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Quantitative Analysis of Electron Transfer between Ce3+(5d1) and Yb3+/Eu3+ Ions in Y3Al5O12 and Lu2Si2O7 Anant A. Setlur* and Joseph J. Shiang GE Global Research Center, 1 Research Circle, Niskayuna, New York 12309 ReceiVed: NoVember 25, 2009; ReVised Manuscript ReceiVed: December 18, 2009
Standard semiclassical, high-temperature models for electron transfer are shown to be able to quantitatively describe the room-temperature electron transfer reactions between Ce3+(5d1) donors and Eu3+/Yb3+ acceptors in insulating oxide hosts. These reactions in Y3Al5O12 and Lu2Si2O7 hosts are analyzed using time-resolved and steady-state measurements of Ce3+ 5d1 f 4f1 luminescence quenching, leading to an exponential distance decay constant, β, of 1.58-1.7 Å-1. In these hosts, the similar values for β infer that the ∆G0 for the electron transfer reaction is the main factor controlling the room-temperature electron transfer rate for RE3+ donors/ acceptors. Initial comparisons to ET in molecular systems are also made. 1. Introduction Electron transfer (ET) reactions between localized donors (D) and acceptors (A) play an important role in chemistry, biology, and physics.1,2 Typically, the ET rate, kET is taken to exponentially decrease with DA distance:2,3
kET ) k0 exp [-β(R - R0)]
(1)
where k0 is the ET rate at the shortest possible DA distance, β is a constant related to a tunneling energy barrier, R is the centerto-center distance, and R0 is the closest possible DA distance. ET reactions can be important for phosphors and scintillators consisting of trivalent rare earth ions (RE3+) in insulating hosts, primarily from quenching by electron transfer from 4fN-15d1 levels to extended conduction band states (or photoionization)4–8 and electron/hole capture by RE3+ ions in scintillation processes.9,10 Whereas photoionization and charge capture involve extended host lattice states, localized ET reactions between RE3+ ions with opposite reduction/oxidation properties can impact the performance of phosphors and scintillators through the absence of nonradiative energy transfer,11–15 quenching from impurity ions,16 and the absence of scintillation in dense, Yb3+-based hosts.17 Apart from direct luminescence quenching, RE3+ ions with opposite reduction/oxidation properties compared to the primary activator(s) can modify afterglow and degradation under high-energy (greater than host bandgap)18 or 4fN f 4fN-15d1 excitation.19 Electron transfer reactions between RE3+ ions with opposite reduction and oxidation properties, such as Ce3+ (5d1) + RE3+ f Ce4+ + RE2+, could be quantitatively analyzed using eq 1 because the donors and acceptors are well-defined, localized ions. However, most analyses have made mostly qualitative comparisons of ET between localized RE3+ ions in crystalline and amorphous hosts. For example, eq 1 has been used to estimate the critical distance for Ce3+ luminescence quenching by Eu3+ with a β value taken from molecular ET experiments.20 Other studies have qualitatively correlated the strength of ET quenching versus RE3+ acceptor composition to the change in the free energy, ∆G, of the ET reaction.13 * To whom correspondence should be addressed. E-mail: setlur@ research.ge.com, Phone: 1-518-387-6305, Fax: 1-518-387-6204.
Figure 1. Schematic configuration coordinate diagram for the Ce3+ (5d1) + Eu3+/Yb3+ f Ce4+ + Eu2+/Yb2+ reaction.
Considering a quantitative analysis for these reactions, eq 1 essentially describes the distance dependence for HAB, the electronic matrix coupling element between the ET reactants and products. In addition to this distance dependence, the relevant energies that need to be estimated for these ET reactions can be seen through a single configuration coordinate (CC) model for ET1,15 (Figure 1). Two separate energies need to be estimated, the change in the free energy for the ET reaction, ∆G0, and the reorganizational energy, λ. In a CC diagram, ∆G0 is represented by the energy difference between the zero-phonon lines for each CC parabola, whereas λ describes the offset between the two CC parabolas due to relaxation after ET. The ability to quantify ∆G0, λ, and HAB (with its distance dependence) would provide a starting point for analysis of these ET reactions. Therefore, in this article, we present a set of experimental data and analysis to estimate ∆G0, λ, and HAB for Ce3+ (5d1) + Eu3+/Yb3+ f Ce4+ + Eu2+/Yb2+ ET reactions in insulating Y3Al5O12 (YAG) and Lu2Si2O7 (LPS) hosts. These reactions are probed using time-resolved photoluminescence of the Ce3+ 5d1 f 4f1 transition and relative quantum yield measurements as a function of temperature. The free energy of the Ce3+ (5d1) + Eu3+/Yb3+ f Ce4+ + Eu2+/Yb2+ ET reaction, ∆G0, is estimated using the energy position of Ce3+/Yb3+/Eu3+ levels within the host bandgap.4–8 The reorganizational energy, λ, is estimated
10.1021/jp911224u 2010 American Chemical Society Published on Web 01/22/2010
J. Phys. Chem. C, Vol. 114, No. 6, 2010 2793 using the saturated dielectric approximation from the Marcus theory for ET reactions in dielectric hosts.1 These estimates for ∆G0 and λ give a high-temperature activation energy for ET, and this estimated activation energy is in reasonable agreement to the activation energy for luminescence quenching, validating the relative values of ∆G0 and λ. Using a semiclassical model for ET1, we then fit the room-temperature Ce3+ 5d1 f 4f1 decay curves and quantum efficiency as a function of acceptor concentration to obtain values for HAB as a function of DA distance. From this analysis, we believe that larger values of |∆G0| is the primary factor that leads to stronger Ce3+ 5d1 f 4f1 luminescence quenching by ET in these oxide hosts. In addition, the values of β for these insulating oxide hosts are comparable to other hosts for ET that have similar absorption edges. Finally, we discuss the limitations of this analysis. 2. Experiments Procedure and Analysis Y3Al5O12 (YAG) and Lu2Si2O7 (LPS) powder samples with Ce3+ and Eu3+/Yb3+ were made using standard solid-state methods in reducing atmospheres and are single-phase materials as determined by powder X-ray diffraction and luminescence spectroscopy. In these samples, the Ce3+ level is kept at 0.1% on the Y3+/Lu3+ sites to minimize energy transfer and migration between Ce3+ ions. Samples made with higher Ce3+ concentrations using similar protocols without Eu3+/Yb3+ acceptor ions have absolute quantum efficiencies of >85%. The samples used in this study have a Ce3+ concentration that is too low for accurate measurements of the absolute quantum efficiency, but the luminescence decay times of the samples prepared without acceptor ions are consistent with Ce3+ radiative rates for high quantum yield phosphors as well as those published in the literature.6,7 In the synthesis of these samples, care must be taken in controlling the reducing atmosphere to avoid the formation of Yb2+/Eu2+21. The absence of Yb2+/Eu2+ was checked by diffuse reflectance measurements using a PerkinElmer Lambda 800 UV-vis spectrometer with BaSO4 (Kodak) as a reflectance standard. All of the samples analyzed in this report have a reflectance matching or exceeding the reflectance of the standard in regions where Ce3+ and Eu3+/Yb3+ do not have electric dipole-allowed absorption transitions, indicating the absence of Yb2+/Eu2+. Time-resolved measurements of the Ce3+ 5d1 f 4f1 luminescence used an Edinburgh F900 spectrometer with a Peltier cooled R928-P Hamamatsu photomultiplier tube (PMT) detector whose detector baseline is due to PMT dark counts. The laser sources for time-resolved measurements were a diode laser at 468 nm (PicoQuant) and a tripled Nd:YAG laser at 355 nm (JDS Uniphase) for YAG and LPS, respectively. For both lasers, the laser pulse convoluted with the system response has a ∼1 ns fwhm. Low-temperature decay profiles were measured on samples that were mounted on a liquid N2 coldfinger cryostat (Oxford). The relative quantum efficiency (QE) of these powders was measured using powders pressed into an Al plaque with a SPEX Fluorolog 2 spectrometer with corrections for sample absorption using BaSO4 (Kodak) as the powder reflectance standard. The relative emission intensity versus temperature below room temperature was measured using the same spectrometer with a closed-cycle He cryostat (Displex). Above room temperature, the emission intensity versus temperature was measured using pressed powders in an Al plaque connected with resistive heaters and a thermocouple that are attached to a standard Watlow temperature controller. The error for the relative QE at room temperature is (10%, including sample-to-sample variation,
TABLE 1: Relative Quantum Efficiencies of Ce3+ (0.1%), RE3+ Co-Doped Powders at Room Temperature composition
relative quantum efficiency
3+
100 66 17 35 13 100 50 10
YAG:Ce YAG:Ce, 1% Yb3+ YAG:Ce, 4% Yb3+ YAG:Ce, 1% Eu3+ YAG:Ce, 2% Eu3+ LPS:Ce LPS:Ce, 1% Yb3+ LPS:Ce, 4% Yb3+
whereas the error for the I(T)/I(10 K) ratio is ( 4% for lowtemperature measurements and (2% for high-temperature measurements. We have assumed a random distribution of Ce3+ and Eu3+/ Yb3+ ions; this is initially supported by the full solubility for Eu3+ and Yb3+ ions in YAG and for Yb3+ in LPS. The luminescence decay was then fit by assuming a random distribution of donors and acceptors and takes each discrete DA distance, Rl, as a spherical coordination shell:22
( )[ ∑
t φ(t) ) exp τ0
k
l)0
l
]
Z Z*exp(-t*kET(Rl))
Zx
(2)
In eq 2, τ0 is the radiative decay time of Ce3+, lZ is the total number of RE3+ sites at a distance of Rl, Z is the total number of sites within the k shells, and x is the relative acceptor concentration. Because the fwhm of the system response is ∼1 ns, subnanosecond quenching is not resolved in these decay profiles. The subnanosecond quenching is incorporated into this analysis by using the steady-state, room-temperature relative QE as a fitting constraint23–25 and assuming that the decay profiles represent the luminescent decay 1 ns after the excitation pulse. The least-squares fitting of the decay profile then minimizes the mean quadratic fitting deviation,22,26 σ ) χj2reduced. 3. Results and discussion In YAG and LPS, relatively low concentrations of Yb3+ and Eu3+ strongly quench Ce3+ 5d1 f 4f1 emission as measured through a reduction in QE (Table 1) and the appearance of multiple, fast-decay components in time-resolved measurements (Figure 2). The multiexponential decay profile indicates that this quenching does occur beyond nearest neighbor sites. We assign the observed quenching to ET reactions for several reasons. There is no spectral overlap between the Ce3+ 5d1 f 4f1 emission and the Yb3+ absorption, eliminating nonradiative energy transfer as a quenching path. Whereas the 7F0 f 5D0,1 and 7F1 f 5D0,1 Eu3+ absorption transitions have spectral overlap with the Ce3+ emission in YAG, these transitions are parity forbidden with extremely low oscillator strengths,13,27 making dipole-dipole energy transfer unlikely. It is possible for energy transfer by (super)exchange as with other rare earth ions but there is virtually no Eu3+ 5D0 f 7FJ emission (4 orders of magnitude larger than typical nearest-neighbor energy transfer rates by (super)exchange (∼107-108 s-1).16
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Figure 3. Schematic diagram detailing the energies used to estimate ∆G0 for the Ce3+ (5d1) + RE3+ f Ce4+ + RE2+ reaction.
SCHEME 1
Figure 2. Ce3+ 5d1 f 4f1 decay profiles at room temperature versus RE3+ concentration for: (a) Y3Al5O12:Ce3+, Yb3+ (λex ) 468 nm, λex ) 560 nm), (b) Y3Al5O12:Ce3+, Eu3+ (λex ) 468 nm, λex ) 560 nm); and (c) Lu2Si2O7:Ce3+,Yb3+ (λex ) 355 nm, λex ) 420 nm). The drawn lines are the least-squares fits using eq 2 that takes eq 6 for kET and eq 2 4 for HAB (R0).
In YAG, ET quenching of Ce3+ luminescence is much stronger for Eu3+ acceptors versus Yb3+ acceptors. For Yb3+
acceptors in different hosts, there is stronger Ce3+ luminescence quenching in LPS versus YAG (Table 1). Stronger ET quenching of Ce3+ luminescence by Eu3+ versus Yb3+ qualitatively agrees with prior experiments measuring Pr3+1S0 luminescence quenching in YF313. To understand some of the differences in these ET reactions, we first estimate ∆G0 for the Ce3+ (5d1) + RE3+ f Ce4+ + RE2+ reaction by taking the energy difference between the Ce3+(5d1) level and the RE3+/RE2+ ground state within the host bandgap. This estimate uses a method similar to a Born-Haber cycle28 that places the energy of RE3+/RE2+ and RE4+/RE3+ ground states within the host lattice bandgap5 (Scheme 1 and Figure 3 In Scheme 1, EPI is the Ce3+(5d1) photoionization threshold, ECTB is the RE3+-O2- charge transfer band (CTB) energy, and Eg is the host lattice bandgap energy. One difficulty when estimating thermodynamic quantities from these measurements is to determine the energy of the zero-phonon line for these broad optical transitions. For YAG, EPI is taken as the onset for excited-state absorption from the lowest Ce3+ 5d1 level to the host conduction band,7 whereas the thermal activation energy for Ce3+ 5d1 f 4f1 emission quenching6 is used for EPI in LPS. ECTB(Yb3+) uses the midpoint between the excitation and emission maxima for Yb3+-O2- charge transfer luminescence,6,29 while ECTB(Eu3+) is estimated using the difference between the position of the Yb3+-O2- and Eu3+-O2- CTBs (∼0.45 eV).5 Finally, the value for Eg is estimated using the maximum in the excitation spectra after the host lattice absorption edge.6,29 When comparing different host lattices, potential errors in these estimates lead to an absolute uncertainty of ∼0.5 eV for ∆G0. However, the error in relative ∆G0 values when comparing different RE3+ acceptors in the same host is relatively small, ∼0.1 eV, because differences in the relative ECTB for different RE3+ ions are more independent of host lattice composition.5 The extent of Ce3+ emission quenching by ET (Table 1) correlates with the estimated values for ∆G0 (Table 2), especially when comparing different acceptors within the same host. In
J. Phys. Chem. C, Vol. 114, No. 6, 2010 2795 TABLE 2: Energetics for the Ce3+ (5d1) + Eu3+/Yb3+ f Ce4+ + Eu2+/Yb2+ Reaction in YAG and LPS material
EPI (eV)
ECTB (eV)
Eg (eV)
YAG:Ce3+,Yb3+ YAG:Ce3+,Eu3+ LPS:Ce3+,Yb3+
1.3 1.3 0.6
4.8 4.35 4.9
7.0 7.0 6.7
∆G0 (eV) -0.90 -1.35 -1.2
addition, it is possible to fit the decay curves and roomtemperature QE with eq 2 (σ < 1.2) using eq 1 for kET (not shown). These fits give a critical distance for ET (where kET is equivalent to the Ce3+ 5d1 f 4f1 radiative rate), Rc, of ∼9 Å (38 neighbor sites) and ∼11.2 Å (90 neighbor sites) for YAG: Ce3+,Yb3+ and YAG:Ce3+, Eu3+. In LPS:Ce3+,Yb3+, the critical distance is ∼9.4 Å (50 neighbor sites). For all of these host/ acceptor combinations, the value for β is ∼1.5 Å-1, slightly larger than previous estimates for β in oxide hosts.20 However, the relative trends and critical distances for these ET reactions are in qualitative agreement with prior work studying Ce3+ quenching by ET.14 The Ce3+ (5d1) + RE3+ f Ce4+ + RE2+ reactions in YAG: Ce3+,Eu3+ and YAG:Ce3+,Yb3+ are also thermally activated with an Arrenhius activation energy of ∼0.05 eV and ∼0.10 eV for YAG:Ce3+,Eu3+ and YAG:Ce3+,Yb3+, respectively (part a of Figure 4). There is again a correlation between these activation energies and the estimated values for ∆G0 (Table 2). However, these ET reactions are not completely frozen out at low temperatures because the decay profiles remain nonexponential at low temperatures (part b of Figure 4). These experimental results are supported by prior measurements of Yb3Al5O12:Ce3+ single crystals where no Ce3+ luminescence was measured at liquid He temperatures.17 The temperature dependence for these ET reactions can be qualitatively described using a configuration coordinate (CC) diagram (Figure 1). The main conclusion from the CC diagram is that ∆G0 must be negative because there is low-temperature ET quenching. If ∆G0 > 0, ET should be completely frozen out at low temperatures because higher-energy vibrational levels are not populated. However, if ∆G0 < 0, lowtemperature ET can occur from tunneling between the nuclear surfaces for the reactants and products; this process is called nuclear tunneling when discussing molecular ET1. As a note, nonradiative transitions similar to nuclear tunneling have been extensively studied within RE3+-based systems for nonradiative transitions that have a large λ.30 Analyzing these ET reactions at low temperatures must include nuclear tunneling and therefore requires a full quantum mechanical treatment of ET. However, at high temperatures (kT/ 2>pω), it is possible to use an approximate semiclassical model.1 Using a semiclassical model simplifies the analysis of the CC diagram by making ((∆G0 + λ)2)/(4λ) a thermal activation energy for ET1. This activation energy has been shown previously to be a reasonable estimate for higher-temperature activation energies.31,32 However, using a semiclassical model for ET requires some understanding of the coupling frequencies for the ET reaction. The IR and Raman spectra for YAG indicate the presence of numerous vibrational modes ranging from 100 to 900 cm-1.33 In addition, for YAG:Ce3+, the vibrational modes that couple to the 4f1 f 5d1 Ce3+ transition are low-frequency optical modes with energies of ∼140-200 cm-1.34 Therefore, we believe that the semiclassical approximation is reasonable for T > 100 K, near the onset of thermally activated luminescence quenching (part a of Figure 4). The comparison between the activation energy for luminescence quenching (part a of Figure 4) with the ((∆G0 + λ)2)/ (4λ) activation energy requires an estimate for the reorganiza-
Figure 4. (a) Relative integrated intensity (λex ) 460 nm) versus temperature for Y3Al5O12:Ce3+, Yb3+ (1%) and Y3Al5O12:Ce3+, Eu3+ (1%) These curves represent two separate measurements from 10 K to room temperature and from room temperature to 493 K. The curves are merged by normalizing to the intensity at room temperature. The drawn line represents a calculated quenching using an Arrenhius relationship for the nonradiative rate. (b) Ce3+ 5d1 f 4f1 decay profiles (λex ) 468 nm, λex ) 560 nm) versus temperature for Y3Al5O12:Ce3+, Eu3+ (2%).
tional energy, λ. We use standard Marcus theory (or the Mott-Austin theory for small polarons35) for electron transfer between isolated ions in a dielectric matrix to estimate the lattice component of this reorganizational energy, λ0:1
λ0 )
[
][
(∆e)2 1 1 1 1 1 + 4πε0 2a1 2a2 R n2 ε
]
(3)
where ∆e is the charge transferred, a1/a2 is the D/A ionic radius, R is the DA separation taken from the YAG36 or LPS37 crystal structure, n is the host refractive index, and is the host static dielectric constant. This estimate treats D/A ions as conducting metal spheres in a dielectric host, making λ0 a charging energy for removing an electron from one ion and placing it onto
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another ion. The Coulomb attraction for these ions with an effective positive and negative charge is also taken into account using the R-1 term in λ0. For YAG, we take n ) 1.83 and ) 11, and for LPS, we take n ≈ 1.7638 and ≈ 8 using the additivity of molecular polarizabilities.39 For Yb3+/Eu3+ acceptor ions, a2 is the Shannon-Prewitt ionic radius for Yb3+ (1.12 Å)/ Eu3+ (1.21 Å).40 One issue is that the Ce3+ Shannon-Prewitt ionic radius is for the Ce3+(4f1) ground state, not the Ce3+(5d1) excited state. However, first-principles calculations for the lowest-energy Ce3+ 5d1 state in YAG:Ce3+ indicate that the Ce3+(5d1)-O2- bond lengths are similar to the Ce3+(4f1)-O2bond lengths.41 Therefore, we use the Ce3+ Shannon-Prewitt ionic radius (1.26 Å)40 for a1. Finally, the relative offset of the lowest Ce3+(5d1) level versus the Ce3+(4f1) ground state is accounted for by subtracting one-half of the Stokes shift (0.15 eV for both YAG:Ce3+ and LPS:Ce3+) from λ0. We note that there is an additional component to λ due to changes in the local vibrational frequencies after ET1. However, we have no methods to estimate this parameter, and previous estimates for this component in the Ce3+-Ce4+ self-exchange reaction in water give values of
