Results of Crystal Analysis. 



75 



Returning to our crystals, we shall first consider the most 

 general type, zircon. In the cell (2dm) . (2a\ o) • (2d n0 ) 

 there should be placed 



one atom of Zr, one atom of Si, and four oxygen atoms. 



The simplest way in which we might arrange the atoms of 

 Zr and Si in the cell would he to suppose the Zr atoms- 

 arranged in a simple elementary lattice, for which we put 

 a=z2diQQ and c = 2a 7 oi, ^ud the Si atoms in a similar lattice 

 with construction-point (a/2, aj2, c/2); but such an arrange- 

 ment would make the spacing of the (100) and (001) planes 

 twice as large as they are actually observed. 



The spacings being inversely proportional to sin 0, we can 

 easily make a comparison with the observed angles and 

 those to be expected for the four types of lattices previously 

 constructed, and we notice at once that the observed spacings 

 have a relation to each other similar to those of equation (6 d) 

 corresponding to the diamond type of lattice, and a calcu- 

 lation will show that within the limit of experimental error 

 the ratios expressed in (6 d) are satisfied by observations,, 

 or 



sin 1OO : sin # oi : sin 0no : sin 1C1 : sin m "I 



= 4: 6*26: 2-83: 3-71: 2-11. 



From equations (6 d) we find for the sides of the 

 elementary lattice : 



a = 4rf 10 o, 



u 



ooi < 



Now in a lattice of the diamond type there are 8 points- 

 associated with a volume equal to that of the elementary 

 lattice (a 2 c), and consequently in a cell (a/4, a/4, c/4) there- 

 should be 1/8, or exactly the number which is found for Zr 

 or Si atoms in the elementary cell d 2 m d 00 i. 



This leads us to the assumption that in zircon the Zr and 

 Si atoms are arranged in a lattice of the diamond type. 



Regarding the relative position 'of the Zr and Si lattices,, 

 it is not necessarily determined from symmetry. The only 

 condition to be fulfilled is that corresponding points of the 

 two lattices must be situated on the tetragonal axis, or the 

 position of one must be derived from the position of the other 

 by a translation parallel to the c-axis. If the construction- 

 point for the Zr atoms has the coordinates (000), the- 



i 



