According to eqn (3) , the average decay time is expressed as the following expression: 4 τ = ( A 1 τ 1 2 + A 2 τ 2 2 ) / ( A 1 τ 1 + A 2 τ 2 ) as the concentration of Dy 3+ increases from 0 to 0.005, the lifetimes of the samples are fitted to be 6.63 ms, 6.48 ms, 6.48 ms, 6.08 ms, 5.99 ms, and 5.97 ms, respectively, indicating a decreasing trend with increasing concentration of Dy 3+ , which can be ascribed to a poor impact stemming from concentration quenching.
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A crystal defect led zero thermal quenching β-NaYF<sub>4</sub> : Eu<sup>3+</sup>,Dy<sup>3+</sup> red emitting phosphor.
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