Radius ratio Rule

 

The radius ratio rule is a concept used in condensed matter physics and inorganic chemistry to determine the stability and structure of ionic compounds. It is based on the idea that cations and anions in an ionic compound will arrange themselves in a way that maximizes the number of cation-anion contacts while minimizing the electrostatic repulsion between ions. The radius ratio is defined as the ratio of the radius of the cation to the radius of the anion, denoted as r+/r-. The rule states that an ionic compound will be stable if the value of the radius ratio falls within a certain range for a given coordination number. The coordination number is the number of anions that surround a cation in the crystal lattice. The critical radius ratio is the value of the radius ratio at which the electrostatic repulsion between ions becomes too strong and the crystal lattice becomes unstable. For coordination number six, the stability limit occurs at a radius ratio of 0.414, where the cation is touching all the anions and the anions are just touching at their edges. It is important to note that the radius ratio rule only applies to ionic substances and not to covalent compounds. Additionally, the rule is a simplified model and does not take into account other factors that can affect the stability and structure of ionic compounds, such as charge density and crystal packing effects.