Perturbed-angular-correlation (PAC) spectroscopy was used to investigate several structural features of the ceramics ${\mathrm{Ba}}_{2}$(${\mathrm{Ti}}_{0.95}$${\mathrm{Hf}}_{0.05}$) ${\mathrm{Ge}}_{2}$${\mathrm{O}}_{8}$ and ${\mathrm{Ba}}_{2}$(${\mathrm{Ti}}_{0.95}$${\mathrm{Hf}}_{0.05}$) (${\mathrm{Ge}}_{0.4}$${\mathrm{Si}}_{1.6}$)${\mathrm{O}}_{8}$, which have technological importance as pyroelectric and piezoelectric materials. Hafnium was introduced into the materials to provide the PAC probe nuclei $^{181}\mathrm{Hf}$${/}^{181}$Ta, and PAC measurements were made over a range of temperatures from 77 to 1380 K. High-frequency, static nuclear-electric-quadrupole interactions were observed in both compounds, and chemical considerations indicated that these interactions occurred at the Ti sites. Because the electric field gradients (EFG's) associated with these interactions were produced primarily by the apical O atoms in the ${\mathrm{TiO}}_{5}$ tetragonal pyramids, neither the strength nor the symmetry of these interactions was very sensitive to the differences in the Ge-Si composition. More importantly, these high-frequency interactions showed similar, nonzero asymmetry parameters \ensuremath{\eta} at low temperatures and small-to-vanishing \ensuremath{\eta} values at high temperatures. This asymmetry was unexpected and is anomalous. Because these results cannot be reconciled by the crystal structure symmetry, a phase change may have occurred between 500 and 700 K. In addition to these high-frequency interactions, each of the two ceramics showed a different second static interaction, but insufficient information was available to identify the specific sites of these interactions.The temperature dependence of the EFG at the Ti site, which was essentially the same for both ceramics, was analyzed using three simple models, which were based on the Debye crystal model. The best description was provided by a (3/2-power dependence of the EFG on temperature. This result indicates that the vibrational motion of the quasi-one-dimensional Ti-O structure was not significantly anharmonic or anisotropic. These exploratory measurements suggest that a better understanding of the electrical-optical properties may be obtained by performing more extensive PAC measurements.