Hollow pyramid crystal shapes

There are two other principal nonplanar habits of polyethylene lamellae chair and ridged crystals. Chair crystals (30) form simultaneously with, and are related to, hollow pyramids their shape may be described as resulting from a hollow pyramid divided in two along the short diagonal, the two halves rotated 180° aroimd their long diagonal and then constrained to rejoin. The proportion of chair to hollow pyramidal crystals appears to vary with crystallization conditions. 

Grainer salt is made by surface evaporation of brine in flat pans open to the atmosphere. Heat usually is furnished by steam pipes located a few inches below tlie tank bottom. Crystals form at the surface of the brine and are held tliere temporarily by surface tension. Thus, they grow laterally for awhile and form thin flakes. But, as they grow, they tend to sink and this process imparts a peculiar, hollow pyramid-like structure to them. Such crystals are called hopper crystals. Ultimately, the crystals sink to the bottom where they are scraped to one end of the pan. The crystals are fragile and during handling they break up, finally assuming a flake-like shape. Thus, tlie term flake salt. 

The hollow pyramid shape typical of a single crystal of polyethylene indicates that the chain axis is not parallel with the normal of the lamella. The chain axis is generally at an angle, about 30°, with respect to the lamella normal. The reason for the chain tilt is essentially that a certain type of regular chain fold requires a small vertical displacement of the linear chain in the adjacent position (Fig. 7.14). 

Polyethylene crystallites are generally not planar rather, they have a hollow-pyramidal shape [134, 135]. A pleat or a trapezoid-shaped structure is observed in the center of the lamellae. By precipitation of crystals from highly diluted solutions, mats are obtained which are very brittle because of the scarcity of interlamellar connections and high crystallinity. 

Figure 3.1 Monolayer crystals of polyethylene grown from 0.1% tetrachloroethylene solution by free cooling from about 120°C. The pleats were formed when the hollow pyramid shape crystals collapsed. A small spiral growth is evident on the largest crystal. Transmission electron micrograph from Reneker and Geil [2] with permission from the American Institute of Physics.

Figure 3.12 (a) TEM of monolayer crystals of polyethylene, M = 10 kDa, grown at 80°C from 0.01 % xylene solution. There are no pleats or creases that indicate a nonplanar shape, (b) Exactly as in (a), except that the polyethylene has M = 120 kDa. The pleat along the b-axis (small diagonal) indicates that the crystal was a hollow pyramid in solution. Note also the spiral growths. From Holland and Lindenmeyer [16] with permission from John Wiley Sons, Inc. 

Figure 3.13 Atomic force microscopy images of M = 32 kDa polyethylene crystals grown from 0.01% solution in xylene at 83°C and sedimented onto a compliant substrate made of 7% poly (vinyl alcohol) dissolved in water. Both (a) hollow pyramid and (b) chair crystals retain their shapes. FromToda et al. [19] with permission from Elsevier.

The crystals of rock-salt are nearly always cubes or small octahedrons. When the crystals form on the surface of evaporating brine, distinctive hopper-shaped crystals resembling hollow quadrilateral pyramids are developed the inner surface appears to be arranged in a series of steps. D. I. Mendeleeff1 explains the formation of hopper salt crystals as follows ... 

---