Investigation of doped calcium aluminosilicate glass: A coupling between thermal-expansion and thermal-diffusion models for assessment of nonradiative relaxation time and characteristic diffusion time

This paper discusses the use of photoacoustic models to obtain the nonradiative relaxation time (τ) and characteristic diffusion time (τβ) for a sample showing visible absorption bands from fluorescent ion-doped low-silica calcium aluminosilicate glass. Two models allowing phase shift analyses, the thermal-expansion and thermal-diffusion models, are briefly reviewed. These models have limitations when the photoacoustic signal depends on both factors, in a coupling mechanism. An alternative model is proposed to take both thermal expansion and thermal diffusion into account with a single temperature solution for the heat-coupled differential equation. This model is simulated for absorbing samples near the thermally thick region. The model is applied to Eu–V codoped glass showing intermediate signal dependence from ω−1.0 to ω−3/2. The nonradiative time and characteristic diffusion time are derived with 33<τ(ms)<39, and τβ(ms)∼70 ms for the Eu-ion and 340<τβ(ms)<710 for the V-ion. Four absorption bands were analyzed (280, 350, 420, and 600 nm), which showed a signal dependence from ω−1.1 to ω−1.52. Absorption coefficients were derived from τβ in the range of 15<β(cm−1)<51, which agreed fairly well with spectrophotometer data for the same ions.