different ion flow speeds and magnetic field strengths. The study shows a fluctuation in DL mode frequency driven by the strength of the particle-wake interaction. The effect of ion flow on polarization of the hybrid wave amplitudes is discussed in detail. Results show a possible mechanism of anomalous phase transition in dusty plasma.