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Competitive cross-relaxation and energy transfer within the shell model: The case of Cs2NaSmxEuyY1 − x − yCl6
JOURNAL OF
LUMINESCENCE Journal
ELSEVIER
of Luminescence
71 (1997) 177-188
Competitive cross-relaxation and energy transfer within the shell model: The case of Cs2NaSmXEuyY1 - x - JjC16 Thomas Luxbacher a,*, Harald P. Fritzer a, Colin D. Flintb aInstitut fir Physikalische und Theoretische Chemie, Technische Universitiit Graz, 8010 Graz, Austria b Laser Laboratory, Department of Chemistry, Birkbeck College, 29, Gordon Square, London WCIH OPP. UK Received
3 June 1996; revised and accepted
16 September
1996
Abstract Electronic energy-transfer processes between Sm3 + (4G,,z) donor ions and Eu 3+ ( ‘FO, ‘F,) acceptor ions in the cubic hexachloroelpasolite crystals Cs2NaSm,Eu,Y1_,_,C16 have been investigated over a wide range of Sm3’ and Eu3+ concentrations at temperatures of 80 and 300K. In these systems the luminescence from the 4G5,2 state of Sm3+ is strongly quenched by both cross-relaxation to nearby Sm 3+ ions and energy transfer to the ‘Do state of Eu3+. The lifetime of the 5D0 state is not affected by the presence of Sm3+. The rates o f cross-relaxation and energy transfer are determined from luminescence decay curve measurements for the Sm3+ 4Gs,2 -+ 6H7,2 emission and the Eu3+ ‘Do -+ ‘Fz emission following excitation into the 4G5,z state of Sm3+. The luminescence decay curves for the 4G5,2 state are analysed in terms of a recently developed discrete shell model for energy transfer assuming electric dipole vibronic-electric dipole vibronic and magnetic dipole-magnetic dipole interaction between Sm3+ donor ions and Eu3+ acceptor ions. Exact agreement is achieved for the energy transfer from Sm3+ donor ions to Eu3+ acceptors without curve fitting. Keywords: Cross relaxation; Energy transfer; Shell model; Luminescence crystals; CszNaSm,Eu,Y,_,_,C1,
dipole allowed electronic transitions. The study of energy-transfer processes in these systems is complicated due to contributions from a large number of possible resonant and near-resonant coupling mechanisms between donor emission and acceptor absorption transitions. In the present study we investigate energy-transfer processes between Sm3+ (4G5,z) donor ions and Eu3+ (‘F,, ‘F1) acceptor ions in the hexachloroelpasolite crystals CszNaSm,Eu,Y i _ _ ,Cl,. The Cs,NaYCl, host lattice has a cubic crystal structure and the rare-earth ions replacing the Y3+ ions are located at perfect octahedral sites surrounded
1. Introduction Electronic energy-transfer processes between trivalent rare-earth ions in crystalline and amorphous solids are of great importance both scientifically and technologically. The kinetics and efficiencies of these energy-transfer processes have been studied theoretically and experimentally using a variety of host materials. In most of these systems the rare-earth ions are located at non-centrosymmetric lattice sites and the optical absorption and emission spectra are dominated by electric * Corresponding
author.
0022-2313/97/$17.00 c> 1997 Elsevier Science B.V. All rights PII SOO22-23 13(96)00124-X
decay curves; Cubic hexachloroelpasolite
reserved
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et al. / Journal of Luminescence
SU13’
71 (1997) 1 V-188
Sd’
Eli”
-
‘D,,
ABCDEF
93 ‘5
7
‘FO Fl Fig. 1. Relevant energy levels and transitions involved in the cross-relaxation Eu,YI _,-,Q. The letters indicate pairs of near-resonant transitions.
by six chloride ions. The nearest neighbour dis7.6.k tance between Y3+ sites is approximately A diagram of the hexachloroelpasolite lattice has been published previously [ 11. This crystalline host lattice provides an excellent model system to study cross-relaxation and energy-transfer processes. The electric-dipole transition moments associated with the 4f -P 4f transitions at octahedral sites are small and therefore excited states of rare-earth ions in centrosymmetric complexes have relatively long relaxation times. The electronic energy levels of Sm3+ and Eu3+ in Cs,NaYCl, are well established both theoretically and experimentally [2-S]. The electronic spectra of Cs,NaSm(Eu)Cl, consist of magnetic dipole allowed electronic transitions and electric dipole allowed vibronic transitions reflecting the perfect centrosymmetric surroundings of the rareearth ions. The 6H5,2 ground state of Sm3+ is split into two crystal-field components in octahedral symmetry, r, (0 cm-‘) and rs (178 cm-‘). The luminescent electronic state 4G5,2 is also split into two components, r, (17 760 cm-‘) and r, (18 105 cm- ‘). The electronic energy levels of Eu3 + involved in the energy-transfer processes considered in this paper are the ‘FO ground state (0 cm-‘) and the 7F, state at 352 cm-‘. The lowest lying luminescent state is 5D, at 17 220 cm-‘.
and
energy-transfer
processes
in Cs2NaSm,
The vibrational properties of Cs,NaSmCl, and Cs,NaEuCl, are also well established [3,8]. The odd parity internal vibrational modes vs(t2J, v4(tlu), and v3(tlu) of the [Ln C1,13- ion (Ln = Sm, Eu) are about 80-90 cm-’ (v& loo-120 cm-’ (v4), (v3). Lattice vibrations are and 240-255 cm-’ found at 40 and 180 cm- ‘. The phonon cut-off frequency corresponds to M 300 cm- ’ so that nonradiative relaxation from an excited state to a lower lying state is slow for a separation between the states of > 2000 cm- ‘. The energy level structure within a 2s+ ‘L, multiplet is comprised of a smaller number of components compared to Sm3+ and Eu3+ ions in noncentrosymmetric crystalline environments such that the number of possible electronic energy levels involved in resonant and near-resonant cross-relaxation and energy-transfer processes is minimised. The cross-relaxation pathways involving the Sm3+ 4 6FJ (J = 2 I,$ and 9) relaxation at the dyi& Gd the Sm3’ 6Hi,2 + ‘jFJ(J =$,$, 3, and y) transitions at the acceptor have been described in detail previously [9]. Fig. 1 shows a selection of near-resonant pathways for crossrelaxation as pairs of transitions AA’, BB’, CC’, and DD’. Beside these there exist numerous phononassisted cross-relaxation processes. In addition to these cross-relaxation processes, energy transfer
T. Luxbacher
et al. I Journal of Luminescence
occurs to the Eu3’ 5Do level. At high temperatures the Sm3+ (4G5,2F,) -+ (6H7,z)F,, r, donor with the transitions are almost resonant (7F1)F4 + (5D0)r1 magnetic dipole allowed electronic transition of the Eu3+ acceptor ion (transitions FF’ in Fig. 1) [2, 51. At low temperatures the main contribution to the energy-transfer at processes involves the 4G5,2 + 6H5,2 transition the Sm3+ donor ion and the 7F0 + 5D0 transition at the Eu3+ acceptor ion where both transitions are of electric dipole allowed vibronic origin [S, lo] (transitions EE’ in Fig. 1). The decay kinetics of the 5D0 state of Eu3+ in Cs,NaEu,Yi _XCl6 (x = 0.01, 1) have been reported by Bettinelli and Flint [ 111. They have observed quenching of emission from the 5D0 state of Eu3+ in Cs,NaEuCl, but not in CszNaEu0.01Y,,g,C16 which implies that energy migration is present in the pure crystal but not in the material with x = 0.01. In a recent series of papers [l, 9, 10, 12-141 we have developed a discrete shell model for energy transfer to understand the kinetics of cross-relaxation processes in cubic crystalline materials and applied this model to the hexachloroelpasolite crystals Cs,NaLn,Y 1_$& and Cs,NaLn,Gd, _Clb (Ln = Pr [l, 131, Sm [9, 10, 121, and Ho [14]). Excellent agreement between the predictions of the shell model and the experimental results was achieved for Pr3 + and Ho3+ whereas some minor aspects of the experimental results on Cs,NaSm,Y, _XC1, cannot yet be reproduced by a priori calculation. In the present study we extend the shell model to include energy transfer between dissimilar lanthanide ions in the hexachloroelpasolite lattice. We have chosen the system Cs,NaSm,Eu,Y 1_x_gClh for a first comparison between calculation and experiment for these energy-transfer processes. In this material the luminescence from the 4G5,2 state of Sm3+ is quenched by both cross-relaxation between nearby Sm 3+ ions and energy transfer from Sm3 + donor ions to Eu3 ’ acceptors. This system is particularly suitable for an experimental investigation of the latter energy-transfer process. Firstly, both the Sm3+ 4Gs,2 state and the Eu3+ 5D, state have slow intrinsic decay rates at temperatures of 80 and 300 K. Secondly, the energy-transfer rate from Sm3+ donor ions to Eu3+ acceptors is comparable to the intrinsic decay rates of the isolated
71 (1997) 177-188
119
ions. Thirdly, both the Sm3+ 4G5,2 state and the Eu3’ 5D0 state may be separately excited in the region 17000 to 18000 cm-’ and the emission from these states may be studied with minimum and Both Cs,NaSmCl, spectral overlap. Cs,NaEuCl, are known to have phase transitions between 80 and 300 K involving a small rotation of the [Ln C1,13- complex ion. As in our previous studies there is no evidence that this minor effect influences the energy-transfer processes. In this paper we focus attention on the crystals Cl, ( y = 0.005, 0.01, 0.02, CszNaSmo.olEu,Yo.ss-,, 0.05, 0.1, 0.25, 0.5, ‘and 0.99) and Cs,Na Sm,Eu0,1Y,.9_,C16 (x = 0.005, 0.01, and 0.1) at temperatures of 80 and 300 K. Results at other temperatures will be reported elsewhere. In crystals of the first type which contain only 1 mol% of Sm3 ’ cross-relaxation between Sm3 + ions is weak but not negligible. The cross-relaxation rate has been determined previously from luminescence decay measurements on Cs2NaSm0.00sYo.995C16, Cs2NaSm,.oolGdo.999Cl~ and Cs,NaSmCl, [9, 121. Since the energy-transfer rate is relatively small it may be deduced from the results obtained on the Cs2NaSm,.,,Eu0,9&16 crystal. The dependence of energy transfer from the Sm3+ donor ion to surrounding Eu3 + acceptors on y is exactly described within the shell model. Energy migration in the ‘DO state is not observed for the compounds which contain lOmol% of Eu3+. The Eu3+ ‘D,, + 7F, emission is not affected by the presence of Sm3’ ions even at a high concentration of the latter.
2. Experimental Large single crystals of high optical quality of compositions CszNaSm0.01Eu,Y,.9,, _ ,Cl, (y = 0.005, 0.01, 0.02, 0.05, 0.1, 0.25, 0.5. and 0.99) and CszNaSm,Eu,.,YO.g_,Clh (x = 0.005, 0.01, and 0.1) were grown by the Bridgman technique as described previously [IS]. Luminescence decay measurements at temperatures of 80 and 300 K were performed as previously reported [9]. Excitation of the Sm3+ ion was carried out directly into the magnetic dipole allowed (6H5,2) I-, -+ (4G5,2)F8 electronic transition at 17760 cm-‘. The (4G5JF, -+ (6H;,~) Fe, F7
180
T Luxbacher
et al. / Journal of Luminescence
emission of Sm3+ was observed at 16 500 + 20 cm-‘. The Eu3+ emission for the ‘D, + 7F2 transition was observed at 16230 f. 20 cm- ‘. Excitation into the (7F,)T1 + (‘De)r, + v4 vibronic transition of Eu3+ at 17310cm-’ does not give emission from the 4G5,2 state of Sm3+. For measurements at 80 K the crystals were cooled using a laboratory built nitrogen cryostat.
3. The shell model for energy transfer In our shell model we assume Fiirster-Dexter multipole-multipole interaction between donor and acceptor ions distributed randomly among the crystalline lattice sites where the rate of resonant energy transfer from a donor ion D to an acceptor ion A may be written [15, 163
x &4E)fo+o, (El dE.
(1)
P, = gn exp( - E,/kB T) is the population of the gafold degenerate initial acceptor state a, and E, is measured from the ground level of the J-manifold with similar notation for the excited donor state d’. The overlap integral contains the normalized line shape functions of donor d’ + d emission and acceptor a --f a’ absorption transitions. In the presence of only one chemical type of optically active ion, the energy-transfer process is due to cross-relaxation and within the shell model the luminescence decay curves from the excited state of the donor ions following a b-function excitation pulse take the form [1] shells 10)
=
4W=p(
-
kd
N.
n
1
n=l
r.=O
x exp[ - Gi(2)rr.kCRt].
C?(x)
(2)
The model assumes that excitation intensities are low, that there is no back transfer of excitation energy from acceptors to the donor, and that energy migration among the donors is negligibly small compared to the sum of the intrinsic decay
71 (I 997) I77- 188
and cross-relaxation processes. x is the mole fraction of the optically active ion, R, is the distance between the donor ion and an acceptor ion in the nth shell determined by the crystal structure, k. is the intrinsic decay rate involving radiative and non-radiative single-ion processes, and kCR is the cross-relaxation rate from a donor ion to a single acceptor in the first shell, s = 6, 8, or 10 for electric dipole vibronic-electric dipole vibronic (EDV EDV) or magnetic dipole-magnetic dipole (MD-MD), electric dipole vibronic-electric quadrupole (EDV-EQ), and electric quadrupoleelectric quadrupole (EQ-EQ) interactions, respectively. In the present system there is no evidence for multipole-multipole interactions involving s > 6. The angular dependence of this dipole-dipole coupling, G,6, is then independent of the value of n [1] and can be included in the definition of kCR. The occupancy factor O>(x) in this system is the statistical probability of there being exactly r, acceptor ions in the nth shell which has a capacity to contain N, acceptors and is readily computed from the equation
@3x) =
N,,! (Nn
_
r”)ir,!xrn(l - xlN.-r. .
The discrete shell model can be extended to include both cross-relaxation and energy transfer to chemically different acceptor ions. The probability P,(t) that the oth donor ion is excited at time t is given by [17]
%(t) -= dt
_
k. + c k;!,D, + c k;:A D’
PD(t).
(4)
A
k. is the intrinsic decay rate of donor ion D involving photon emission and (multi-) phonon relaxation processes. kg?+,, denotes the total cross-relaxation rate from the excited donor ion D to a chemically identical acceptor ion D’ and kETA represents the rate of energy transfer to the chemically different acceptor ion A. Introducing the occupancy numbers r, for the acceptor ions D’ and q,, for the acceptor ions A in the nth shell, the intensity of the emission from a specific set of excited donor ions D with identical distributions of acceptors at
T. Luxbacher
et al. I Journal of Luminescence
Table I Occupancy factors Oz.,,(x, y) /lo-’ for the first acceptor shell with x = 0.25 and y = 0.5 (the total number of combinations (r.. y.) is given by $(N,, + 1)(X + 2))
r,
0
0000 1 0 2 0 3 0 4 0 5 0 6 1 7 0 8027 9 0 10 11 ,2
0 0 0
1
0
I 2 5 7 7 5
3
4
5
6
7
8
9
1 2 9 7 38 19 88 33 132 40 132 33 88 19 38 9
5 38 132 264 330 264 132 38 5
15 106 317 529 529 317 106 15 _
35 211 529 705 529 211 35 ~ ._~
60 302 604 604 302 60 --~ _
16 302 453 302 76 _
61 201 201 76 ~ _
40 15 81 15 40 ~ ~ -~-~ - ~ ~ -_-_
.~
_
~
_
_
___
_ _
.._ ~~
_ _
_ -_
_ ~
_~__ _ -
r,kzR
+
2
1 2
, ~
0 0 0 ~~ _.. ._~ ~~ ~~
~ _
10 11 12 2 ~ ~-~ ~
_
time t is given by shells
k,
+
shells
1
c
q,,kfT
.
The total emission decay curve is then obtained by summing over all possible sets of donor ions. This may be converted into a tractable form by making use of the occupancy factors OE:,“(x, y) which give the probability of there being r, ions chemically identical to the donor and qn ions of the chemically different acceptor in the nth shell and are calculated as
o’“.qn(x’ ‘) =
_
x
x’nyqn(l
r,
_
qn)!r,!q,! _
x
_
4.1. Cs2NaSm,Y,
y)N.-r.-q,.
shells =
I(O)ev(
-
W
n
N. C
n= 1 i-,=0
x exp
N.-r. 1
Oi?,:q,(x,.d
q.=o
(11
- G,“(r,kCR + qnkET) $
‘t
n
_xCl,
and Cs2NaSm,Gdl
__Jlh
(6)
Occupancy factors for the first shell of acceptor ions for x = 0.25 and y = 0.5, OiB7,n(0.25, 0.5) are given in Table 1. Eq. (5) then takes the form l(t)
where for simplicity of notation we have assumed that the same value of s applies to both the crossrelaxation and the energy transfer as occurs for the system considered in this paper. The more general case will be treated elsewhere. As for kCR, the energy-transfer rate k ET is the rate that a donor ion transfers its energy to a chemically different acceptor which occupies a nearest-neighbour lattice site. As above, in the elpasolite lattice the angular dependence of the coupling between the donor emission and the acceptor absorption transitions, G,“, can be included in kET for dipole-dipole interaction (s = 6). For the elpasolite lattice and assuming s = 6, more than 94% of the energy-transfer processes are described by using the first three shells [12]. The successive terms in the products of Eqs. (2) and (7) respectively, approach unity more rapidly for dipole-quadrupole interaction (s = 8) because of the factor (1/R,)8 in the exponential term so that 99% of the energy-transfer processes to the acceptors occur within the first three shells. We therefore truncate the expansion in Eq. (7) at this point. Within the three-shell model assuming dipole-dipole interaction among donor and acceptor ions for both cross-relaxation and energy transfer, 88% of the coupling is due to interaction with nearest neighbours, 5.5% due to transfer to next nearest neighbours, and 6.5% of the energy is transferred to acceptors in the third shell. All values of the occupancy factor Ot:,jx, y) have been included which represents a summation over about 8.3 x lo5 acceptor distributions.
4. Results
N,!
(N,
181
71 (I 997) 177-l?%
(7)
Luminescence decay curves of the 4Gs,2 -+ ‘HTi2 emission of an isolated Sm3+ ion have been recorded in CszNaSmo,ooIGdo.9&l~ and Cs2Na Sm o.oo5Yo.9&16 over the temperature range lo-300 K [12]. The decay curves are exactly exponential over ten half-lives and give the value of the decay constants k. as 66 s- ’ at 80 K increasing to k. = 107 s-l at 300 K. As the concentration of Sm3 + is increased, cross-relaxation involving the
182
T. Luxbacher
et al. /Journal
4G,,,-+ 6FJ (J
= $,$, 3, and y) transitions at the donor and the 6Hsi2 + 6F, (J = 4, 4, 4, and q) transitions at the acceptor becomes increasingly important (e.g., pairs of transitions AA’, BB’, CC’, and DD’ in Fig. 1). As described previously, the cross-relaxation rate kCR may be determined from the exponential decay of luminescence from the 4G5,2 state of Sm3+ in Cs,NaSmCl, Cl, 123. Truncating the cross-relaxation processes at three shells, the decay constant for the pure material can be expanded as k. + (12 + 618 + 24/27) x kCR = k. + 13.64 x kCR for dipole-dipole interaction [l]. The measured exponential decay constant for x = 1 at 80K is 173OOs-’ corresponding to kCR (DD) = 1270 s-r. This increases by a factor of 1.8 at 300 K. The decay curve for x = 0.01 is identical to that for x = 0.001 and x = 0.005, respectively, at times greater than 2.5 x 10e3 s. At short times there is a small faster component consistent with the value of O:‘(O.Ol) = 0.1 and kCR determined from the exponential luminescence decay curve of the pure crystal. Over the whole concentration range there is no evidence for energy migration among the Sm3+ ions in the 4G 5,2 state at a rate competitive with the cross-relaxation processes. Migration would lead to the exponential decay rate being faster than the calculated rate and the long time decay rates not being asymptotic to the decay of the isolated ion which is not observed even at times > 10e2 s. There is no evidence for a change in the relaxation mechanism occurring in this compound over the whole temperature and concentration range studied. This would appear to exclude energy migration as a significant contributor to the decay kinetics of the 4GS,2 state of Sm3+ donor ions. 4.2. Cs,NaEu,Y,
_xCl6
Bettinelli and Flint have measured the decay of the ?Da state of Eu3+ in Cs2NaEu,YI_.C16 for x = 0.01 and x = 1 [ll]. At 12 K for x = 0.01 the decay curves are exactly exponential with a rate constant of 90 s- ‘. At higher temperatures this rate increases according to the coth law and the decay curves remain exponential. These results are essentially ,unchanged over the concentration range 0.001 d x < 0.1 [ 181. For x = 1 the decay curves
of Luminescence
71 (1997) 177-188
are strongly non-exponential and the long-term tail of the decay curve corresponds to a rate constant of 180 s-l at 12 K. This rate increases to 300 s-l at 80 K and 830 s- ’ at 300 K. Clearly, a process that is not present in the dilute material with x = 0.01 is quenching the emission in Cs,NaEuCl,. The two most likely processes in stoichiome tric crystals are cross-relaxation or quenching by a defect site. The lowest-order many-body cross-relaxation process between Eu3+ ions would involve the coupling of the 5D0 + 7F6 donor transition to at least three other 7F0 -+ 7F6 acceptor transitions and therefore may be neglected. The above decay curves have been interpreted as indicating energy migration in the 5D0 state in the pure compound followed by energy transfer to short-lived Eu3+ defect sites. The defect probably involves the presence of a nearby water molecule and/or 0’ - anion. The lower symmetry of these defect sites relaxes the selection rules for electricdipole transitions and the presence of high-frequency vibrations provides an efficient relaxation pathway. Such sites have therefore short lifetimes and the decay of the excitation at these sites competes efficiently with back transfer to octahedral sites. The concentration of these defects depends on the method of preparation and cannot be controlled quantitatively [ 181. These decay curves cannot therefore be directly calculated. 4.3. Cs2NaSmxEu,Y,_x-yC16 The
80 K
emission
decay curve for from the 5D0 state of Eu3+ excited resonantly at 17310 cm-’ and observed at 16 230 _+20 cm- ’ is shown in Fig. 2. The luminescent decay is strictly exponential over more than 10 half-lives with an intrinsic decay rate of k. = 120 s-l. At both 80 and 300 K the decay curves are identical to those for Cs2NaEu,,01 Y0,9&l6. Similarly, for Cs2NaSm0.01Eu0,9&16 the decay curves and decay rates closely resemble the non-exponential decay curves for Cs,NaEuCl,. At higher Sm3+ concentrations there is little change in the decay curves (Fig. 3). No emission is observed from the Sm3+ 4Gs,2 state at any concentration after excitation into the Eu3+ 5D, state. This shows clearly that the introduction of Sm3+ CS2NaSm~.o~EU~.o~Y~.~~cl6
T. Luxbacher
et al. / Journal of Luminescence
emm. Et?+: 5D, - ‘F, I
\ 7’\.X-.-,, c.._..,_.,.,,, \
.=.\,
Cs2NaSm,o,Eu,,,Y,,,CI
6
\ \,,
i
‘=, ‘...,,, i \
‘1 \
“\
--.
,.’~
i ‘r r. >$Cs,NaSm,,,Eu,,,CI, 76, .‘: ‘G.. :. ‘$. :;,
t
I
0
IO
:v 20
183
electric dipole, magnetic dipole, and electric quadrupole moments in octahedral symmetry and the vibronic transitions carry very little transition dipole. Even at room temperature the overlap of the Sm3’ the Eu3+ 5Do --+‘F. and vibronic sidebands will be (6H~,z)r: --+(4G~,& small. Excrtatton mto the 4GS:2 state of Sm”’ in CS2NaSmo.01EU,Y,.,,_,C16 (y = 0.005 to L’ = 0.99) produces strong emission from the Eu3+ 5Do state. The decay curves show pronounced slow risetimes followed by a decay equal to the decay rate of the 5Do state in the Cs,NaEu,Yr_,Cl, compounds (Fig. 4). The 5 x lop3 s rise time of the emission in CszSmo.olEuo,lYo.s9C16 reflects the distribution of the lifetimes within the shell model of the Sm3+ (4G5,2) donor ion and is consistent with the rate of luminescence decay from the 4Gsj2 state as independently monitored at 16 500 f 20 cm- ‘. The probability PA(t) that the A th Eu3+ acceptor ion is excited by energy transfer from a Sm3+ donor ion at time t is given by
80 K ext. Et?+: ‘F, - 5D,
k_
71 (1997) 177-188
30
Time / 1V3s Fig. 2. Luminescence decay of the ‘De -+ ‘Fa emission in Cs,NaSmo.o,Eu,Yo.99_,C16 (y = 0.01 and y = 0.99) after direct excitation into the ‘D,, state of Eu3+ at 80 K.
into the lattice has little effect on the lifetime of the ‘Do state of Eu3+. This is not surprising since the 5D,, state lies 530 cm-’ beneath the 4G,,z state of Sm3+. The 5Do -+ 7Fo transition is forbidden for
where p,(t) is introduced by Eq. (4). Under our experimental conditions ( y $0.15) migration amongst the acceptors and energy transfer from the Cs2NaW% ,Y, 9_,rCl, 300 K ext. Err’-: ‘F,-‘D, emm. Eus’: ‘D0-7F,
0
5
10
15
20
25
30
Time / 10.‘~ Fig. 3. Luminescence decay of the ‘Da + ‘FZ emission into the sD, state of Eu3+ at 80 K.
in CstNaSm,Eu
01 Y09 _ XCl, (x = 0.005, 0.01, and 0.1) after direct excitation
i? Luxbacher et al. /Journal
1
~%Na%l.,,%,ycl8s 300K ext. Sm”: ‘H,,, - 4G,,,
emm. Eu3’: ‘D, - ‘F,
:
I
IO
0
20
30
4
40
Time / I O-3s Fig. 4. Time evolution of the emission from the ‘Do state of Eu3+ in Cs,NaSmo.olEuo.lY,s9Cl~ following excitation into the Sm3+ 4G5,z state at 300 K.
acceptors to defects may be neglected. Moreover at low excitation intensities the probability of two nearby Sm 3+ ions being initially excited is small. The saturation of an acceptor will not influence the energy-transfer rate from the donors. We may therefore sum over the probability distributions in a way analogous to Eq. (7) so that the time evolution of the emission intensity Z,,(t) from the ‘D, state of Eu3+ acceptor ions excited by non-radiative energy transfer from Sm3+ (4Gs,2) donor ions in Cs,NaSm,Eu,Y, _,_,C16 can be calculated by ZEu(t) = Z’(0)
exp( - kE”t) i
shells
N.
N.-r.-
1
-@mt-(rnkCR+q,kET)
x exp [
and is therefore designed Z’(0). The first term in the main bracket corresponds to the decay of the Eu3+ 5D0 emission excited by energy transfer from the Sm3+ ions and is independent of the environment of the Eu3+ ions. The second term is the excitation of the Eu3+ ions by energy transfer from Sm3+ ions averaged over all possible occupancy factors Ot:,n(x, y) for all shells. As before we have assumed that the same value of s is applicable to crossrelaxation and energy transfer. This equation does not include the excitation migration among the Eu3+ ions nor their quenching of emission by the defect sites and is therefore restricted to the concentration range y GO.15 where the directly excited Eu3+ emission decays exponentially. In Eq. (9) the rates kf”, ki”, and kCR are known. In principle, kET may be found by curve-fitting but for this system there is a more direct method of independently determining the energy-transfer rate. Introduction of Eu3’ into the Cs,NaSm,Y, _$l, crystal with x = 0.01 results in an increase in the rate of relaxation from the 4G5,2 state of Sm3+ due to energy transfer to the 5D, state of Eu3+. Results on samples with higher Sm3+ concentrations are similar to those reported here although the effect of the energy-transfer process between Sm3+ donor ions and Eu3+ acceptor ions is less especially when x > y. Fig. 1 shows possible pathways for these additional energy-transfer processes as the pairs of transitions EE’ and FF’. At 80 K the main contribution to the energy-transfer process involves the EDV transition at the Sm3’ donor 4G~,z --f %2 ion and the ‘F, --t 5D0 EDV transition at the Eu3+ acceptor ion (transitions EE’ in Fig. 1). At 300 K the Sm3+ (4G,,,)T7 -(6H7,2)r7, r, donor transitions almost are resonant with the (‘Fi)r, -+ (‘DO)rl magnetic dipole allowed electronic transition of the Eu3+ acceptor ions (transitions FF’ in Fig. 1). Fig. 5 shows a selection of luminescence decay curves from the 4G5,, state of Sm3+ in Cl, for 0 6 y 6 0.99 at C+NaSmo.oiEu,Yo.+, 80 K. The decay curves for y < 0.1 and y = 0.99 are essentially exponential at times > 2.5 x low3 s. At intermediate concentrations the long-time decay curves deviate significantly from pure exponential behaviour but are exactly described by Eq. (7). In Fig. 5 the a priori calculated decay curves for
. ( n111 $
‘I
(9) Note that the pre-exponential now weighted by a branching
of Luminescence 71 (1997) 177-188
intensity factor is ratio of decay rates
T. Luxbacher et al. 1 Journal
185
qf Luminescence 71 (1997) 177-188
0 0.05 0.1
0.25 0
20
60
40
80
Time / 10.‘s Fig. 5. Dependence of the luminescence decay from the %5/z state of Sm3+ in Cs,NaSmo.o,Eu,Y,.,P-,Clb on 4’.Note that the solid lines are calculated a priori using the independently measured values k0 = 66 s-‘, kCR (DD) = 1350 s-‘, and kET (DD) = 7.5 s-- ‘.
Cl6 (y = 0.05, 0.1, 0.25, Cs2NaSmo.olEu,Yo.99-, 0.5, and 0.99) assuming s = 6 in Eq. (7) are superimposed on the measured curves. For reasons discussed in Section 3 only the first three shells have been included in our model using the exponential decay constants k0 = 66 s-l and 18 400 s- ’ from our previous measurements on Cs2NaSm,.,,lGdo.999Cl~ and Cs,NaSmCl, at 80 K, respectively [9, 121. Within the three-shell model the latter constant has been calculated to be k, + 13.64 x kCR for dipole-dipole interaction giving a cross-relaxation rate kCR(DD) = 1350 s- ‘. The rate kET(DD) = 7.5 s-r for energy transfer from Sm3’ donor ions to a single Eu3+ acceptor in the first shell at a distance of 7.6 8, has been determined from the measured luminescence decay Eu,,&l, at 80 K. This value curve of CszNaSm,,,r has been used to calculate the decay curves for all other Eu3+ concentrations shown in Fig. 5. We emphasise that in Fig. 5 no curue fitting is involved. The agreement between the calculated and experimental curves is remarkable and provides very strong evidence for the assumptions made both in the shell model in general and its application to this particular system. The behaviour at 300 K is similar but the energytransfer rate increases much more rapidly than either k,, or kCR. The luminescence decay curve
from the 4Gs,2 state of Sm3+ in Cs,NaSmO.OI Eu 0.9&16 at 300 K is also shown in Fig. 5. The energy-transfer rate extracted from this curve corresponds to kET(DD) = 50 s-l. We note that the main contribution to the temperature dependence of the Sm3+ 4Gs,2 luminescence quenching is due to the energy transfer from Sm3+ donor ions to nearest-neighbour Eu3+ acceptors. A detailed study of the temperature dependence of luminescence decay curves from the 4GS,z state of Sm3+ in Cs,NaSm,Eu,Y, _X_yC16 will be presented elsewhere.
5. Discussion In a previous paper [9] we showed that in order to model the cross-relaxation process in Cs,NaSm,Y, -$X6 within the shell model it, was necessary to reduce the contribution from the shells other than n = 1. We attributed this reduction to the selective shielding of the Sm3+ acceptor in shells n 3 2 from the Sm3+ donor by the intervening ions. No such screening effect is observable for the Sm3+ + Eu3+ energy-transfer processes described in this paper. The agreement between experiment and independent calculation demonstrated by Fig. 5 is perfect. An explanation of this
186
T. Luxbacher et al. /Journal
10’ 0
2
4
6
8
10
Time / I O?S
Fig. 6. Computed decay curves for different ratios of the energytransfer rate kET and the intrinsic decay rate k. (x = 0.25, k. = 66 SK’). The measured decay curves of luminescence from the 4Gs,Z state of Sm 3* in CszNaSmO.,,Y,,,=,C1, (x = 0.25) and Cs,NaSmo.olEuo.zsYo.74Cls (y = 0.25) are superimposed on the calculated curves.
apparent difference between the Sm3+ + Sm3+ cross-relaxation and the Sm3+ + Eu3+ energy transfer can be found by comparing the Sm3+ decay curves for CszNaSmo.olEuo.zsYo.74C16 and CszNaSm,,,SYO,,,C1,. In both cases the excited Sm3+ ion is relaxed by energy transfer to acceptors distributed in accordance with the occupancy factor 0:(0.25) and the behaviour of these systems might therefore expected to be comparable. The 80 K decay curves for the above two systems are shown in Fig. 6 and superimposed on these curves are the three-shell model calculations assuming dipole-dipole interaction for differing ratios of the energy-transfer (or cross-relaxation) rate constants. For kET < k0 the decay curves are virtually exponential but for kET > k. they become markedly non-exponential. The deviation from exponential behaviour in the latter regime may only be modelled on the assumptions that there is an anisotropic dielectric but for the case of
of Luminescence
71 (1997) 177-188
Cs2NaSmo.olEuo.25Yo.74Cls the deviation from exponential behaviour is very small and only present at very short times. The order of magnitude of the cross-relaxation rate kCR and the energy-transfer rate kET can be estimated from Fig. 6 as 10ko < kCR < lOOk and O.lko < kET < ko, respectively. The values for kCR(DD) = 1350 s-l and kET(DD) = 7.5 s-l obtained from measurements on Cs,NaSmCl, and Cs2NaSm0.01Eu0.9&16 crystals reflect these magnitudes as kCR/k,, = 20.5 and kETJkO= 0.114 at 80 K. Note that the experimental decay curves shown in Fig. 6 become almost parallel to the intrinsic decay of Sm3 + at times > 2 x 10m3 s. The reasons for this differ in the two cases. In Cs,Na Sm o.olEu 0.25Y0.74Cl~the energy-transfer rate is so low that the decay curves remain nearly exponential since a large number of small terms with different rate constants add to the intrinsic decay. This behaviour is comparable to the cross-relaxation from the 3P0 state of Pr3+ in Cs,NaPr,Y,_,Cl, [l]. For Cs2NaSm0.25Y0,75C16the cross-relaxation rate is so fast that almost all of the excited Sm3+ ions that have a nearby acceptor are relaxed and only the emission from almost isolated Sm3+ ions is observed. It is convenient to define cross-relaxation and energy-transfer efficiencies Y/CRand VET from an excited donor state of an optically active ion as parameters to characterise the applicability of a crystal containing a certain concentration of these ions as a laser material or an optical device. The overall efficiency of energy transfer from an excited electronic energy level of the donor can be calculated by using the expression [ 19, 201 o(, VET=
gdt
1 -ko
(10)
s 0
where the intrinsic decay rate k. is the sum of radiative and non-radiative relaxation processes occurring at an isolated donor ion which is determined experimentally from the exponential decay curve of a very dilute crystal. Z(t) represents the time evolution of luminescence in the presence of acceptor ions and 17 1(t) is the integrated area of
T. Luxbacher
et al. i Journal of Luminescence
71 11997) 177-188
187
6. Conclusions In this paper we have derived kinetic expressions for the decay of excited rare-earth ions undergoing both cross-relaxation processes and also energy transfer to dissimilar acceptors. The cross-relaxation rate may be determined by measurements on crystals containing only the donor species. The energy-transfer rate may be determined by kinetic measurements on crystals containing a large concentration of acceptors. The decay kinetics at all other concentrations of both donor and acceptor may then be exactly predicted from these measurements. This provides very strong evidence for the assumptions implicit within the shell model.
0
+
0
O.O ~h&-a--y--+ 0.01
acceptor
concentration
x (y)
Fig. 7. Concentration dependence of the efficiencies of crossrelaxation and energy transfer in Cs,NaSm,Y(Gd), _XCI, and CszNaSmo 0,E~gY0.99_,Clh at 300 K.
the donor decay curve, normalized such that I(0) = 1. In the pure crystal the decay Z(t) is exponential with a decay rate k and relation (10) reduces to
Acknowledgements This work has been supported in part under the collaborative ARC scheme of The British Council and the Bundesministerium fiir Wissenschaft and Forschung.
References kT
=
1 - Wk.
(11) [II S.O. Vasquez and CD. Flint, Chem. Phys. Lett. 238 (1995)
Using this expression the efficiency qCR of the Sm3 + + Sm3+ cross-relaxation in Cs,NaSmCl, is calculated to be > 99.6% at 300 K and z 99.5% at 10 K. These efficiencies are comparable to those found for the Ho3+ + Tb3+ energy transfer in Cs2NaHo0.1Tb0,1Y0,8Cl~ [21]. Fig. 7 shows the dependence of the efficiency of cross-relaxation between Sm3+ ions in CszNaSm,Y(Gd), _,Clh (x=0.001 tox=l)onxat300K. Replacing Y 3 + ions successively by Eu3 ’ in CszNaSmO,OIY,.y&l, the lifetime of luminescence from the 4G5,2 state of Sm3+ is further decreased. The efficiency of the additional energy-transfer processes is calculated from the ratio of luminescence of Sm3+ donor ions in the presence of Eu3+ acceptor ions to the luminescence of Sm3+ ions alone. The energy-transfer efficiencies so obtained are also shown in Fig. 7 for varying concentrations of Eu3+ acceptor ions at 300 K.
378.
PI D.R. Foster, F.S. Richardson
and R.W. Schwartz, J. Chem. Phys. 82 (1985) 618. c31 A.K. Banerjee and R.W. Schwartz. Chem. Phys. 58 (1981) 255. II41 P.A. Tanner, Chem. Phys. Lett. 155(1989) 59. [51 M. Bettinelli and CD. Flint, Chem. Phys. Lett. 167 (1990) 45. 161 R.W. Schwartz. Mol. Phys. 30 (1975) 81. Inorg. Chem. 15 (1976) c71 O.A. Serra and L.C. Thompson, 504. Mol. Phys. 44 (1981) PI C.D. Flint and F.L. Stewart-Darling, 61. H.P. Fritzer. R. Sabry-Grant and C.D. II91T. Luxbacher, Flint, Chem. Phys. Lett. 241 (1995) 103. 1101T. Luxbacher, K. Gatterer, H.P. Fritzer and C.D. Flint, J. Appl. Spectrosc. 62 (1995) 27. 1111 M. Bettinelli and C.D. Flint. J. Phys.: Condens. Matter 3 (1991) 7053. H.P. Fritzer and C.D. Flint, J. Phys.: ConCl21 T. Luxbacher, dens. Matter 7 (1995) 9683. 1131 S.O. Vasquez and C.D. Flint. J. Appl. Spectrosc. 62 (1995) 213.
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i? Luxbacher et al. / Journal of Luminescence
[14] R. Sabry-Grant
[15] [16] [17] [18]
and C.D. Flint, J. Appl. Spectrosc. 62 (1995) 155. T. Fiirster, Ann. Phys. 2 (1948) 55. D.L. Dexter, J. Chem. Phys. 21 (1953) 836. D.L. Huber, Phys. Rev. B 20 (1979) 2307. M. Duckett and C.D. Flint, to be published.
71 (1997) 177-188
[19] R. Reisfeld and N. Lieblich-Sofler, J. Solid State Chem. 28 (1979) 391. [20] A. Lupei, V. Lupei, S. Georgescu and W.M. Yen, J. Appl. Phys. 66 (1989) 3792. [21] A.K. Banerjee, F. Stewart-Darling, CD. Flint and R.W. Schwartz, J. Phys. Chem. 85 (1981) 146.
LUMINESCENCE Journal
ELSEVIER
of Luminescence
71 (1997) 177-188
Competitive cross-relaxation and energy transfer within the shell model: The case of Cs2NaSmXEuyY1 - x - JjC16 Thomas Luxbacher a,*, Harald P. Fritzer a, Colin D. Flintb aInstitut fir Physikalische und Theoretische Chemie, Technische Universitiit Graz, 8010 Graz, Austria b Laser Laboratory, Department of Chemistry, Birkbeck College, 29, Gordon Square, London WCIH OPP. UK Received
3 June 1996; revised and accepted
16 September
1996
Abstract Electronic energy-transfer processes between Sm3 + (4G,,z) donor ions and Eu 3+ ( ‘FO, ‘F,) acceptor ions in the cubic hexachloroelpasolite crystals Cs2NaSm,Eu,Y1_,_,C16 have been investigated over a wide range of Sm3’ and Eu3+ concentrations at temperatures of 80 and 300K. In these systems the luminescence from the 4G5,2 state of Sm3+ is strongly quenched by both cross-relaxation to nearby Sm 3+ ions and energy transfer to the ‘Do state of Eu3+. The lifetime of the 5D0 state is not affected by the presence of Sm3+. The rates o f cross-relaxation and energy transfer are determined from luminescence decay curve measurements for the Sm3+ 4Gs,2 -+ 6H7,2 emission and the Eu3+ ‘Do -+ ‘Fz emission following excitation into the 4G5,z state of Sm3+. The luminescence decay curves for the 4G5,2 state are analysed in terms of a recently developed discrete shell model for energy transfer assuming electric dipole vibronic-electric dipole vibronic and magnetic dipole-magnetic dipole interaction between Sm3+ donor ions and Eu3+ acceptor ions. Exact agreement is achieved for the energy transfer from Sm3+ donor ions to Eu3+ acceptors without curve fitting. Keywords: Cross relaxation; Energy transfer; Shell model; Luminescence crystals; CszNaSm,Eu,Y,_,_,C1,
dipole allowed electronic transitions. The study of energy-transfer processes in these systems is complicated due to contributions from a large number of possible resonant and near-resonant coupling mechanisms between donor emission and acceptor absorption transitions. In the present study we investigate energy-transfer processes between Sm3+ (4G5,z) donor ions and Eu3+ (‘F,, ‘F1) acceptor ions in the hexachloroelpasolite crystals CszNaSm,Eu,Y i _ _ ,Cl,. The Cs,NaYCl, host lattice has a cubic crystal structure and the rare-earth ions replacing the Y3+ ions are located at perfect octahedral sites surrounded
1. Introduction Electronic energy-transfer processes between trivalent rare-earth ions in crystalline and amorphous solids are of great importance both scientifically and technologically. The kinetics and efficiencies of these energy-transfer processes have been studied theoretically and experimentally using a variety of host materials. In most of these systems the rare-earth ions are located at non-centrosymmetric lattice sites and the optical absorption and emission spectra are dominated by electric * Corresponding
author.
0022-2313/97/$17.00 c> 1997 Elsevier Science B.V. All rights PII SOO22-23 13(96)00124-X
decay curves; Cubic hexachloroelpasolite
reserved
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et al. / Journal of Luminescence
SU13’
71 (1997) 1 V-188
Sd’
Eli”
-
‘D,,
ABCDEF
93 ‘5
7
‘FO Fl Fig. 1. Relevant energy levels and transitions involved in the cross-relaxation Eu,YI _,-,Q. The letters indicate pairs of near-resonant transitions.
by six chloride ions. The nearest neighbour dis7.6.k tance between Y3+ sites is approximately A diagram of the hexachloroelpasolite lattice has been published previously [ 11. This crystalline host lattice provides an excellent model system to study cross-relaxation and energy-transfer processes. The electric-dipole transition moments associated with the 4f -P 4f transitions at octahedral sites are small and therefore excited states of rare-earth ions in centrosymmetric complexes have relatively long relaxation times. The electronic energy levels of Sm3+ and Eu3+ in Cs,NaYCl, are well established both theoretically and experimentally [2-S]. The electronic spectra of Cs,NaSm(Eu)Cl, consist of magnetic dipole allowed electronic transitions and electric dipole allowed vibronic transitions reflecting the perfect centrosymmetric surroundings of the rareearth ions. The 6H5,2 ground state of Sm3+ is split into two crystal-field components in octahedral symmetry, r, (0 cm-‘) and rs (178 cm-‘). The luminescent electronic state 4G5,2 is also split into two components, r, (17 760 cm-‘) and r, (18 105 cm- ‘). The electronic energy levels of Eu3 + involved in the energy-transfer processes considered in this paper are the ‘FO ground state (0 cm-‘) and the 7F, state at 352 cm-‘. The lowest lying luminescent state is 5D, at 17 220 cm-‘.
and
energy-transfer
processes
in Cs2NaSm,
The vibrational properties of Cs,NaSmCl, and Cs,NaEuCl, are also well established [3,8]. The odd parity internal vibrational modes vs(t2J, v4(tlu), and v3(tlu) of the [Ln C1,13- ion (Ln = Sm, Eu) are about 80-90 cm-’ (v& loo-120 cm-’ (v4), (v3). Lattice vibrations are and 240-255 cm-’ found at 40 and 180 cm- ‘. The phonon cut-off frequency corresponds to M 300 cm- ’ so that nonradiative relaxation from an excited state to a lower lying state is slow for a separation between the states of > 2000 cm- ‘. The energy level structure within a 2s+ ‘L, multiplet is comprised of a smaller number of components compared to Sm3+ and Eu3+ ions in noncentrosymmetric crystalline environments such that the number of possible electronic energy levels involved in resonant and near-resonant cross-relaxation and energy-transfer processes is minimised. The cross-relaxation pathways involving the Sm3+ 4 6FJ (J = 2 I,$ and 9) relaxation at the dyi& Gd the Sm3’ 6Hi,2 + ‘jFJ(J =$,$, 3, and y) transitions at the acceptor have been described in detail previously [9]. Fig. 1 shows a selection of near-resonant pathways for crossrelaxation as pairs of transitions AA’, BB’, CC’, and DD’. Beside these there exist numerous phononassisted cross-relaxation processes. In addition to these cross-relaxation processes, energy transfer
T. Luxbacher
et al. I Journal of Luminescence
occurs to the Eu3’ 5Do level. At high temperatures the Sm3+ (4G5,2F,) -+ (6H7,z)F,, r, donor with the transitions are almost resonant (7F1)F4 + (5D0)r1 magnetic dipole allowed electronic transition of the Eu3+ acceptor ion (transitions FF’ in Fig. 1) [2, 51. At low temperatures the main contribution to the energy-transfer at processes involves the 4G5,2 + 6H5,2 transition the Sm3+ donor ion and the 7F0 + 5D0 transition at the Eu3+ acceptor ion where both transitions are of electric dipole allowed vibronic origin [S, lo] (transitions EE’ in Fig. 1). The decay kinetics of the 5D0 state of Eu3+ in Cs,NaEu,Yi _XCl6 (x = 0.01, 1) have been reported by Bettinelli and Flint [ 111. They have observed quenching of emission from the 5D0 state of Eu3+ in Cs,NaEuCl, but not in CszNaEu0.01Y,,g,C16 which implies that energy migration is present in the pure crystal but not in the material with x = 0.01. In a recent series of papers [l, 9, 10, 12-141 we have developed a discrete shell model for energy transfer to understand the kinetics of cross-relaxation processes in cubic crystalline materials and applied this model to the hexachloroelpasolite crystals Cs,NaLn,Y 1_$& and Cs,NaLn,Gd, _Clb (Ln = Pr [l, 131, Sm [9, 10, 121, and Ho [14]). Excellent agreement between the predictions of the shell model and the experimental results was achieved for Pr3 + and Ho3+ whereas some minor aspects of the experimental results on Cs,NaSm,Y, _XC1, cannot yet be reproduced by a priori calculation. In the present study we extend the shell model to include energy transfer between dissimilar lanthanide ions in the hexachloroelpasolite lattice. We have chosen the system Cs,NaSm,Eu,Y 1_x_gClh for a first comparison between calculation and experiment for these energy-transfer processes. In this material the luminescence from the 4G5,2 state of Sm3+ is quenched by both cross-relaxation between nearby Sm 3+ ions and energy transfer from Sm3 + donor ions to Eu3 ’ acceptors. This system is particularly suitable for an experimental investigation of the latter energy-transfer process. Firstly, both the Sm3+ 4Gs,2 state and the Eu3+ 5D, state have slow intrinsic decay rates at temperatures of 80 and 300 K. Secondly, the energy-transfer rate from Sm3+ donor ions to Eu3+ acceptors is comparable to the intrinsic decay rates of the isolated
71 (1997) 177-188
119
ions. Thirdly, both the Sm3+ 4G5,2 state and the Eu3’ 5D0 state may be separately excited in the region 17000 to 18000 cm-’ and the emission from these states may be studied with minimum and Both Cs,NaSmCl, spectral overlap. Cs,NaEuCl, are known to have phase transitions between 80 and 300 K involving a small rotation of the [Ln C1,13- complex ion. As in our previous studies there is no evidence that this minor effect influences the energy-transfer processes. In this paper we focus attention on the crystals Cl, ( y = 0.005, 0.01, 0.02, CszNaSmo.olEu,Yo.ss-,, 0.05, 0.1, 0.25, 0.5, ‘and 0.99) and Cs,Na Sm,Eu0,1Y,.9_,C16 (x = 0.005, 0.01, and 0.1) at temperatures of 80 and 300 K. Results at other temperatures will be reported elsewhere. In crystals of the first type which contain only 1 mol% of Sm3 ’ cross-relaxation between Sm3 + ions is weak but not negligible. The cross-relaxation rate has been determined previously from luminescence decay measurements on Cs2NaSm0.00sYo.995C16, Cs2NaSm,.oolGdo.999Cl~ and Cs,NaSmCl, [9, 121. Since the energy-transfer rate is relatively small it may be deduced from the results obtained on the Cs2NaSm,.,,Eu0,9&16 crystal. The dependence of energy transfer from the Sm3+ donor ion to surrounding Eu3 + acceptors on y is exactly described within the shell model. Energy migration in the ‘DO state is not observed for the compounds which contain lOmol% of Eu3+. The Eu3+ ‘D,, + 7F, emission is not affected by the presence of Sm3’ ions even at a high concentration of the latter.
2. Experimental Large single crystals of high optical quality of compositions CszNaSm0.01Eu,Y,.9,, _ ,Cl, (y = 0.005, 0.01, 0.02, 0.05, 0.1, 0.25, 0.5. and 0.99) and CszNaSm,Eu,.,YO.g_,Clh (x = 0.005, 0.01, and 0.1) were grown by the Bridgman technique as described previously [IS]. Luminescence decay measurements at temperatures of 80 and 300 K were performed as previously reported [9]. Excitation of the Sm3+ ion was carried out directly into the magnetic dipole allowed (6H5,2) I-, -+ (4G5,2)F8 electronic transition at 17760 cm-‘. The (4G5JF, -+ (6H;,~) Fe, F7
180
T Luxbacher
et al. / Journal of Luminescence
emission of Sm3+ was observed at 16 500 + 20 cm-‘. The Eu3+ emission for the ‘D, + 7F2 transition was observed at 16230 f. 20 cm- ‘. Excitation into the (7F,)T1 + (‘De)r, + v4 vibronic transition of Eu3+ at 17310cm-’ does not give emission from the 4G5,2 state of Sm3+. For measurements at 80 K the crystals were cooled using a laboratory built nitrogen cryostat.
3. The shell model for energy transfer In our shell model we assume Fiirster-Dexter multipole-multipole interaction between donor and acceptor ions distributed randomly among the crystalline lattice sites where the rate of resonant energy transfer from a donor ion D to an acceptor ion A may be written [15, 163
x &4E)fo+o, (El dE.
(1)
P, = gn exp( - E,/kB T) is the population of the gafold degenerate initial acceptor state a, and E, is measured from the ground level of the J-manifold with similar notation for the excited donor state d’. The overlap integral contains the normalized line shape functions of donor d’ + d emission and acceptor a --f a’ absorption transitions. In the presence of only one chemical type of optically active ion, the energy-transfer process is due to cross-relaxation and within the shell model the luminescence decay curves from the excited state of the donor ions following a b-function excitation pulse take the form [1] shells 10)
=
4W=p(
-
kd
N.
n
1
n=l
r.=O
x exp[ - Gi(2)rr.kCRt].
C?(x)
(2)
The model assumes that excitation intensities are low, that there is no back transfer of excitation energy from acceptors to the donor, and that energy migration among the donors is negligibly small compared to the sum of the intrinsic decay
71 (I 997) I77- 188
and cross-relaxation processes. x is the mole fraction of the optically active ion, R, is the distance between the donor ion and an acceptor ion in the nth shell determined by the crystal structure, k. is the intrinsic decay rate involving radiative and non-radiative single-ion processes, and kCR is the cross-relaxation rate from a donor ion to a single acceptor in the first shell, s = 6, 8, or 10 for electric dipole vibronic-electric dipole vibronic (EDV EDV) or magnetic dipole-magnetic dipole (MD-MD), electric dipole vibronic-electric quadrupole (EDV-EQ), and electric quadrupoleelectric quadrupole (EQ-EQ) interactions, respectively. In the present system there is no evidence for multipole-multipole interactions involving s > 6. The angular dependence of this dipole-dipole coupling, G,6, is then independent of the value of n [1] and can be included in the definition of kCR. The occupancy factor O>(x) in this system is the statistical probability of there being exactly r, acceptor ions in the nth shell which has a capacity to contain N, acceptors and is readily computed from the equation
@3x) =
N,,! (Nn
_
r”)ir,!xrn(l - xlN.-r. .
The discrete shell model can be extended to include both cross-relaxation and energy transfer to chemically different acceptor ions. The probability P,(t) that the oth donor ion is excited at time t is given by [17]
%(t) -= dt
_
k. + c k;!,D, + c k;:A D’
PD(t).
(4)
A
k. is the intrinsic decay rate of donor ion D involving photon emission and (multi-) phonon relaxation processes. kg?+,, denotes the total cross-relaxation rate from the excited donor ion D to a chemically identical acceptor ion D’ and kETA represents the rate of energy transfer to the chemically different acceptor ion A. Introducing the occupancy numbers r, for the acceptor ions D’ and q,, for the acceptor ions A in the nth shell, the intensity of the emission from a specific set of excited donor ions D with identical distributions of acceptors at
T. Luxbacher
et al. I Journal of Luminescence
Table I Occupancy factors Oz.,,(x, y) /lo-’ for the first acceptor shell with x = 0.25 and y = 0.5 (the total number of combinations (r.. y.) is given by $(N,, + 1)(X + 2))
r,
0
0000 1 0 2 0 3 0 4 0 5 0 6 1 7 0 8027 9 0 10 11 ,2
0 0 0
1
0
I 2 5 7 7 5
3
4
5
6
7
8
9
1 2 9 7 38 19 88 33 132 40 132 33 88 19 38 9
5 38 132 264 330 264 132 38 5
15 106 317 529 529 317 106 15 _
35 211 529 705 529 211 35 ~ ._~
60 302 604 604 302 60 --~ _
16 302 453 302 76 _
61 201 201 76 ~ _
40 15 81 15 40 ~ ~ -~-~ - ~ ~ -_-_
.~
_
~
_
_
___
_ _
.._ ~~
_ _
_ -_
_ ~
_~__ _ -
r,kzR
+
2
1 2
, ~
0 0 0 ~~ _.. ._~ ~~ ~~
~ _
10 11 12 2 ~ ~-~ ~
_
time t is given by shells
k,
+
shells
1
c
q,,kfT
.
The total emission decay curve is then obtained by summing over all possible sets of donor ions. This may be converted into a tractable form by making use of the occupancy factors OE:,“(x, y) which give the probability of there being r, ions chemically identical to the donor and qn ions of the chemically different acceptor in the nth shell and are calculated as
o’“.qn(x’ ‘) =
_
x
x’nyqn(l
r,
_
qn)!r,!q,! _
x
_
4.1. Cs2NaSm,Y,
y)N.-r.-q,.
shells =
I(O)ev(
-
W
n
N. C
n= 1 i-,=0
x exp
N.-r. 1
Oi?,:q,(x,.d
q.=o
(11
- G,“(r,kCR + qnkET) $
‘t
n
_xCl,
and Cs2NaSm,Gdl
__Jlh
(6)
Occupancy factors for the first shell of acceptor ions for x = 0.25 and y = 0.5, OiB7,n(0.25, 0.5) are given in Table 1. Eq. (5) then takes the form l(t)
where for simplicity of notation we have assumed that the same value of s applies to both the crossrelaxation and the energy transfer as occurs for the system considered in this paper. The more general case will be treated elsewhere. As for kCR, the energy-transfer rate k ET is the rate that a donor ion transfers its energy to a chemically different acceptor which occupies a nearest-neighbour lattice site. As above, in the elpasolite lattice the angular dependence of the coupling between the donor emission and the acceptor absorption transitions, G,“, can be included in kET for dipole-dipole interaction (s = 6). For the elpasolite lattice and assuming s = 6, more than 94% of the energy-transfer processes are described by using the first three shells [12]. The successive terms in the products of Eqs. (2) and (7) respectively, approach unity more rapidly for dipole-quadrupole interaction (s = 8) because of the factor (1/R,)8 in the exponential term so that 99% of the energy-transfer processes to the acceptors occur within the first three shells. We therefore truncate the expansion in Eq. (7) at this point. Within the three-shell model assuming dipole-dipole interaction among donor and acceptor ions for both cross-relaxation and energy transfer, 88% of the coupling is due to interaction with nearest neighbours, 5.5% due to transfer to next nearest neighbours, and 6.5% of the energy is transferred to acceptors in the third shell. All values of the occupancy factor Ot:,jx, y) have been included which represents a summation over about 8.3 x lo5 acceptor distributions.
4. Results
N,!
(N,
181
71 (I 997) 177-l?%
(7)
Luminescence decay curves of the 4Gs,2 -+ ‘HTi2 emission of an isolated Sm3+ ion have been recorded in CszNaSmo,ooIGdo.9&l~ and Cs2Na Sm o.oo5Yo.9&16 over the temperature range lo-300 K [12]. The decay curves are exactly exponential over ten half-lives and give the value of the decay constants k. as 66 s- ’ at 80 K increasing to k. = 107 s-l at 300 K. As the concentration of Sm3 + is increased, cross-relaxation involving the
182
T. Luxbacher
et al. /Journal
4G,,,-+ 6FJ (J
= $,$, 3, and y) transitions at the donor and the 6Hsi2 + 6F, (J = 4, 4, 4, and q) transitions at the acceptor becomes increasingly important (e.g., pairs of transitions AA’, BB’, CC’, and DD’ in Fig. 1). As described previously, the cross-relaxation rate kCR may be determined from the exponential decay of luminescence from the 4G5,2 state of Sm3+ in Cs,NaSmCl, Cl, 123. Truncating the cross-relaxation processes at three shells, the decay constant for the pure material can be expanded as k. + (12 + 618 + 24/27) x kCR = k. + 13.64 x kCR for dipole-dipole interaction [l]. The measured exponential decay constant for x = 1 at 80K is 173OOs-’ corresponding to kCR (DD) = 1270 s-r. This increases by a factor of 1.8 at 300 K. The decay curve for x = 0.01 is identical to that for x = 0.001 and x = 0.005, respectively, at times greater than 2.5 x 10e3 s. At short times there is a small faster component consistent with the value of O:‘(O.Ol) = 0.1 and kCR determined from the exponential luminescence decay curve of the pure crystal. Over the whole concentration range there is no evidence for energy migration among the Sm3+ ions in the 4G 5,2 state at a rate competitive with the cross-relaxation processes. Migration would lead to the exponential decay rate being faster than the calculated rate and the long time decay rates not being asymptotic to the decay of the isolated ion which is not observed even at times > 10e2 s. There is no evidence for a change in the relaxation mechanism occurring in this compound over the whole temperature and concentration range studied. This would appear to exclude energy migration as a significant contributor to the decay kinetics of the 4GS,2 state of Sm3+ donor ions. 4.2. Cs,NaEu,Y,
_xCl6
Bettinelli and Flint have measured the decay of the ?Da state of Eu3+ in Cs2NaEu,YI_.C16 for x = 0.01 and x = 1 [ll]. At 12 K for x = 0.01 the decay curves are exactly exponential with a rate constant of 90 s- ‘. At higher temperatures this rate increases according to the coth law and the decay curves remain exponential. These results are essentially ,unchanged over the concentration range 0.001 d x < 0.1 [ 181. For x = 1 the decay curves
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71 (1997) 177-188
are strongly non-exponential and the long-term tail of the decay curve corresponds to a rate constant of 180 s-l at 12 K. This rate increases to 300 s-l at 80 K and 830 s- ’ at 300 K. Clearly, a process that is not present in the dilute material with x = 0.01 is quenching the emission in Cs,NaEuCl,. The two most likely processes in stoichiome tric crystals are cross-relaxation or quenching by a defect site. The lowest-order many-body cross-relaxation process between Eu3+ ions would involve the coupling of the 5D0 + 7F6 donor transition to at least three other 7F0 -+ 7F6 acceptor transitions and therefore may be neglected. The above decay curves have been interpreted as indicating energy migration in the 5D0 state in the pure compound followed by energy transfer to short-lived Eu3+ defect sites. The defect probably involves the presence of a nearby water molecule and/or 0’ - anion. The lower symmetry of these defect sites relaxes the selection rules for electricdipole transitions and the presence of high-frequency vibrations provides an efficient relaxation pathway. Such sites have therefore short lifetimes and the decay of the excitation at these sites competes efficiently with back transfer to octahedral sites. The concentration of these defects depends on the method of preparation and cannot be controlled quantitatively [ 181. These decay curves cannot therefore be directly calculated. 4.3. Cs2NaSmxEu,Y,_x-yC16 The
80 K
emission
decay curve for from the 5D0 state of Eu3+ excited resonantly at 17310 cm-’ and observed at 16 230 _+20 cm- ’ is shown in Fig. 2. The luminescent decay is strictly exponential over more than 10 half-lives with an intrinsic decay rate of k. = 120 s-l. At both 80 and 300 K the decay curves are identical to those for Cs2NaEu,,01 Y0,9&l6. Similarly, for Cs2NaSm0.01Eu0,9&16 the decay curves and decay rates closely resemble the non-exponential decay curves for Cs,NaEuCl,. At higher Sm3+ concentrations there is little change in the decay curves (Fig. 3). No emission is observed from the Sm3+ 4Gs,2 state at any concentration after excitation into the Eu3+ 5D, state. This shows clearly that the introduction of Sm3+ CS2NaSm~.o~EU~.o~Y~.~~cl6
T. Luxbacher
et al. / Journal of Luminescence
emm. Et?+: 5D, - ‘F, I
\ 7’\.X-.-,, c.._..,_.,.,,, \
.=.\,
Cs2NaSm,o,Eu,,,Y,,,CI
6
\ \,,
i
‘=, ‘...,,, i \
‘1 \
“\
--.
,.’~
i ‘r r. >$Cs,NaSm,,,Eu,,,CI, 76, .‘: ‘G.. :. ‘$. :;,
t
I
0
IO
:v 20
183
electric dipole, magnetic dipole, and electric quadrupole moments in octahedral symmetry and the vibronic transitions carry very little transition dipole. Even at room temperature the overlap of the Sm3’ the Eu3+ 5Do --+‘F. and vibronic sidebands will be (6H~,z)r: --+(4G~,& small. Excrtatton mto the 4GS:2 state of Sm”’ in CS2NaSmo.01EU,Y,.,,_,C16 (y = 0.005 to L’ = 0.99) produces strong emission from the Eu3+ 5Do state. The decay curves show pronounced slow risetimes followed by a decay equal to the decay rate of the 5Do state in the Cs,NaEu,Yr_,Cl, compounds (Fig. 4). The 5 x lop3 s rise time of the emission in CszSmo.olEuo,lYo.s9C16 reflects the distribution of the lifetimes within the shell model of the Sm3+ (4G5,2) donor ion and is consistent with the rate of luminescence decay from the 4Gsj2 state as independently monitored at 16 500 f 20 cm- ‘. The probability PA(t) that the A th Eu3+ acceptor ion is excited by energy transfer from a Sm3+ donor ion at time t is given by
80 K ext. Et?+: ‘F, - 5D,
k_
71 (1997) 177-188
30
Time / 1V3s Fig. 2. Luminescence decay of the ‘De -+ ‘Fa emission in Cs,NaSmo.o,Eu,Yo.99_,C16 (y = 0.01 and y = 0.99) after direct excitation into the ‘D,, state of Eu3+ at 80 K.
into the lattice has little effect on the lifetime of the ‘Do state of Eu3+. This is not surprising since the 5D,, state lies 530 cm-’ beneath the 4G,,z state of Sm3+. The 5Do -+ 7Fo transition is forbidden for
where p,(t) is introduced by Eq. (4). Under our experimental conditions ( y $0.15) migration amongst the acceptors and energy transfer from the Cs2NaW% ,Y, 9_,rCl, 300 K ext. Err’-: ‘F,-‘D, emm. Eus’: ‘D0-7F,
0
5
10
15
20
25
30
Time / 10.‘~ Fig. 3. Luminescence decay of the ‘Da + ‘FZ emission into the sD, state of Eu3+ at 80 K.
in CstNaSm,Eu
01 Y09 _ XCl, (x = 0.005, 0.01, and 0.1) after direct excitation
i? Luxbacher et al. /Journal
1
~%Na%l.,,%,ycl8s 300K ext. Sm”: ‘H,,, - 4G,,,
emm. Eu3’: ‘D, - ‘F,
:
I
IO
0
20
30
4
40
Time / I O-3s Fig. 4. Time evolution of the emission from the ‘Do state of Eu3+ in Cs,NaSmo.olEuo.lY,s9Cl~ following excitation into the Sm3+ 4G5,z state at 300 K.
acceptors to defects may be neglected. Moreover at low excitation intensities the probability of two nearby Sm 3+ ions being initially excited is small. The saturation of an acceptor will not influence the energy-transfer rate from the donors. We may therefore sum over the probability distributions in a way analogous to Eq. (7) so that the time evolution of the emission intensity Z,,(t) from the ‘D, state of Eu3+ acceptor ions excited by non-radiative energy transfer from Sm3+ (4Gs,2) donor ions in Cs,NaSm,Eu,Y, _,_,C16 can be calculated by ZEu(t) = Z’(0)
exp( - kE”t) i
shells
N.
N.-r.-
1
-@mt-(rnkCR+q,kET)
x exp [
and is therefore designed Z’(0). The first term in the main bracket corresponds to the decay of the Eu3+ 5D0 emission excited by energy transfer from the Sm3+ ions and is independent of the environment of the Eu3+ ions. The second term is the excitation of the Eu3+ ions by energy transfer from Sm3+ ions averaged over all possible occupancy factors Ot:,n(x, y) for all shells. As before we have assumed that the same value of s is applicable to crossrelaxation and energy transfer. This equation does not include the excitation migration among the Eu3+ ions nor their quenching of emission by the defect sites and is therefore restricted to the concentration range y GO.15 where the directly excited Eu3+ emission decays exponentially. In Eq. (9) the rates kf”, ki”, and kCR are known. In principle, kET may be found by curve-fitting but for this system there is a more direct method of independently determining the energy-transfer rate. Introduction of Eu3’ into the Cs,NaSm,Y, _$l, crystal with x = 0.01 results in an increase in the rate of relaxation from the 4G5,2 state of Sm3+ due to energy transfer to the 5D, state of Eu3+. Results on samples with higher Sm3+ concentrations are similar to those reported here although the effect of the energy-transfer process between Sm3+ donor ions and Eu3+ acceptor ions is less especially when x > y. Fig. 1 shows possible pathways for these additional energy-transfer processes as the pairs of transitions EE’ and FF’. At 80 K the main contribution to the energy-transfer process involves the EDV transition at the Sm3’ donor 4G~,z --f %2 ion and the ‘F, --t 5D0 EDV transition at the Eu3+ acceptor ion (transitions EE’ in Fig. 1). At 300 K the Sm3+ (4G,,,)T7 -(6H7,2)r7, r, donor transitions almost are resonant with the (‘Fi)r, -+ (‘DO)rl magnetic dipole allowed electronic transition of the Eu3+ acceptor ions (transitions FF’ in Fig. 1). Fig. 5 shows a selection of luminescence decay curves from the 4G5,, state of Sm3+ in Cl, for 0 6 y 6 0.99 at C+NaSmo.oiEu,Yo.+, 80 K. The decay curves for y < 0.1 and y = 0.99 are essentially exponential at times > 2.5 x low3 s. At intermediate concentrations the long-time decay curves deviate significantly from pure exponential behaviour but are exactly described by Eq. (7). In Fig. 5 the a priori calculated decay curves for
. ( n111 $
‘I
(9) Note that the pre-exponential now weighted by a branching
of Luminescence 71 (1997) 177-188
intensity factor is ratio of decay rates
T. Luxbacher et al. 1 Journal
185
qf Luminescence 71 (1997) 177-188
0 0.05 0.1
0.25 0
20
60
40
80
Time / 10.‘s Fig. 5. Dependence of the luminescence decay from the %5/z state of Sm3+ in Cs,NaSmo.o,Eu,Y,.,P-,Clb on 4’.Note that the solid lines are calculated a priori using the independently measured values k0 = 66 s-‘, kCR (DD) = 1350 s-‘, and kET (DD) = 7.5 s-- ‘.
Cl6 (y = 0.05, 0.1, 0.25, Cs2NaSmo.olEu,Yo.99-, 0.5, and 0.99) assuming s = 6 in Eq. (7) are superimposed on the measured curves. For reasons discussed in Section 3 only the first three shells have been included in our model using the exponential decay constants k0 = 66 s-l and 18 400 s- ’ from our previous measurements on Cs2NaSm,.,,lGdo.999Cl~ and Cs,NaSmCl, at 80 K, respectively [9, 121. Within the three-shell model the latter constant has been calculated to be k, + 13.64 x kCR for dipole-dipole interaction giving a cross-relaxation rate kCR(DD) = 1350 s- ‘. The rate kET(DD) = 7.5 s-r for energy transfer from Sm3’ donor ions to a single Eu3+ acceptor in the first shell at a distance of 7.6 8, has been determined from the measured luminescence decay Eu,,&l, at 80 K. This value curve of CszNaSm,,,r has been used to calculate the decay curves for all other Eu3+ concentrations shown in Fig. 5. We emphasise that in Fig. 5 no curue fitting is involved. The agreement between the calculated and experimental curves is remarkable and provides very strong evidence for the assumptions made both in the shell model in general and its application to this particular system. The behaviour at 300 K is similar but the energytransfer rate increases much more rapidly than either k,, or kCR. The luminescence decay curve
from the 4Gs,2 state of Sm3+ in Cs,NaSmO.OI Eu 0.9&16 at 300 K is also shown in Fig. 5. The energy-transfer rate extracted from this curve corresponds to kET(DD) = 50 s-l. We note that the main contribution to the temperature dependence of the Sm3+ 4Gs,2 luminescence quenching is due to the energy transfer from Sm3+ donor ions to nearest-neighbour Eu3+ acceptors. A detailed study of the temperature dependence of luminescence decay curves from the 4GS,z state of Sm3+ in Cs,NaSm,Eu,Y, _X_yC16 will be presented elsewhere.
5. Discussion In a previous paper [9] we showed that in order to model the cross-relaxation process in Cs,NaSm,Y, -$X6 within the shell model it, was necessary to reduce the contribution from the shells other than n = 1. We attributed this reduction to the selective shielding of the Sm3+ acceptor in shells n 3 2 from the Sm3+ donor by the intervening ions. No such screening effect is observable for the Sm3+ + Eu3+ energy-transfer processes described in this paper. The agreement between experiment and independent calculation demonstrated by Fig. 5 is perfect. An explanation of this
186
T. Luxbacher et al. /Journal
10’ 0
2
4
6
8
10
Time / I O?S
Fig. 6. Computed decay curves for different ratios of the energytransfer rate kET and the intrinsic decay rate k. (x = 0.25, k. = 66 SK’). The measured decay curves of luminescence from the 4Gs,Z state of Sm 3* in CszNaSmO.,,Y,,,=,C1, (x = 0.25) and Cs,NaSmo.olEuo.zsYo.74Cls (y = 0.25) are superimposed on the calculated curves.
apparent difference between the Sm3+ + Sm3+ cross-relaxation and the Sm3+ + Eu3+ energy transfer can be found by comparing the Sm3+ decay curves for CszNaSmo.olEuo.zsYo.74C16 and CszNaSm,,,SYO,,,C1,. In both cases the excited Sm3+ ion is relaxed by energy transfer to acceptors distributed in accordance with the occupancy factor 0:(0.25) and the behaviour of these systems might therefore expected to be comparable. The 80 K decay curves for the above two systems are shown in Fig. 6 and superimposed on these curves are the three-shell model calculations assuming dipole-dipole interaction for differing ratios of the energy-transfer (or cross-relaxation) rate constants. For kET < k0 the decay curves are virtually exponential but for kET > k. they become markedly non-exponential. The deviation from exponential behaviour in the latter regime may only be modelled on the assumptions that there is an anisotropic dielectric but for the case of
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71 (1997) 177-188
Cs2NaSmo.olEuo.25Yo.74Cls the deviation from exponential behaviour is very small and only present at very short times. The order of magnitude of the cross-relaxation rate kCR and the energy-transfer rate kET can be estimated from Fig. 6 as 10ko < kCR < lOOk and O.lko < kET < ko, respectively. The values for kCR(DD) = 1350 s-l and kET(DD) = 7.5 s-l obtained from measurements on Cs,NaSmCl, and Cs2NaSm0.01Eu0.9&16 crystals reflect these magnitudes as kCR/k,, = 20.5 and kETJkO= 0.114 at 80 K. Note that the experimental decay curves shown in Fig. 6 become almost parallel to the intrinsic decay of Sm3 + at times > 2 x 10m3 s. The reasons for this differ in the two cases. In Cs,Na Sm o.olEu 0.25Y0.74Cl~the energy-transfer rate is so low that the decay curves remain nearly exponential since a large number of small terms with different rate constants add to the intrinsic decay. This behaviour is comparable to the cross-relaxation from the 3P0 state of Pr3+ in Cs,NaPr,Y,_,Cl, [l]. For Cs2NaSm0.25Y0,75C16the cross-relaxation rate is so fast that almost all of the excited Sm3+ ions that have a nearby acceptor are relaxed and only the emission from almost isolated Sm3+ ions is observed. It is convenient to define cross-relaxation and energy-transfer efficiencies Y/CRand VET from an excited donor state of an optically active ion as parameters to characterise the applicability of a crystal containing a certain concentration of these ions as a laser material or an optical device. The overall efficiency of energy transfer from an excited electronic energy level of the donor can be calculated by using the expression [ 19, 201 o(, VET=
gdt
1 -ko
(10)
s 0
where the intrinsic decay rate k. is the sum of radiative and non-radiative relaxation processes occurring at an isolated donor ion which is determined experimentally from the exponential decay curve of a very dilute crystal. Z(t) represents the time evolution of luminescence in the presence of acceptor ions and 17 1(t) is the integrated area of
T. Luxbacher
et al. i Journal of Luminescence
71 11997) 177-188
187
6. Conclusions In this paper we have derived kinetic expressions for the decay of excited rare-earth ions undergoing both cross-relaxation processes and also energy transfer to dissimilar acceptors. The cross-relaxation rate may be determined by measurements on crystals containing only the donor species. The energy-transfer rate may be determined by kinetic measurements on crystals containing a large concentration of acceptors. The decay kinetics at all other concentrations of both donor and acceptor may then be exactly predicted from these measurements. This provides very strong evidence for the assumptions implicit within the shell model.
0
+
0
O.O ~h&-a--y--+ 0.01
acceptor
concentration
x (y)
Fig. 7. Concentration dependence of the efficiencies of crossrelaxation and energy transfer in Cs,NaSm,Y(Gd), _XCI, and CszNaSmo 0,E~gY0.99_,Clh at 300 K.
the donor decay curve, normalized such that I(0) = 1. In the pure crystal the decay Z(t) is exponential with a decay rate k and relation (10) reduces to
Acknowledgements This work has been supported in part under the collaborative ARC scheme of The British Council and the Bundesministerium fiir Wissenschaft and Forschung.
References kT
=
1 - Wk.
(11) [II S.O. Vasquez and CD. Flint, Chem. Phys. Lett. 238 (1995)
Using this expression the efficiency qCR of the Sm3 + + Sm3+ cross-relaxation in Cs,NaSmCl, is calculated to be > 99.6% at 300 K and z 99.5% at 10 K. These efficiencies are comparable to those found for the Ho3+ + Tb3+ energy transfer in Cs2NaHo0.1Tb0,1Y0,8Cl~ [21]. Fig. 7 shows the dependence of the efficiency of cross-relaxation between Sm3+ ions in CszNaSm,Y(Gd), _,Clh (x=0.001 tox=l)onxat300K. Replacing Y 3 + ions successively by Eu3 ’ in CszNaSmO,OIY,.y&l, the lifetime of luminescence from the 4G5,2 state of Sm3+ is further decreased. The efficiency of the additional energy-transfer processes is calculated from the ratio of luminescence of Sm3+ donor ions in the presence of Eu3+ acceptor ions to the luminescence of Sm3+ ions alone. The energy-transfer efficiencies so obtained are also shown in Fig. 7 for varying concentrations of Eu3+ acceptor ions at 300 K.
378.
PI D.R. Foster, F.S. Richardson
and R.W. Schwartz, J. Chem. Phys. 82 (1985) 618. c31 A.K. Banerjee and R.W. Schwartz. Chem. Phys. 58 (1981) 255. II41 P.A. Tanner, Chem. Phys. Lett. 155(1989) 59. [51 M. Bettinelli and CD. Flint, Chem. Phys. Lett. 167 (1990) 45. 161 R.W. Schwartz. Mol. Phys. 30 (1975) 81. Inorg. Chem. 15 (1976) c71 O.A. Serra and L.C. Thompson, 504. Mol. Phys. 44 (1981) PI C.D. Flint and F.L. Stewart-Darling, 61. H.P. Fritzer. R. Sabry-Grant and C.D. II91T. Luxbacher, Flint, Chem. Phys. Lett. 241 (1995) 103. 1101T. Luxbacher, K. Gatterer, H.P. Fritzer and C.D. Flint, J. Appl. Spectrosc. 62 (1995) 27. 1111 M. Bettinelli and C.D. Flint. J. Phys.: Condens. Matter 3 (1991) 7053. H.P. Fritzer and C.D. Flint, J. Phys.: ConCl21 T. Luxbacher, dens. Matter 7 (1995) 9683. 1131 S.O. Vasquez and C.D. Flint. J. Appl. Spectrosc. 62 (1995) 213.
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[14] R. Sabry-Grant
[15] [16] [17] [18]
and C.D. Flint, J. Appl. Spectrosc. 62 (1995) 155. T. Fiirster, Ann. Phys. 2 (1948) 55. D.L. Dexter, J. Chem. Phys. 21 (1953) 836. D.L. Huber, Phys. Rev. B 20 (1979) 2307. M. Duckett and C.D. Flint, to be published.
71 (1997) 177-188
[19] R. Reisfeld and N. Lieblich-Sofler, J. Solid State Chem. 28 (1979) 391. [20] A. Lupei, V. Lupei, S. Georgescu and W.M. Yen, J. Appl. Phys. 66 (1989) 3792. [21] A.K. Banerjee, F. Stewart-Darling, CD. Flint and R.W. Schwartz, J. Phys. Chem. 85 (1981) 146.