STRUCTURE OF CRYSTALS — WYCKOFF. 203 



Powder reflections. — It has just been seen that diffraction, or "re- 

 flection," effects with X rays result either from passing them through 

 a thin section of a crystal (the Laue experiment) or by "reflecting" 

 them from the face of a crystal. In both of these cases a single 

 crystal of considerable size and perfection is required. There is one 

 other way in which definite diffraction can be obtained: by "re- 

 flecting " the X rays from a haphazard arrangement of crystals such 

 as is furnished by a fine powder. 10 In such a completely chaotic 

 grouping of crystalline particles some of them will be in a position 

 to reflect X rays from each important crystal plane. Thus interfer- 

 ence effects from all of the possible planes in the crystal will be pro- 

 duced at the same time. This third method of obtaining diffraction 

 effects makes available for study the large group of substances which 

 can not be obtained as crystals of appreciable size. 



The structure of sodium chloride. — The reflection of X rays by 

 crystals gives a means of obtaining information about the arrange- 

 ment of the atoms in the crystal. If the structure of a crystal is 

 known, then the wave length of X rays can be determined. From 

 equation (1) it is seen that if X rays of the same wave length are em- 

 ployed, the relative distance apart of like planes of atoms in different 

 directions can be derived from a measurement of the angles of reflec- 

 tion. From such measurements it appears that the spacings of like 

 planes normal to the cube, dodecahedrai and octahedral, (100), (110), 

 and (111), planes of sodium chloride stand in the ratio of 



1 • -±- • 4- 



' V2 ' V3 



W. H. and W. L. Bragg pointed out " that these observations can be 

 accounted for if the atoms of sodium chloride have the positions 

 shown in figure 22. (See p. 217.) 



The wave lengths of X rays. — A knowledge of the arrangement of 

 the atoms in any crystal makes possible a determination of the abso- 

 lute length of X rays. The necessary procedure is somewhat as fol- 

 lows: A crystal may be imagined as made up of a vast number of 

 units of structure, all alike in size and shape and similarly oriented ; 

 for instance a cubic crystal will be divisible into cubes, a hexagonal 

 crystal into either hexagonal prisms or rhombohedrons, and so on. 

 Figure 22 shows such a unit for the structure assumed for sodium 

 chloride. That four chemical molecules are associated with this cube 

 will be clear from the following considerations. The eight sodium 

 atoms at the corners of the unit are each shared by eight cubes ; all of 

 them thus place within the unit the equivalent of the mass of a single 



10 P. Debye u. P. Scherrer, Phys. Z., 17, 277, 191G. A. W. Hull, Phys. Rev., 10, 661, 

 1917. 



11 W. H. and W. L. Bragg, op. cit., chap. vil. 



