December i, 3914] 



SCIENCE 



801 



heavy. A grating specially ruled for us at the 

 National Physical Laboratory shows this OjEEect 

 very well. This difference between rocksalt 

 and sylvine and its explanation in this way 

 constituted an important link in W. Lawrence 

 Bragg's argument as to their structure. 



When, therefore, we are observing the reflec- 

 tions in the different faces of a crystal in 

 order to obtain data for the determination of 

 its structure, we have more than the values of 

 the angles of reflection to help us; we have 

 also variations of the relative intensities of 

 the spectra. In the case just described we 

 have an example of the effect produced by 

 want of similarity between the planes, which 

 are, however, uniformly spaced. 



In the diamond, on the other hand, we have 

 an example of an effect due to a peculiar 

 ' arrangement of planes which are otherwise 

 similar. The diamond crystallizes in the 

 form of a tetrahedron. When any of the four 

 faces of such a figure is used to reflect X-rays, 

 it is found that the second order spectrum is 

 missing. The analogous optical effect can be 

 obtained by ruling a grating so that, as com- 

 pared with a regular grating of the usual kind, 

 the first and second, fifth and sixth, ninth and 

 tenth alone are drawn. To put it another 

 way, two are drawn, two left out, two drawn, 

 two left out, and so on. The National Phys- 

 ical Laboratory has ruled a special grating of 

 this kind also for us, and the effect is obvious. 

 The corresponding inference in the case of the 

 diamond is that the planes parallel to any 

 tetrahedral face are spaced in the same way as 

 the lines of the grating. Every plane is three 

 times as far from its neighbor on one side as 

 from its neighbor on the other. There is only 

 one way to arrange the carbon atoms of the 

 crystal so that this may be true. Every atom 

 is at the center of a regular tetrahedron com- 

 posed of its four nearest neighbors, an arrange- 

 ment best realized by the aid of a model. It is 

 a beautifully simple and uniform arrange- 

 ment, and it is no matter of surprise that the 

 symmetry of the diamond is of so high an 

 order. Perhaps we may see also, in the perfect 

 symmetry and consequent effectiveness of the 



forces which bind each atom to its place, an 

 explanation of the hardness of the crystal. 



Here, then, we have an example of the way 

 in which peculiarities of spacing can be de- 

 tected. There are other crystals in which want 

 of uniformity both in the spacings and in the 

 effective value of the planes combine to give 

 cases stiU more complicated. Of these are iron 

 pyrites, calcite, quartz and many others. It 

 would take too long to explain in detail the 

 method by which the structures of a large 

 number of crystals have already been deter- 

 mined. Yet the work done already is only a 

 fragment of the whole, and it will take no 

 doubt many years, even though our methods 

 improve as we go on, before the structures of 

 the most complicated crystals are satisfactorily 

 determined. 



On this side then we see the beginning of a 

 new crystallography which, though it draws 

 freely on the knowledge of the old, yet builds 

 on a firmer foundation since it concerns itself 

 with the actual arrangement of the atoms 

 rather than the outward form of the crystal 

 itseH. We can compare with the internal ar- 

 rangements we have now discovered the ex- 

 ternal forms which crystals assume in growth, 

 and the modes in which they tend to come 

 apart under the action of solvents and other 

 agents. By showing how atoms arrange and 

 disarrange themselves under innumerable 

 variations of circumstances we must gain 

 knowledge of the nature and play of the forces 

 that bind the atoms together. 



There is yet a third direction in which en- 

 quiry may be made, though as yet we are only 

 at the beginning of it. In the section just 

 considered we have thought of the atoms as at 

 rest. But they are actually in motion, and the 

 position of an atom to which we have referred 

 so frequently must be an average position 

 about which it is in constant movement. Since 

 the atoms are never exactly in their places, 

 the precision of the joint action on which the 

 reflection effect depends suffers materially. 

 The effect is greater the higher the order of 

 the spectrum. When the crystal under exam- 

 ination is contained within a suitable electric 

 furnace and the atoms vibrate more violently 



