DISCOVERY 



37 



surrounding it by the diffracted beams. The symmetry 

 of the patterns of spots is that of the crystal used, 

 and this shows that it is the molecular pattern of the 

 crystal which is causing the diffraction. 

 This discover^' has led to investigations which have 



FIG. 3.— REFLECTION OF A ■WAVE-TRAIN FROM THE PLANES OF 

 A CRYSTAL STRCCTrRE. CONDITION FOR REINFORCEMENT 



greatly enlarged our knowledge both of X-rays and of 

 crystal structure. We now know how the atoms are 

 arranged in a large number of the simpler crystal 

 structures ; we can make a model showing their 

 positions in the pattern, and these models explain those 

 features of crystal symmetry which have, so far, been 

 studied by means of the crystal's external appearance 

 only. Using tlie crystal as a diffraction grating, we can, 

 on the other hand, measure the wave-length of the 

 X-rays, just as the wave-length of visible light can be 

 measured with a diffraction grating. 



Let us suppose that a beam of X-rays is allowed 

 to fall on the face of a crystal. We have seen how the 

 face may be considered as being built up, as the crystal 

 grows, by layers upon layers of molecules arranged 

 in planes one on top of the other. Consideration shows 

 that each of these layers is capable of reflecting a very 

 small proportion of the train of waves constituting the 

 X-rays, so that a number of reflected wave-trains are 

 produced as shown in Fig. 3. 



If A, B, c, D represent the planes of a crystal structure, 

 then waves coming in the direction of the arrow will 

 be partly reflected at each plane. The waves reflected 

 from the plane b have gone a greater distance than 

 those reflected at a, those reflected at c a still greater 

 distance, and we have here the same conditions for 

 the interference of the waves as we have in the case 

 of a grating and light waves. If the extra distance 

 which is traversed by the waves reflected from b, as 

 compared with those reflected from a, is exactly one 

 wave-length, the two sets of waves will reinforce each 

 other. So also will those reflected from c, D, and the 

 other planes, and the combined reflected beam will be 

 strong. If, however, the crystal is set at such an angle 

 that the waves do not reinforce each other, they will 

 interfere and reflection will not take place. The condi- 

 tion that reflection should take place depends on the 

 distance between the crystal planes and on the angle 

 at which the X-rays fall on it. Measurement of the 

 angle when X-rays of a known wave-length are used 

 tells at once the distance between the layers of molecules 

 parallel to a face. 



If we measure this distance for various faces of the 

 crj'stal, we can find out the way in which the molecules 

 are arranged. For instance, referring again to the 

 two-dimensional model shown in Fig. i, if the dis- 

 tances between the rows of molecules which are 

 parallel to various faces are found, it will be clear that 

 the arrangement of the molecules in that figure can be 

 deduced. The measurements tell us the framework. 



FIG. 4a.-ARRAXGEiIENT OF C.VREON ATOMS IN FIG. 46.— ARKANGEJIENT OF ATOJIS IN £1^. 4c. -MODEL OF ROCK-SALT STOLCT^ 



A DIAilON-D. A ROCK SALT (NaO) CRYSTAL. WHITE THE L^GECIRt^E* REPRESENT M^^ 



CIRCLES REPRESENT SODIUM ATOMS, ■-'>">= -"^ <=""t ,~„to=,x.ij «t^v.<: 

 BL.^CK CHLORINE. 



ATOMS, THE SMAI,L CHLORINE .\TOMS. 



