Random Packing Of Hard Spheres Research Articles

Folded network and structural transition in molten tin

The fundamental relationships between the structure and properties of liquids are far from being well understood. For instance, the structural origins of many liquid anomalies still remain unclear, but liquid-liquid transitions (LLT) are believed to hold a key. However, experimental demonstrations of LLTs have been rather challenging. Here, we report experimental and theoretical evidence of a second-order-like LLT in molten tin, one which favors a percolating covalent bond network at high temperatures. The observed structural transition originates from the fluctuating metallic/covalent behavior of atomic bonding, and consequently a new paradigm of liquid structure emerges. The liquid structure, described in the form of a folded network, bridges two well-established structural models for disordered systems, i.e., the random packing of hard-spheres and a continuous random network, offering a large structural midground for liquids and glasses. Our findings provide an unparalleled physical picture of the atomic arrangement for a plethora of liquids, shedding light on the thermodynamic and dynamic anomalies of liquids but also entailing far-reaching implications for studying liquid polyamorphism and dynamical transitions in liquids.

Structural Characteristics of a Small Group of Fixed Particles and the Maximum Density of a Random Packing of Hard Spheres

Structural Characteristics of a Small Group of Fixed Particles and the Maximum Density of a Random Packing of Hard Spheres

Local constriction around minor elements in Al86Ni7X1Y6 metallic glass (X: Ag, Au, Pt)

The local structure around Ag, Au and Pt atoms in Al86Ni7X1Y6 (X: Ag, Au, Pt) bulk amorphous alloy was studied by X-ray absorption spectroscopy. Strong bond-shortening and a concomitant reduction of Al nearest neighbors around Ag, Au and Pt atoms compared to a dense random packing of hard spheres (based on the metallic radii of the elements) were observed suggesting strong covalent (Ag, Au, Pt) — Al bonds. This is ascribed to charge transfer from first-shell Al atoms to the X atoms resulting in s–p hybridization of the bonds. This causes opposite changes of the effective radii of X and Al atoms. Our results suggest that models using the metallic radii of elements are not appropriate to describe Al-based metallic glasses which contain Ag, Au or Pt atoms.

Impact of microstructure on the effective diffusivity in random packings of hard spheres

We present results of computer simulations of the effective diffusion coefficient in bulk random packings of hard monosized spheres with solid volume fraction between 0.54 (random-loose packing) and 0.634 (maximally random jammed). Six types of sphere packings were generated with different protocols and parameters resulting in a systematically varied degree of microstructural heterogeneity. The packing morphology is qualitatively characterized by statistical analyses of Voronoi cells obtained from spatial tessellation of the packing space. Diffusive transport of point-like tracers in the pore space of the packings was simulated with a random-walking particle-tracking technique. Our results indicate that the effective transport characteristics of the random sphere packings are not fully defined from the solid volume fraction but also depend on the packing microstructure. For the first time, we compared (i) the values of the effective diffusion coefficient Deff simulated in packings with different morphologies, and (ii) the corresponding values of Deff obtained from an approximate analytical formula involving the three-point microstructural parameter ζ2. This analysis reveals that this approximation involving ζ2 clearly reflects key morphological specificity of individual sphere packings and provides a sufficiently accurate estimate of the effective diffusion coefficient.

Structural Study of Zr<SUB>50</SUB>Cu<SUB>50</SUB> Amorphous Alloy by Anomalous X-ray Scattering Coupled with Reverse Monte-Carlo Simulation

Anomalous X-ray scattering (AXS) analysis was applied for the structural analysis of a rapidly quenched Zr50Cu50 amorphous alloy. The present AXS analysis provided the environmental structural information round Cu and Zr, and the subsequent reverse Monte Carlo (RMC) simulation allowed us to obtain three partial pair distribution functions together with a three-dimensional structural model. The Voronoi polyhedral analysis of the nearest-neighbor region confirms that the structural features are similar to those of the dense random packing of hard spheres (DRPHS) model. The chemical oscillatory structure composed of alternating Cu-rich and Zr-rich coordination shells was realized in the middle range, up to 0.8 nm. The shell structure is suggested to be one of the fundamental structural features of medium-range ordering in the Zr50Cu50 amorphous alloy. [doi:10.2320/matertrans.MAW201016]

Local organization and atomic clustering in multicomponent amorphous steels

The characteristics of atom packing in multicomponent metallic alloys with distinct short- and mediumrange order SMRO are notoriously difficult to provide as the local structure is made up of multiple overlapping pair correlations. In the case of binary glasses, several cluster models have been proposed that can describe the SMRO well going beyond models of dense random packing of hard spheres. By combining the pair density function analysis of neutron-diffraction data and modeling using ab initio computational techniques, the tendency for local atomic clustering is investigated and properties of multicomponent bulk Fe78x-yTMxREyC22zBz amorphous alloys transition metal TM and rare earth RE are studied going beyond simple binary systems. The results are relevant to most bulk metallic glass forming alloys with more than one kind of solute ion.

A phase diagram for jammed matter

The problem of finding the most efficient way to pack spheres has a long history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal. Apart from its mathematical interest, the problem has practical relevance in a wide range of fields, from granular processing to fruit packing. There are currently numerous experiments showing that the loosest way to pack spheres (random loose packing) gives a density of approximately 55 per cent. On the other hand, the most compact way to pack spheres (random close packing) results in a maximum density of approximately 64 per cent. Although these values seem to be robust, there is as yet no physical interpretation for them. Here we present a statistical description of jammed states in which random close packing can be interpreted as the ground state of the ensemble of jammed matter. Our approach demonstrates that random packings of hard spheres in three dimensions cannot exceed a density limit of approximately 63.4 per cent. We construct a phase diagram that provides a unified view of the hard-sphere packing problem and illuminates various data, including the random-loose-packed state.

Statistical modeling of the geometrical structure of the system of artificial air pores in autoclaved aerated concrete

The geometrical structure of the system of artificial air pores in autoclaved concrete is studied, based on samples from laboratory and industry. The single pores are approximated by spheres, the corresponding radius distribution is determined by means of stereological methods. The resulting distribution is not a classical standard distribution, but instead requires a mixture of three components, one of them Gaussian. The pore system as a whole is approximated by the penetrable-concentric-shell or “cherry-pit” model, which consists of spheres that are partially penetrable. The corresponding hard cores form a random packing of hard spheres. The goodness-of-fit of the model is tested by means of information available from planar sections: the section profile radius distribution and the pair correlation function of profile centers.

Small-angle scattering investigations of cobalt-ferrofluids using polarised neutrons

Combining contrast variation using polarised neutrons and various H/ D mixtures of solvents allowed different structural units in Co-ferrofluids to be identified by small-angle scattering. In diluted liquids, the magnetic core behaves as a non-interacting single-domain. The core is encapsulated by a shell of surfactant molecules which was found to be impenetrable for the solvent. In more concentrated samples aggregation appears in an external magnetic field which is described by a densely random packing of hard spheres.

Voronoï tessellation reveals the condensed matter character of folded proteins.

The packing geometry of amino acids in folded proteins is analyzed via a modified Voronoï tessellation method which distinguishes bulk and surface. From a statistical analysis of the Voronoï cells over 40 representative proteins, it appears that the packings are in average similar to random packings of hard spheres encountered in condensed matter physics, with a quite strong fivefold local symmetry. Moreover, the statistics permits one to establish a classification of amino acids in terms of increasing propensity to be buried in agreement with what is known from chemical considerations.

The structure and properties of sputter-deposited Co-Si alloy thinfilms

The structural and magnetic properties of Co1-xSix alloythin films in the composition range 0 < x < 0.9 are investigated. Thesputter-deposited thin films show a single phase hcp structure up to x~0.25. For Si compositions beyond this, but with x < 0.6, electrondiffraction implies a single amorphous phase with features in thediffraction patterns typical of a dense random packing of hard spheres(DHRPS). These alloys are ferromagnetic. For 0.6 < x < 0.8 additionaldiffraction maxima are observed that suggest the formation of at least twoamorphous phases. Magnetic measurements suggest the presence of thermallyunstable magnetic particles. For x>0.7-0.8, Co atoms are incorporated inthe covalent random network structure of Si and paramagnetism is observed.A correlation of the PEELS Co L2/L3 edge loss intensityratio with the effective Co moment suggests that the magnetic changes couldarise from differing local environments as Si is added, rather than achange in the particle size. Compositional mapping shows that some of thefilms have a composition that is not spatially uniform.

Elastic Properties of Tenuous Networks

A disordered cubic network of springs is introduced as a model of 3-dimensional tenuous networks. It presents an unusual elastic behavior since it does not resist shear but only shear coupled to compression by a type of bending rigidity. Numerical simulations of the elastic behavior of random packings of hard spheres and of disordered cubic networks show a similar stress distribution, which can be partially understood by considering the appearance of buckling.

A model for high-frequency acoustic backscatter from gas bubbles in sandy sediments at shallow grazing angles

A model for acoustic backscatter from trapped bubbles in sandy sediments was developed. The model combines a Biot acoustic penetration model with a resonance scattering mechanism from trapped bubbles. The bubble size distribution is assumed to mirror the size distribution of the fluid pores that exist between sand grains. An estimate of the pore size distribution is constructed from the grain size distribution, based on the known pore structure between dense random packings of hard spheres. The principle of acoustic reciprocity is employed to compute backscattered acoustic pressure in terms of the incident pressure and the scattering cross section of a bubble distribution. The model is applied to data from experiments recently taken at sea. It is concluded that trapped gas is often a likely cause of observed backscatter from sandy sediments. Very small amounts of gas appear to be sufficient to produce significant backscatter.

Nanostructured amorphous SiAu alloys — Structure and atomic correlations

Nanostructured amorphous Si 1− x Au x alloys ( 0.1 ⪕ x Au ⪕ 0.35 ) were produced by an inert gas condensation and in situ consolidation technique. Small-angle neutron scattering (SANS), density measurements and wide-angle neutron scattering (WANS) were employed to characterize the microstructure and local atomic order. The SANS results are interpreted in terms of a microstructure which consists of nanometre-sized amorphous grains embedded in a matrix of lower density, formed by grain boundaries and free volumes. The relative densities depend on the average particle size, but not on the alloy composition. In all samples, the SANS intensity decreases at low Q according to a power law − Q −3.37, which is attributed to a surface fractal structure of dimension D s = 2.63. WANS reveals two contributions: (a) a continuously decreasing part resulting from the presence of about 10 at.% hydrogen, and (b) a modulation of the intensity as a function of the scattering angle, characteristic of amorphous material. The total pair correlation function g( R) presents maxima corresponding to the first and second atomic neighbours. Nanostructured amorphous SiAu alloys exhibit a reduced short-range order compared with systems with dense random packing of hard spheres, e.g. metallic glasses, or continuous random network structures, e.g. covalent systems.

On the determination of the structure of metallic glasses by reverse Monte Carlo simulation: comparison with hard sphere Monte Carlo results

Reverse Monte Carlo (RMC) simulation has recently been used for modelling the atomic level structure of several amorphous metallic alloys. Using the particle configuraitons that were provided by the RMC calculations, characteristics of the short-range structure were evaluated. Standard (Metropolis) Monte Carlo simulations on hard sphere systems mimicking three of the metallic glassy materials modelled by RMC have also been carried out. Particle configurations obtained by these two methods were compared. It was shown that dense random packing of hard spheres is most similar to “real” metallic glassy structures when the chemical nature of the components differs the least.

Porosity and microstructure of polydisperse random packing of hard spheres

Abstract The statistical theory of porosity of polydisperse random packing of hard spheres has been derived. The relationship of porosity and average gaps between spheres has been obtained. The nonmonotonic behavior of mean values of gaps between different types of spheres as functions of packing composition has been derived for the bidisperse systems.

Computer simulation of random packing of hard spheres

A computer simulation which can randomly pack hard spheres for gravitationally stable lattices ranging from random loose packing to random close packing is described. The algorithm tests a model for random packing which proposes that the characteristics of a lattice are determined by its local interstices and that the shape of these interstices is formed by bridging and the angular separation of contacting spheres. The model predicts that random packings form a quadrilateral in the packing density/mean coordination plane with packing densities ranging from 0.509 to 0.638 and mean coordination numbers ranging from 4.4 to 5.9.

Dipolar Energy Transfer and Knudsen Diffusion Inside Disordered Porous Media: Interfacial Geometry and Chord Distributions.

AbstractThe interfacial geometry of a disordered porous medium strongly influences Knudsen diffusion of gases and interfacial dipolar energy transfer. Some interesting comparison can be made between these two transport processes, involving statistical properties of chords belonging either to the solid matrix or to the pore network. A quantitative analysis of these two mechanisms is proposed, based on a chord distribution model. In a first part, we discuss how chord distribution functions contribute to the stastistical characterization of a porous medium. We show that a direct connection between imaging techniques and small angle scattering provides, in many cases, a reliable description of theses functions. In a second part, interfacial direct energy transfer is analyzed. This one step excitation transfer strongly relies on the interfacial autocorrelation function φ2s(r). An analytic expression of φ2s(r) is given and theoretical predictions compared with available experiments. In a third part and following the seminal work of Derjaguin on the Knudsen diffusion, we critically examine how the self diffusion coefficient can be related to the two first moments of the pore chord distribution. A direct comparison with experimental results and numerical simulations is presented in the case of a model porous medium: the random packing of hard spheres. Finally, we analyze a trapping reaction where an excited gas molecule, diffusing in the Knudsen regime, relaxes primarily by wall effects. We show how the chord distribution of the pore network permits to compute the survival probability of the tagged molecules. Two situations are more closely analyzed: the strong and the very weak wall quenching efficiency.

Atomistic simulation of liquid-vapour coexistence: binary mixtures

Liquid-vapour coexistence and surface tension of binary mixtures is studied by Monte Carlo simulation. Both mixtures with a difference in the size parameters and mixtures with a difference in the energy parameters of the Lennard-Jones potential are investigated. The results for the surface tension and the coexisting liquid density are compared with the predictions of one-fluid models. The van der Waals model is found to be quite accurate, except in cases of strong interfacial adsorption. An interpretation of this accuracy is given, by developing a one-fluid model based on random packing of hard spheres. It is found that the predictions of this random-packing model are close to predictions of the van der Waals one-fluid model. The authors also present a simulation of the argon-krypton liquid-vapour interface.

Geometrical properties of a random packing of hard spheres

Some geometrical properties of a random packing of identical hard spheres generated by a ballistic deposition model with complete restructuring are investigated. The length distribution of chords in the space between spheres is numerically calculated and is shown to have an exponential form (up to chord lengths of about five diameters) as conjectured by Dixmier. The anisotropic properties of the packing are numerically investigated and are shown to modify the Dixmier relation between the packing fraction and the average coordination number.