“…The decay curves are monitored for the Pr 3+ emission. All curves are fitted well to the biexponential decay model based on the following formula: 44 I t = I 0 + A 1 exp(− t / τ 1 ) + A 2 exp(− t / τ 2 ),where I t and I 0 are the emission intensities, A 1 and A 2 are the fitting constants, t is the time, and τ 1 and τ 2 are the lifetimes of the exponential component. The average decay time value τ is acquired as: τ = ( A 1 τ 1 2 + A 2 τ 2 2 )/( A 1 τ 1 + A 2 τ 2 ).The corresponding average lifetimes are calculated to be 1.85 μs (320 nm), 21.75 μs (486 nm) and 13.75 μs (618 nm), respectively.…”