The time-resolved optical measurements reveal rate-dependent ML emission behaviors under rapid compression at 0–10 GPa, namely, diffuse-like ML behavior with broad peaks at the rate below 1.2 GPa/s and oscillatory ML emission with a series of the peaks at the critical rate of ~ 1.2–1.5 GPa/s. It means the compression rates has significant influence on the mechanically-excited process of ML. Before discussing rate-dependent emission kinetics, let us recall the self-recoverable ML mechanism previously reported18,29,32–34. The piezoelectric SrZnOS: Mn2+ ion has a non-centrosymmetric hexagonal structure (P63mc) with excellent piezoelectric and EML properties6,37,41, similar to the wurtzite zinc ZnS: Mn2+. Based on previously reported de-trapping mechanism in ZnS: Mn2+/Cu2 + 1,15–17,20,35, here, the ML emission process is proposed for SrZnOS: Mn2+ through PIE of the luminescent Mn2+ in the 4T1 to 6A1 transition (Fig. 5a). Upon rapid compression with deviatoric stress at a given rate, a piezoelectric field is generated via deformation-induced polarization, accompanied by the de-trapping process with the separation of the trapped electrons and holes around the activator of Mn2+. The escaped de-trapped electron may be thermally activated into the conduction band. The thermoluminescence (TL) results for SrZnOS: Mn2+ at ambient pressure confirm the existence of the defect traps with the trap-depth at 0.73–0.85 eV, following Gaussian-shaped trap-depth distribution42–43 (Supplementary Fig. 11). Under piezoelectrical perturbation, the conduction band is tilted due to the piezoelectric effect, leading to a recombination of the de-trapped electrons and holes with the release of radiative energy. The luminescent Mn2+ is excited from the ground state (6A1) to the excited state (4T1) by the energy transfer, and then the photon emission occurs in the 4T1 to 6A1 transition of Mn2+. The above ML kinetic process, given by the piezoelectrically-induced de-trapping mode, describes a cycle of the PIE and photon emission process of the luminescent ions, in which an emission peak will appear in the ML curve. This has been confirmed by the ML experiments17,19–20,31-34. Self-recovery that may involve re-trapping (or energy re-charging) of the carriers is required for multi-cyclic PIE processes. It can be speculated that a series of oscillatory ML emission peaks with adjacent ones distinguished will be observed during the multi-cyclic PIE and self-recovery processes if the time scale required for the PIE and self-recovery is comparable to or longer than that of the width of the emission peaks.
Combined with previous studies in the MPa pressure range1,15–20,28-34, the following conditions may lead to the occurrence of the oscillatory ML emission peaks in the time-dependent instantaneous intensity: Multi-cyclic PIE and self-recovery processes that the carriers and luminescent ions involve (i) under ramp compression at a given rate, (ii) during multi-cyclic compression-decompression processes at a given frequency, and (iii) under continuous stepwise compression; (iv) ML peaks will appear if the trap-depth of the carriers have an oscillatory distribution in the GPa pressure range. In our experiments, we compressed sample continuously at a given rate, and the derivative stress should increase with pressure, ruling out the possibilities of (ii) and (iii) (Supplementary Fig. 12)18,29. For the case of (iv), we checked the ML emission under compression from different initial pressure to ~ 10 GPa at a given rate, and found the ML intensity did not follow the oscillatory change with initial pressure, excluding the oscillatory distribution of the trap-depth (Supplementary Fig. 13). Therefore, we believe that the oscillatory ML emission under rapid compression at the critical rates should stem from the multi-cyclic processes of the PIE and self-recovery, viz, the first possibility.
Here, the ML emission peaks in the time-dependent instantaneous ML intensity of SrZnOS: Mn2+ are interpreted tentatively using the equation proposed by Chandra et al (Fig. 5b, c)17,19. The Chandra’s model predicted a ML peak in the time-dependent instantaneous ML intensity, viz, the cumulative ML intensity has a sigmoidal profile over time19. The ML peak corresponds to a process in which the luminescent ions involved undergo a cyclic PIE and photon emission process. The characteristic time (τML), determined by the peak width, is predicted to decrease linearly with increasing rate. The fitting result at ~ 1.25 GPa/s shows that the model can describe the time-dependent ML intensity very well, implying that the oscillatory emission peaks correspond to multi-cyclic processes of the PIE and self-recovery that the luminescent ions involve. The characteristic time (τc) corresponds to the time required for the PIE and self-recovery process. Below the critical rate, the ML curve may consist of several broad emission peaks which are hardly distinguished due to the large τML (Fig. 5c). It is difficult to determine how many cycles the luminescent ions have been piezoelectrically excited.
The above analysis shows that the oscillatory ML behavior is the result of the competition between τc and τML. The measurement of the PL lifetime shows the time scale of ~ 2 ms for the photon emission, much shorter than τML and τc (Fig. S9). This means the PIE and self-recoverable processes is much longer than the photon-excitation in PL. The shorter the τML and τc, the faster the PIE and self-recovery processes. The minimum value of τML and τc observed at the critical rates of ~ 1.2–1.5 GPa/s implies the shortest time required for the PIE and self-recovery process, a limit in the dynamic response to the rapid compression. To study the temperature effect, τML and τc at the critical rate are plotted as a function of temperature (Fig. 5d, e). When Fig. 5(c) is plotted with the natural logarithm of the critical τML and inverse temperature, the result shows an approximately linear relationship between τML and 1/T, i.e., there is an Arrhenius relationship between the critical τML and temperature with 1/τ = C*exp(-Q/kBT)45–47, where C is a constant and Q is the thermal activation energy required to be overcome for the PIE processes. Fitting the experimental data yields Q of 0.042(1) eV. Q is close to the thermal energy (kBT), but much smaller than the trap-depth (0.73–0.85 eV) of the carriers. This indicates that the thermal effect exerts a subtle, favorable influence on the PIE process.
On contrast, τc almost changes negligibly with temperature. However, the difference between τc and τML, that corresponds to the self-recovery process, increases slightly over temperature. This suggests unfavorable effect of temperature on the self-recovery process (Fig. 5e). Previous studies indicate the self-recovery process is related to the re-trapping of the carriers or recharging of the piezoelectric field29,31–34. Regardless of them, the mechanical work (W = P*ΔV) per unit cell is calculated to be ~ 0.04 eV if assuming that the sample is compressed from ambient pressure to 1 GPa, significantly smaller than the photon energy of ~ 2.0 eV emitted in ML. This implies the mechanical work contributed by the atoms around the luminescent ions will be essential for photon emission. Meanwhile, the ML light emission only occurs when pressure changes continuously at a given rate, indicating the mechanical work needs to be accumulated over time. Therefore, the self-recovery may be a process of the energy accumulation in time and space for the mechanical-photon energy conversion. The temperature dependence of the difference between the τc and τML shows the thermal effect may disturb the energy accumulation in the self-recovery process (Fig. 5e). It should be noted that the above interpretation is based on the de-trapping model, but more theoretical and experimental work is required to confirm it.
In summary, we reveal a compression rate-dependent distinct ML kinetics in the Mn2+ dopped SrZnOS at different rates and various temperatures. The optical fluorescent, PMT and imaging measurements present a diffuse-like emission with broad peaks in the ML intensity as a function of time (or pressure) at compression rate below ~ 1.2 GPa/s, and resonant ML emission character with the distinguishable oscillatory peaks at critical compression rate between 1.2 GPa/s and1.5 GPa/s. The oscillatory ML emission is gradually suppressed with increasing compression rates above ~ 5 GPa/s, where the number of the emission peaks and total ML intensities decrease. It could be counted for the multi-cycles of the PIE and self-recoverable processes that the luminescent ions undergo during the compression process when the compression time is comparable to the intrinsic time scales of the piezoelectrically-induced excitation and light emission. The rate dependence of the characteristic time in the ML kinetics indicates the limit of the ML light emission in the dynamic response to the rapid compression. The present work offers new technical methods and notions for the study of the ML in the GPa pressure range, and uncovers rate-dependent distinctive kinetics of the ML emission, presenting new perspectives for understanding the mechanoluminescent mechanism that facilitates the design and development of high-performance ML materials in materials science, and opening new research direction for high-pressure science.