晶体离子质量差异对激活离子声子参助能量传递几率的影响

在已有理论模型的基础上讨论了基质晶体离子质量差异对激活离子声子参助能量传递几率的影响。结果表明基质离子的质量差异除了导致声子频率的变化从而影响其声子参助能量传递几率,还直接改变其传递几率的显式。对单声子参助能量传递过程,其传递几率必须乘以质量差异因子D²,对双声子参助能量传递过程其传递几率则乘以因子D⁴。文中给出了两种不同质量离子组成的晶体的因子D的表示式和p种不同质量的离子组成的晶体的因子D的一般表达式。

Effect of Mass Difference between Host Ions on the Phonon Assisted Energy Transfer Rates of the Active Ions in Crystals

Emission efficiency of the laser and luminescence materials depends directly on the concentration of active centers. In order to obtain a high efficient material, one usually hopes to increase the concentration to as a high level as possible. However, the energy transfer between active ions at a high concentration level often causes fluorescence quenching. Therefore, the study of energy transfer processes including resonant and phonon-assisted processes is important in both theory and practice. The effect of mass difference between ions of the host crystals on the phonon assisted energy transfer rates of activeions in the crystals has been discussed in this paper. Besides that resulted from the change of phonon frequency, this effect can be expressed as a multiplication factor D² for the single-phonon assisted energy transfer and D⁴ for the two-phonon assisted energy transfer. The expressions of factor D for the case when the crystal is composed by two kinds of ions,i.e.n ions with mass m and n ions with mass m is where n=n+n and m=nm+nm. Generally, when the crystal composed by p kinds of ion,one have It is clear that one can use this equation to take into account the influence of the mass difference on the energy transfer rates.