SEPT. 19, 1921 WYCKOFF: WAVE LENGTHS OF X-RAYS 369 



found to give effects in what must correspond with the first order 

 region, and (2) the confirmatory observation (from spectrometer 

 measurements) that the first observable reflections from the (100), 

 (110) and (111) faces stand in the ratio of 



' V2 ' V3 



The familiar "sodium chloride arrangement" (Fig. 2), with four 

 chemical molecules associated with the unit cell, is in agreement with 

 the above data, so that it has been taken as the structure of this 

 crystal. Accepting such an identification as correct, a substitution 

 of m = 4 in expression (2) yields dioo, and since the value of n is also 

 directly determinable from a knowledge of the crystal structure, it is 

 but a step to obtain the wave length of the X-rays (diffracted through 

 the angle 6) . 



Other possible structures for sodium chloride. — The most serious 

 objection to this determination of the wave length of X-rays obviously 

 rests in the implied statement that because it agrees with these rather 

 meager data, the "sodium chloride arrangement" is the correct one 

 for this salt. 



It will now be shown that other structures are possible. The 

 effect of this observ^ation will of course be to render this determination 

 of the wave length of X-rays based upon the study of the structure of a 

 crystal indeterminate (and along with it all determinations of the 

 structures of crystals), 



A factor which gives the effect of phase differences between the waves 

 scattered by the atoms in any arrangement and which is therefore 

 proportional, under certain conditions, to the intensity of the X-rays 

 seemingly "reflected" by a plane of atoms can be written as* 



I ^ ^[pm cos 2 irn ihxm + kym + Izm) Y -\- 



m 



S]p „, sin 2 irn {hx,n + ky^ + IzJ ]-, 



m 



where / is the intensity of reflection from planes hkl having the same 

 relative spacings, 



p is the scattering power of the atom m whose coordinate 

 position is Xj^ymZmt and 



n is the order of the reflection. 



« Ralph W, G. Wyckoff. Amer. Journ. Sci. 50: 317. 1920. 



