How does coordination number vary with the radius ratio?

The coordination number of a metal ion in a crystal structure generally increases with the radius ratio, which is the ratio of the radius of the cation to that of the anion. As the radius ratio increases, larger cations can accommodate more neighboring anions, resulting in higher coordination numbers. For example, a radius ratio of approximately 0.414 corresponds to a coordination number of 4 (tetrahedral), while a radius ratio closer to 0.732 corresponds to a coordination number of 6 (octahedral). However, this relationship can also be influenced by factors such as ionic charge and the specific crystal structure.