Analyses of the R₁-line thermal shifts for Bi₂Al₄O₉: Cr³⁺ and Bi₂Ga₄O₉: Cr³⁺ crystals with a complete equation

ABSTRACT

The thermal red-shifts of R₁-line for Cr³⁺-doped Bi₂Al₄O₉ and Bi₂Ga₄O₉ crystals are analyzed with a complete equation containing not only the dynamic factor (used previously) due to electron–phonon interaction, but also the static factor caused by lattice thermal expansion. From the analysis, the static parameters A (charactering the static factor), the more reasonable electron–phonon coupling parameters${\alpha }^{\mathrm{\prime }}$(charactering the dynamic factor) and hence the more accurate quadratic coupling constants w for the two crystals are gained. It is found that the static factors are about 17% and 9% of the dynamic factors for Bi₂Al₄O₉: Cr³⁺ and Bi₂Ga₄O₉: Cr³⁺ crystals, respectively. So, in the accurate and reasonable analysis of R₁-line thermal shifts in the two crystals (or other spectral line thermal shifts in crystals), the static factor needs to be considered and the complete equation including both factors should be adopted.

KEYWORDS:

• Luminescence
• thermal shifts
• Cr³⁺
• Bi₂Al₄O₉
• Bi₂Ga₄O₉

Disclosure statement

No potential conflict of interest was reported by the authors.