368 



SCIENCE PROGRESS 



assemblage possesses the property that, with a given density of 

 distribution of the centres, a maximum distance prevails between 

 nearest centres. This result has been arrived at by the geomet- 

 rical artifice of employing spherical surfaces for the derivation 

 of the close-packed assemblages. It must be clearly understood 

 that the atomic domain in a crystal structure is not to be regarded 

 as spherical or else we should be making a physical distinction 

 between portions of space lying within the spheres and the 

 portions forming the interstices between them ; there is no justi- 

 fication for any such distinction. The portion of space dominated 

 by each atom must rather be looked upon as polyhedral. 



Fig. 4. 



Fig. 5. 



If, however, we consider the crystals of elements to be close- 

 packed arrangements of so-called atomic spheres of influence, 

 it is evident that we can expect crystals of but two types — cubic 

 and hexagonal, the latter to exhibit the ratio a:c\= i : 0-8165 ; 

 as already stated, the expectation is realised to a great extent. 



The following elements all crystallise in the cubic system : 

 copper, silver, gold, carbon, silicon, lead, arsenic, vanadium, 

 iron, platinum, iridium, osmium, palladium, titanium, thorium, 

 germanium, mercury, gallium, chromium and nickel ; and 

 consequently their crystalline structure must be represented 

 by the cubic closest-packed assemblage of equal spheres : 

 50 per cent, of the crystalline elements are thus accounted 

 for. Another 35 per cent, crystallise in the hexagonal system 

 with the axial ratios a-.c approximating to i :o'8i65 or r6330 



