Growth-deviation model to understand the perceived variety of falling snow

What is the source of snow-crystal variety? This question is answered using a model of snow-crystal growth in a cloud. In the model, crystals start under various initial cloud-crystal conditions, and then encounter growth perturbations from random air-temperature deviations along simple crystal trajectories. To obtain distributions of these deviations, I analyzed recent high-resolution measurements of cloud updrafts and temperatures. The trajectories and distributions are used to estimate the number of possible snow crystal shapes, to a given viewing resolution, from a range of initial conditions. The logarithm of this number, defined here as the perceived shape variety or "diversity", is dominated not by the range of conditions, but rather by the air-temperature deviations along a trajectory. This qualitative result is independent of the viewing resolution. Thus, temperature deviations are the main source of crystal diversity. When plotted against the crystal's initial temperature (here –11 to –19°C), the curve is mitten-shaped, with a main peak at –15.4°C and a smaller, sharper peak near –14.4°C. The mitten shape arises from temperature trends in the crystal's terminal fallspeed and prism-face growth rate. Specifically, the two diversity peaks are due to maxima in growth-rate sensitivity to temperature near –15.4 and –14.0°C. Applying the results to all snow crystals ever formed, then, to 1-μm resolution, all crystals that began near –15°C would appear unique, but some that began near –11°C would not.

Yttrotungstite

SummaryYttrotungstite occurs at Kramat Pulai mine, and at Tapah, Kinta, Perak, Malaysia, as yellow earthy material and as monoclinic laths, elongated along [001], flattened, and always twinned, on {100} to pseudo-orthorhombic symmetry, and frequently bevelled by {110}; crystals are very rarely terminated by {101}. γ = [010], α:[001] = 26°, probably in β acute, and 2Vα ≃ 68°. A thermal weight loss curve and an infra-red absorption spectrum are given and discussed. Accessory minerals include raspite and stolzite.The yttrotungstite unit cell has a 6·95, b 8·64, c 5·77, β 104° 56′, space group P21/m; cell contents are (Yt, Ln, Ca, Mg)2(W, Al, Si, Ti, Fe)4(O, OH)14(OH)2·2H2O. Indexed X-ray powder data are given. Microprobe studies show that Al and Si replace W and are concentrated in zones showing larger values of a sin β (6·75 Å instead of 6·72 Å) but with no other appreciable difference in cell dimensions. Crystal structure studies show that the structure consists of WO6 octahedra sharing non-opposite edges in zig-zag chains running parallel to [010]. Yttrium is in approximately trigonal prismatic coordination between the chains, with the water molecule as a seventh neighbour at one prism face. The water molecule is accommodated in the angle between zig-zags in the WO6 chains; it is probably hydrogen bonded to chain oxygen atoms, and becomes coordinated to the yttrium by a shear between chains away from strict close-packing of the oxygen atoms. The shear is related to the change in a sin β in (Al, Si)-rich zones; arguments based on this and on details of the chemical analysis suggest that SiO4 replaces WO6 with a local oxygen deficit.Oxygen atom peaks on partial Fourier difference syntheses for our data for yttrotungstite are only slightly larger than the troughs in the syntheses due to experimental error. Methods of testing the significance of the positive peaks are described in an appendix.

The variation with temperature of the magnetic leakage field in cobalt

The variation with temperature of the magnetic leakage field of an unmagnetized crystal of hexagonal cobalt has been investigated by means of an electron beam. Both the prism and hexagonal faces were examined in the temperature range of 20 to 380 °C by a new method using a divergent electron beam. In addition, the prism face was studied from 20 to — 170 °C. It was found that the strength of the magnetic leakage field decreased steadily with increasing temperature. It became negligible at about 260 °C and this condition persisted up to 380 °C. It was also found that the basic domain spacings did not change during heating or cooling of the crystal.

An example of porphyry-quartz, from the Esterel Mtns., France, twinned on face (1012)

It is now well recognized that quartz undergoes a sudden change near 575° C., and Wright and Larsen (1) have shown that the characteristics of quartz formed above or below this point are so marked that they can be utilized to determine the temperature of formation of rocks containing quartz. Quartz formed above 575° so-called β-quartz, is of distinctly hexagonal development, and occurs generally as regular hexagonal bipyramids with or without a subordinate prism-face. These external characteristics are of course preserved on cooling, and the bipyramids are converted into apseudomorphous aggregate of α-quartz.