J. Phys. Chem. B 2001, 105, 4181-4187
4181
Dual Luminescence and Excited-State Dynamics in Ti2+ Doped NaCl Oliver S. Wenger and Hans U. Gu1 del* Departement fu¨ r Chemie und Biochemie, UniVersita¨ t Bern, Freiestrasse 3, CH-3000 Bern 9, Switzerland ReceiVed: NoVember 14, 2000; In Final Form: January 23, 2001
Single crystals of Ti2+ doped NaCl were grown by the Bridgeman technique. High resolution variable temperature absorption, continuous-wave emission, and time-dependent measurements were performed for the spectroscopic characterization of the title compound. At T < 100 K excitation of Ti2+:NaCl in the red spectral region around 647 nm results in two broad emission bands centered at about 1850 and 780 nm, respectively, originating from the 3T2g(t2geg) first excited state and from the 3T1g(t2geg) higher excited state, respectively. Rate constants for the individual depopulation processes of the two metastable excited states are determined. The calculated 15 K 3T2g(t2geg) f 3T1g(t2g2) and 3T1g(t2geg) f 3T1g(t2g2) luminescence quantum yields are 1 and ≈0.26, respectively.
I. Introduction Most of the transition metal ions follow Kasha’s rule,1 which states that luminescence occurs, if at all, only from the energetically lowest lying excited state. The reason is that nonradiative relaxation from higher excited states to the first excited state usually occurs extremely fast, i.e., on a picosecond time scale. Radiative emission is therefore usually not a competitive deactivation process for higher excited states. Up to now, there have been only very few transition metal ions known which exhibit higher excited state luminescence in octahedral coordination. When Mo3+,2 Re4+,2,3 or Os4+ 4 is doped into octahedral sites of chloride and bromide host lattices, luminescence is observed from more than one excited state. What all the emitting states in these ions have in common is the fact that they are energetically separated from their next lower lying states by several thousand wavenumbers, and the fact that all the states between the highest energetic emitting state and the ground state derive from the same electron configuration as the ground state. The nuclear distortions in these so-called spin-flip excited states with respect to each other and with respect to the ground state are very small. In that regard the situation in MoX63-, ReX62-, and OsX62- (X ) Cl, Br) resembles rare earth ions, in which luminescence from multiple excited states is a common phenomenon.5 At present there are only two examples of octahedrally coordinated transition metal ions known, which exhibit higher excited-state luminescence from a state with different electron configuration than the ground state, namely, the 3d ions Ni2+ and Ti2+. Their broad higher excited state emission bands are in clear contrast to the sharp luminescence features observed in MoX63-, ReX62-, or OsX62- or in the rare earths. In this sense Ni2+ and Ti2+ show unique photophysical properties among the octahedrally coordinated d ions. Of these two ions, Ni2+ is clearly the spectroscopically more thoroughly studied: Higher excited-state emission has been observed in Ni2+ doped oxides,6 fluorides,7 chlorides,8 and bromides.9 By contrast, there is only one material in which dual luminescence from Ti2+ has so far been reported, namely, Ti2+:MgCl2.10 The MgCl2 lattice is a rather exceptional host for Ti2+, since the latter experiences a very strong ligand field in this matrix. In particular, due to the small size of Mg2+ the crystal field
acting on the Ti2+ is such that the energy level order in Ti2+: MgCl2 corresponds to a situation to the right of the 3T2g(t2geg)/ 1T (t 2) crossing point in the d2 Tanabe-Sugano diagram of 2g 2g Figure 1.11 This manifests itself in the observation of long-lived 1T (t 2) f 3T (t 2) sharp-line luminescence in the near2g 2g 1g 2g infrared.11 The second metastable level in Ti2+:MgCl2 is 3T (t e ), from which broad-band visible emission to the 1g 2g g ground state was observed at temperatures below 40 K.10 Whether or not 3T1g(t2geg) luminescence is restricted to Ti2+ in strong ligand field environments is only one of the questions we wanted to answer with the present study on Ti2+:NaCl. Our further aims were to get a detailed picture of the nature of the emitting states in Ti2+:NaCl and, more generally, increase our understanding of the radiative and in particular the nonradiative processes between excited states of transition metal ions in crystals. Pump and probe experiments using picosecond and femtosecond laser pulses are often used to characterize the photophysical properties of coordination complexes.12 With two long-lived metastable states the title system offers the possibility to obtain a very detailed characterization of the various competing relaxation processes without these techniques. II. Experimental Section A. Crystal Growth. NaCl single crystals doped with x% Ti2+ (x ) 0.2, 0.8) were grown from the melt by the Bridgeman technique. The actual dopant concentrations were determined on the basis of published -values for Ti2+:NaCl.13 The optical quality of the 0.2% doped crystals was very good; the 0.8% doped crystals were slightly opaque. The Ti2+ ions were generated in the melt by oxidation of Ti metal with ZnCl2. The Zn metal produced in this reaction was deposited on the surfaces of the crystal in the Bridgeman ampule. The ionic radii of Na+ and Ti2+ are 1.02 and 0.86 Å, respectively. We assume that Ti2+ substitutes for Na+ and that charge compensation occurs in the form of a Cl- vacancy. As will be shown in section IVB, there is spectroscopic evidence that the Ti2+ coordination geometry is almost perfectly octahedral. B. Spectroscopic Measurements. Except for the survey absorption measurement, all experiments were carried out on the same 0.2% Ti2+:NaCl single crystal.
10.1021/jp004183n CCC: $20.00 © 2001 American Chemical Society Published on Web 04/13/2001
4182 J. Phys. Chem. B, Vol. 105, No. 19, 2001
Wenger and Gu¨del
Figure 2. (a) The 15 K survey absorption spectrum of 0.8% Ti2+: NaCl and (b) 15 K survey emission spectrum of 0.2% Ti2+:NaCl after excitation at 15 454 cm-1. Figure 1. Tanabe-Sugano energy level diagram for octahedrally coordinated d2 ions. The vertical dashed line represents the ligand field strength in Ti2+ doped NaCl.
Absorption spectra were recorded on a Cary 5e (Varian) spectrometer. For continuous-wave luminescence spectroscopy the sample was excited with the 647.1 nm line of a Kr+ laser (Coherent CR 500K). For the excitation spectrum an Ar+ laser (Spectra Physics 2060-10 SA) pumped Ti3+:sapphire laser (Spectra Physics 3900S) was used. The sample luminescence was dispersed by a 0.75 m single monochromator (Spex 1702) equipped with 750 nm/1250 nm/1600 nm blazed (600 grooves/ mm) gratings. The 3T1g(t2geg) emission was recorded with a cooled photomultiplier tube (RCA C31034) and a Stanford Research 400 photon counting system. Part of the 3T2g(t2geg) luminescence was measured with a liquid nitrogen cooled Ge detector (ADC 403L). Survey luminescence spectra were recorded with a dry ice cooled PbS detector (Hamamatsu P3337). The Ge/PbS detector signals were processed by a lockin amplifier (Stanford Research 830). For the measurement of the 3T1g(t2geg) lifetime rectangular excitation pulses were generated by passing the Kr+ laser beam through an acoustooptic modulator (Coherent 305) connected to a function generator (Stanford Research DS 345). The luminescence decay of the sample was detected as described above and recorded on a multichannel scaler (Stanford Research 430). For the measurement of the 3T2g(t2geg) lifetime the sample was excited with a pulsed Nd3+:YAG laser (Quanta Ray DCR 3, 20 Hz, 1064 nm). The sample luminescence decay was detected with a fast-response Ge detector (ADC 403HS, response time 1 µs) and recorded on an oscilloscope (Tektronix TDS 540 A). Sample cooling was achieved with a closed-cycle refrigerator (Air Product Displex) for the absorption measurements and with a helium gas flow technique for the emission experiments. Luminescence spectra are corrected for the sensitivity of the detection system and are displayed as photon counts versus energy. III. Results The upper trace in Figure 2 shows the 15 K survey absorption spectrum of 0.8% Ti2+:NaCl. This relatively high dopant concentration was needed in order to detect the 3T1g(t2g2) f 3T (t e ) absorption transition. The lower trace (displayed 2g 2g g
Figure 3. (a) Temperature dependence of the 3T1g(t2g2) f 3T1g(t2geg) absorption bandwidth (fwhm) of 0.2% Ti2+:NaCl. The solid line is a fit with eqs 1 and 2 to the experimental data with the parameters ν ) 175 cm-1 and S ) 9.8. (b) High-resolution absorption spectrum of the 3T (t 2) f 3T (t e ) absorption transition in 0.2% Ti2+:NaCl at 15 1g 2g 1g 2g g K. The solid vertical lines represent the predicted band shape using eq 3 and the parameter S ) 9.8.
upside down) shows the 15 K overview luminescence spectrum of 0.2%Ti2+:NaCl obtained after excitation at 15 454 cm-1. The visible and near-infrared luminescence transitions shown here were recorded with individual highly sensitive detection systems (see section II). The photon output ratio of visible:near-infrared luminescence is 1:4 and has been determined in a separate luminescence experiment with a detection system sensitive in both spectral regions (see section II). Figure 3a shows the width (full width at half-maximum, fwhm) of the 3T1g(t2g2) f 3T1g(t2geg) absorption band in 0.2% Ti2+:NaCl as a function of temperature. Figure 3b shows the high-resolution absorption spectrum of this transition in 0.2% Ti2+:NaCl at 15 K. Differences in the 3T1g(t2geg) absorption bands in Figures 2a and 3b are due to the better optical quality of the 0.2% Ti2+:NaCl (Figure 3b) crystal. In Figure 4a the high resolution 15 K 3T1g(t2geg) f 3T1g(t2g2) emission spectrum of a 0.2% Ti2+:NaCl crystal is presented. Figure 4b shows the 15 K emission (left trace) and excitation spectra (right trace) in the spectral region of the electronic origin. In the upper part of Figure 5a the temperature dependence of the 3T1g(t2geg) luminescence lifetime and in the lower part
Excited-State Dynamics in Ti2+ Doped NaCl
Figure 4. (a) High-resolution emission spectrum of 0.2% Ti2+:NaCl at 15 K showing the 3T1g(t2geg) f 3T1g(t2g2) transition after excitation at 15 454 cm-1. The brackets indicate the members of a vibrational 165 cm-1 progression built on three different origins at 13 648, 13 689, and 13 757 cm-1, respectively, as indicated by the arrows in (b). (b) 15 K emission and excitation spectra in the spectral region of the electronic origin and structured sidebands of the 3T1g(t2g2) f 3T1g(t2geg) transitions.
Figure 5. Temperature dependences of (a) the 3T1g(t2geg) lifetime (circles) and the integrated 3T1g(t2geg) f 3T1g(t2g2) emission intensity (triangles) and (b) the 3T2g(t2geg) lifetime (circles) and the integrated 3T (t e ) f 3T (t 2) emission intensity (triangles) in 0.2% Ti2+:NaCl 2g 2g g 1g 2g after excitation at 15 454 cm-1.
the integrated intensity are shown as a function of temperature. The emission intensity has been normalized to 1 at 10 K and corrected for the temperature dependence of the absorption cross section at the laser excitation wavelength. In Figure 5b analogous data for the 3T2g(t2geg) state are presented. Note the different scales in the upper parts (lifetimes) of Figure 5a and Figure 5b, respectively. IV. Analysis and Discussion A. Energy Level Sequence and Luminescence Transitions. There exist several detailed studies on the absorption spectra of the octahedrally coordinated d2 ion V3+.14 By contrast, there are only relatively few optical absorption studies on the isoelectronic Ti2+. Ti2+:MgCl2 and Ti2+:MnCl2 have been most thoroughly investigated.11,15 The studies of the absorption spectra of Ti2+:MgBr2 and Ti2+:NaCl are much less detailed.11,13,16 The 15 K survey absorption spectrum of 0.8% Ti2+:NaCl presented in Figure 2a shows the typical features of an octahedral d2 system: Two broad absorption transitions with maxima at 8170 cm-1 and 15 100 cm-1, respectively, and oscillator strengths
J. Phys. Chem. B, Vol. 105, No. 19, 2001 4183 on the order of 10-5 are observed. According to the d2 TanabeSugano diagram of Figure 1, they can readily be assigned to the spin-allowed one-electron transitions from the 3T1g(t2g2) ground state to the 3T2g(t2geg) and 3T1g(t2geg) excited states, respectively. According to Figure 1 there is a third spin-allowed transition in d2 systems, namely the 3T1g(t2g2) f 3A2g(eg2) transition. This corresponds to a two-electron excitation, and as such is expected to be weak. We do not observe it in our absorption spectra of 0.8% Ti2+:NaCl. Also unobserved are all the spin-forbidden triplet-singlet absorption transitions. This is not unexpected since in nonmagnetic materials such as the title compound the spin-forbidden transitions gain their intensity via spin-orbit coupling to energetically nearby spin-allowed transitions. For Ti2+ this intensity-gaining mechanism is particularly inefficient due to its weak spin-orbit coupling. (The spin-orbit coupling parameter for the free Ti2+ ion is 123 cm-1,17 and in Ti2+:MgCl2 it was found to be reduced to 93 cm-1.11) With a simple d2 ligand field calculation, we made a fit of calculated to experimental excited-state energies. Using C/B ) 3.76 as in Ti2+:MgCl2,11 the following values for the octahedral ligand field parameters of Ti2+:NaCl are obtained: 10 Dq ) 9064 cm-1 and B ) 530 cm-1. Thus we calculate a 10 Dq/B ratio of 17.1 which places the Ti2+:NaCl system close to the 3T (t e )/1T (t 2) crossing point in the d2 Tanabe-Sugano 2g 2g g 2g 2g diagram; see the dashed vertical line in Figure 1. As shown in Figure 2b, excitation at 15 K into 3T1g(t2geg) at 15 454 cm-1 leads to two luminescence bands. Their broadness indicates that the electronic transitions occur between states with different equilibrium geometries. Time-dependent measurements (section IVC) show that the two luminescence transitions have different decay behaviors, and consequently they have their origin in different excited states. On the basis of their positions with respect to the two absorption bands, the lower energy emission band is assigned to the 3T2g(t2geg) f 3T1g(t2g2) transition and the higher energy band is assigned to the 3T1g(t2geg) f 3T (t 2) transition. This is in clear contrast to the luminescence 1g 2g behavior of Ti2+:MgCl2, in which dual luminescence from the 3T (t e ) and 1T (t 2) excited states of Ti2+ has been 1g 2g g 2g 2g reported.10 Thus we observe for the first time dual spin-allowed luminescence in a Ti2+ system. We do not observe any inter-excited-state luminescence transitions from the 3T1g(t2geg) higher excited state to the 3T2g(t2geg), 1T (t 2), or 1E (t 2) intermediate states. The 3T (t e ) f 2g 2g g 2g 1g 2g g 1T (t 2)/1E (t 2) transitions are strictly spin-forbidden in this 2g 2g g 2g system. In contrast, the 3T1g(t2geg) f 3T2g(t2geg) transition is spin-allowed. This intraconfigurational transition is expected to occur as a relatively sharp feature at about 6757 cm-1, i.e., at the energy difference between the electronic origins of the 3T (t e ) (13 757 cm-1; see section IVB) and the 3T (t e ) 1g 2g g 2g 2g g (≈7000 cm-1) states. No band is observed in this spectral region, and we estimate that the 3T1g(t2geg) f 3T2g(t2geg) inter-excitedstate transition is at least 2 orders of magnitude weaker than the 3T1g(t2geg) f 3T1g(t2g2) transition. Thus, for the 3T2g(t2geg) f 3T1g(t2geg) excited-state absorption transition, we estimate an oscillator strength of 10-7 as an upper limit. This compares to an oscillator strength of ≈5 × 10-5 for the 3T1g(t2g2) f 3T (t e ) ground-state absorption transition. At first sight, such 1g 2g g a large difference between the oscillator strengths of two spinallowed transitions in the same ion seems puzzling. There is a dearth of knowledge about spin-allowed intraconfigurational transitions in 3d transition metal ions because such transitions cannot be observed in absorption spectra from the ground state. Excited state absorption and inter-excited-state emission mea-
4184 J. Phys. Chem. B, Vol. 105, No. 19, 2001 surements are needed for their characterization. In the very few examples which have been explored, transitions between states deriving from the same electron configuration have been found to be weak: the 3T1g(t2geg) f 3T2g(t2geg) transition in Ti2+: MgCl210 and the 2E(t2g3) f 2T2g(t2g3) transition in ruby.18 What these transitions have in common is the fact that they are formally zero-electron transitions in an orbital picture. As a consequence, they do not involve significant electron density redistributions and are thus accompanied by small changes in the dipole moment. This leads to small transition moments and thus oscillator strengths. We are not aware of any theoretical work in the literature to back up this qualitative argument about zero-electron transitions. B. Absorption and Emission Band Shapes: Excited-State Distortions. The 3T1g(t2g2) f 3T1g(t2geg) absorption band of 0.2% Ti2+:NaCl at 15 K presented in Figure 3b shows a vibrational progression with ν ) 165 cm-1. The fact that this 165 cm-1 mode couples so strongly to the electronic transition of the Ti2+ ion indicates that it is a TiCl64- local mode rather than a NaCl lattice mode. Typical vibration energies of such octahedral MCl64- units are ≈250 cm-1 for the a1g and ≈160 cm-1 for the eg mode.19 Therefore we conclude that the 3T1g(t2g2) f 3T (t e ) transition couples to the TiCl 4- e mode. This is a 1g 2g g 6 g manifestation of a Jahn-Teller effect, indicating that the 3T1g degeneracy is not lifted by symmetry, and consequently the coordination geometry of the Ti2+ ion in the NaCl lattice must be almost perfectly octahedral. At the lowest temperatures the vibrational progression in the eg mode (νeg ) 165 cm-1) is also observed in the reverse transition, i.e., 3T1g(t2geg) f 3T1g(t2g2) luminescence (Figure 4a), but it is much better resolved in the absorption spectrum. A close inspection of the origin region of the emission spectrum (Figure 4b) reveals that in emission progressions in ν ) 165 cm-1 are built on three origins at 13 757, 13 689, and 13 648 cm-1, respectively (arrows in Figure 4b), and these progressions are indicated by the brackets in Figure 4a. With excitation spectroscopy it is possible to resolve some fine structure in the spectral region of the weak 3T1g(t2geg) origin; see Figure 4b. It is found that there is a coincidence of the lowest energy feature in excitation with the highest energy feature in emission at 13 757 cm-1. We assign this to an electronic origin. In absorption, only a very weak 165 cm-1 progression is built on this origin. The shape of the absorption spectrum in Figure 3b is largely dominated by an eg progression which starts at 13 822 cm-1, i.e., 65 cm-1 above the electronic origin, and we assign this to a vibronic origin. In the emission spectrum the corresponding vibronic origin is observed at 13 689 cm-1, i.e., 68 cm-1 below the electronic 3T1g(t2geg) origin. The different degree of resolution in the 3T1g(t2g2) T 3T1g(t2geg) absorption and emission spectra is due to the fact that the absorption spectrum is largely dominated by one single eg progression, whereas in emission three eg progressions with comparable intensities are observed, and in particular their relative energetic separation is such that their superposition leads to an overall smoothing of the emission relative to the absorption band shape. From the fact that the vibrational eg progression is observed in 3T1g(t2g2) T 3T1g(t2geg) absorption and emission spectra, it is not a priori clear in which of these two states the corresponding Jahn-Teller distortion occurs. However, eg electron density is more susceptible to nuclear distortions along the eg coordinate than electron density located in t2g orbitals.20 The eg Jahn-Teller active state is therefore more likely 3T1g(t2geg) than 3T1g(t2g2). We now examine the 3T1g(t2g2) T 3T2g(t2geg) transitions. The 3T (t e ) f 3T (t 2) luminescence transition (Figure 2) shows 2g 2g g 1g 2g
Wenger and Gu¨del four members of a vibrational progression in a 170 cm-1 mode. This is reasonably close to the 165 cm-1 progression in the 3T1g(t2g2) T 3T1g(t2geg) transitions discussed above, and consequently we attribute this 170 cm-1 vibrational progression to the same eg mode and conclude that also the 3T2g(t2geg) state undergoes an eg Jahn-Teller distortion. The 15 K 3T1g(t2g2) f 3T2g(t2geg) high-resolution absorption spectrum of 0.2% Ti2+:NaCl (data not shown) exhibits a vibrational 120 cm-1 progression, which we assign to the t2g mode of TiCl64-. We note that the 3T1g(t2g2)-3T2g(t2geg) potentials are displaced with respect to each other not only along the eg coordinate but also along the t2g coordinate. We turn our attention back to the 3T1g(t2g2) T 3T1g(t2geg) transitions in order to perform a more detailed analysis of the eg Jahn-Teller effect in the 3T1g(t2geg) state. In Figure 3a the temperature dependence of the 3T1g(t2g2) f 3T1g(t2geg) absorption bandwidth (full width at half-maximum, fwhm) is presented. The full line in Figure 3a shows the best fit of these data by
ΓFWHM ) ΓFWHM(T0)
xcoth(2kTν )
(1)
which describes this temperature dependence as resulting from thermal population of excited vibrational eg levels of the electronic ground state.21 ν represents the energy of the progression mode and ΓFWHM(T0) is the bandwidth (fwhm) at T ) 0 K. Equation 1 can be applied equally to allowed transitions or, as is the case here, to transitions with vibronically induced intensity. ΓFWHM(T0) is related to the Huang-Rhys parameter S via eq 2:21
ΓFWHM(T0) ) 2x2 ln 2 ν xS
(2)
The prefactor in this equation derives from the conversion of 2 times the standard deviation of a Gaussian into full width at half-maximum. The fit with these equations to the experimental data in Figure 3a yields ν ) 175 cm-1 and S ) 9.8. The vibrational energy we obtain is reasonably close to the energy of the eg mode (165 cm-1; see above), which we have already identified as the progression mode in the 3T1g(t2g2) f 3T1g(t2geg) transition. For Franck-Condon transitions at the lowest temperatures, absorption (and emission) band shapes may be calculated using eq 3:22
In )
[exp(- S)]Sn n!
(3)
where In is the intensity of the nth member of the vibrational progression. We use this equation to test our Huang-Rhys parameter obtained above, by comparing the experimental 15 K 3T1g(t2g2) f 3T1g(t2geg) absorption spectrum with the intensity distribution calculated using eq 3 and S ) 9.8. As shown in Figure 3b, calculation (vertical lines) and experiment (full trace) agree very well, and we conclude that our Seg value is accurate. This Huang-Rhys parameter can now be used to calculate the displacement of the 3T1g(t2geg) excitedstate potential relative to the 3T1g(t2g2) ground-state potential along the eg coordinate. This displacement is related to the Huang-Rhys parameter by
|∆Qi| )
x( ) 2Si hνi fi
(4)
where h is Planck’s constant and fi the force constant of mode i with energy νi.22 For the stretching vibrations of an octahedral
Excited-State Dynamics in Ti2+ Doped NaCl
Figure 6. Single configurational coordinate (SCC) diagram of the relevant states of Ti2+:NaCl.
MX6 complex the force constant fi depends on the atomic masses of M and X, respectively, as well as on the energy of the relevant vibration.23 We calculate feg based on νeg ) 165 cm-1 and obtain |∆Qeg| ) 0.44 Å for the displacement of the 3T1g(t2g2)/3T1g(t2geg) potentials relative to each other along eg. This result is illustrated in the single configurational coordinate (SCC) diagram in Figure 6. The 3T1g(t2geg) potential has its minimum 13 757 cm-1 above the minimum of the 3T1g(t2g2) ground-state potential (see above). To complete this SCC diagram, we calculated the displacement of the 3T2g(t2geg) potential relative to the 3T1g(t2g2) groundstate potential from a fit with eq 3 to the 15 K 3T2g(t2geg) f 3T (t 2) emission spectrum (fit not shown). As discussed above, 1g 2g the vibrational progression in this spectrum is due to the eg mode, and consequently we determine Seg in this procedure. With eq 4 we calculate |∆Qeg| ) 0.38 Å for the displacement of the 3T (t 2)/3T (t e ) potentials relative to each other. The 1g 2g 2g 2g g electronic origin of the 3T1g(t2g2) T 3T2g(t2geg) transition is at about 7 000 cm-1 above the 3T1g(t2g2) ground-state potential. The relative distortion of the two excited triplet states 3T2g(t2geg) and 3T1g(t2geg) is thus very small, reflecting the fact that both states derive from the same electron configuration. Finally, we consider the 1T2g(t2g2) and 1Eg(t2g2) potentials. Both states derive from the same electron configuration as the ground state, and consequently we assume |∆Qeg| ≈ 0 Å for these potentials. Based on the ligand field parameters from section IVA, we calculate E ≈ 7 500 cm-1 for the energy of the 1T2g(t2g2) state relative to the ground state. The 1Eg(t2g2) state is energetically very close to the 1T2g(t2g2) state and has therefore been omitted in Figure 6. The 1T2g(t2g2) potential minimum is thus roughly 500 cm-1 above the 3T2g(t2geg) potential minimum. This accounts for the observation of broad-band 3T2g(t2geg) f 3T (t 2) instead of sharp-line 1T (t 2) f 3T (t 2) near1g 2g 2g 2g 1g 2g infrared luminescence as in the case of Ti2+:MgCl2,11 where the ligand field is stronger and therefore the 3T2g(t2geg) potential minimum is above the 1T2g(t2g2) potential minimum. This SCC model will be used in section IVE to rationalize the observed excited-state dynamics. C. Temperature Dependence of the Luminescence Lifetimes and Intensities: Decay Mechanisms. The 3T2g(t2geg) lifetime at 15 K is 1.4 ms. When the temperature is raised, this lifetime is reduced and reaches a value of 0.4 ms at 150 K; see Figure 5b, top. In contrast, as shown in the lower part of Figure 5b, the integrated 3T2g(t2geg) f 3T1g(t2g2) emission intensity stays relatively constant in the 10-150 K temperature range. From this we conclude that 3T2g(t2geg) depopulation is essentially radiative below 150 K. Above 150 K the integrated 3T2g(t2geg) f 3T1g(t2g2) emission intensity is drastically reduced, and at 300
J. Phys. Chem. B, Vol. 105, No. 19, 2001 4185 K it is essentially zero. We attribute this to nonradiative multiphonon relaxation processes. The 3T1g(t2geg) higher excited state has a very contrasting behavior already at the lowest temperatures. At 7 K the 3T (t e ) lifetime of 0.2% Ti2+:NaCl is 15 µs, roughly 2 orders 1g 2g g of magnitude shorter than the 3T2g(t2geg) lifetime. This indicates that nonradiative processes contribute significantly to the 3T1g(t2geg) depopulation already at 7 K. The steep decrease of the 3T (t e ) lifetime between 30 and 100 K is paralleled by a 1g 2g g corresponding decrease of the integrated 3T1g(t2geg) f 3T1g(t2g2) emission intensity, as seen in Figure 5a. This is a direct proof for the presence of a nonradiative relaxation process which becomes increasingly efficient at temperatures above 30 K, and which finally quenches the 3T1g(t2geg) f 3T1g(t2g2) luminescence completely at temperatures above 150 K. This nonradiative relaxation can occur by two fundamentally different mechanisms, namely multiphonon relaxation and cross-relaxation. In a cross-relaxation process a highly excited (donor) ion transfers part of its excitation energy to an (acceptor) ion which is in an electronic state of lower energy. In our specific case this could occur as follows: One Ti2+ ion in the 3T1g(t2geg) higher excited state transfers part of its excitation energy to a Ti2+ ion in the 3T1g(t2g2) ground state, with the net result of two ions in the 3T2g(t2geg) first excited state. In the case of electric multipole-multipole interactions the cross-relaxation rate depends not only on the distance between donor and acceptor ion, but also on the spectral overlap of the donor emission profile with the acceptor absorption profile, as well as on the oscillator strengths of the respective transitions.22 In our specific case these transitions are 3T1g(t2geg) f 3T2g(t2geg) emission and 3T1g(t2g2) f 3T2g(t2geg) absorption, respectively. Our analysis in section IVA shows that the spectral overlap of these two transitions is zero at 15 K. Additionally we estimated an upper limit of only 10-7 for the oscillator strength of the 3T (t e ) f 3T (t e ) transition at 15 K. From these two facts 1g 2g g 2g 2g g we conclude that at 15 K there is no 3T1g(t2geg)/3T1g(t2g2) f 3T (t e )/3T (t e ) cross-relaxation in Ti2+:NaCl. Both the 2g 2g g 2g 2g g above spectral overlap and the 3T1g(t2geg) f 3T2g(t2geg) oscillator strength are temperature dependent. Experimentally there is no evidence for an increasing oscillator strength of the 3T1g(t2geg) f 3T2g(t2geg) transition with increasing temperature; i.e. this transition stays undetectable also at elevated temperatures. Furthermore, based on our energy considerations in section IVA, we estimate that thermal energies of more than 100 cm-1 are required in order to lead to a nonzero spectral overlap of the 3T (t e ) f 3T (t e ) emission with the 3T (t 2) f 3T (t e ) 1g 2g g 2g 2g g 1g 2g 2g 2g g absorption. Therefore, we exclude cross-relaxation and we conclude that multiphonon relaxation is responsible for the 3T (t e ) quenching. 1g 2g g D. Excited-State Dynamics: Quantitative Evaluation of the Various Competing Deactivation Processes. In Figure 7 we have simplified the energy level structure of Ti2+ to a diagram which neglects nuclear distortions of the various states relative to each other. The 3T1g(t2g2) ground state (|0〉) as well as the two metastable states 3T2g(t2geg) (|1〉) and 3T1g(t2geg) (|2〉) are shown. The 1T1g(t2g2) and 1Eg(t2g2) states are irrelevant for the present purpose and have been omitted in Figure 7. Our aim in this section is to quantify as many of the 3T2g(t2geg)- and 3T (t e )-deactivation processes as possible, to get a detailed 1g 2g g picture of the competition between radiative and nonradiative processes in Ti2+:NaCl. In Figure 7 the solid and wavy arrows represent all possible radiative and nonradiative (multiphonon) relaxation processes, respectively, leading to depopulation of the two metastable excited states in 0.2% Ti2+:NaCl. Since we
4186 J. Phys. Chem. B, Vol. 105, No. 19, 2001
Wenger and Gu¨del
dN1 ) krad21N2 + knr21N2 - krad10N1 - knr10N1 dt
Figure 7. Energy level diagram and relevant deactivation processes from the two metastable excited states of Ti2+:NaCl. Solid arrows represent radiative emission; wavy arrows represent nonradiative multiphonon relaxation processes.
TABLE 1: Rate Constants of Radiative and Nonradiative Transitions from the 3T2g(t2geg) (|1〉) and 3T1g(t2geg) (|2〉) States in 0.2 % Ti2+:NaCl at 15 Ka 714 s-1 0 s-1 17 271 s-1 69 085 s-1
krad10 knr10 krad20 krad21 + knr21
a The labels used here correspond to those shown in Figure 7. The values were derived from the experimental data as described in detail in section IVD.
have already excluded a 3T1g(t2geg)/3T1g(t2g2) f 3T2g(t2geg)/ 3T (t e ) cross-relaxation process in section IVC, this process 2g 2g g is not included in Figure 7. In the following analysis we determine the rate constants of the individual relaxation processes for T ) 15 K. The results are summarized in Table 1. As shown by the temperature-dependent 3T2g(t2geg) lifetime and emission data (Figure 5b), the 3T2g(t2geg) population decays purely radiative at 15 K (section IV C). Consequently knr10 ) 0 s-1 and krad10 ) τ[3T2g(t2geg)]-1 ) 714 s-1. The ratio of the 3T1g(t2g2) f 3T2g(t2geg) (|0〉 f |1〉):3T1g(t2g2) f 3T1g(t2geg) (|0〉 f |2〉 absorption oscillator strengths is 1:4.3 (Figure 2a). We neglect the splitting of the different 3T states due to spin-orbit interaction and note that absorption oscillator strengths are directly proportional to radiative decay rate constants;22 this ratio directly relates to the ratio krad10:krad20. Taking the average 3T2g(t2geg) f 3T1g(t2g2) (|1〉 f |0〉) and 3T (t e ) f 3T (t 2) |2〉 f |0〉 emission wavelengths of 1 850 1g 2g g 1g 2g and 780 nm, respectively (Figure 2b), into account, we obtain krad20 ) 4.3(1850/780)2krad10 ) 17 271 s-1. The survey emission spectrum in Figure 2b shows that, after 3T1g(t2geg) excitation at 15 K, 3T2g(t2geg) f 3T1g(t2g2) luminescence (|1〉 f |0〉) is 4 times stronger than 3T1g(t2geg) f 3T1g(t2g2) luminescence (|2〉 f |0〉), or in other words, the radiative |2〉 f |0〉 emission rate is a factor of 4 larger than the radiative |2〉 f |0〉 emission rate. Mathematically expressed this means
krad20N2 1 ) krad10N1 4
(5)
The absolute values of the population densities Ni are unknown. However, the ratio N2:N1 in the steady state can be calculated using the following differential rate equation for level |1〉 (3T2g(t2geg)):
(6)
As shown above, the last term in eq 6 is zero. Under steadystate conditions the whole expression 6 equals zero and can be solved for N2/N1. Combination with eq 5 then yields krad21 + knr21 ) 4krad20 ) 69 085 s-1 for the total 3T1g(t2geg) f 3T2g(t2geg) relaxation rate constant. As discussed in section IVA, the 3T (t e ) f 3T (t e ) inter-excited-state luminescence is at 1g 2g g 2g 2g g least 2 orders of magnitude weaker than 3T1g(t2geg) f 3T1g(t2g2) luminescence and consequently krad21 , knr21. Finally, the inverse of the 3T1g(t2geg) lifetime must equal the sum of all individual rate constants of the four 3T1g(t2geg) depopulation processes shown in Figure 7. The sum krad20 + krad21 + knr21 is 30% larger than the experimentally determined decay rate constant of 3T1g(t2geg) at 15 K. Considering the experimental uncertainties in the input data needed for the above calculations, this is a very reasonable agreement. E. Multiphonon Relaxation from the 3T1g(t2geg) Higher Excited State. The light output of a system on a specific transition is best described by the luminescence quantum yield η, which is defined as the ratio of the number of emitted photons to the number of absorbed photons.24 In practice, the measurement of absolute quantum yields is a very difficult task. η is therefore often calculated from the ratio of the radiative rate constant and the total (radiative plus nonradiative) depopulation rate constant of the emitting state.22 In the specific case of 3T1g(t2geg) f 3T1g(t2g2) emission in 0.2% Ti2+:NaCl at 15 K we find η ) krad20/τ(3T1g(t2geg))-1 ≈ 0.26. Considering the fact that we are dealing with higher excited state emission in a 3d transition metal ion, this quantum yield is high, but it is not without precedent, because in Ti2+:MgCl2 at 15 K the corresponding value is 0.7. We now attempt to rationalize this result on the basis of the SCC diagram in Figure 6. knr21 is the sum of the rate constants of two relaxation pathways: Multiphonon relaxation from 3T1g(t2geg) directly to 3T (t e ), as well as multiphonon relaxation from 3T (t e ) 2g 2g g 1g 2g g via the 1T2g(t2g2)/1Eg(t2g2) states to the 3T2g(t2geg). We consider the latter pathway first. Generally, the nonradiative rate Wba for a transition from a state |b〉 to a state |a〉 can be expressed in terms of Fermi’s Golden Rule for nonradiative transitions:22
Wba )
2π |H |2F(Ea,V) δ(Ea,V - Eb,V′) h ba
(7)
where V and V′ denote the vibrational levels in the |a〉 and |b〉 states, respectively, and F(Ea,V) is the density of final states. The δ term ensures energy conservation. |Hba|2 is the so-called electronic factor, which is the important factor for our consideration here. In cubic symmetry the only operator connecting the 3T1g(t2geg) and 1T2g(t2g2)/1Eg(t2g2) states is the spin-orbit coupling operator. We have already discussed the weakness of spin-orbit coupling in the case of Ti2+ in section IVA (ζFreeIon ) 123 cm-1).17 Due to this weak spin-orbit coupling the matrix elements |Hba| between the 3T1g(t2geg) and 1T2g(t2g2)/1Eg(t2g2) states must be particularly small for Ti2+, and we conclude that this is why, at the lowest temperatures, 3T1g(t2geg) f 1T2g(t2g2)/ 1E (t 2) f 3T (t e ) multiphonon relaxation is relatively g 2g 2g 2g g inefficient in Ti2+:NaCl. Regarding multiphonon relaxation from 3T1g(t2geg) directly to 3T2g(t2geg), we refer to the SCC diagram in Figure 6. The 3T (t e ) and the 3T (t e ) potentials have very similar 1g 2g g 2g 2g g equilibrium distortions with respect to the main distortion coordinate Qeg. Thus, the two potentials relative to each other
Excited-State Dynamics in Ti2+ Doped NaCl are in the so-called weak coupling limit. In this case the nonradiative multiphonon relaxation rate is given by the socalled energy gap law,22 which simply states that the multiphonon rate decreases with increasing reduced energy gap p. p is the energy gap in terms of quanta of the highest frequency vibration, usually the a1g mode. Using a value of 250 cm-1 for the energy of the a1g mode,11 we calculate p ≈ 25 for the reduced energy gap between the 3T1g(t2geg) and the 3T2g(t2geg) states in Ti2+:NaCl. Recent systematic studies on Mo3+,24 Re4+,3 and Os4+ 25 have shown that, among weakly distorted states in transition metal ions, multiphonon relaxation processes become inefficient typically with reduced energy gaps above 10. Therefore, we conclude that multiphonon relaxation from 3T1g(t2geg) directly to 3T2g(t2geg) is inefficient and thus knr21 is relatively small. V. Conclusions So far there has existed only one compound where dual luminescence from an octahedral d2 system has been observed, namely, Ti2+:MgCl2.10 In this compound the ligand field strength is such that the Ti2+ energy level structure corresponds to a situation to the right of the 3T2g(t2geg)/1T2g(t2g2) crossing point in the d2 Tanabe-Sugano diagram of Figure 1. Consequently, spin-forbidden sharp-line near-infrared emission occurs on the 1T (t 2) f 3T (t 2) transition. Additionally, emission from 2g 2g 1g 2g the 3T1g(t2geg) higher excited state has been observed in Ti2+: MgCl2 below 40 K.10 In this paper we reported the first observation of dual spin-allowed luminescence of Ti2+. With the example of Ti2+:NaCl we have established that 3T1g(t2geg) higher excited-state emission is not restricted to Ti2+ in strong ligand field environments (10Dq/B > 16), although the energetic position of the 3T1g(t2geg) state itself is strongly ligand field dependent. This is a remarkable finding because it means that the identity of the first excited state can be controlled by means of chemistry while 3T1g(t2geg) higher excited state emission remains maintained. This is particularly interesting in view of photon upconversion.26,27
J. Phys. Chem. B, Vol. 105, No. 19, 2001 4187 Acknowledgment. We thank the Swiss National Science Foundation for financial support, and Rafael Valiente and Markus Wermuth for helpful discussions. References and Notes (1) Kasha, M. Discuss. Faraday Soc. 1950, 9, 14. (2) Gamelin, D. R.; Gu¨del, H. U. J. Am. Chem. Soc. 1998, 120, 12143. (3) Gamelin, D. R.; Gu¨del, H. U. Inorg. Chem. 1999, 38, 5154. (4) Wermuth, M.; Gu¨del, H. U. Chem. Phys. Lett. 1997, 281, 81. (5) Blasse, G.; Grabmaier, B. C. Luminescent Materials, SpringerVerlag: Berlin, 1994. (6) Iverson, M. V.; Sibley, W. A. J. Lumin. 1979, 20, 311. (7) May, P. S.; Gu¨del, H. U. Chem. Phys. Lett. 1990, 175, 488. (8) May, P. S.; Gu¨del, H. U. Chem. Phys. Lett. 1989, 164, 612. (9) de Viry, D.; Tercier, N.; Denis, J. P.; Blanzat, B.; Pelle´, F. J. Chem. Phys. 1990, 97, 2263. (10) Jacobsen, S. M.; Gu¨del, H. U. J. Lumin. 1989, 43, 125. (11) Jacobsen, S. M.; Gu¨del, H. U. J. Am. Chem. Soc. 1988, 110, 7610. (12) Rullie´re, C.; Armand, T.; Marie, X. In Femtosecond Laser Pulses; Rullie´re, C., Ed.; Springer, Berlin, 1998. (13) Brown, D. H.; Hunter, A.; Smith, W. E. J. Chem. Soc., Dalton Trans. 1979, 79. (14) Reber, C.; Gu¨del, H. U. J. Lumin. 1988, 42, 1 and references therein. (15) Jacobsen, S. M.; Gu¨del, H. U.; Smith, W. E. Inorg. Chem. 1987, 26, 2001. (16) Smith, W. E. J. Chem. Soc., Chem. Commun. 1987, 1121. (17) Figgis, B. Introduction to Ligand Fields; Interscience: New York, 1966; p 60. (18) Sugano, S.; Tanabe, Y.; Kamimura, H. Multiplets of Transition Metal Ions in Crystals; Academic Press: New York/London, 1970. (19) May, P. S.; Gu¨del, H. U. J. Lumin. 1990, 46, 277. (20) Sturge, M. D. Solid State Phys. 1967, 20, 91. (21) Fowler, W. B. Physics of Color Centers; Academic Press: New York, 1968; p 72. (22) Brunold, T. C.; Gu¨del, H. U. In Inorganic Electronic Structure and Spectroscopy; Solomon, E. I., Lever, A. B. P., Eds.; Wiley: New York, 1999; pp 259-306. (23) Venkateswartu, K.; Sundaram, S. Z. Phys. Chem. Neue Folge 1956, 9, 174. (24) Gamelin, D. R.; Gu¨del, H. U. J. Phys. Chem. B 2000, 104, 10222. (25) Wermuth, M.; Gu¨del, H. U. J. Am. Chem. Soc. 1999, 121, 10102. (26) Wright, J. C. Topics in Applied Physics: Radiationless Processes in Molecules and Condensed Phases; Fong, F. K., Ed.; Springer: Berlin, 1976; p 239. (27) Downing, E.; Hesselink, L.; Ralston, J.; Macfarlane, R. Science 1996, 273, 1185.
