Alternating anion-cation bond strengths in ${\mathrm{CdGeAs}}_2$: Application to the family of ternary pnictides

We have investigated in great detail the low-temperature infrared (ir) transmission and polarized-Raman-scattering spectra of ${\mathrm{CdGeAs}}_2$. We identified all vibrational modes predicted from group-theory arguments and compared them with predictions of three- and four-parameter valence-force-field models. Assuming only nearest-neighbor interactions for the two different series of anion-cation bonds that define the ternary pnictide structure, we have found the resulting series of force constants to be in very good agreement with predictions of the semiempirical tight-binding method. This results in an inverse scaling of the force constants versus the fourth power of the bond length which, together with the use of a simple molecular model, has provided enough physical insight to allow simple but accurate predictions to be made. This shows that there is a one-to-one correspondence between the identity of chemical species that enter a given compound and the experimental phonon frequencies that dominate the ir and Raman spectra. This correspondence is found to hold true for the whole family of ternary pnictides.