470 Ichikawa — Etched Figures of Japanese Quartz. 



Fig. 2 is a theoretical figure showing the structure of a 

 crystal-molecule of left-handed quartz, in which it is assumed 

 that six molecules of silica (Si0 9 ) go to form the six faces of 

 the trapezohedral form produced by etching; the atom of 

 silicon (Si) with the positive ion takes its place in the direction 

 of the positive lateral axes, and the atom of oxygen (O) with 

 the negative ion takes its place in the direction of the negative 

 lateral axes. The dotted hexagon shows the position of the 

 axes and its internal part represents the limit of area of the 

 crystal-molecule (6Si0 2 ). A is a horizontal projection on a 

 pole of the vertical axis of the crystal-molecule ; B that on a 

 pole seen from the other pole. Fig. 3 is a theoretical figure 

 showing the structure of the crystal molecule of right-handed 

 quartz crystal ; A and B correspond to A and B of ^. 1. 

 Fig. 4 shows a left-handed trapezohedron (in a position opposed 

 to that of fig. 2), supposed to be formed by natural etching 

 (K.CO,). _ 



Fig. 5 is a theoretical figure showing the structure of the 

 crystal-molecules of a simple left-handed crystal ; seven crystal- 

 molecules are grouped regularly in the direction of the 

 intermediate axes, and they are combined with each other by 

 the energy of the positive and negative ions. Fig. 6 shows 

 the same on a right-handed quartz crystal. 



Fig. 7 is a theoretical figure showing the molecular structure 

 of a left-handed Dauphine twin, in which it is assumed that 

 the crystal-molecule at the end of each negative lateral axis is 

 revolved 60° about the vertical axis. Fig. 8 is a similar figure 

 of a Brazilian twin of rock crystal in wmich it is assumed that 

 the crystal-molecule belonging to the area of the negative 

 lateral axes of a right-handed quartz penetrates into the area 

 of the positive lateral axes of a left-handed quartz. 



The symmetry of the crystal-molecule (six molecules of 

 silica (Si 2 0) with geometric arrangement) in the above figs. 2 

 and 3 corresponds to the symmetry of the trapezohedron, and 

 the crystal -molecule thus reveals the trigonal symmetry by the 

 revolution about the vertical axis, and the binary symmetry 

 by the revolution about the lateral axes, and it has neither 

 center nor plane of symmetry. 



In the above models the structures of simple crystals and 

 twin crystals of the given quartz are readily understood, and 

 there are also numerous cases where the physical and chemical 

 reactions by which the molecules act upon other adjacent mole- 

 cules can be well explained by the models; a few examples are 

 mentioned in the following: 



When a quartz crystal is kept in strong hydrofluoric acid, a 

 groove will be found on each positive edge of its prism (see 

 Plate II, figs. 1 and 2, etc.) ; if we assume that the prismatic 



