Using the Born-von Karman and rigid-ion models of Elcombe for the optical phonons in $\alpha$-quartz, we have analyzed the Raman spectra of isomorphic AlP${\mathrm{O}}_4$ (berlinite). The resulting analysis yields several physical parameters which are not accessible to any other experimental measurement; for example, the dispersion of phonon branches in the high-frequency region. Since the AlP${\mathrm{O}}_4$ Brillouin zone is halved in the [$00\zeta$] direction compared with that of quartz, phonons characteristic of critical point $A$ in quartz are Raman active in AlP${\mathrm{O}}_4$. The near equivalence of Al + P and 2Si masses and of phonon frequencies experimentally determined in Si${\mathrm{O}}_2$ and AlP${\mathrm{O}}_4$ demonstrates that a significant amount of charge compensation exists in AlP${\mathrm{O}}_4$, such that Al and P each have a nominal valence of ∼ +4, rather than +3 and +5. This is confirmed by the measured LO/TO splitting of modes which would be described as having wave vector ($0,0,\frac{\pi }{c}$) in quartz: If Al and P charges and masses were identical, these degeneracies would remain unsplit by the lattice Coulomb field. The small splittings we observe (7-19 ${\mathrm{cm}}^{-1\mathrm{}}$) for each transverse/longitudinal doublet allow us to determine the difference in effective charge for Al and P ions. An estimate of $Z\left(\mathrm{P}\right)-Z\left(\mathrm{Al}\right)\approx 0.2e$ is obtained from the rigid-ion expression $4{\pi }^2\Sigma j^{}({\omega }_{\mathrm{LO},j}^2-{\omega }_{\mathrm{TO},j}^2)=\left(\frac{4\pi }{V}\right)\Sigma k^{}\frac{Z_k^{}{}_{}{}^2}{m_k}$, and values $Z\left(\mathrm{P}\right)=2.4e$, $Z\left(\mathrm{Al}\right)=2.2e$, $Z\left(\mathrm{O}\right)=-1.15e$ deduced.

• Received 4 December 1970

DOI:https://doi.org/10.1103/PhysRevB.4.1360