Numerical Simulation of the Flow Field and Concentration Distribution in the Bulk Growth of Silicon Carbide Crystals

The physical vapor transport (PVT) method is being widely used to grow large-size single SiC crystals. The growth process is associated with heat and mass transport in the growth chamber, chemical reactions among multiple species as well as phase change at the crystal/gas interface. The current paper aims at studying and verifying the transport mechanism and growth kinetics model by demonstrating the flow field and species concentration distribution in the growth system. We have developed a coupled model, which takes into account the mass transport and growth kinetics. Numerical simulation is carried out by employing an in-house developed software based on finite volume method. The results calculated are in good agreement with the experimental observation.

Investigation Of Mode Ii Crack Growth Following A Very High Speed Impact

A recoverable plate impact testing technology has been developed for studying fracture mechanisms of mode II crack. With this technology, a single duration stress pulse with submicrosecond duration and high loading rates, up to 10(8) MPam(1/2)s(-1), can be produced. Dynamic failure tests of Hard-C 60# steel were carried out under asymmetrical impacting conditions with short stress-pulse loading. Experimental results show that the nucleation and growth of several microcracks ahead of the crack tip, and the interactions between them, induce unsteady crack growth. Failure mode transitions during crack growth, both from mode I crack to mode II and from brittle to ductile fracture, were observed. Based on experimental observations, a discontinuous crack growth model was established. Analysis of the crack growth mechanisms using our model shows that the shear crack extension is unsteady when the extending speed is between the Rayleigh wave speed c(R) and the shear wave speed c(S). However, when the crack advancing speed is beyond c(S), the crack grows at a steady intersonic speed approaching root 2c(S). It also shows that the transient mechanisms, such as nucleation, growth, interaction and coalescence among microcracks, make the main crack speed jump from subsonic to intersonic and the steady growth of all the subcracks causes the main crack to grow at a stable intersonic speed.

Growth of liquid bridge in AFM

Capillary forces are dominant in adhesive forces measured with an atomic force microscope (AFM) in ambient air, which are thought to be dependent on water film thickness, relative humidity and the free energy of the water film. In this paper, besides these factors, we study the nature of the 'pull-off' force on a variety of atmospheres as a function of the contact time. It is found that capillary forces strongly depend on the contact time. In lower relative humidity atmosphere, the adhesion force is almost independent of the contact time. However, in higher relative humidity, the adhesion force increases with the contact time. Based on the experiment and a model that we present in this paper, the growth of the liquid bridge can be seen as undergoing two processes: one is water vapour condensation; the other is the motion of the thin liquid film that is absorbed on the substrate. The experiment and the growth model presented in this paper have direct relevance to the working mechanism of AFM in ambient air.

Discontinuous growth mechanisms of mode II crack under high-speed impact conditions

A recoverable plate impact testing technology has been used for studying the growth mechanisms of mode II crack. The results show that interactions of microcracks ahead of a crack tip cause the crack growth unsteadily. Failure mode transitions of materials were observed. Based on the observations, a discontinuous crack growth model was established. Analysis shows that the shear crack grows unsteady as the growth speed is between the Rayleigh wave speed c(R) and the shear wave speed c(s); however, when the growth speed approaches root 2c(s), the crack grows steadily. The transient microcrack growth makes the main crack speed to jump from subsonic to intersonic and the steady growth of all the sub-cracks leads the main crack to grow stably at an intersonic speed.

Simulation of growth process of thin film on non-planar substrate

In (2 + 1) dimension, growth process of thin film on non-planar substrate in Kuramoto-Sivashinsky model is studied with numerical simulation approach. 15 x 15 semi-ellipsoids arranged orderly on the surface of substrate are used to represent initial rough surface. The results show that at the initial stage of growth process, the surface morphology of thin film appears to be grid-structure, and the interface width constantly decreases with the growth time, then reaches minimum. However, the grid-structure becomes ambiguous, and granules of different sizes distribute evenly on the surface of thin film with the increase of growth time. Thereafter, the average size of granules and the interface width gradually increase, and the surface morphology of thin film presents fractal properties. The numerical results of height-height correlation functions of thin film verify the surface morphology of thin film to be fractal for a longer growth time. By fitting of the height-height correlation functions of thin film with different growth times, the growth process is described quantitatively. (c) 2004 Elsevier B.V. All rights reserved.

Age and Growth of an Endemic Tibetan Fish, Schizothorax o'connori, in the Yarlung Tsangpo River

We investigated the age and growth of Schizothorax o'connori in the Yarlung Tsangpo River by examination of annuli from otoliths. The von Bertalanffy model was the most acceptable statistical growth model. Its parameters were as follows: SL infinity = 492.4 mm, K = 0.1133, t(0) = -0.5432 year and W-infinity = 1748.9 g for females; SL infinity = 449.0 mm, K = 0.1260, t(0) = -0.4746 year and W-infinity = 1287.0 g for males. Theoretical longevity was 25.9 years for the female and 23.3 years for the male. Moreover, females had larger asymptotic length and weight compared with males.

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Collective evolution characteristics and computer simulation of short fatigue cracks

Fatigue testing was conducted using a kind of triangular isostress specimen to obtain the short-fatigue-crack behaviour of a weld low-carbon steel. The experimental results show that short cracks continuously initiate at slip bands within ferrite grain domains and the crack number per unit area gradually increases with increasing number of fatigue cycles. The dispersed short cracks possess an orientation preference, which is associated with the crystalline orientation of the relevant slip system. Based on the observed collective characteristics, computer modelling was carried out to simulate the evolution process of initiation, propagation and coalescence of short cracks. The simulation provides progressive displays which imitate the appearance of experimental observations. The results of simulation indicate that the crack path possesses a stable value of fractal dimension whereas the critical value of percolation covers a wide datum band, suggesting that the collective evolution process of short cracks is sensitive to the pattern of crack site distribution.

Spall damage in aluminum-alloy

A void growth relations for ductile porous materials under intense dynamic general loading condition is presented. The mathematical model includes the influence of inertial effects, material rate sensitivity, as well as the contribution of void surface energy and material work-hardening. Numerical analysis shows that inertia appears to resist the growth of voids. The inertial effects increase quickly with the loading rates. The theoretical analysis suggests that the inertial effects cannot be neglected at high loading rates. Plate-impact tests of aluminum alloy are performed with light gas gun. The processes of dynamic damage in aluminum alloy are successfully simulated with a finite-difference dynamic code in which the theoretical model presented in this paper is incorporated.

The effect of diffusion and overhangs/vacancies on the microstructure of zig-zag thin film

Basing on some growth models of thin film, we have investigated the growth mechanism of glancing angle deposition (GLAD) film. The simulation verifies that the overhangs/vacancies also contribute to the columnar growth as well as the self-shadowing effect for GLAD thin film. Besides, we have studied the effect of the deposition rate, surface and bulk diffusions on the microstructure of thin film using the time-dependent Monte Carlo method. The results show that the surface and bulk diffusions can significantly enhance the packing density of thin film in GLAD growth, and the increase of the deposition rate induce the moderate decrease of the packing density. (c) 2006 Elsevier B.V. All rights reserved.

Influence of ion energy and deposition temperature on the surface morphology of carbon films deposited by ion beams

Carbon films were deposited by mass-selected ion beam technique with ion energies 50-200eV at a substrate temperature from room temperature to 80 degreesC,. For the energies used, smooth diamond-like carbon films were deposited at room temperature. When the substrate temperature was 600 degreesC,rough graphitic films were produced. But highly oriented carbon tubes were observed when the energies were larger than 140eV at 800 degreesC. They were perpendicular to the surface and parallel to each other. preferred orientation of graphite basic plane was observed by high-resolution electron microscopy. Shallow ion implantation and stress are responsible for this orientation.

Effects of Thickness on Properties of ZnO Films Grown on Si by MOCVD

High quality ZnO films are successfully grown on Si（100） substrates by metal-organic chemical vapor deposition at 300℃. The effects of the thickness of the ZnO films on crystal structure, surface morphology,and optical properties are investigated using X-ray diffraction, scanning probe microscopy,and photoluminescence spectra, respectively. It is shown that the ZnO films grown on Si substrates have a highly-preferential C-axis orientation,but it is difficult to obtain the better structural and optical properties of the ZnO films with the increasing of thickness. It is maybe due to that the grain size and the growth model are changed in the growth process.

Crystallization kinetics in shearing-induced oriented and stretched poly(ethylene oxide)

Isothermal crystallization kinetics in the melting of poly(ethylene oxide) (PEO) were investigated as a function of the shear rate and crystallization temperature by optical microscopy. The radial growth rates of the spherulites are described by a kinetics equation including shearing and relaxation combined effects and the free energy for the formation of a secondary crystal nucleus. The free-energy difference between the liquid and crystalline phases increased slightly with rising shearing rates. The experimental findings showed that the influence of the relaxation of PEO, which is related to the shear-induced orientation and stretch in a PEO melt, on the rate of crystallization predominated over the influence of the shearing. This indicated that the relaxation of PEO should be more important so that the growth rates increase with shearing, but it was nearly independent of the shear rate within the measured experimental range.

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90degrees and 180degrees is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress sigma(infinity) and electric field E-infinity or (sigma(infinity), E-infinity) is replaced by strain e and electric displacement D-infinity or (epsilon(infinity), D-infinity). Mixed conditions (sigma(infinity),D-infinity) and (epsilon(infinity),E-infinity) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E-y(infinity),sigma(y)(infinity)) for negative E-y(infinity) and (D-y(infinity), epsilon(y)(infinity)) for positive D-y(infinity) while the mechanical conditions sigma(y)(infinity) or epsilon(y)infinity are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth. (C) 2002 Published by Elsevier Science Ltd.

A constitutive model for cavitation and cavity growth in rubber-like materials under arbitrary tri-axial loading

In this paper, we attempted to construct a constitutive model to deal with the phenomenon of cavitation and cavity growth in a rubber-like material subjected to an arbitrary tri-axial loading. To this end, we considered a spherical elementary representative volume in a general Rivlin's incompressible material containing a central spherical cavity. The kinematics proposed by [Hou, H.S., Abeyaratne, R., 1992. Cavitation in elastic and elastic-plastic solids. J. Mech. Phys. Solids 40, 571-722] was adopted in order to construct an approximate but optimal field. In order to establish a suitable constitutive law for this class of materials, we utilized the homogenisation technique that permits us to calculate the average strain energy density of the volume. The cavity growth was considered through a physically realistic failure criterion. Combination of the constitutive law and the failure criterion enables us to describe correctly the global behaviour and the damage evolution of the material under tri-axial loading. It was shown that the present models can efficiently reproduce different stress states, varying from uniaxial to tri-axial tensions, observed in experimentations. Comparison between predicted results and experimental data proves that the proposed model is accurate and physically reasonable. Another advantage is that the proposed model does not need special identification work, the initial Rivlin's law for the corresponding incompressible material is sufficient to form the new law for the compressible material resulted from cavitation procedure. (C) 2007 Elsevier Ltd. All rights reserved.