Fractal structure of fullerite

We have obtained macroscopic fractal aggregates of fullerite ranging in size from 100 to 400 μm. The fractal structure of fullerite is formed by microscopic (30–100 nm) fullerite crystals in the presence of a temperature gradient under conditions of diffusion-limited aggregation. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 684–685 (10 May 1998)     

Simulation of the formation of porous-silicon structures

The formation of porous silicon is investigated by the Monte Carlo method in a model that takes account of the nonuniformity of the charge distribution over the silicon-electrolyte interface, hole diffusion, generation, and recombination processes, and size quantization. The structures obtained in a computer simulation for various doping levels of the crystalline substrate, temperatures, HF concentrations, and anode current densities are presented. Analysis of nanoporous structures shows that the porosity depends on the depth and reveals the presence of a fractal dimensionality on scales of less than 10 nm. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 685–690 (10 May 1997)     

Structure, internal friction, and Young’s modulus of fractal carbon deposits

We have observed that carbon deposits obtained by atomizing graphite in an electric arc in an atmosphere of argon and helium exhibit porosity and possess fractal structure. The results of measurements of the internal friction Q ⁻¹ and the effective Young’s modulus E as a function of temperature are presented. Data on the resistivity, density, and microhardness of the carbon deposits are presented. A possible mechanism for formation of fractal structures in carbon deposits is discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 584–586 (March 1998)     

Copper nanoclusters in amorphous hydrogenated carbon

A study of the geometric characteristics of copper nanoclusters incorporated in an amorphous hydrogenated carbon matrix is reported. It makes use of small-angle x-ray scattering and transmission electron microscopy (100 keV). The fractal dimension and nanocluster diameter have been determined from the x-ray scattering indicatrix for different copper concentrations. TEM images of copper nanoclusters have been analyzed, and a cluster distribution function in size constructed. The shape of the distribution function is discussed in terms of the theory of nucleation of a new phase. Fiz. Tverd. Tela (St. Petersburg) 40, 568–572 (March 1998)     

Manifestation of glass-crack fractal geometry in Raman spectra

A Raman spectroscopic investigation of the fractal structure on the surface of cracks of different size scales in glassy SiO₂ is reported. A study was made of the crack surface and of the distorted layer formed after grinding and polishing and comminution. The parameters of the fractal structure thus found reflect the properties of the material and the crack nature; namely, fractal dimension is of greater importance for more compact materials, and the geometric size of fractal units (i.e., the size in real space) correlates with crack dimensions. Fiz. Tverd. Tela (St. Petersburg) 41, 1030–1034 (June 1999)     

Cluster structure and superlattices in Co and Fe films

The process of dendritic crystallization of Co and Fe films is investigated. Electron-diffraction methods show that fractal growth of dendrites in Co and Fe films proceeds by multiple twinning of the elements of a nanostructure consisting of different clusters with close-packing. The formation of superstructures is explained by a shell model of a cluster structure forming nanocrystallites. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 12, 872–875 (25 June 1997)     

Formation and magnetic properties of fractal aggregates of cobalt

Macroscopic fractal aggregates of cobalt are obtained by thermal evaporation of cobalt metal in an argon atmosphere and subsequent deposition on a silicon substrate heated to 1000 K. It is established that the fractal structure is formed by diffusion-limited aggregation of cobalt particles. The macroscopic fractal cobalt aggregates are ferromagnetic. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 8, 556–558 (25 October 1997)     

Statistical theory of the diffusion of a passive tracer in a random velocity field

A passive tracer on the surface of an incompressible liquid behaves like a tracer in two-dimensional compressible flows, whose characteristic feature is the formation of cluster structures, i.e., compact regions of increased density surrounded by vast low-density regions. The cluster formation dynamics are studied, and statistical spatiotemporal characteristics of the density fields, which faithfully reflect the properties of the cluster structures, are calculated. Zh. éksp. Teor. Fiz. 111, 1297–1313 (April 1997)     

Production of fullerenes in gas discharge plasmas. I. Kinetics of fullerene formation from polycyclic structures

A model is proposed for the formation of fullerenes from three-ring structures. It is shown that under arc discharge conditions, fullerenes are more efficiently formed through the capture of C₂ molecules from the surrounding space by a growing cluster. A system of equations is written down for calculating the kinetics of fullerene structure formation under these assumptions and is then used in some calculations. Zh. Tekh. Fiz. 69, 104–109 (September 1999)     

Synthesis, structure, and dielectric properties of KH2PO4 fractal aggregates

Macroscopic fractal aggregates of KH₂PH₄ (KDP) measuring up to 500 μm have been obtained. The fractal structure forms as a result of the precipitation of KDP particles from a supersaturated aqueous solution in the presence of a temperature gradient followed by a diffusioncontrolled mechanism of aggregation. The electron-microscopic analysis performed has shown that the fractals are formed predominantly from crystallites of the tetragonal modification measuring ∼1 μm. The dielectric constant (ɛ) of fractal KH₂PO₄ has been measured in the temperature range 80–300 K. A characteristic anomaly has been discovered on the ɛ(T) curve in the vicinity of 122 K, which attests to a ferroelectric phase transition. The absolute value of ɛ is significantly smaller than the components ɛ ₁₁ and ɛ ₃₃ for KH₂PO₄. Fiz. Tverd. Tela (St. Petersburg) 41, 2059–2061 (November 1999)     

Diagnostics of two-dimensional fractal structures using scanning coherent beams

A method of studying two-dimensional random structures such as amplitude screens with fractal properties using scanning focused and wide collimated beams is discussed. An analysis is made of the interrelation between the parameters of the structure functions of the intensity fluctuations detected at a fixed observation point and the structural characteristics of the particular screens. Results of experimental investigations of model samples of random amplitude screens with fractal properties are presented. Zh. Tekh. Fiz. 67, 101–112 (November 1997)     

Mechanisms for long-range forces in the “three atoms+electron” system

The Born-Oppenheimer approximation is used to obtain an equation for the effective interaction of three atoms bound by a single electron. For low binding energies long-range forces arise between the atoms in an “electron + atom pair” that lead to bound states when the size of the three-atom cluster is several tens of angstroms. A system made up of alkali metal atoms is considered as an example. Zh. éksp. Teor. Fiz. 111, 1229–1235 (April 1997)     

Lagrange formalism for particles moving in a space of fractal dimension

Analogs of the Lagrange equation for particles evolving in a space of fractal dimension are obtained. Two cases are considered: 1) when the space is formed by a set of material points (a so-called fractal continuum), and 2) when the space is a true fractal. In the latter case the fractional integrodifferential formalism is utilized, and a new principle for devising a fractal theory, viz., a generalized principle of least action, is proposed and used to obtain the corresponding Lagrange equation. The Lagrangians for a free particle and a closed system of interacting particles moving in a fractal continuum are derived. Zh. Tekh. Fiz. 68, 7–11 (February 1990)     

Electron-beam-induced fluorescence of carbon dioxide clusters. II. Molecular beam with clusters

The fluorescence of CO₂ clusters excited by an electron beam in a molecular beam formed from a free jet expansion of carbon dioxide is investigated. Data on the fluorescence of the clusters are obtained by comparing the electron-beam-induced fluorescence with the signal appearing in an electronic-fluorescence detector as a result of reflection of the cluster beam from an obstacle placed after the electron beam, as well as with the intensity of the cluster beam. It is established that, unlike a jet expansion, for CO₂ clusters in a molecular beam the fluorescence yield from a cluster decreases significantly with increasing cluster size and is very small for clusters of large size. It is concluded on the basis of the results from an investigation of the fluorescence of CO₂ clusters that the electron-beam-induced fluorescence technique can be used for measurements in molecular beams with CO₂ clusters. Zh. Tekh. Fiz. 67, 63–71 (July 1997)     

MINDO/3 calculation of the electronic structure of silicon nitride

The electronic structure of silicon nitride has been calculated by the semiempirical quantumchemical method MINDO/3 in the cluster approximation. The effect of cluster size and of boundary conditions on the partial density of one-electron states is analyzed. The results of the calculation are compared with experimental data on amorphous silicon nitride. The origin of a peak in the upper part of the valence band, which is seen in the SiL2,3 spectrum but not reproduced in the calculations is discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 1342–1347 (August 1997)     

Fractal structure of ultradisperse-diamond clusters

Ultradisperse-diamond clusters are shown to be fractal objects, and the character of variation of the fractal dimension in the course of the diamond-graphite phase transition under annealing in an inert atmosphere is studied. Fiz. Tverd. Tela (St. Petersburg) 40, 776–780 (April 1998)     

Two-component model for the growth of porous subsurface layers

This paper studies a kinetic model that describes the interaction of two fluctuating densities. The model makes it possible to stably reproduce the growth of dense, porous, and fractal structures near the surface of solids placed in an active medium. The solutions of local and nonlocal equations of the model are studied, and the results are used to comment on the possible scenarios of the evolution of systems whose behavior can be reduced to such a model. Finally, the exponents of the growth of the front width in a steady-state regime are calculated for various values of the parameters. Zh. éksp. Teor. Fiz. 114, 1500–1515 (October 1998)     

The structure of diamond nanoclusters

A model describing the structure of diamond nanoclusters produced by explosive shocks is proposed. The model is based on experimental data obtained from x-ray diffraction and small-angle x-ray scattering. This model considers the diamond nanocluster as a crystalline diamond core coated by a carbon shell having a fractal structure. The shell structure depends both on the cooling kinetics of the detonation products and on the method used to extract from them the diamond fraction. Fiz. Tverd. Tela (St. Petersburg) 41, 740–743 (April 1999)     

Structure and melting of dipole clusters

Two-dimensional microclusters made up of particles repelled by the dipole law and confined by an external quadratic potential are considered. The model describes a number of physical systems, in particular, electrons in semiconductor structures near a metallic electrode, indirect excitons in coupled semiconductor dots etc. Two competing types of particle ordering in clusters have been revealed: formation of a triangular lattice and of a shell structure. Equilibrium configurations of clusters with N=1–40 particles are calculated. Temperature dependences of the structure, potential energy, and mean-square radial and angular displacements are studied. These characteristics are used to investigate cluster melting. Melting occurs in one or two stages, depending on N. Melting of a two-shell microcluster takes place in two stages: at low temperatures—from the frozen phase to a state with rotationally reoriented “crystalline” shells with respect to one another, followed by a transition involving breakdown of radial order. Melting in a cluster made up of a larger number of shells occurs in one stage. This is due to the fact that the potential barrier to intershell rotation is substantially lower than that to particle jumping from one shell to another for small N, and of the same order of magnitude for large N. A method is proposed for predicting the character of melting in shell clusters by comparing the potential barriers for shell rotation and intershell particle jumping. Fiz. Tverd. Tela (St. Petersburg) 40, 1379–1386 (July 1998)     

Nature of fractal formations at the surface of ferroelectric crystals having a broad phase transition

The nature of fractal surface formations observed in studies of small-angle light scattering from ferroelectric perovskites such as lead magnesium niobate is discussed. It is postulated that these formations may be caused by helical growth steps on the crystal faces. Fiz. Tverd. Tela (St. Petersburg) 40, 1305–1306 (July 1998)