Although the ions of such a structure are in equilibrium in electric fields produced by the surrounding ions, it seems probable from the position of the cleavage planes and from the distances of closest approach of the metallic ions to the oxygen ions that one metal ion of each kind belongs to each SO, group to form the molecule. Fig. 3 represents the molecule of potassium sulphate as it occurs in these crystals. The potassium, sulphur, and two oxygen atoms

lie in a plane. The other two oxygen atoms, which are equidistant from that plane, are also represented as lying in that plane, and have been displaced to prevent the electron systems from intersecting in the diagram.

6. The crystals of this series show repeated twinning, which results in interpenetrating groups which are almost indistinguishable from simple hexagonal crystals. Fig 4 A

shows a section of such a crystal built from three crystals, I., II., and III.* Figures of characteristic triplets of potassium selenate are given by Tutton †. The external faces of the crystal are the planes p (110) and p' (130). The twinning plane (130) is nearly at right angles to the plane (110). If the re-entrant angles formed by the planes (130) vanish by the growth of the crystal, there results an almost true hexagonal prism terminated by a hexagonal pyramid. Each face is however composed of two halves, which are inclined at a small angle to one another. This inclination can be detected by reflecting light from the face of the crystal.

Section of Potassium Sulphate perpendicular to "C"axis twinned on (130)

A twining plane must have special characteristics. The cases hitherto observed show twinning planes to be planes of closely-packed atoms. It must also be such that, if the crystal is built up to this plane, its continuance on the other side of the plane may follow one or more alternatives. One of these is correct and continues the plan of the crystal. Physikalische Krystallographie,' Groth, p. 406.

+Crystalline Structure and Chemical Constitution,' A. E. H. Tutton, p. 93.

The others are not so easy to follow.

satisfies these conditions.

The plane (130)

Fig. 4 B, which is a section of potassium sulphate perpendicular to the "c" axis, explains the process of twinning in these crystals. The figure shows the 3-potassium atoms in the projection lying inside a nearly true hexagon of oxygen atoms, which in turn lie inside a larger hexagon of S atoms. These potassium atoms lie in the reflexion planes parallel to (100). Their positions relative to the oxygen atoms are shown in fig. 4 C. If these potassium atoms are rotated through nearly 60° into the plane (130), they would occupy positions relative to oxygen atoms illustrated in fig. 4 D. The crystal would now grow in that direction as the (100) plane of the twin. The potassium atoms might equally well be rotated through nearly 60° in the opposite direction into the plane (130). Arcanite (K2SO4) is described in Dana's System of Mineralogy' as giving repeated twins on the planes (110) and also on (130) resembling aragonite.

The diagonal of the " hexagon" of S atoms parallel to the plane (100) is slightly longer than that parallel to (130) or (130). The lengths are 6.67 and 6-63 A.U. The longer direction is the correct direction for the potassium atoms. The section between the lines y and 8 would serve as origin for the growth of either system on each side of it.

7. Models of SO, groups were made with spheres of 1.5 cm. diameter to represent both S and O. The distance S-0=1.5 cm. The K2SO4 unit was then constructed with SO, models and with spheres of 2.7 cm. diameter to represent K atoms. The radii of these spheres were not intended to represent "atomic radii." A similar model of the (NH4)2SO4 unit was made, taking a sphere of 15 cm. diameter to represent N and a sphere of 10 cm. diameter to represent H. The whole NH, group would then lie within a sphere of 1.75 cm. radius.

Two views of the (100) planes of each of these models are given in Pl. V. (figs. 5 A & B) and in Pl. VI. (figs. 6 A & B).

It can be seen from the model that, if ammonium sulphate were to twin like potassium sulphate, not only would the NH, group have to be rotated through nearly 60° about an axis parallel to "c," but the groups would also have to be inverted; i. e., rotated through 180° about an axis through its centre parallel to "b."

SUMMARY.

The structures of the isomorphous sulphates of potassium, ammonium, rubidium, and cæsium have been investigated. The structure is based on a simple orthorhombic lattice having four molecules to the unit cell, and the space-group is V 16. The positions of the atoms in the structures have been determined. An explanation of the characteristic twinning of these crystals has been given.

In conclusion, I wish to express my thanks to Dr. A. E. H. Tutton, F.R.S., for supplying me with certain crystals for this investigation, to the South African Research Grant Board for some financial assistance, and to Mr. J. A. Linton for skilful assistance in making models and diagrams.

XXXV. Energy Distribution among Secondary Electrons from Nickel, Aluminium, and Copper. By D. A. WELLS, Assistant Professor of Physics, University of Cincinnati*.

REVIEW of experimental work indicates that results

A do not always agree as to the energy distribution

of secondary electrons. The highest velocities found by Barber working with copper correspond to from 2 to 5 volts. The results of McAllister ‡, using practically the same apparatus and continuing the work of Barber, indicate that there are a few electrons reflected or emitted with velocities approaching the velocity of the primary stream. Davisson and Kunsman §, investigating the maximum velocity of secondary electrons from aluminium, platinum, and magnesium, found that secondary electrons with velocities "not appreciably less than that of the primaries proceed from the platinum and magnesium for all bombarding potentials up to the highest investigated in each case, 1000 volts and 1500 volts respectively."

* Communicated by the Author.

I. G. Barber, "Secondary Electron Emission from Copper and Copper Oxide," Phys. Rev. vol. xvii. pp. 322-338 (1921).

L. E. McAllister, "The Effect of Ageing on the Secondary Electron Emission from Copper Surfaces," Phys. Rev. vol. xix. p. 246 (1922).

C. Davisson and C. H. Kunsman, Phys. Rev. vol. xxii. p. 242 (1923).

Description of Apparatus.

Fig. 1 gives a diagram of apparatus and connexions. F, a flat spiral tungsten filament (Coolidge X-ray cathode) heated by means of lead storage-cells, was used as the source of primary electrons. A nickel shield S served as an anode and allowed a narrow beam of primary electrons to fall on d, the metal from which secondaries were to be studied. The large disk D, carrying the small disks d, could be rotated from the outside by the action of an electromagnet on a short iron bar attached to the extreme end of the axle.

Fig. 1.

TO PUMP

The

APPARATUS

FIGURE 1

AND DIAGRAM OF CONNECTIONS

Faraday cylinder G could be put at any potential with respect to d by moving the point N. The primary electrons could be given any desired energy by moving the contact M. From the diagram it may be seen that the galvanometer reads I-I, the difference between the primary current striking and the secondary current leaving d. Therefore the complete energy distribution among secondary electrons for a given value of primary accelerating potential E, may be obtained by moving N from A to B.

The aluminium cathode C was used for bombarding the metals to remove adsorbed gases. The negative terminal of 7-inch induction coil was connected to this cathode, and

a