The orthosilicate phosphors Sr_xBa_2–xSiO₄:Eu²⁺ have now been known for over four decades and have found extensive recent use in solid-state white lighting. It is well-recognized in the literature and in practice that intermediate compositions in the solid-solutions between the orthosilicates Sr₂SiO₄ and Ba₂SiO₄ yield the best phosphor hosts when the thermal stability of luminescence is considered. We employ a combination of synchrotron X-ray diffraction, total scattering measurements, density functional theory calculations, and low-temperature heat capacity measurements, in conjunction with detailed temperature- and time-resolved studies of luminescence properties to understand the origins of the improved luminescence properties. We observe that in the intermediate compositions, the two cation sites in the crystal structure are optimally bonded as determined from bond valence sum calculations. Optimal bonding results in a more rigid lattice, as established by the intermediate compositions possessing the highest Debye temperature, which are determined experimentally from low-temperature heat capacity measurements. Greater rigidity in turn results in the highest luminescence efficiency for intermediate compositions at elevated temperatures.