This paper makes a contribution towards understanding recent extended x-ray-absorption fine-structure (EXAFS) measurements on the mixed-valence solid ${\mathrm{Sm}}_x{\mathrm{Y}}_{1-x}\mathrm{S}$. These experiments have been interpreted as showing that the difference $\delta R$ between the nearest-neighbor distances ${\mathrm{Sm}}^{2+}$-${\mathrm{S}}^{2-}$ and ${\mathrm{Sm}}^{3+}$-${\mathrm{S}}^{2-}$ is less than 0.05 Å. The difference between the ionic radii of ${\mathrm{Sm}}^{2+}$ and ${\mathrm{Sm}}^{3+}$ is much larger, 0.18 Å. We show that in the fluctuating-valence solid the large electronic hybridization energy (enhanced by the sixfold degeneracy of the ${\mathrm{Sm}}^{3+}$ configuration), tends to strongly reduce the dependences of the positions of ${\mathrm{S}}^{2-}$ ions on the valency of the Sm ions. We find that $\delta R$ lies in the range between 0.045 and 0.06 Å, and could possibly be even smaller if a better estimate of the crucial hybridization matrix element $\frac{\Delta }{\pi }$ should become available.

• Received 17 August 1981

DOI:https://doi.org/10.1103/PhysRevB.25.3557