240 Wychoff — Crystal Structure of Alahandite. 



of calcite and the (100) face of the crystal of alahandite 

 was prepared in the usual manner. From the known 

 reflection from calcite an accurate measurement was 

 obtained of the distance from the reflecting crystals to 

 the photographic plate ; this determination was then used 

 in the calculation of the spacing of alahandite. From 

 the application of these measurements to the usual 

 equation 



71/. = 2cl sin e^ (l) 



a mean value of d^oo/n, where d^Qo is the length of the 

 side of the unit cube and n is the order of the reflection, 

 for this crystal of alahandite was found to he 



d^^„/n = 2.607 X 10-' cm. 



The density of this mineral is variously stated to lie 

 between p=3.95 and /3=4.04.'^ From a knowledge of the 

 spacing against the cube face and of the density of the 

 substance the ratio of the cube of the order of the reflec- 

 tion, n, to m, the number of chemical molecules associated 

 with the unit cube, becomes with the aid of 



nym = M/{cl,^/ny X p (2) 



(where M is the weight of a single chemical molecule of 

 the compound) 



n'/m = 2.038 when p = 3.95, or 

 n'/m = 1.994 when p — 4.04. 



From this it is evident that the measured reflection is 

 either the second-order one from a crystal whose unit 

 contains four chemical molecules or a fourth-order reflec- 

 tion from one having a unit composed of thirty-two 

 chemical molecules. 



The Possible Arrangements of the Atoms within the 

 Unit Cube. — If alahandite has tetrahedral cubic symme- 

 try then it must be assignable to one of the space groups 

 showing a hemimorphic hemihedry; if tetartohedral, it 

 must have the symmetry of one of the space groups T^"^. 



Four Molecules in the Unit. — Two space groups, T a ' 

 and Td ^, having the symmetry of the hemimorphic hemi- 

 hedry, furnish two special cases with four equivalent 

 positions within the unit cell.^ Three tetartohedral 



*P. Grotli, Chemisclie Krystallographie, I, p. 146. 



^ These results are taken from tables, yet unpublished, which give a com- 

 plete analytical representation of the theory of space groups. 



