An empirical relation fitting the position in energy of the lower d-band edge for Eu2+ OR Ce3+ in various compounds

For most divalent and some trivalent rare earth ions in suitable matrices, stimulated emission may occur from the low energy edge of the d-band. The position of the d-band edge (E) in energy for rare earth ions that fluoresce with broad emission bands is known to be sensitive to electron-electron repulsion between the “active” cation and its surrounding anions. Indeed for any one of a number of these “active” ions, emission color range from the ultraviolet to the infrared. It is shown that the relation

$\text{E=Q1?}\text{V}\text{4}{}^{\mathrm{<mtext>1</mtext><mtext>V</mtext>}}\text{10}{}^{\mathrm{<mtext>?(near)</mtext><mtext>80</mtext>}}\text{]}$

provides a good fit to the emission peak and/or excitation edge data for Eu²⁺ and Ce³⁺. Here Q is the position in energy for the lower d-band edge for the free ion (obtained from spark data), V is the valence of the “active” cation, n is the number of anions in the immediate shell about this ion, ea is the electron affinity of the atoms that form anions, and r is the radius of the host cation replaced by the “active” cation. The relation has predictive capabilities for estimating an unknown from the remaining variables and should apply to other rare earth ions as well.