Spiral Layers Research Articles

Observation and interpretation of eccentric growth spirals

Eccentric growth spirals were observed on the (0001) face of SiC crystals synthesized by the Lely method at the Toshiba Central Research Laboratories. Originating from one screw dislocation, mono-molecular spiral layers (step height 15 Å, 6H polytype), show increasingly wider step separation in the direction towards the inner portion of the furnance where temperature is lower, and hence supersaturation is higher. Contrary to this, step separations become increasingly narrower approaching the base of the crystal which is more close to the wall of the furnace. This eccentricity is interpreted as due to a supersaturation gradient over the surface. In addition, an observed eccentric growth spiral with a hollow core will be presented and interpreted.

On the micropolar ekman problem

Microfluid theory is applied to the classic Ekman problem. A general solution for the time dependent case is obtained. The characteristics of this solution are investigated by examining the complex response. Typically, the response is very similar to the complex response of the Ekman solution, thus suggesting that there is an equivalent Ekman time response for nearly any set of micropolar parameters. It is shown that for the steady state case, the two solutions exhibit significantly different features. With inhomogeneous boundary conditions for the gyration, the micropolar solution can produce a velocity profile that is virtually logarithmic with height near the lower boundary but which merges into a spiral Ekman-like layer and then finally into geostrophic flow. This profile is very similar to solutions obtained in studies of the atmospheric planetary layer which piece together boundary layer and Ekman layer solutions. Conceptually, the micropolar solution is much simpler in that an eddy viscosity which is an empirical function of height is not required.

A rationale for determining spacing of levels in numerical models of the atmospheric boundary layer

It is suggested that since diffusion is the principal vertical transfer mechanism in the boundary layer, the mixing-length concept can be used to determine the spacing between levels in numerical models. An analysis of the Wangara Experiment boundary-layer data suggests that for that location, a vertical spacing of about 1% of the smallest horizontal scale is appropriate in the spiral layer and that this is constant with height.

The characteristics of a laboratory produced turbulent Ekman layer

The characteristics of the atmospheric turbulent Ekman boundary layer have been qualitatively simulated in an annular rotating wind tunnel. Observed velocity spirals found to exist within the wind tunnel resembled qualitatively those found in the atmosphere in that a two-layer structure was evident, consisting of a log-linear portion topped by an outer spiral layer. The magnitude of the friction velocity u * obtained from the log-linear profile agreed with that measured directly, i.e., that obtained from the relation: u * = (u′w′)1/2. Also, the effects of surface roughness on the characteristics of the boundary layer agreed with expected results. In cases where the parametric behaviour predicted by theory departed from the observed behaviour, the probable cause was the inherent size limitations of the wind tunnel. The ability to maintain dynamic similarity is constrained by the limited radius of curvature of the wind tunnel. The vertical distribution of turbulent intensity in the wind tunnel was found to agree qualitatively with an observed atmospheric distribution. Also, a vertical distribution of eddy diffusivity was calculated from tunnel data and found to give qualitatively what one might expect in the atmosphere.

Cone-helix growth forms of graphite

Various kinds of filamentary growth of graphite from the gas phase have structures that can be interpreted in terms of curved basal sheets of graphite arranged in the form of cone-helices. In these arrangements successive spiral basal layers are rotated relative to one another, but only those geometries occur in which this rotation is a multiple of 60° (thus restoring the graphite basal stacking in the “c” direction) or alternatively 21.8° which is one of the optimum coincidence configurations for “c” axis rotation faults in graphite. This type of growth form occurs in solid filaments prepared under various experimental conditions, and also in hollow filamentary tubes. There is some evidence that it might also occur in semi-fibrous and spherulitic forms of crystallization from metal solution.

Study of microstructure of chrysotile asbestos by high-resolution electron microscopy

Several samples of chrysotile asbestos from different localities, including a synthetic sample, were electron-microscopically observed by the lattice imaging method along two directions parallel and perpendicular to the fibre axis. The results are as follows: (a) The lattice fringes of 4.5 Å corresponding to 020 were often tilted to the edge of the fibrils with an angular distribution ranging up to about 10° with a peak value at a few degrees, depending on the sample. (b) Most of the fibrils examined were hollow cylinders and their circumferential lattice layers form spiral or multi-spiral layers. The perfectly concentric cylindrical layers were also found with a frequency depending on the sample. (c) Unusual growth patterns which cannot be explained by Jagodzinski and Kunze's model were observed. (d) The lattice images of the cortical fibrils (cone-in-cone shape) were observed in the synthetic sample. (e) Most fibrils greater than about 350 Å in diameter showed traces of discontinuous growth in two or three steps, depending on the growth conditions, and this gave rise to various distributions of the fibril diameters.

The geometry of peripheral myelin sheaths during their formation and growth in rat sciatic nerves.

In rat sciatic nerves, a small bundle of fibers was identified in which myelin sheaths were absent at birth, appeared within 3 days, and grew rapidly for 2 wk. During this interval, nerves were removed from littermates and were sectioned serially in the transverse plane. Alternating sets of thin and thick sections were used to prepare electron micrograph montages in which single myelinating axons could be identified and traced distally. During the formation of the first spiral turn, the mesaxon's length and configuration varied when it was studied at different levels in the same Schwann cell. The position of the mesaxon's termination shifted while its origin, at the Schwann cell surface, remained relatively constant. Along myelin internodes composed of two to six spiral turns, there were many variations in the number of lamellae and their contour. Near the mesaxon's origin, longitudinal strips of cytoplasm separated the myelin layers. Thicker sheaths were larger in circumference, more circular in transverse sections, and more uniform at different levels. Irregularities were confined to the paranodal region, and separation of lamellae by cytoplasm occurred at Schmidt-Lantermann clefts. Approximate dimensions of the bundle, its largest fibers, and their myelin sheaths were measured and calculated. The myelin membrane's transverse length and area increased exponentially with time; the growth rate increased rapidly during the formation of the first four to six spiral layers and remained relatively constant during the subsequent enlargement of the compact sheath.

Surface microstructures of crystals grown from molten salts

Surface structures of the following crystals grown from various molten salts were studied by means of phase contrast microscopy; emerald, corundum, hematite, spinel, magnetoplumbite, YIG, ZrO 2, ZnO, UO 2 and U 3O 8. Most of these crystals exhibit growth spirals. Four types of spirals were observed; 1) spirals having mono-molecular step height and wide and regular spacings between the successive arms, 2) spirals having mono-molecular step height and narrow and regular spacings, 3) conical growth hills which also consist of narrow but irregularly spaced spiral layers, and 4) minute growth hills consisting of narrow but irregularly spaced spiral layers. Their morphologies are explained on the basis of structural characteristics and growth conditions. The characteristics of growth spirals on these crystals are compared with those on the crystals of the same compound grown from the vapour, solution or unicomponent melt, and the difference in the growth mechanism between these methods is discussed.

Instability of the Ekman Spiral with Applications to the Planetary Boundary Layers

The Ekman spiral boundary layer occurs in rotating systems near boundary surfaces perpendicular to the rotation axis when the flow is slow compared to the speed of rotation. New results are presented for the instability of the Ekman layer with a free boundary and for shear‐flow instability in the presence of density stratification: (1) For the Ekman boundary layer caused by wind stress on a free water surface the critical Reynolds number is much less than for the case of flow over a smooth rigid boundary. An example of this instability from a laboratory experiment is presented. (2) For the free‐surface case the distortion of the basic Ekman flow by finite‐amplitude motion is very large. (3) With unstable density stratification either shear‐flow instability or thermal convection may dominate according to the relative values of Rayleigh and Reynolds numbers. (4) With stable density stratification the shear‐flow instability may be resonant with internal gravity‐wave oscillations so that damping of the cellular circulations is minimized. Some of the implications of these results for the planetary boundary layers of the atmosphere and ocean are considered.

Ekman drift currents in the Arctic Ocean

Current observations from a drifting ice floe in the central Arctic Ocean give clear evidence of a clockwise spiral structure in the upper layers. The data for steady conditions show a boundary layer just beneath the ice and an Ekman spiral layer below it. The depth of frictional influence is 18 m for winds of 4 m/sec. This is apparently the first detailed confirmation of the Ekman spiral in deep waters.

Observations sur Nummulites millecaput Boubee (forme macrospherique)

Abstract A statistical study of the measurements of macrospheric forms of Nummulites millecaput from Lutetian (Tertiary) deposits of the Gibret area, Landes, France. The values for the thickness of the shell, the diameter of the initial chamber, and the ratio of the diameter of the third whorl to the diameter of the initial chamber are normally distributed around the mean. The thickness of the spiral layer increases to the third whorl, then decreases. The diameter of the initial chamber correlates with the diameter rather than the thickness of the shell.

On the Theory of the Progressive Universal Winding

The rigorous theory previously developed by the author for the ordinary or stationary universal winding is extended to the progressive universal winding; in particular, an exact formula for calculating the gear ratio to be employed in winding a progressive universal coil is deduced, and, by neglecting certain terms therein, formulas representing various degrees of approximation of the same are derived and shown to be equivalent of those previously given by the author, by Joyner and Landon, and by Hershey. The theory of the spiral ridges and close-packed layers of progressive universal coils is developed, and formulas giving the slope of the spiral ridge and the dimensions of the close-packed layers are deduced. The principles underlying the selection of the optimum number of crossovers per turn are discussed, and an example of the application of the formulas to the design of a progressive universal coil is given.