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Absorption, emission and lifetime data on Cu+ in some alkali halides
Journal of Luminescence 14 (1976) 281-294 © North-Holland Publishing Company
ABSORPTION, EMISSION AND LIFETIME DATA ON Cu + IN SOME ALKALI HALIDES M. BERTOLACCINI, P. G A G L I A R D E L L I , G. PADOVINI lstituto di Fisica del Politecnico di Milano and Gruppo Nazionale di Struttura della Materia del C.N.R., Milano, Italy and G. SPINOLO lstituto di Fisica dell'Universith degli Studi di Milano and Gruppo Nazionale di Struttura della Mate~ffa del C.N.R., Milano, ltaly Received 22 October 1975 Revised manuscript received 3 May 1976
The lifetime of the 3d94s ~ 3d 1o transition of Cu+ in several alkali halides has been measured as a function of temperature from L.He.T. (---8 K) to R.T. Original instrumentation was developed allowing the automatic continuous recording, as a function of temperat-ure, of single decay time constants even if varying at a rather high rate. Accurate fixedpoint measurements by the single photon technique were also performed at R.T., L.N.T. and L.He.T. Two regions of variation of r versus T have been observed. The interpretation which seems more plausible is that the Cu+ ion in its relaxed excited state is essentially incenter in the lower temperature region while for T > 40 K it goes off-center even if not so strongly as in the ground state. In NaCI the behaviour of Cu+ is quite similar with the difference that in the ground state it is in-center over the whole temperature range from L.He.T to R.T..
1. Introduction In the last decade, together with a considerable interest in the relaxed excited states o f color centers in alkali halides, some attention has also been paid to excited states of heavy metal impurities. Here we will be concerned with the lifetime o f t h e relaxed excited state o f Cu + in alkali halides. An interesting feature about Cu + is that in several host matrices it does not occupy the position o f the ion it substitutes; in other terms, it goes "off-center". This fact has important bearings b o t h on the oscillator strength of the upwards transition and on the lifetime of the luminescence. Further, it has been noticed, on grounds o f emission lifetime studies, that the position of the unexcited ion may be different from the position of the ion when the electron is in the relaxed excited state [1,2]. 281
282
M. Bertolaccini et al. / Lifetime data on Cu ÷ fl~ some alkafi halides
In two former papers by our group [1,2] the lifetime has been studied from 4.2 K up to 700 K with single pulse excitation and oscillographic detection. Unfortunately, the clipping time of the preamplifier perturbed the readings of unexpectedly long lifetimes and this fact, together with a lowering of the amplitude of the signal at the lower temperature end and some scattering from the exciting light, introduced strong errors in our results below 30 K in KBr and RbBr. This became evident few months later when a box-car integrator was used as the main block of the detection system
[3]. Later on [4], when it was clearly established that lifetimes near liquid helium temperature are of the order of milliseconds, we performed some excited state spectroscopy measurements, since it appeared possible to maintain a non-zero populatibn in the relaxed excited state. Before going into further work in this area, we thought it useful to obtain precise data on the lifetimes of Cu + in several alkali halide matrices. A suitable technique and an original electronic instrument were therefore developed for this purpose. The measuring apparatus will be described in some detail in the section 2. In section 3, together with the data on lifetime, we shall also present some new results of absorption measurements which, in the case of NaBr : Cu, are of particular interest. Absorption and luminescence data will be put together in table la,b. In section 4 absorption and luminescence lifetime data will be discussed in relation to the wave function mixing produced by the perturbation due to the "off-center" position of the ion or to the odd parity phonons.
2. Experimental techniques The Cu doped alkali halides we used, were prepared either growing them from the doped melt or by diffusion of copper into pure crystal samples ( ' 1 h at ~600°C in nitrogen atmosphere). The content of Cu in freshly quenched samples was checked before each luminescence and lifetime measurement by recording the optical absorption in a Cary 14 automatic spectrophotometer. D.C. excitation and luminescence spectra were measured with a standard apparatus. Temperature was measured by means of a cryogenic linear temperature sensor (C.L.T.S.) by Oxford Instruments, inserted into a fixed Kirchoff bridge; current through the temperature sensor was kept constant so as to obtain an unbalance voltage output from the bridge proportional to the temperature variation. Temperature was continuously monitored and recorded through all the measurements. The lifetime measurements were performed using two different techniques; the reason for doing this will become apparent in the following discussion. A very precise and powerful tool in many experimental investigations on the lifetime of excited color centers in solids is the single photon technique [5]. This technique can be used only if the varying parameter, in our case temperature, is held con-
34. Bertolaccini et al. / Lifetime clata on Cu + in some alkali halides
283
stant for a sufficiently long time (generally some hours), in order to achieve reasonably high statistical accuracy. A compromise between total measurement time and number of fixedpoints explored is therefore unavoidable. Besides, feedback stabilization of the working point is necessary; otherwise only a very low number of naturally stable fixed points can be explored. A technique has therefore been developed, allowing a continuous and automatic recording, as a function of temperature, of the lifetime, that is, of the time constant of repetitive, low level, statistically fluctuating, exponential waveforms, which are the output signals of a detector (photomultiplier) viewing the sample excited by repetitive light flashes. The accuracy of the single measurement point is generally poorer than with the aforementioned single photon technique, but this drawback is counterbalanced by the resulting interpolation between a much greater number of measurements and by the much more detailed information one gets. Besides, temperature may be allowed to vary even at a rather high rate and no knowledge of the law of variation is necessary. A block diagram of the measuring apparatus is given in fig. 1. The sample, enclosed within a liquid helium cryostat, is excited by a high pressure mercury lamp - Osram HBO 200 W - operated in a relaxation oscillator mode (P.L.S.), and thus giving pulses of sufficient intensity at a repetition rate adjustable from 2 - 3 to 200-300 pulses per second; duration of the light pulse was below i/as. The light emitted by the sample is collected by a low noise 56 DVP Philips photomultiplier (P.M.), whose output signal is sent to the time constant measuring unit (T.C.M.U.). The output from the temperature sensing device (C.L.T.S.) is amplified (A) and sent, together with the analog output of the T.C.M.U., to a two pen strip chart recorder. Due to the weak luminescence, pulses at the output of the photomultiplier are of very low amplitude and statistical fluctuation both in the charge collected and in the waveshape are very strong (the waveform is practically resolved into single photon spikes); integration of the output pulses is therefore necessary and the rise time constant of the integrated waveform is measured by the T.C.M.U.
FILTER~ t/F/ILTER SAMPLE
CRYOSTAT
,
CLrS
1
Fig.1. Block diagram of the apparatus for the continuous recording of lifetime as a function of temperature (T.C.M.U.).
284
M. Bertolaccini et al. / Lifethne data on Cu + hi some alkali halides
Basically, the working principle of the T.C.M.U. is the following. The exponential waveform is sent to a gated integrator whose gating interval is Tg >> r (where r is the time constant to be measured). A sample of the integrated waveform is taken at some time T < Tg while a second sample is taken at the end of the gating time. The amplitude of the two samples is compared and a digital step-up or step-down system shifts T on subsequent pulses in the proper direction, in a succession of equal duration steps until the first sample is equal to a pre-determined fraction (for instance 1/e or ½) of the second one. The time T at which this happens is of course equal or proportional to r and both an analog and a digital measure of it is displayed by the T.C.M.U. These outputs can be used to drive a strip chart recorder or to feed a computer or a punched type recorder. The input pulses do not need to be of constant amplitude. This is important in our case where the pulsed light source displays short and long term instability and where statistical fluctuations in the charge collected at the anode of the photomultiplier are important because the luminescence is very weak. One important limitation (which can be overcome by a somewhat more sophisticated logic design of the T.C.M.U.) is that only single exponential decays can be measured. The presence in the waveform to be analysed of more than one decay time constant can give rise to .non-negligible errors. The instrument is capable of measuring time constants from some/as to some ms with variation rates as fast as 10 3/as/s. A complete description has been published elsewhere [6]. In order to have precise reference values and to make sure that luminescence decays are characterized by single time constants, also fixed point measurements were performed by the single photon technique [5]. Due to the rather long lifetime to be measured, the apparatus had to be modified with respect to conventional start-stop systems. To avoid distortions [7] and to improve measuring efficiency, a multistop
CRYOSTAT~ SAMPLE~_,~ FIL TER
/
FILTER
•
:
= ~o
scarer"
Fig. 2. Block diagram of the apparatus for lifetime measurements with the single photon technique.
M.. Bertolaccini et al. / Lifet#ne data on Cu + in some alkali halides
285
time-to-amplitude converter (M.S.T.A.C.) had to be used instead of a single stop converter. A block diagram of the measuring apparatus is shown in fig. 2. An electrical pulse is obtained from the light source and suitably shaped within the lamp pulse shaper (L.P.S.). This pulse is passed through a fan out (F.O.) and sent to start the M.S.T.A.C. The output pulse from the photomultiplier is sent through a preamplifier (P.A.) and an amplifier (A) to a single channel pulse height analyzer (S.C.P.H.A.) where optimum ratio of single photon pulses to thermal background pulses is achieved [5]. The output pulses provided by the S.C,P.H.A. are passed through a gate (G) and sent as stop pulses to the M.S.T.A.C. The output from the M.S.T.A.C. is used to feed a multichannel pulse height analyzer. The fan out provides pulses which are sent in anticoincidence to the gate to cancel stop pulses which are almost timecoincident with start pulses; this is necessary because some light from the source, despite every possible precaution, reaches the photomultiplier directly by reflection or diffusion from the sample. In order to fulfill the following requirements: (a) ensure that the decay is given by a single exponential process; (b) have a reference value for the recording with the T.C.M.U., measurements were performed as follows. A fixed point measurement was performed at L.He.T. after determination of the absorption spectrum. Temperature was then allowed to rise to L.N.T. and during this period the lifetime was continuously recorded by means of the apparatus already described. When L.N.T. was reached, a second fixed point measurement was performed. Analysis of fixed point data was
"^lu'~
I
=
~%~
i
Na Br
:
Cu
L. H e . T. 215 I J s / c h a n n e l ¢n I0"~
•
~ = 3.901 ms
IO s c) ¢j
I0
1
I
5O
. . . .
tO0 CHANNELS
-
150
....
Fig. 3. An example of the decay curves obtained with the single photon technique.
286
M. Bertolaccini et al. / Lifetime data on Cu + in some alkali halMes
Fig. 4. Typical recorder trace obtained from the T.C.M.U.
automatically performed by a computer [5], an example being shown in fig. 3. In fig. 4 a typical recorder trace o f the signal from the T.C.M.U. as a function of temperature is presented. As already said, the T.C.M.U. works correctly only if dealing with single lifetime decays. If more than one process is involved, the result must be corrected paying due attention to the relative intensity o f the different components, according to the following relation [6]
1+13 2/3
e-X-e-X/~"
,
/3- A2 -
,
~
r2
1"1
r'l
x = 0 . 6 9 3 ~ -I
(1)
valid in the case of two components of intensity A 1 and A 2 and decay time constants I 7"1 and 7-2 , 1-1 is the lifetime measured without correction. As it is apparent from the formula given above,/3 and 6 must be known and the same correction can be applied to the whole measurement cycle on a single specimen only if these parameters remain constant (in our case independent of temperature). Errors in the measurements using the T.C.M.U. may arise from different causes. The digitization error due to the digital nature of the T.C.M.U. is 1%. Errors in calibration, errors due to thermal drifts and long term instability and errors arising from the statistical nature of the signal analyzed may be estimated to be lower than 5%. The most important source of error is probably due to the temperature sensing device and stems chiefly from calibration uncertainties and from the dynamic behaviour of the sample holder and the sensing device itself. Errors in the fixed point measurements arise from statistical limits in the accu-
M. Bertolaccini et al. / Lifetime data on Cu + in some alkali halides
287
mulation of data, from limitations in the computer program for the evaluation of the lifetime and from calibration inaccuracy of the time axis. The first two sources of error are often negligible; they can become important only in the case of multiple time constant decay or in the case of high background. The third contribution to errors is of the order of some percent.
3. Experimental results and discussion 3.1. A b s o r p t i o n a n d h t m i n e s c e n c e
Several absorption parameters have already been reported in literature (see references in table 1). We thought it useful, however, to complete these data on Cu + in alkali halides and so we performed detailed measurements on RbC1 : Cu, RbBr : Cu and NaBr : Cu whose absorption curves - to our knowledge - have not yet been published. Our results are shown in fig. 5. In table la we have collected the best available data on the width at half height and peak position of the absorption bands. The oscillator strength f ( T ) of the samples we have been more interested in, is given in fig. 6 as a function of temperature. It is apparent that f(T) for RbC1 : Cu and RbBr : Cu is essentially temperature independent; in NaC1 : Cu, on the contrary, it strongly increases with increasing temperature. These behaviours have already been discussed [8] and have been explained on the basis of an off-center (RbBr : Cu and RbCI : Cu) and in-center situation (NaC1 : Cu) for Cu ÷ in its ground state. The anomalous behaviour o f f ( T ) in NaBr : Cu should be related to the growth at low temperatures of the band peaked at 5.1 eV (L.He.T. value). It seems clear that the presence of this band splitted from the main one (at 4.7 eV) is due to the lowering of symmetry of the local field acting on Cu +. The wave function mixing due to this change of the local symmetry at temperature lower than L.N.T., should be responsible for the increase of the oscillator strength. From the fact that f(T) is essentially constant from L.N.T. to R.T., we may infer that the offcenter displacement of the Cu ÷ ion, at low temperatures, has a different crystallographic direction with respect to the one at high temperatures. The NaI : Cu absorption spectra below 80 K show a similar behaviour, although the proximity of the intrinsic absorption edge does not allow an analysis as accurate as that for NaBr : Cu. As a last remark we observe that the two main absorption peaks of NaBr : Cu shift towards lower energies with decreasing temperature, starting from about 80 K. The Cu + luminescence peak positions and band widths are also collected in table lb. The emission peak positions and their shift as a function of temperature do not deserve particular comments with the exception of RbBr : Cu. In the latter crystal we have found two emission bands centered respectively at L.N.T., at 2.83 and 2.97 eV (L.He.T. 3.1 eV). From excitation spectra we have been able to associate these emission bands to the L.N.T. absorption peaks at 4.92 and 4.55 eV. We have meas-
288
3£. gertolaccini et al. / Lifetime data on Cu + in some alkali halides
Table 1 a Absorption peak energies and band halfwidth at half height at various temperatures. The values are given in eV. Abs. peak energies
Abs. halfwidth energies
L.He.T.
L.N.T.
R.T.
L.He.T.
L.N.T.
R.T.
NaCI : Cu NaBr : Cu NaI : Cu
4.81 a) 4.69 4.9 b)
4.85 a) 4.775 4.86b)
4.86 a) 4.78 4.79 b)
0.25t 0.02 a) 0.33 ± 0.02 0.32 ± 0.02
0.31 ± 0.02 a) 0.44 _+0.02 0.37 +- 0.02b)
0.57 ± 0.02 0.63 ± 0.02 0.51 ± 0.02 b)
KC1 : Cu KBr : Cu KI : Cu
4.75 c) 4.70 c) 4.73 e)
4.75 c) 4.70 c) 4.72 c)
4.75 c) 4.66 c) 4.66 c)
0.32 -+ 0.02 a-c) 0.36 a) 0.22 +_0.02 a-c) 0.26 d) 0.15 ± 0.02 a-c) 0.18 d)
0.48 d) 0.40 d) 0.32 d)
RbCI : Cu RbBr : Cu RbI:Cu
4.69 4.62 4.64b)
4.66 4.55 4.62b)
4.64 4.52 4.65b)
0.34 ± 0.02 0.31 ± 0.02 0.25±0.03b)
0.48 -+ 0.02 0.40 ± 0.02
0.42 ± 0.02 0.38 ± 0.02 0.26±0.03b)
Table lb Emission peak energies and band halfwidth at half height at various temperatures. The values are given in eV. Emission peak energies
Emission halfwidth energies
L.He.
L.N.T.
R.T.
L.He.T.
L.N.T.
R.T.
NaCI : Cu NaBr : Cu NaI : Cu
3.55 3.47 3.32 e)
3.54 3.46 3.31 e)
3.46 3.41 3.28 e)
0.14 +- 0.02 0.10 _+0.02 0.11 ± 0.02 e)
0.17 ± 0.02 0.14 ± 0.02 0.14 ± 0.02 e)
0.255 ± 0.02 0.24 ± 0.02 0.23 + 0.02 e)
KCI : Cu KBr : Cu KI : Cu
3.16
3.146 d) 3.12 d) 3.16 d) 3.137 d) 0.12 ± 0.02 3.13 d) 3.114 d)
0.16 d) 0.14 ± 0.02 0.124 d)
0.26 d) 0.23 ± 0.02 0.23 d)
RbBr : Cu
3.1 ± 0.02
2.97 +- 0.02
0.23 ± 0.02
RbI : Cu
3.05 3.05 3.03 0.12 ± 0.02 e) ± 0.02 e) ± 0.02 e) ± 0.02 e)
0.22 _+0.02
a) K. Fussgaenger, Phys. Stat. Sol. 34 (1966) 157. b) G. Spinolo, unpublished. c) E. Kriitzig et al., Phys. Stat. Sol. 10 (1965) 709. d) R. Oggioni.e.t al., Phys. Stat. Sol. 9 (1965) 411. e) S.A. Mack et al., Phys. Stat. Sol. 46b (1971) 193.
0.16 + 0.02 e)
0.32 ± 0.02 e)
M. Bertolaccini et aL / Lifetime data on Cu+ h7 some alkali halides
289
1.5 Rb Cl : Cu ,.o ~ \
--
\ \
o.r.
.... c Nr
L.He.T 0.5
1.5
...j 0.5
~
~
~
~
x
\
Iii,
RbBr : Cu
h
t~ o 0
Na Br : Cu 1.5
,o
PHOTON ENERGY (eY) Fig. 5. Absorption spectra at R.T., LN.T. and L.He.T. of NaBr : Cu, RbBr : Cu, RbC! : Cu.
ured two different lifetime values. We think that the processes arising from the absorption of the photon of 2.83 eV are probably due to some impurity already present in the pure RbBr before the Cu addition. We have focused our attention on the absorption band at 4.55 eV and the corresponding emission which we think is connected with the presence of Cu in the pure crystal. Table lb shows that the values of the half-widths at half-height of the emission bands are always smaller than those corresponding to absorption. Since the width of absorption and emission bands is strictly related to the electron-ohonon coupling
290
M. Bertolaccini et al. / L i f e t i m e data on Cu + in s o m e alkali ha~ides I
I
I
Na B r : Cu
:
= tO
li RbBr: Cu
~
-
NaCI : Cu
O~
-
- RbCI
Cu
~J ~J (J ~3
, 0
100
200
300
T (K)
Fig. 6. Relative oscillator strength as a function of temperature for RbCI : Cu, NaCI : Cu, RbBr : Cu and NaBr : Cu. Data on NaCI : Cu are taken from ref. [8]. s t r e n g t h , t h e i n t e r a c t i o n w i t h lattice field for t h e o f f - c e n t e r Cu + ion is clearly larger t h a n for an i n - c e n t e r s i t u a t i o n . We c a n t h e r e f o r e infer t h a t Cu + in its relaxed e x c i t e d state, even if still o f f - c e n t e r , is m o r e nearly i n - c e n t e r t h a n in its g r o u n d state.
3.2. Lffetime In table 2 the lifetime data we obtained on Cu doped NaC1, NaBr, KBr and RbBr, both with the single photon technique and the T.C.M.U. are shown. Table 2 Lifetime data at fixed temperatures. Values are given in text. Two values are given when the time decay can be decomposed in two components. R.T. a)
L.N.T. a)
~8 K a)
~ 8 K b)
NaCI : Cu
0.038
0.082
f 1.66 c) 3.39 "4.24 c)
3.088
NaBr : Cu
0.142
0.356
3.90
4.04
KBr : Cu
0.091
0.137
3.62
3.77
RbBr : Cu
0.044 d) 0.094 e)
0.063 d) 0.134 e)
2.2 d) 3.41 e)
2.83
a) Single photon technique. b) Data from T.C.M.U. e) Lifetime values from a two-components reduction of the S.P. spectrum. d) Lifetime of the component excited at 2.83 eV (L.N.T. value). e) Lifetime of the component excited at 2.97 eV (L.N.T. value).
M. Bertolaccini et al. / Lifetime data on Cu + in some alkali halides
291
s s
i0 t
103
J
0
I
20
40
I
60
I
80
I..
I00
I
280 300 T (K)
Fig. 7. Reciprocal lifetime as a function o f temperature as obtained from the T.C.M.U. for NaC1 : Cu, NaBr : Cu, KBr : Cu.
In fig. 7 we report 7" - 1 as a function of T, with the exception o f RbBr : Cu. It has already been outlined that in the RbBr : Cu crystals we used, two emission bands are present. We have been able to associate the r value o f 3.41 ms (low temperature value) to the band peaked at 3.1 eV selecting the light emitted from the sample with a Kodak 34 filter. This filter was not used when performing the measurements with the T.C.M.U The value at' L.He.T. shown in table 2 must therefore be analyzed by means o f formula (1) given in section 2. In the case o f RbBr at L.He.T. we have: /3 = 1.55,
8 = 1.55,
!
7-1 = 2.83 ms,
and substituting into formula (1) we obtain: x = 1.13
that is
7-1 =2"2 ms,
7-2 = 3 " 4 m s '
in good agreement with the values obtained by the fixed point technique. The above correction can be performed only if/3 and/i are known with sufficient accuracy. As for NaBr : Cu and KBr : Cu, the L.He.T. data obtained with the S.P. technique and the T.C.M.U. show that the agreement between the results of the two methods is good, within the experimental error. For NaCI : Cu the discrepancy is a little greater. It could be explained if we admit that there are two decay constants instead of one, as some of our measurements seem t o indicate. Unfortunately, it is rather difficult to separate two such components in
292
M. Bertolaccini et al. / Lifetime data on
Cu+in some alkali halides
our fixed point measurements, due to the fact that, if present, the second component is a rather long-lived one and the strong contribution of background in the tail of the decay curve produces a high statistical inaccuracy. The question remains therefore an open one and further work on fixed point data is necessary to reach a conclusive statement. The r -1 dependence versus T can be explained, in our opinion, with reference to two different situations at low (<40 K) and at high temperature ( > 4 0 K). The emission transition 3d94s --> 3d 10 is forbidden unless static (off-center) or dynamic mixing with wave functions of different parity occurs. The extremely long L.He.T. lifetime of Cu + in the matrices we have studied, suggests that in that temperature region the mixing is very low. The values of ~- at L.He.T. for the various samples we have considered are rather similar; this should imply that Cu + preserves its identity and the interaction with the host lattice is not particularly relevant. As a consequence of these observations, we propose that at L.He.T. Cu + is essentially in-center: in the relaxed excited state the balance between stabilizing (repulsive, mainly) and destabilizing (mainly dipolar) forces is in favour of the former ones. As the temperature rises, this balance is rapidly altered; the Cu + ion goes offcenter and the lifetime becomes considerably shorter due to the static mixing. For a further increase of temperature, above 50 K, r keeps decreasing but at a much slower rate. This'model implies that, in all the temperature range we studied, the only decay channel, from the lowest relaxed excited state to the ground state, is through spontaneous emission. Certainly the decay probability will be very different if the relaxed excited state of interest is a pure 4s or is mixed with 4p (in this case we will call it 4s'): the second situation may occur if the ion moves off-center. The jump of Cu + to the off-center position may be reached through a thermal activation process involving an activation energy; there will also be an activation energy AE, for the related process in the electronic levels. Analytically we may describe l / r , the total decay probability, as follows: 1_ 1 + 1 _ ~ c c ~ l (--~0 7" (rR)in (rR)of f r R ~ S ~ d ~ + r R ~ S ' ~ d j
e-aE/kT) '
where AE represents the barrier the electron has to overcome to go from the 3d94s level in the in-center position, to the corresponding level in the off-center position; I[r 0 the frequency.of the jump trials (whose probability of success goes as e - ~ E / k T and 1/rR(S --> d) the probability of radiative decay when Cu + is in the off-center position. In fig. 8 the analysis through which AE can be derived is shown. In fig. 9 our experimental results are fitted for higher temperatures (>L.N.T.) with the function: 1
1
~6o
- = coth 7" ref f 2kT " The hypothesis is made that, when Cu + is in an off-center position the electron-
M. Bertolaccini et al. / Lifetime data on Cu + in s o m e alkali halides
293
I0 ~
~- ¢'sec'9
10~
Na~:Cu .KBr : Cu NaSr:Cu
10 2
AE=O.4eV .4E=O.3Z,eV
AE=O.325eV
\
10
0
2
I,
6
8
I/T•
10
12
14
16
I0 ~ (K-11
Fig. 8. Plot of 1
1
r
rR(S~d)
_
1
1 e-Z~E/kT
~'R(S'--* d) r 0
(heavy straight lines) in the low-temperature range. Light traces are the experimental data obtained by means of the T.C.M.U. (see fig. 7).
phonon interaction (and the related wave function mixing) is responsible for the increase of the decay probability. The fitting is rather good for NaCI : Cu and KBr : Cu at T > I00 K. The conclusion we can draw from all the reported experiments and their analysis, is that in general Cu + in the relaxed excited state is more in-center than in the ground state (with the exception of NaC1). This may be caused by a stronger effect of repulsive forces in the excited state, due to a more extended wave function. Further, while in the ground state Cu + is either in center (NaCI) or off-center (most of alkali halides) with the only possible exception of NaBr, up to 300 K, in the relaxed excited state, the cases in which Cu+ moves from an in-center position to an off-center position with increasing temperature are rather common.
294
M. Bertolaccini et al. / Lifetime data on
-~ (s.c-,)
f
toZ l
0
I
I
I00
I
I
200
Cu +
in some alkali halides I
I
300
T (K)
Fig. 9. Fit of experimental results (see fig. 7) with the function 1/r = (1/%if) coth (17w/kT) in the temperature range from L.N.T. to R.T.
References [1] [21 [3] [4] [5 ]
G. B',ddini, A. Jean and G. Spinolo, Phys. Stat. Solidi 25 (1968) 557. M. Piccirilli and G. Spinolo, Phys. Rev. B4 (1971) 1339. G. Spinolo, Errata, Phys. Rev. B6 (1972) 759. C. Bussolati, P. Gagliardelli and G. Spinolo, Solid State Commun. 12 (1973) 1253. M. Bertolaccini, L. Bosi, C. Bussolati and G. Spinolo, Color centers in alkali halides, International Symposium (Roma, 1968) p. 32; unpublished abstracts. L. Bosi, C. Bussolati and G. Spinolo, Phys. Rev. B1 (1970) 890; S. Cova, M. Bertolaccini and C. Bussolati, Phys. Stat. Sol. 18a (1973) 11. [6] M. Bertolaccini and G. Padovini, Nucl. Instr. Methods 129 (1975) 59. [7] M. Bertolaccini and S. Cova, Nucl. Instr. Methods 121 (1974) 547. [8] K. Fussgaenger, Phys. Stat. Sol. 34 (1965) 157; 36 (1969) 645.
ABSORPTION, EMISSION AND LIFETIME DATA ON Cu + IN SOME ALKALI HALIDES M. BERTOLACCINI, P. G A G L I A R D E L L I , G. PADOVINI lstituto di Fisica del Politecnico di Milano and Gruppo Nazionale di Struttura della Materia del C.N.R., Milano, Italy and G. SPINOLO lstituto di Fisica dell'Universith degli Studi di Milano and Gruppo Nazionale di Struttura della Mate~ffa del C.N.R., Milano, ltaly Received 22 October 1975 Revised manuscript received 3 May 1976
The lifetime of the 3d94s ~ 3d 1o transition of Cu+ in several alkali halides has been measured as a function of temperature from L.He.T. (---8 K) to R.T. Original instrumentation was developed allowing the automatic continuous recording, as a function of temperat-ure, of single decay time constants even if varying at a rather high rate. Accurate fixedpoint measurements by the single photon technique were also performed at R.T., L.N.T. and L.He.T. Two regions of variation of r versus T have been observed. The interpretation which seems more plausible is that the Cu+ ion in its relaxed excited state is essentially incenter in the lower temperature region while for T > 40 K it goes off-center even if not so strongly as in the ground state. In NaCI the behaviour of Cu+ is quite similar with the difference that in the ground state it is in-center over the whole temperature range from L.He.T to R.T..
1. Introduction In the last decade, together with a considerable interest in the relaxed excited states o f color centers in alkali halides, some attention has also been paid to excited states of heavy metal impurities. Here we will be concerned with the lifetime o f t h e relaxed excited state o f Cu + in alkali halides. An interesting feature about Cu + is that in several host matrices it does not occupy the position o f the ion it substitutes; in other terms, it goes "off-center". This fact has important bearings b o t h on the oscillator strength of the upwards transition and on the lifetime of the luminescence. Further, it has been noticed, on grounds o f emission lifetime studies, that the position of the unexcited ion may be different from the position of the ion when the electron is in the relaxed excited state [1,2]. 281
282
M. Bertolaccini et al. / Lifetime data on Cu ÷ fl~ some alkafi halides
In two former papers by our group [1,2] the lifetime has been studied from 4.2 K up to 700 K with single pulse excitation and oscillographic detection. Unfortunately, the clipping time of the preamplifier perturbed the readings of unexpectedly long lifetimes and this fact, together with a lowering of the amplitude of the signal at the lower temperature end and some scattering from the exciting light, introduced strong errors in our results below 30 K in KBr and RbBr. This became evident few months later when a box-car integrator was used as the main block of the detection system
[3]. Later on [4], when it was clearly established that lifetimes near liquid helium temperature are of the order of milliseconds, we performed some excited state spectroscopy measurements, since it appeared possible to maintain a non-zero populatibn in the relaxed excited state. Before going into further work in this area, we thought it useful to obtain precise data on the lifetimes of Cu + in several alkali halide matrices. A suitable technique and an original electronic instrument were therefore developed for this purpose. The measuring apparatus will be described in some detail in the section 2. In section 3, together with the data on lifetime, we shall also present some new results of absorption measurements which, in the case of NaBr : Cu, are of particular interest. Absorption and luminescence data will be put together in table la,b. In section 4 absorption and luminescence lifetime data will be discussed in relation to the wave function mixing produced by the perturbation due to the "off-center" position of the ion or to the odd parity phonons.
2. Experimental techniques The Cu doped alkali halides we used, were prepared either growing them from the doped melt or by diffusion of copper into pure crystal samples ( ' 1 h at ~600°C in nitrogen atmosphere). The content of Cu in freshly quenched samples was checked before each luminescence and lifetime measurement by recording the optical absorption in a Cary 14 automatic spectrophotometer. D.C. excitation and luminescence spectra were measured with a standard apparatus. Temperature was measured by means of a cryogenic linear temperature sensor (C.L.T.S.) by Oxford Instruments, inserted into a fixed Kirchoff bridge; current through the temperature sensor was kept constant so as to obtain an unbalance voltage output from the bridge proportional to the temperature variation. Temperature was continuously monitored and recorded through all the measurements. The lifetime measurements were performed using two different techniques; the reason for doing this will become apparent in the following discussion. A very precise and powerful tool in many experimental investigations on the lifetime of excited color centers in solids is the single photon technique [5]. This technique can be used only if the varying parameter, in our case temperature, is held con-
34. Bertolaccini et al. / Lifetime clata on Cu + in some alkali halides
283
stant for a sufficiently long time (generally some hours), in order to achieve reasonably high statistical accuracy. A compromise between total measurement time and number of fixedpoints explored is therefore unavoidable. Besides, feedback stabilization of the working point is necessary; otherwise only a very low number of naturally stable fixed points can be explored. A technique has therefore been developed, allowing a continuous and automatic recording, as a function of temperature, of the lifetime, that is, of the time constant of repetitive, low level, statistically fluctuating, exponential waveforms, which are the output signals of a detector (photomultiplier) viewing the sample excited by repetitive light flashes. The accuracy of the single measurement point is generally poorer than with the aforementioned single photon technique, but this drawback is counterbalanced by the resulting interpolation between a much greater number of measurements and by the much more detailed information one gets. Besides, temperature may be allowed to vary even at a rather high rate and no knowledge of the law of variation is necessary. A block diagram of the measuring apparatus is given in fig. 1. The sample, enclosed within a liquid helium cryostat, is excited by a high pressure mercury lamp - Osram HBO 200 W - operated in a relaxation oscillator mode (P.L.S.), and thus giving pulses of sufficient intensity at a repetition rate adjustable from 2 - 3 to 200-300 pulses per second; duration of the light pulse was below i/as. The light emitted by the sample is collected by a low noise 56 DVP Philips photomultiplier (P.M.), whose output signal is sent to the time constant measuring unit (T.C.M.U.). The output from the temperature sensing device (C.L.T.S.) is amplified (A) and sent, together with the analog output of the T.C.M.U., to a two pen strip chart recorder. Due to the weak luminescence, pulses at the output of the photomultiplier are of very low amplitude and statistical fluctuation both in the charge collected and in the waveshape are very strong (the waveform is practically resolved into single photon spikes); integration of the output pulses is therefore necessary and the rise time constant of the integrated waveform is measured by the T.C.M.U.
FILTER~ t/F/ILTER SAMPLE
CRYOSTAT
,
CLrS
1
Fig.1. Block diagram of the apparatus for the continuous recording of lifetime as a function of temperature (T.C.M.U.).
284
M. Bertolaccini et al. / Lifethne data on Cu + hi some alkali halides
Basically, the working principle of the T.C.M.U. is the following. The exponential waveform is sent to a gated integrator whose gating interval is Tg >> r (where r is the time constant to be measured). A sample of the integrated waveform is taken at some time T < Tg while a second sample is taken at the end of the gating time. The amplitude of the two samples is compared and a digital step-up or step-down system shifts T on subsequent pulses in the proper direction, in a succession of equal duration steps until the first sample is equal to a pre-determined fraction (for instance 1/e or ½) of the second one. The time T at which this happens is of course equal or proportional to r and both an analog and a digital measure of it is displayed by the T.C.M.U. These outputs can be used to drive a strip chart recorder or to feed a computer or a punched type recorder. The input pulses do not need to be of constant amplitude. This is important in our case where the pulsed light source displays short and long term instability and where statistical fluctuations in the charge collected at the anode of the photomultiplier are important because the luminescence is very weak. One important limitation (which can be overcome by a somewhat more sophisticated logic design of the T.C.M.U.) is that only single exponential decays can be measured. The presence in the waveform to be analysed of more than one decay time constant can give rise to .non-negligible errors. The instrument is capable of measuring time constants from some/as to some ms with variation rates as fast as 10 3/as/s. A complete description has been published elsewhere [6]. In order to have precise reference values and to make sure that luminescence decays are characterized by single time constants, also fixed point measurements were performed by the single photon technique [5]. Due to the rather long lifetime to be measured, the apparatus had to be modified with respect to conventional start-stop systems. To avoid distortions [7] and to improve measuring efficiency, a multistop
CRYOSTAT~ SAMPLE~_,~ FIL TER
/
FILTER
•
:
= ~o
scarer"
Fig. 2. Block diagram of the apparatus for lifetime measurements with the single photon technique.
M.. Bertolaccini et al. / Lifet#ne data on Cu + in some alkali halides
285
time-to-amplitude converter (M.S.T.A.C.) had to be used instead of a single stop converter. A block diagram of the measuring apparatus is shown in fig. 2. An electrical pulse is obtained from the light source and suitably shaped within the lamp pulse shaper (L.P.S.). This pulse is passed through a fan out (F.O.) and sent to start the M.S.T.A.C. The output pulse from the photomultiplier is sent through a preamplifier (P.A.) and an amplifier (A) to a single channel pulse height analyzer (S.C.P.H.A.) where optimum ratio of single photon pulses to thermal background pulses is achieved [5]. The output pulses provided by the S.C,P.H.A. are passed through a gate (G) and sent as stop pulses to the M.S.T.A.C. The output from the M.S.T.A.C. is used to feed a multichannel pulse height analyzer. The fan out provides pulses which are sent in anticoincidence to the gate to cancel stop pulses which are almost timecoincident with start pulses; this is necessary because some light from the source, despite every possible precaution, reaches the photomultiplier directly by reflection or diffusion from the sample. In order to fulfill the following requirements: (a) ensure that the decay is given by a single exponential process; (b) have a reference value for the recording with the T.C.M.U., measurements were performed as follows. A fixed point measurement was performed at L.He.T. after determination of the absorption spectrum. Temperature was then allowed to rise to L.N.T. and during this period the lifetime was continuously recorded by means of the apparatus already described. When L.N.T. was reached, a second fixed point measurement was performed. Analysis of fixed point data was
"^lu'~
I
=
~%~
i
Na Br
:
Cu
L. H e . T. 215 I J s / c h a n n e l ¢n I0"~
•
~ = 3.901 ms
IO s c) ¢j
I0
1
I
5O
. . . .
tO0 CHANNELS
-
150
....
Fig. 3. An example of the decay curves obtained with the single photon technique.
286
M. Bertolaccini et al. / Lifetime data on Cu + in some alkali halMes
Fig. 4. Typical recorder trace obtained from the T.C.M.U.
automatically performed by a computer [5], an example being shown in fig. 3. In fig. 4 a typical recorder trace o f the signal from the T.C.M.U. as a function of temperature is presented. As already said, the T.C.M.U. works correctly only if dealing with single lifetime decays. If more than one process is involved, the result must be corrected paying due attention to the relative intensity o f the different components, according to the following relation [6]
1+13 2/3
e-X-e-X/~"
,
/3- A2 -
,
~
r2
1"1
r'l
x = 0 . 6 9 3 ~ -I
(1)
valid in the case of two components of intensity A 1 and A 2 and decay time constants I 7"1 and 7-2 , 1-1 is the lifetime measured without correction. As it is apparent from the formula given above,/3 and 6 must be known and the same correction can be applied to the whole measurement cycle on a single specimen only if these parameters remain constant (in our case independent of temperature). Errors in the measurements using the T.C.M.U. may arise from different causes. The digitization error due to the digital nature of the T.C.M.U. is 1%. Errors in calibration, errors due to thermal drifts and long term instability and errors arising from the statistical nature of the signal analyzed may be estimated to be lower than 5%. The most important source of error is probably due to the temperature sensing device and stems chiefly from calibration uncertainties and from the dynamic behaviour of the sample holder and the sensing device itself. Errors in the fixed point measurements arise from statistical limits in the accu-
M. Bertolaccini et al. / Lifetime data on Cu + in some alkali halides
287
mulation of data, from limitations in the computer program for the evaluation of the lifetime and from calibration inaccuracy of the time axis. The first two sources of error are often negligible; they can become important only in the case of multiple time constant decay or in the case of high background. The third contribution to errors is of the order of some percent.
3. Experimental results and discussion 3.1. A b s o r p t i o n a n d h t m i n e s c e n c e
Several absorption parameters have already been reported in literature (see references in table 1). We thought it useful, however, to complete these data on Cu + in alkali halides and so we performed detailed measurements on RbC1 : Cu, RbBr : Cu and NaBr : Cu whose absorption curves - to our knowledge - have not yet been published. Our results are shown in fig. 5. In table la we have collected the best available data on the width at half height and peak position of the absorption bands. The oscillator strength f ( T ) of the samples we have been more interested in, is given in fig. 6 as a function of temperature. It is apparent that f(T) for RbC1 : Cu and RbBr : Cu is essentially temperature independent; in NaC1 : Cu, on the contrary, it strongly increases with increasing temperature. These behaviours have already been discussed [8] and have been explained on the basis of an off-center (RbBr : Cu and RbCI : Cu) and in-center situation (NaC1 : Cu) for Cu ÷ in its ground state. The anomalous behaviour o f f ( T ) in NaBr : Cu should be related to the growth at low temperatures of the band peaked at 5.1 eV (L.He.T. value). It seems clear that the presence of this band splitted from the main one (at 4.7 eV) is due to the lowering of symmetry of the local field acting on Cu +. The wave function mixing due to this change of the local symmetry at temperature lower than L.N.T., should be responsible for the increase of the oscillator strength. From the fact that f(T) is essentially constant from L.N.T. to R.T., we may infer that the offcenter displacement of the Cu ÷ ion, at low temperatures, has a different crystallographic direction with respect to the one at high temperatures. The NaI : Cu absorption spectra below 80 K show a similar behaviour, although the proximity of the intrinsic absorption edge does not allow an analysis as accurate as that for NaBr : Cu. As a last remark we observe that the two main absorption peaks of NaBr : Cu shift towards lower energies with decreasing temperature, starting from about 80 K. The Cu + luminescence peak positions and band widths are also collected in table lb. The emission peak positions and their shift as a function of temperature do not deserve particular comments with the exception of RbBr : Cu. In the latter crystal we have found two emission bands centered respectively at L.N.T., at 2.83 and 2.97 eV (L.He.T. 3.1 eV). From excitation spectra we have been able to associate these emission bands to the L.N.T. absorption peaks at 4.92 and 4.55 eV. We have meas-
288
3£. gertolaccini et al. / Lifetime data on Cu + in some alkali halides
Table 1 a Absorption peak energies and band halfwidth at half height at various temperatures. The values are given in eV. Abs. peak energies
Abs. halfwidth energies
L.He.T.
L.N.T.
R.T.
L.He.T.
L.N.T.
R.T.
NaCI : Cu NaBr : Cu NaI : Cu
4.81 a) 4.69 4.9 b)
4.85 a) 4.775 4.86b)
4.86 a) 4.78 4.79 b)
0.25t 0.02 a) 0.33 ± 0.02 0.32 ± 0.02
0.31 ± 0.02 a) 0.44 _+0.02 0.37 +- 0.02b)
0.57 ± 0.02 0.63 ± 0.02 0.51 ± 0.02 b)
KC1 : Cu KBr : Cu KI : Cu
4.75 c) 4.70 c) 4.73 e)
4.75 c) 4.70 c) 4.72 c)
4.75 c) 4.66 c) 4.66 c)
0.32 -+ 0.02 a-c) 0.36 a) 0.22 +_0.02 a-c) 0.26 d) 0.15 ± 0.02 a-c) 0.18 d)
0.48 d) 0.40 d) 0.32 d)
RbCI : Cu RbBr : Cu RbI:Cu
4.69 4.62 4.64b)
4.66 4.55 4.62b)
4.64 4.52 4.65b)
0.34 ± 0.02 0.31 ± 0.02 0.25±0.03b)
0.48 -+ 0.02 0.40 ± 0.02
0.42 ± 0.02 0.38 ± 0.02 0.26±0.03b)
Table lb Emission peak energies and band halfwidth at half height at various temperatures. The values are given in eV. Emission peak energies
Emission halfwidth energies
L.He.
L.N.T.
R.T.
L.He.T.
L.N.T.
R.T.
NaCI : Cu NaBr : Cu NaI : Cu
3.55 3.47 3.32 e)
3.54 3.46 3.31 e)
3.46 3.41 3.28 e)
0.14 +- 0.02 0.10 _+0.02 0.11 ± 0.02 e)
0.17 ± 0.02 0.14 ± 0.02 0.14 ± 0.02 e)
0.255 ± 0.02 0.24 ± 0.02 0.23 + 0.02 e)
KCI : Cu KBr : Cu KI : Cu
3.16
3.146 d) 3.12 d) 3.16 d) 3.137 d) 0.12 ± 0.02 3.13 d) 3.114 d)
0.16 d) 0.14 ± 0.02 0.124 d)
0.26 d) 0.23 ± 0.02 0.23 d)
RbBr : Cu
3.1 ± 0.02
2.97 +- 0.02
0.23 ± 0.02
RbI : Cu
3.05 3.05 3.03 0.12 ± 0.02 e) ± 0.02 e) ± 0.02 e) ± 0.02 e)
0.22 _+0.02
a) K. Fussgaenger, Phys. Stat. Sol. 34 (1966) 157. b) G. Spinolo, unpublished. c) E. Kriitzig et al., Phys. Stat. Sol. 10 (1965) 709. d) R. Oggioni.e.t al., Phys. Stat. Sol. 9 (1965) 411. e) S.A. Mack et al., Phys. Stat. Sol. 46b (1971) 193.
0.16 + 0.02 e)
0.32 ± 0.02 e)
M. Bertolaccini et aL / Lifetime data on Cu+ h7 some alkali halides
289
1.5 Rb Cl : Cu ,.o ~ \
--
\ \
o.r.
.... c Nr
L.He.T 0.5
1.5
...j 0.5
~
~
~
~
x
\
Iii,
RbBr : Cu
h
t~ o 0
Na Br : Cu 1.5
,o
PHOTON ENERGY (eY) Fig. 5. Absorption spectra at R.T., LN.T. and L.He.T. of NaBr : Cu, RbBr : Cu, RbC! : Cu.
ured two different lifetime values. We think that the processes arising from the absorption of the photon of 2.83 eV are probably due to some impurity already present in the pure RbBr before the Cu addition. We have focused our attention on the absorption band at 4.55 eV and the corresponding emission which we think is connected with the presence of Cu in the pure crystal. Table lb shows that the values of the half-widths at half-height of the emission bands are always smaller than those corresponding to absorption. Since the width of absorption and emission bands is strictly related to the electron-ohonon coupling
290
M. Bertolaccini et al. / L i f e t i m e data on Cu + in s o m e alkali ha~ides I
I
I
Na B r : Cu
:
= tO
li RbBr: Cu
~
-
NaCI : Cu
O~
-
- RbCI
Cu
~J ~J (J ~3
, 0
100
200
300
T (K)
Fig. 6. Relative oscillator strength as a function of temperature for RbCI : Cu, NaCI : Cu, RbBr : Cu and NaBr : Cu. Data on NaCI : Cu are taken from ref. [8]. s t r e n g t h , t h e i n t e r a c t i o n w i t h lattice field for t h e o f f - c e n t e r Cu + ion is clearly larger t h a n for an i n - c e n t e r s i t u a t i o n . We c a n t h e r e f o r e infer t h a t Cu + in its relaxed e x c i t e d state, even if still o f f - c e n t e r , is m o r e nearly i n - c e n t e r t h a n in its g r o u n d state.
3.2. Lffetime In table 2 the lifetime data we obtained on Cu doped NaC1, NaBr, KBr and RbBr, both with the single photon technique and the T.C.M.U. are shown. Table 2 Lifetime data at fixed temperatures. Values are given in text. Two values are given when the time decay can be decomposed in two components. R.T. a)
L.N.T. a)
~8 K a)
~ 8 K b)
NaCI : Cu
0.038
0.082
f 1.66 c) 3.39 "4.24 c)
3.088
NaBr : Cu
0.142
0.356
3.90
4.04
KBr : Cu
0.091
0.137
3.62
3.77
RbBr : Cu
0.044 d) 0.094 e)
0.063 d) 0.134 e)
2.2 d) 3.41 e)
2.83
a) Single photon technique. b) Data from T.C.M.U. e) Lifetime values from a two-components reduction of the S.P. spectrum. d) Lifetime of the component excited at 2.83 eV (L.N.T. value). e) Lifetime of the component excited at 2.97 eV (L.N.T. value).
M. Bertolaccini et al. / Lifetime data on Cu + in some alkali halides
291
s s
i0 t
103
J
0
I
20
40
I
60
I
80
I..
I00
I
280 300 T (K)
Fig. 7. Reciprocal lifetime as a function o f temperature as obtained from the T.C.M.U. for NaC1 : Cu, NaBr : Cu, KBr : Cu.
In fig. 7 we report 7" - 1 as a function of T, with the exception o f RbBr : Cu. It has already been outlined that in the RbBr : Cu crystals we used, two emission bands are present. We have been able to associate the r value o f 3.41 ms (low temperature value) to the band peaked at 3.1 eV selecting the light emitted from the sample with a Kodak 34 filter. This filter was not used when performing the measurements with the T.C.M.U The value at' L.He.T. shown in table 2 must therefore be analyzed by means o f formula (1) given in section 2. In the case o f RbBr at L.He.T. we have: /3 = 1.55,
8 = 1.55,
!
7-1 = 2.83 ms,
and substituting into formula (1) we obtain: x = 1.13
that is
7-1 =2"2 ms,
7-2 = 3 " 4 m s '
in good agreement with the values obtained by the fixed point technique. The above correction can be performed only if/3 and/i are known with sufficient accuracy. As for NaBr : Cu and KBr : Cu, the L.He.T. data obtained with the S.P. technique and the T.C.M.U. show that the agreement between the results of the two methods is good, within the experimental error. For NaCI : Cu the discrepancy is a little greater. It could be explained if we admit that there are two decay constants instead of one, as some of our measurements seem t o indicate. Unfortunately, it is rather difficult to separate two such components in
292
M. Bertolaccini et al. / Lifetime data on
Cu+in some alkali halides
our fixed point measurements, due to the fact that, if present, the second component is a rather long-lived one and the strong contribution of background in the tail of the decay curve produces a high statistical inaccuracy. The question remains therefore an open one and further work on fixed point data is necessary to reach a conclusive statement. The r -1 dependence versus T can be explained, in our opinion, with reference to two different situations at low (<40 K) and at high temperature ( > 4 0 K). The emission transition 3d94s --> 3d 10 is forbidden unless static (off-center) or dynamic mixing with wave functions of different parity occurs. The extremely long L.He.T. lifetime of Cu + in the matrices we have studied, suggests that in that temperature region the mixing is very low. The values of ~- at L.He.T. for the various samples we have considered are rather similar; this should imply that Cu + preserves its identity and the interaction with the host lattice is not particularly relevant. As a consequence of these observations, we propose that at L.He.T. Cu + is essentially in-center: in the relaxed excited state the balance between stabilizing (repulsive, mainly) and destabilizing (mainly dipolar) forces is in favour of the former ones. As the temperature rises, this balance is rapidly altered; the Cu + ion goes offcenter and the lifetime becomes considerably shorter due to the static mixing. For a further increase of temperature, above 50 K, r keeps decreasing but at a much slower rate. This'model implies that, in all the temperature range we studied, the only decay channel, from the lowest relaxed excited state to the ground state, is through spontaneous emission. Certainly the decay probability will be very different if the relaxed excited state of interest is a pure 4s or is mixed with 4p (in this case we will call it 4s'): the second situation may occur if the ion moves off-center. The jump of Cu + to the off-center position may be reached through a thermal activation process involving an activation energy; there will also be an activation energy AE, for the related process in the electronic levels. Analytically we may describe l / r , the total decay probability, as follows: 1_ 1 + 1 _ ~ c c ~ l (--~0 7" (rR)in (rR)of f r R ~ S ~ d ~ + r R ~ S ' ~ d j
e-aE/kT) '
where AE represents the barrier the electron has to overcome to go from the 3d94s level in the in-center position, to the corresponding level in the off-center position; I[r 0 the frequency.of the jump trials (whose probability of success goes as e - ~ E / k T and 1/rR(S --> d) the probability of radiative decay when Cu + is in the off-center position. In fig. 8 the analysis through which AE can be derived is shown. In fig. 9 our experimental results are fitted for higher temperatures (>L.N.T.) with the function: 1
1
~6o
- = coth 7" ref f 2kT " The hypothesis is made that, when Cu + is in an off-center position the electron-
M. Bertolaccini et al. / Lifetime data on Cu + in s o m e alkali halides
293
I0 ~
~- ¢'sec'9
10~
Na~:Cu .KBr : Cu NaSr:Cu
10 2
AE=O.4eV .4E=O.3Z,eV
AE=O.325eV
\
10
0
2
I,
6
8
I/T•
10
12
14
16
I0 ~ (K-11
Fig. 8. Plot of 1
1
r
rR(S~d)
_
1
1 e-Z~E/kT
~'R(S'--* d) r 0
(heavy straight lines) in the low-temperature range. Light traces are the experimental data obtained by means of the T.C.M.U. (see fig. 7).
phonon interaction (and the related wave function mixing) is responsible for the increase of the decay probability. The fitting is rather good for NaCI : Cu and KBr : Cu at T > I00 K. The conclusion we can draw from all the reported experiments and their analysis, is that in general Cu + in the relaxed excited state is more in-center than in the ground state (with the exception of NaC1). This may be caused by a stronger effect of repulsive forces in the excited state, due to a more extended wave function. Further, while in the ground state Cu + is either in center (NaCI) or off-center (most of alkali halides) with the only possible exception of NaBr, up to 300 K, in the relaxed excited state, the cases in which Cu+ moves from an in-center position to an off-center position with increasing temperature are rather common.
294
M. Bertolaccini et al. / Lifetime data on
-~ (s.c-,)
f
toZ l
0
I
I
I00
I
I
200
Cu +
in some alkali halides I
I
300
T (K)
Fig. 9. Fit of experimental results (see fig. 7) with the function 1/r = (1/%if) coth (17w/kT) in the temperature range from L.N.T. to R.T.
References [1] [21 [3] [4] [5 ]
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