The Intensity of Reflexion of X-Rays by Rock-Salt. 335 



modal must be taken which has a greater concentration of 



electrons near the centre than that in the case o£ a uniform 



distribution. 



An important distinction must be made between the 



diffraction of X-rays by a crystal and the scattering of 



X-rays by an amorphous mass of material. In the formula 



e 

 for the intensity of reflexion, the quantity F — § represents 



the amplitude of a polarized wave diffracted by a single atom 

 m various directions. This amplitude must not be supposed to 

 be necessarily the same as that which determines the amount 

 of radiation scattered in various directions by an amorphous 

 mass of the same atoms in a random arrangement. It is 

 justifiable to consider the scattering by an amorphous sub- 

 stance as the summation of the intensities due to the separate 

 atoms. If the electrons are in vibration, as has been 

 supposed in the third atom model, their movements will be- 

 slow as compared with the frequency of the X-radiation. 

 In the case of a single atom which is scattering the radia- 

 tion, the arrangement of electrons in the atom at any one 

 moment may be a random one, and the displacements may 

 be so large and arbitrary that we may simply consider the 

 scattering as due to a random arrangement of Z electrons, 

 Z being the atomic number. If the amplitude of the 



e 2 — 



scattered wave is F' — - S5 F ; may be nearly equal to V 7 Z for 



all angles of scattering, except for very small angles where 



all the electrons are in phase and " excess scattering " comes 



into play. 



The factor F' will not be the same as the factor F in 



the case of the atoms of a crystalline substance. When 



examining the reflexion from a crystal, we have a large 



number of atoms diffracting waves which are exactly in 



e 2 

 phase with each other. F — =■ is now the amplitude scattered 



mr L 



by what we may term the "statistical" atom. In this case 

 the movements of the electrons are allowed for by supposing 

 that diffraction takes place, not at single electron points 

 displaced from their mean positions, but from all over a 

 certain region for each electron in which all its possible 

 positions lie, due weight being given to each element of the 

 region. This has been done in calculating F for the third 

 atom model. This region may be so large that the effect of 

 the outer electrons is practically zero for the higher orders, 

 and this illustrates the essential difference between the two 



