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

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This paper discusses the use of photoacoustic models to obtain the nonradiative relaxation time () and characteristic diffusion time () 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 ^−1.0 to ^−3/2. The nonradiative time and characteristic diffusion time are derived with 33<(ms)<39, and (ms)~70  ms for the Eu-ion and 340<(ms)<710 for the V-ion. Four absorption bands were analyzed (280, 350, 420, and 600 nm), which showed a signal dependence from ^−1.1 to ^−1.52. Absorption coefficients were derived from in the range of 15<(cm⁻¹)<51, which agreed fairly well with spectrophotometer data for the same ions. ©2009 American Institute of Physics