In case of tetrahedral arrangement, the angle ABC is 109 ° 28´ . Hence, the angle ABD is half of the angle ABC = 54 ° 44 ´
Sin ABD = AD/AB = r − / r + + r − = 0.8164
or, r + + r − / r − = 1.225
or, r + / r − = 1.225-1.000 = 0.225
Coordination number 6 (octahedral):
Figure 2.4. Cross section of an octahedral arrangement.
In this case, the angle BAC = 45 ° .
cos BAD = AD/AB = r − / r + + r − = 0.7071
or, r + + r − / r − = 1.414
or, r + / r − = 1.414-1.000 = 0.414
