646 
CHEMISTRY: BURDICK AND ELLIS 
1 : 0.707: 0.573; 1 : 0.707 
2$ 
Interpretation of the Results. — In determining the atomic structure of 
chalcopyrite, we will first attempt to fix the type of lattice on which it 
is constructed. For approximate purposes its crystals may be regarded 
as isometric, since the axial ratio a: c (1: 0.985) is nearly unity. 
The interplanar distance d (that is, the distance between like planes 
of atoms) is by the fundamental law of reflection {n\ = 2d sin B) in- 
versely proportional to the sine of the angle of reflection {S). For the 
three fundamental planes (100) (101) (111) the angles were 6°25', 
9°V , and 5°32'. The reciprocals of the sines of these angles stand to 
one another in the ratio 1 : 0.706 : 1.152. The ratios of the interplanar 
distances in the three possible types of isometric lattice, known as the 
cubic, the face-centered, and the cube-centered^ are respectively 
1.146; and 1 : 1,414: 0.573. The lattice in- 
volved in the chalcopyrite crystal is 
therefore obviously the face-centered 
type; and we may infer that the heavy 
atoms, which predominate in determin- 
ing the reflection, must be the points in 
this lattice. 
Since there is only a small difference 
in the atomic weights of iron and copper, 
their reflecting powers, like those of potas- 
sium and chlorine in potassium chloride, 
will not be greatly different. The atoms 
of iron and copper will therefore be prac- 
tically indistinguishable in their effect on the X-rays. The observations 
then show that the basic lattice formed by the iron atoms must intersect 
that formed by the copper atoms in such a way as to form together a 
single face-centered lattice. 
A study with the aid of a model of possible arrangements by which 
two different kinds of atoms, present in equal numbers, could together 
form a single face-centered lattice shows that there is only one such 
arrangement; namely, that shown in the accompanying figure, in which 
the iron atoms and copper atoms are represented by the solid and 
annular circles. It is evident, moreover, from the symmetries of the 
atomic arrangements that the vertical axis in the figure corresponds to 
the tetragonal or c axis in the crystal. 
These conclusions are corroborated by the fact that the observed 
angles of reflections agree closely with the 'calculated' angles (given in 
the table), which were computed geometrically from the assumed loca- 
COPPER AND IRON ATOMS IN CHAL- 
COPYRITE LATTICE. 
