PROF. W. H. BRAGG ON X-RAYS AND CRYSTAL STRUCTURE. 



257 



a point in each group is chosen to represent that group it must be similarly 

 situated in each group the points will lie at the intersections of such a set of lines 

 as are shown in fig. 5. If they do not do so the unit chosen must be incomplete and 

 is indeed not a unit at all. The figure may be regarded as composed of rhomboidal 

 cells, and in the most general case three unequal edges of each cell meet at every 

 corner and include three unequal angles. 



The determination of the form of this fundamental lattice is a necessary preliminary 

 in any investigation of crystal structure. It involves the measurement of the three 

 edges and three angles of the elementary rhomboidal cell. 



But the form of the crystal structure is not fully known until we have also deter- 

 mined the disposition of the atoms about the representative point in each unit. 



There are thus two stages in such an investigation, and the X-ray method operates 

 in entirely different ways in the two. 



^ ^ 



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 _^1 / >7 / ,>? / ,>/ 



i/iu/rm 



I 



LK / /^/ / 



v / / // / / 7, . . 



/ ~Z'-77 / / 



Fig. 5. 



Fig. 6. 



Let us first consider the determination of the fundamental lattice. 



If we knew what faces of the crystal, if any, were parallel to the faces of the cell, 

 we should merely have to measure the spacings perpendicular to the faces and our 

 work would be done. It might not even be necessary to make more than one such 

 measurement because the relative values of the spacings might be known from con- 

 siderations of crystalline form. The same knowledge of form which told us the faces 

 to measure, would give us also the angles of the cell, and so all the quantities would 

 be known. 



Although, however, a knowledge of crystalline form gives the most valuable 

 suggestions as to the dimensions of the elementary cell, its indications are not always 

 definite. A very interesting and important example occurs in the case of cubic 

 crystals. If the elementary cell were a cube, we ' should certainly expect the form of 

 the crystal to be cubic ; but there are also two other forms of lattice which may lead 

 to the cubic habit and one of these is of the greatest importance to us. If the three 

 edges are all equal, and the three angles are all 60 degrees, we have the cell shown in 

 the dotted lines of fig. 6, and the distribution of points which it gives may also be 



