Diffusion limited aggregation. The role of surface diffusion

ibstract. The angular and energy dependence of the dynamical diffraction of gamma rays was studied experimentally in the symmetric Brag case. Mossbauer diffraction spectra were measured with high angular resolution in a pure nuclear Bragg reflection of a nearly perfect 57FeB0, single crystal. In the spectrum taken at the exact Bragg position, very broad hyperfine resonance peaks were observed. In the spectra just above and below the Bragg angle the reflection peaks were much smaller and were shifted to energy positions above and below resonance respectively. The results were interpreted by means of the dynamical theory and compared with computer calculations. The measurements represent the first direct observation of the enhancement of nuclear resonance scattering in the case of a thick crystal reflection. Furthermore the angular dependence of the resonance scattering by a perfect single crystal has been measured for the first time. Soon after the discovery of the Mossbauer effect the dynamical diffraction of gamma radiation by a regular ensemble of resonant nuclei was considered theoretically. First the diffraction of gamma rays incident on a thin perfect single-crystal film near the Bragg angle was studied (Trammell 1961). It was found that in this case the halfwidth of the resonance scattering is larger than for an isolated nucleus and increases with the thickness of the crystal film. The energy broadening of the resonance scattering was called the enhancement effect. A general treatment of the dynamical diffraction of resonant gamma rays in thick perfect single crystals was given for the hue case (Afanas’ev and Kagan 1965) and also for the Bragg case (Kagan et al1968). In the latter paper it was shown that in the case of a Bragg reflection by an infinitely thick perfect crystal, under certain conditions, an angular position can be found where the reflection becomes total in spite of the presence of a strong inelastic channel and independent of the energy distance from resonance. In the region around this angular position the reflectivity falls off rapidly. Thereby the reflectivity remains unchanged when the energy distance from resonance and the angular deviii:ion are both changed in sign. Also the Bragg reflection by thin perfect crystals was treated in a general way (Hannon and Trammell 1969). The contributions of other authors may be found summarised in review articles (Belyakov 1975, Champeney 1979). Recently the problem of filtering of

The diffraction of high‐energy characteristic x‐ray lines, which have relatively large intrinsic widths, by perfect single crystals, which have acceptance angles much less than these line widths, is discussed. Experiments using Bi Kα 1 , which has an equivalent FWHM of 0.0013°, and an asymmetrically cut Si (111) crystal, having acceptance angles of 0.0002° and 0.0004°, showed that only a small fraction of the total characteristic line was, in fact, diffracted by the crystal.

Crystal perfection in Czochralski grown nickel single crystals

Fracture of brittle and ductile crystals in the generalized stress state. Strength and strain fracture criteria

Parametric X-rays and diffracted transition radiation in perfect and mosaic crystals

Synchrotron radiation has opened new possibilities for experimental investigations in condensed matter physics. The high intensities of the emitted X-rays allows scattering experiments with an energy resolution high enough to study ionic excitations and dynamics, directly. 1–3 So far, this was only possible by means of inelastic neutron scattering. In that method the probe is coupling to the nuclei in the sample, whereas in case of X-rays the coupling occurs to the electrons. Therefore, X-ray scattering experiments with high resolution in energy and momentum allow to determine the dynamical structure factor which is the fourier transform in time and space of the time dependent electron density–density correlation function. Within the validity of the adiabatic approximation this function is proportional to the ion density–density correlation function This means, peaks in of a liquid, for example, can be interpreted either as localized density fluctuations around or as propagating sound modes for The latter excitations correspond to the well known phonon excitations observable in solids. Since the coupling of the energy to the momentum transfer is negligible, inelastic X-ray scattering has almost no restrictions in the accessible space. Hence this method is extremely attractive for investigations at small Q-values of the coherent part of the dynamical structure factor for liquids and amorphous solids with high sound velocities. In contrast to this, inelastic neutron scattering is strongly limited by the mass of the neutron itself just in this part of the space. Conventional triple axis spectrometer can be optimized for high energy resolution by Bragg scattering from perfect single crystals in extreme backscattering geometry at the monochromator and the analyzer. This technique was used to build the inelastic X-ray spectrometer INELAX 2,3 at the synchrotron radiation laboratory at DESY, Hamburg and the second generation instrument 4 at the ESRF in Grenoble. Energy resolution values of 10 meV down to 1 meV can be achieved by using high order reflections from perfect silicon crystals. The energy transfer in an inelastic scattering experiment is established by an energy shift between the monochromator and the analyzer crystals. This is done by thermal tuning of the lattice parameter of the analyzer or the monochromator crystal. Using the (7 7 7) Bragg reflection of silicon with a primary energy of 13.8 keV, a temperature difference of 0.01 K between both crystals corresponds to an energy transfer of 0.35 meV. The resolution function

Growth of strontium sulphate single crystals by chemically reacted flux method and their dislocation configuration

Optimized growth and characterization of cadmium oxalate single crystals in silica gel

Simulation of mechanical damping in nanostructures

Based on detailed investigations on morphology (evolution and variation in external forms), surface microtopography of crystal faces (spirals and etch figures), internal morphology (growth sectors, growth banding and associated impurity partitioning) and perfection (dislocations and other lattice defects) in single crystals, we can deduce how and by what mechanism the crystal grew and experienced fluctuation in growth parameters through its growth and post-growth history under unconstrained condition. The information is useful not only in finding appropriate way to growing highly perfect and homogeneous single crystals, but also in deciphering letters sent from the depth of the Earth and the Space. It is also useful in discriminating synthetic from natural gemstones. In this chapter, available methods to obtain molecular information are briefly summarized, and actual examples to demonstrate the importance of this type of investigations are selected from both natural minerals (diamond, quartz, hematite, corundum, beryl, phlogopite) and synthetic crystals (SiC, diamond, corundum, beryl).

Miniaturization of optical components is one major task for the further development of high tech equipment. Perfect single crystals or glasses can be structured with femtosecond-lasers. Thus e. g. waveguides can be created and used as laser resonator [1–3]. In order to improve performance it is necessary to obtain detailed information about the local physical properties in the patterned area and its surrounding. While the bulk properties of a crystal are well known it is very difficult to obtain information about basic physical quantities like crystal structure, density and refractive index in the patterned area.

This study reports evidence for barite (BaSO4) formation from aqueous solution via nonclassical pathways. Our observations support the occurrence of a liquid–liquid separation in the absence of any additive as the initial stage of the crystallization process. The first solid (primary) particles or nuclei seem to form within the initially formed liquidlike precursor phase. TEM and SEM observations of the nanostructure evolution of samples quenched at successive stages of crystallization indicate two levels of oriented aggregation of nanosized solid particles. The first is the aggregation of crystalline primary nanoparticles of ca. 2–10 nm length to give larger but still nanometer-sized particles (ca. 20–100 nm length). For the first time, clear evidence of crystallographically oriented aggregation of secondary, nanometer-sized particles to form a barite single crystal is reported. During the second aggregation step of these secondary nanoparticles, most of the porosity in the largest, micron-sized aggregates is annealed, resulting in perfect single crystals. Once an amount of 50 ppm of additive, in our case a maleic acid/allyl sulfonic acid copolymer with phosphonate groups, is present in the solution, the dense liquid precursor phase seems to be stabilized, forming a PILP (polymer induced liquid precursor) and then secondary nanoparticles are temporarily stabilized against recrystallization. Growth by classical monomer addition, ripening processes or nanoparticle attachment also seems to contribute to barite formation during the latest stages of the processes.

The possibility of pions and muons being used as probe particles for defects studies in materials research has been investigated for the past thirty years or so. We discuss here the similarities of π+ and µ+ with positrons and tritons so that they can be treated as light hydrogen isotopes. Incident pions occupy a lattice site (substitutional or interstitial) and then decay into muons of energy 4.12 MeV which undergo channeling effects. The scattering cross-section of pions in tantalum single crystal with oxygen impurities has been evaluated applying Born approximation and using a double screened potential. The same calculation is applicable for muons after making some relativistic corrections. This model should also be applicable in various other situations where dechanneling by heavy ion impurities existing in multiple charge states takes place in an otherwise perfect single crystal.

Ultrasonic velocity measurements are reported for dislocation-free benzophenone single crystals cut and polished to coincide with the principal crystal directions. The measurements were performed at 38.5 MHz and over a temperature range from 228 to 318 K. Expansivity measurements made over a similar temperature range allowed the calculation of both the elastic and the Grüneisen constants for the lattice. The data are discussed in relationship to the molecular configuration of the benzophenone crystalline state.

Critical currents and relaxation in Bi-based ceramic superconductors