Emission Decay Research Articles

Enhancement of Circularly Polarized Luminescence Brightness of Schiff‐Base Diphenylboron and 9‐Borafluoren‐9‐yl Complexes

AbstractA series of diphenylboron and 9‐borafluoren‐9‐yl complexes with chiral Schiff‐base ligands was synthesized and characterized by NMR spectroscopy. X‐ray diffraction analysis revealed that their boron centers were adapted to tetrahedral coordination geometry. Although boron complexes with salicylideneimine backbones exhibited a weak circularly polarized luminescence (CPL), the CPL brightness (BCPL) was enhanced more than 9‐fold by the π‐extension of the Schiff base ligands. Time‐resolved emission decay analysis and theoretical calculations based on density functional theory (DFT) were conducted to further understand their luminescent properties.

Colloidal down-shifting Gd2O3:Eu3+/SiO2 phosphors nanocomposites using one-pot modified surfactants-based soft templates for catalytic applications

The application of rare earth (RE)-based phosphor materials faces a significant challenge in adopting strategies to bring down the cost without compromising their properties. The most straightforward approach is to minimize the use of RE elements. Herein, we demonstrate the use of SiO2 as an economical solid nano-matrix for lanthanides-based phosphor nanomaterials. Gd2O3:Eu3+(x%) and Gd2O3:Eu3+(x%)/SiO2 nanophosphor composites were prepared through a modified soft templating technique using cetyltrimethylammonium bromide (CTAB) as the surfactant. The photoluminescence properties were studied by excitation, emission, and luminescence decay investigations. Upon excitation in the O2−(2p)→Eu3+(4f6) LMCT state, these nanophosphors exhibited predominantly red emission from the 5D0→7FJ transition (where J = 0–4) of the Eu3+ ion. Moreover, the synthesized low-cost Gd2O3Eu3+(5 %)/SiO2 composites, with a small number of lanthanides, exhibited excellent photocatalytic degradation activity for organic dye (methylene blue) under visible light (λ ≥ 420 nm), showing promising potential for photocatalytic wastewater treatment.

Energy Transfer of a New Self-Activating Ba<sub>3</sub>TaGa<sub>3</sub>Si<sub>2</sub>O<sub>14</sub>: ySm<sup>3+</sup>, xNb<sup>5+</sup> Phosphor Obtained by a Small Substitution of Nb<sup>5+</sup> for Ta<sup>5+</sup>

Self-activated multicolor phosphors are being used in more and more emerging fields. In order to explore the energy transfer between [NbO6]7- coordination groups and Sm3+ ions, a series of Ba3-ySmyTa1-xNbxGa3Si2O14 samples co-doped with Nb5+ and Sm3+ were prepared in this work, and the changes of luminous intensity under the condition of fixed Nb5+ concentration regulating Sm3+ concentration and fixed Sm3+ concentration regulating Nb5+ concentration were obtained respectively. By further fitting the emission decay curves of Sm3+ under two conditions, the decreasing average lifetime is obtained. Thermal stability tests of the samples also hinted the presence of such energy transfer. This regular change can provide a good reference for developing new self-activated phosphors.

Er3+/Tm3+ codoped CaF2 based oxyfluoroborosilicate glass-ceramics for fiber laser applications

Transparent Er3+/Tm3+ codoped CaF2 based oxyfluoroborosilicate glass-ceramics (BSEr1TmxGCs) with variable Tm3+ concentration were prepared through melt quench process followed by reheat treatment at 450 °C/1h. They were characterized through differential scanning calorimetry (DSC), powder X-ray diffraction (XRD), Fourier transform infrared (FTIR) Raman spectroscopy, near infrared (NIR) emission and luminescence decay. The formation of CaF2 nanocrystallites against oxyfluoroborosilicate glassy phase was confirmed by scanning electron microscopic (SEM) and hi-resolution transmission electron microscopic (HRTEM) studies. The NIR emission properties were investigated at 460 nm diode laser pumping. The applicability of BSEr1TmxGCs were examined by evaluating effective bandwidth (Δλeff), stimulated emission cross-section (σe), gain bandwidth (σe × Δλeff), figure of merit (σe × τR) and quantum efficiency (ηQE). The energy transfer efficiency (ηET), rate of energy transfer (WET) between Er3+ and Tm3+ and the rate of non-radiative transitions (WNR) were also calculated. The comparative NIR emission performance suggests that the BSEr1Tm1GC has proficiency for 1530 nm broadband fiber lasers and optical amplifiers in short wavelength and conventional wavelength (S + C) band communication window.

Luminescence and Faraday rotation properties of Tb2O3 and Tb:Y2O3 single crystals

Heavily-doped and fully concentrated 2.78% Tb:Y2O3 and Tb2O3 single crystals with high optical quality and very low levels of impurities have been grown and studied for their luminescence and Faraday rotation properties. Absorption, emission and fluorescence decay measurements performed vs excitation wavelength and temperature and their confrontation with Judd-Ofelt and crystal-field calculations show the contributions of two types of luminescent centers: dominant ones with a 5D4 emission lifetime of 23 μs corresponding to coupled near-neighbor Tb3+ ions, all in C2 symmetry sites, and minority ones with a 5D4 emission lifetime of about 2 ms corresponding to coupled Tb3+ ions in C2 and C3i near-neighbor symmetry sites. Faraday rotation measurements confirm Tb2O3 as the Tb-based Faraday crystalline material with the largest ever measured Verdet constant, at all temperatures and from the visible to the near-infrared. They also show that the dominant luminescent centers contribute more particularly to this large Verdet constant thanks to a favorable crystal-field splitting of their 7F6 ground multiplet and also to the contributions of both types of spin-allowed and spin-forbidden 4f-5d absorption bands.

Synthesis of low-dimensional metal halide CsAgCl2 for X-ray scintillation applications

Low-dimensional metal halides, which possess efficient luminescent properties, have garnered significant interest in the fields of optoelectronics and radiation detection. This study introduces novel lead-free silver-based metal halide material, CsAgCl2 microcrystals (MCs). These MCs have a one-dimensional atomic chain structure and a unique [AgCl5]4- tetragonal shared triangular configuration. CsAgCl2 MCs exhibit excellent performance as X-ray scintillators due to their bright broadband yellow emission and fast decay time in the microsecond range. The large Stokes shift of 350 nm is produced by self-trapped exciton emission. In X-ray scintillation applications, CsAgCl2 MCs demonstrate a high light yield of 13280 photons/MeV and a wide range of linear scintillation response. It is noteworthy that the CsAgCl2 MCs maintain good stability under both atmospheric conditions and continuous X-ray irradiation. The sample was used in an X-ray imaging screen, which clearly presented the X-ray projection image of a wooden stick. As a result, this research not only contributes to the collection of lead-free metal halide scintillators but also indicates that CsAgCl2 MCs have a wide range of future applications and potential in areas such as medical imaging, scientific research, and diagnostic and detection technologies.

Concentration- and temperature-dependent luminescence mechanisms and fluorescence dynamic temperature sensing of NaY(MoO4)2:Tb3+ phosphors

High-temperature solid-state reaction technique was used to prepare NaY(MoO4)2:Tb3+ phosphors with different Tb3+ concentrations. XRD patterns showed that the prepared samples contained only single-phased compound NaY(MoO4)2. The concentration-dependent green luminescent intensity of Tb3+ was studied, and it was found that the concentration quenching process is in charge of Ozawa's model. The concentration-effect of luminescence decay of 5D4 level was explained by the Auzel's self-generated quenching theory. Starting from the Reisfeld's theory, the analysis on the luminescence decays also indicated exchange interaction was responsible for the concentration quenching. Temperature dependences of the green emission intensity and decay were comprehended based on the crossover mechanism. A novel temperature sensing technique rooting in the fluorescence dynamics of 5D4 level of Tb3+ in NaY(MoO4)2 was proposed, and the absolute and relative sensitivities were deduced and assessed.

Blue and white light emissions and energy transfer in Tm3+ and Dy3+/Tm3+ doped lithium-aluminum-zinc phosphate glasses

Lithium-aluminum-zinc phosphate glasses doped with thulium and dysprosium ions are characterized by using spectroscopy techniques. The Judd-Ofelt parameters were evaluated to calculate the radiative parameters of thulium 1D23F4 and 1G43H6 visible transitions and 3H43F4 near infrared transition, which shows the highest optical amplification parameters. Upon 356 nm excitation, the Tm3+ doped phosphate glass emits blue light with CIE1931 chromaticity coordinates x = 0.1540 and y = 0.0283 and color purity around 96.8%. With excitations at 347 and 350 nm, the Dy3+/Tm3+ doped phosphate glass emits neutral and cold white light with correlated color temperature values of 4716 and 6628 K, respectively. The dysprosium emission decay time in the codoped glass is shorter than that in the Dy3+ single-doped glass, indicating a non-radiative energy transfer from Dy3+ to Tm3+. The dominant electrical interaction involved in the energy transfer, following the model Inokuti-Hirayama, is of dipole-dipole type. The energy transfer probability and efficiency are 769.0 s-1 and 0.53, respectively. Tm3+ doped and Dy3+/Tm3+co-doped lithium-aluminum-zinc phosphate glasses could be appropriate for blue and neutral/cold white light-emitting device applications.

Hard X-ray nanoprobe to study the emission properties of Ce-doped YAG wafer by using XEOL and TR-XEOL

In this study, the valent state, emission properties, and decay lifetime of Ce-doped yttrium aluminum garnet (Y3Al5O12, YAG) wafer have been probed using X-ray absorption (XAS), X-ray excited optical luminescence (XEOL), and time-resolved XEOL (TR-XEOL). The XAS spectrum demonstrates that Ce ions are in the trivalent state, and the XEOL spectrum exhibits typical 5 d1-4f1(2F5/2) and 5 d1-4f1(2F7/2) transitions of Ce3+ ions, with emission peaks at ∼528 nm and 582 nm, respectively. From the TR-XEOL measurements, the decay lifetimes of 5 d1-4f1(2F5/2) and 5 d1-4f1(2F7/2) transitions are about ∼90 ns and ∼100 ns, respectively. We found that the reabsorption effects will not only make the 5 d1-4f1(2F7/2) transitions have longer decay lifetime, but also the higher emission intensity. By comparison with photoluminescence (PL) and time-resolved PL using a pulsed laser at 375 nm, we found that the emission spectra and decay lifetime of Ce-doped YAG (111) wafer are different when using X-ray irradiation. The longer decay lifetime measured by TR-XEOL compared TR-PL are caused by high X-ray dose irradiation. In addition, high X-ray doses provided by the nano-focus X-ray beam will be influenced the emission behaviors of Ce-doped YAG (111) wafer. Which phenomena have been demonstrated by using time-dependent XEOL with irradiation for 10 h. These peculiar emission behaviors observed with a hard X-ray nanoprobe may be able to provide important information on quantum technologies and scintillators used in hard X-ray detectors.

Spectral deconvolution approach for Beryllium-7 detection: Evaluating soil redistribution with NaI(Tl) detectors

Beryllium-7 is a cosmogenic radionuclide produced in the upper atmosphere through the spallation of cosmic rays and falls to Earth mainly by wet deposition. Given its short half-life (53 days) and strong adsorption to the clay present in the soil, 7Be inventory can be evaluated to obtain information about soil redistribution over periods of up to 6 months. By performing these measurements, one can infer the efficiency of soil management and conservation procedures. The isotope presence is measured using gamma-ray spectrometry to detect its decay emission, specifically a photon with an energy of 477.6 keV. Since other isotopes found in soil emit photons with similar energies, it is common to use High-Purity Germanium (HPGe) detectors due to their high energy resolution. However, these detectors are expensive and require cryogenic cooling during operation. An alternative is the Thallium-Activated Sodium Iodide (NaI(Tl)) detector, which is less costly and does not require cryogenic cooling, but has poorer resolution and cannot separate the emissions from 228Ac (463.0 keV), 7Be, and 208Tl (510.7 keV). This work aims to apply spectral deconvolution to quantify 7Be in soil samples collected from an agricultural mega-parcel situated on a hill slope and evaluate the soil redistribution experienced within. The activities of the interfering isotopes were quantified using other emissions, and the results were used to calculate the corresponding area in the desired region of the spectra. From this, 7Be activities were calculated and compared with the HPGe results to validate the deconvolution technique. The calculated activities for the three radioisotopes showed similar correspondence between the two detectors, indicating that the applied method is adequate for evaluating soil redistribution at lower costs. The calculated net soil deposition was 36.4 ± 6.4 kgm−2 for the NaI(Tl) detector and 26.4 ± 7.9 kgm−2 for the HPGe detector during the evaluated period. Furthermore, these results suggest that a similar approach can be applied to quantify other isotopes using NaI(Tl) detectors as an alternative to HPGe detectors.

Hybrid metal halide family with color-time-dual-resolved phosphorescence for multiplexed information security applications

Luminescent materials with engineered optical properties play an important role in anti-counterfeiting and information security technology. However, conventional luminescent coding is limited by fluorescence color or intensity, and high-level multi-dimensional luminescent encryption technology remains a critically challenging goal in different scenarios. To improve the encoding capacity, we present an optical multiplexing concept by synchronously manipulating the emission color and decay lifetimes of room-temperature phosphorescence materials at molecular level. Herein, we devise a family of zero-dimensional (0D) hybrid metal halides by combining organic phosphonium cations and metal halide tetrahedral anions as independent luminescent centers, which display blue phosphorescence and green persistent afterglow with the highest quantum yields of 39.9 % and 57.3 %, respectively. Significantly, the luminescence lifetime can be fine-tuned in the range of 0.0968–0.5046 μs and 33.46–125.61 ms as temporary time coding through precisely controlling the heavy atomic effect and inter-molecular interactions. As a consequence, synchronous blue phosphorescence and green afterglow are integrated into one 0D halide platform with adjustable emission lifetime acting as color- and time-resolved dual RTP materials, which realize the multiple applications in high-level anti-counterfeiting and information storage. The color-lifetime-dual-resolved encoding ability greatly broadens the scope of luminescent halide materials for optical multiplexing applications.

Ln3+ Induced Thermally Activated Delayed Fluorescence of Chiral Heterometallic Clusters Ln2Ag28.

A series of TADF-active compounds: 0D chiral Ln-Ag(I) clusters L-/D-Ln2Ag28-0D (Ln=Eu/Gd) and 2D chiral Ln-Ag(I) cluster-based frameworks L-/D-Ln2Ag28-2D (Ln=Gd) has been synthesized. Atomic-level structural analysis showed that the chiral Ag(I) cluster units {Ag14S12} in L-/D-Ln2Ag28-0D and L-/D-Ln2Ag28-2D exhibited similar configurations, linked by varying numbers of [Ln(H2O)x]3+ (x=6 for 0D, x=3 for 2D) to form the final target compounds. Temperature-dependent emission spectra and decay lifetimes measurement demonstrated the presence of TADF in L-Ln2Ag28-0D (Ln=Eu/Gd) and L-Gd2Ag28-2D. Experimentally, the remarkable TADF properties primarily originated from {Ag14S12} moieties in these compounds. Notably, {Ag14S12} in L-Eu2Ag28-0D and L-Gd2Ag28-2D displayed higher promote fluorescence rate and shorter TADF decay times than L-Gd2Ag28-0D. Combined with theoretical calculations, it was determined that the TADF behaviors of {Ag14S12} cluster units were induced by 4 f perturbation of Ln3+ ions. Specially, while maintaining ΔE(S1-T1) small enough, it can significantly increase k(S1→S0) and reduce TADF decay time by adjusting the type or number of Ln3+ ions, thus achieving the purpose of improving TADF for cluster-based luminescent materials.

Ln3+ Induced Thermally Activated Delayed Fluorescence of Chiral Heterometallic Clusters Ln2Ag28

AbstractA series of TADF‐active compounds: 0D chiral Ln−Ag(I) clusters L‐/D‐Ln2Ag28‐0D (Ln=Eu/Gd) and 2D chiral Ln−Ag(I) cluster‐based frameworks L‐/D‐Ln2Ag28‐2D (Ln=Gd) has been synthesized. Atomic‐level structural analysis showed that the chiral Ag(I) cluster units {Ag14S12} in L‐/D‐Ln2Ag28‐0D and L‐/D‐Ln2Ag28‐2D exhibited similar configurations, linked by varying numbers of [Ln(H2O)x]3+ (x=6 for 0D, x=3 for 2D) to form the final target compounds. Temperature‐dependent emission spectra and decay lifetimes measurement demonstrated the presence of TADF in L‐Ln2Ag28‐0D (Ln=Eu/Gd) and L‐Gd2Ag28‐2D. Experimentally, the remarkable TADF properties primarily originated from {Ag14S12} moieties in these compounds. Notably, {Ag14S12} in L‐Eu2Ag28‐0D and L‐Gd2Ag28‐2D displayed higher promote fluorescence rate and shorter TADF decay times than L‐Gd2Ag28‐0D. Combined with theoretical calculations, it was determined that the TADF behaviors of {Ag14S12} cluster units were induced by 4 f perturbation of Ln3+ ions. Specially, while maintaining ΔE(S1–T1) small enough, it can significantly increase k(S1→S0) and reduce TADF decay time by adjusting the type or number of Ln3+ ions, thus achieving the purpose of improving TADF for cluster‐based luminescent materials.

New Insights in Luminescence and Quenching Mechanisms of Ag2S Nanocrystals through Temperature-Dependent Spectroscopy.

Bright near-infrared-emitting Ag2S nanocrystals (NCs) are used for in vivo temperature sensing relying on a reversible variation in intensity and photoluminescence lifetime within the physiological temperature range. Here, to gain insights into the luminescence and quenching mechanisms, we investigated the temperature-dependent luminescence of Ag2S NCs from 300 to 10 K. Interestingly, both emission and lifetime measurements reveal similar and strong thermal quenching from 200 to 300 K, indicating an intrinsic quenching process that limits the photoluminescence quantum yield at room temperature, even for perfectly passivated NCs. The low thermal quenching temperature, broadband emission, and multiexponential microsecond decay behavior suggest the optical transition involves strong lattice relaxation, which is consistent with the recombination of a Ag+-trapped hole with a delocalized conduction band electron. Our findings offer valuable insights for understanding the optical properties of Ag2S NCs and the thermal quenching mechanism underlying their temperature-sensing capabilities.

Synthesis and Photophysical Properties of Small Helical Carbon Nanohoops Combined with Computational Studies on Racemization Pathway.

We herein report the facile synthesis of two helical carbon nanorings with small ring sizes, cyclo[6]paraphenylene-1,5-naphthylene ([6]CPPNap1,5), and cyclo[6]paraphenylene-1,5-anthrylene ([6]CPPAn1,5). The structures were determined by NMR and HR-MS. X-ray single-crystal data of [6]CPPNap1,5 was also achieved. The strain energy and racemization processes were investigated by DFT calculations. The reduced ring sizes result in increased ring strain and elevated energy barriers. The photophysical properties were studied by UV-Vis absorption, fluorescence emission, and time-resolved fluorescence decay.

Study α decay and proton emission based on data-driven symbolic regression

α decay and proton emission were combined using symbolic regression to improve the accuracy of predicting their respective half-lives using two theoretical formulations: (1) adjustable parameters for the universal decay law and universal decay law for proton emission are obtained by regressions with fully-constrained symbolic regressions. (2) New theoretical formulas for calculating the half-life of proton emission and α decay are obtained using unconstrained symbolic regressions combined with nuclear data. Our computational analysis indicates that fully-constrained symbolic regressions and unconstrained symbolic regressions are reliable for specific and general nuclei, respectively, in terms of replicating experimental results, and are sufficiently robust to produce accurate half-life predictions. Unlike other machine learning methods that generate complex and opaque results, our approach integrates physics and machine learning to create interpretable formulas that provide intuitive parametric outcomes and transparent and dependable inferences of half-lives, even in areas with limited experimental data. The test results show that the equation yields accurate results, and can be easily applied to future α decay and proton emission studies.

Deciphering the Nd3+ environment and energy-transfer mechanisms in thermally stable novel calcium aluminate glasses: elucidation of broadband high-gain performance for laser applications

Rare-earth-doped barium calcium aluminate (BCA) glasses, having extended infrared (IR) transmission (6 μm), are attractive materials for near IR (NIR) photonic applications. Nd2O3-doped BCA glasses display broadband emission at 1.07 µm, but they are limited, with poor glass-forming ability (GFA) and low emission cross sections. In the present study, four different barium zinc calcium aluminate (BZCA) glasses are synthesized with varied ZnO concentrations (from 9.5 to 24.5 mol%) and doped with 0.5 mol% Nd2O3 to decipher the effect on GFA and spectroscopic properties. The addition of ZnO enhances the GFA, and the NdBZCA20 glass shows the maximum GFA. Ultraviolet (UV)–visible (Vis)–NIR absorption spectra reveal a decreasing trend in the nephelauxetic effect, while J–O parameters, emission, and gain properties lead to no significant alteration with increasing ZnO, and the structure–properties correlation is established accordingly. However, the emission cross sections for all ZnO concentrations are found ∼4.5 × 10−20 cm2 accompanied by broadband emission (Δλ eff ∼ 40 nm), which ensures the potentiality of these glasses for low-threshold high-gain laser applications as well as ultrashort pulse laser applications. Furthermore, a thorough analysis of 1.06 µm emission as a function of Nd concentration in the BZCA20 glass is reported here. The emission spectra and decay time indicate that 0.5 mol% is the optimized doping concentration. Inokuti–Hirayama and Burshtein equations are adopted to study the decay kinetics and energy-transfer mechanisms, which confirm that the energy-transfer process due to cross-relaxation is dominant up to 0.5 mol% concentration, whereas, beyond that concentration, excitation energy migration via the hopping mechanism supersedes.

The origins of dual-peak emission and anomalous exciton decay in 2D Sn-based perovskites.

Two-dimensional (2D) Sn-based perovskites exhibit significant potential in diverse optoelectronic applications, such as on-chip lasers and photodetectors. Yet, the underlying mechanism behind the frequently observed dual-peak emission in 2D Sn-based perovskites remains a subject of intense debate, and there is a lack of research on the carrier dynamics in these materials. In this study, we investigate these issues in a representative 2D Sn-based perovskite, namely, PEA2SnI4, through temperature-, excitation intensity-, angle-, and time-dependent photoluminescence studies. The results indicate that the high- and low-energy peaks originate from in-face and out-of-face dipole transitions, respectively. In addition, we observe an anomalous increase in the non-radiative recombination rate as temperature decreases. After ruling out enhanced electron-phonon coupling and Auger recombination as potential causes of the anomalous carrier dynamics, we propose that the significantly increased exciton binding energy (Eb) plays a decisive role. The increased Eb arises from enhanced electronic localization, a consequence of weakened lattice distortion at low temperatures, as confirmed by first-principles calculations and temperature-dependent x-ray diffraction measurements. These findings offer valuable insights into the electronic processes in the unique 2D Sn-based perovskites.

Optical, vibrational, and photoluminescence properties of holmium-doped boro-bismuth-germanate glasses.

Holmium (Ho3+)-doped boro-bismuth-germanate glasses having the chemical composition (30-x)B2O3 + 20GeO2 + 20Bi2O3 + 20Na2O + 10Y2O3 + xHo2O3, where x = 0.1, 0.5, 1.0, and 2.0 mol% were prepared by melt-quenching technique. The prepared glasses were examined for thermal, optical, vibrational, and photoluminescent properties. The prepared glasses were found to be thermally very stable. The optical bandgap and Urbach energies of 0.1 mol% Ho2O3-doped boro-bismuth-germanate glass were calculated to be 3.3 eV and 377 MeV, respectively, using the absorption spectrum. The Judd-Ofelt analysis was performed on the 0.1 mol% Ho2O3-doped glass and compared the obtained parameters with literature. The branching ratio (β) and emission cross-section (σem) of the green band were determined to be 0.7 and 0.24 × 10-20cm2, respectively. Under 450 nm excitation, a strong green emission around 550 nm was observed and assigned to the (5S2 + 5F4) → 5I8 (Ho3+) transition. Upon an increase of Ho2O3 content from 0.1 to 2.0 mol%, the intensities of all observed emission bands as well as decay time of the (5S2 + 5F4) → 5I8 transition have been decreased gradually. The reasons behind the decrease in emission intensity and decay time were discussed. The strong green emission suggests that these glasses may be a better option for display devices and green emission applications.

Overcoming Temperature Limits in the Optical Cooling of Solids Using Light-Dressed States.

Laser cooling of solids currently has a temperature floor of 50-100K. We propose a method that could overcome this using defects, such as diamond color centers, with narrow electronic manifolds and bright optical transitions. It exploits the dressed states formed in strong fields which extend the set of phonon transitions and have tunable energies. This allows an enhancement of the cooling power and diminishes the effect of inhomogeneous broadening. We demonstrate these effects theoretically for the silicon vacancy and the germanium vacancy, and discuss the role of background absorption, phonon-assisted emission, and nonradiative decay.