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Temperature dependence of luminescence decay from the 4G52 state of Sm3+ in Cs2NaSmxY1 − xCl6 and Cs2NaSmxEuyY1 − x − yCl6
JOURNAL OF
LUMINESCENCE ELSEVIER
Journal
of Luminescence
71 (1997) 313-319
Temperature dependence of luminescence decay from the 4G5j2 state of Sm3+ in Cs,NaSm,Y 1 _ $1, and Cs,NaSm,Eu,Y 1_ x_ ,C16 Thomas Luxbachera,*, Harald P. Fritzef,
Colin D. Flintb
“Institut,fiir Physikalische und Theoretische Chemie, Technische Universitiit Graz, Rechhauerstraje 12, 8010 Graz. Austria bLaser Laboratory. Department of Chemistry, Birkheck College, 29, Gordon Square, London WCIH OPP, UK Received
29 October
1996; accepted
15 January
1997
Abstract Luminescence decay curves for the 4Gsiz + 6H712 emission of Sm 3+ in the cubic hexachloroelpasolite crystals Cs2NaSm,Y1 -+C16 (X = 0.005-l) and CszNaSm,Eu,YI -X-yC16 (X = 0.01P0.95, y = 0.05-0.99) have been measured over the temperature range lo-300 K using pulsed laser excitation into the (6H5j2)r7 + (4Gs,z)rs magnetic-dipole-allowed electronic transition of Sm3’. The luminescence from the 4G 512state is strongly quenched by both cross relaxation to nearby Sm”’ ions and energy transfer to the 5D~ state of Eu3+ acceptors. The temperature dependence of cross relaxation and energy transfer is discussed in terms of the involved mechanisms. Keywords:
Cross
relaxation;
crystals; CszNaSm,Eu,Y
Energy
transfer;
Shell model;
Luminescence
1. Introduction
the temperature range lo-300 K. The intrinsic decay rate k, of the isolated Sm3’ donor ion is measured as the exponential decay rate of the Cs2NaSmo.oosYo,995C16 crystal which is k. = 58.4 s-l at 10 K increasing to k0 = 109 S-I at 300 K [2]. According to our shell model the crossrelaxation rate kCR to a single Sm3 ’ acceptor in the first shell is determined from the measured exponential decay constant for Cs,NaSmCl,[ 1) which is 11 600 s- ’ at 10 K increasing by a factor of 2.7 at 300 K. In the elpasolite crystals it is sufficient to include only acceptors of shells n = l-3 and within this three-shell model for dipole-dipole interaction the cross-relaxation rate kCR = 832 s- 1 at 10 K increasing to kCR = 2120 s-’ at 300 K [2]. The energy-transfer rate is determined from results obtained for Cs,NaSm,.01Euo.9&16 with a small concentration of donor ions and almost
In a series of papers a recently developed shell model for energy transfer [l] has been applied to understand the luminescence decay curves for the emission from the 4G5,2 state of Sm3+ in the hexachloroelpasolite crystals Cs,NaSm,Y 1_J&, (x = 0.005 to x = 1) [2-41 and Cs2NaSm,Euy Y, _x_yClh (X = 0.01-0.95, y = 0.05-0.99) [S]. In the latter material the emission from the 4Gs,2 state of Sm3+ is strongly quenched by both cross relaxation to nearby Sm 3+ ions and energy transfer to the ‘D 0 state of Eu3+. In this paper, attention is focused on the crystals Cs,NaSm,Y 1_,Cls (x = 0.005-l) and CszNaSmo.olEu,Yo.99_,C1, (y = 0.05-0.99) over *Corresponding
author.
decay curves; Cubic hexachloroelpasolite
1-xm,c16
Fax:
+ 43 316 8738225.
0022-23131971S17.00 m$>1997 Elsevier Science B.V. All rights PII SOO22-23 13(97)00097-5
reserved
314
T. Luxbacher et al. 1 Journal of Luminescence
100 mol% of the acceptor as kET = 5.5 s-l at 10 K increasing to 49.9 s-’ at 300 K. The stronger temperature dependence of kET indicates that two different mechanisms for energy transfer are involved. The temperature dependencies of ko, kCR, and kET are discussed in terms of resonant and phonon-assisted relaxation and energy-transfer processes.
2. The shell model for cross relaxation and energy transfer Within the shell model for simultaneous treatment of cross-relaxation and energy-transfer processes, luminescence decay curves following a 6function excitation pulse take the form [S] shells r(t)
=
I(Wv(
x
-bt)
N.
N. -rn
n
1
1
n=l
r,=O
q.=o
- G;(rnkCR + qnkET)
exp C
O~,n(x,
Y)
71 (1997) 313-319
and energy transfer. In the particular system Cs,NaSm,Eu,Y 1-X-J& there is no evidence to include higher-order multipole-multipole interaction with s > 6. For dipole-dipole interaction the geometric factor, G,“, is independent of the shell number IZ[S] and will therefore be included in the definitions of kCR and kET. As discussed in a previous paper [4] the expansion in Eq. (1) may be truncated at n = 3 for the elpasolite lattice.
3. Experimental Crystals of high optical quality were grown using a vertical Bridgman technique [a]. Luminescence curves were measured for the decay (4GS,z)Ts -+ (6H7,2)r,, Ts emission of Sm3+ at 16 500 cm-’ after pulsed laser excitation into the (6Hs,2)r, + (4Gs,z)rs transition at 17 760 cm-’ as described in detail previously [2].
(1)
4. Results
k. is the intrinsic decay rate of the isolated donor
ion including radiative and non-radiative relaxation processes, k CR is the cross-relaxation rate from the donor to a chemically identical acceptor ion in the first shell, and kET is the rate of energy transfer to a n = 1 acceptor chemically different from the donor. The distance dependence of the multipolar interaction between donor and-acceptor ions which is assumed in our model is introduced by the ratio (RJR,)S where R, is the distance between the donor and an acceptor in the nth shell and s = 6, 8, or 10 for electric dipole vibronicelectric dipole vibronic (EDV-EDV) or magnetic dipole-magnetic dipole (MD-MD), electric dipole vibronic-electric quadrupole (EDV-EQ), and electric quadrupole-electric quadrupole (EQ-EQ) interaction, respectively. The occupancy factor O[:,“((x, y) is the probability of finding I, acceptor ions chemically identical to the donor and q,, chemically different acceptors in the nth shell which has a capacity to contain N, acceptors [S]. G”, is a geometric factor containing the angular dependence of cross-relaxation and energy-transfer processes. In Eq. (1) we have assumed the same mechanisms to occur for both cross relaxation
The spectroscopic and vibrational properties of Cs,NaSmC16 and CspNaEuC16 have been investigated both experimentally and theoretically [6-121. The electronic spectra are dominated by magnetic dipole allowed electronic origins and electric-dipole-allowed vibronic origins. In the Cs,NaSm,Eu,Y I _ x j& crystals a variety of cross-relaxation and energy-transfer pathways exist involving the 6F, (J = 3, $, $,y) intermediate states of Sm3+ and the 7F1 and 5D0 states of Eu3+ [4]. The kinetic data for the relaxation of the 4Gs,2 state of Sm3 + in Cs,NaSm,Eu,Y, _*_ $16 is given in Table 1. Fig. 1 shows the temperature dependence of luminescence decay from the 4Gs,2 state of Sm3+ in Cs,NaSm 0.25Y0.75c16. At all temperatures the decay curves consist of an initial non-exponential fast process followed by a slightly non-exponential slower region. The proportion of the fast process increases with increasing temperature. There is no evidence for a change in the mechanism occurring in this compound over the whole temperature and concentration ranges studied. This would appear to exclude energy migration among the 4G5,z state of
T. Luxbacher et al. 1 Journal of Luminescence
Table 1 Kinetic data for the relaxation of the 4Gs,2 state of Sm3’ Cs,NaSm,Eu,.Y, _X_,Cl, as a function of temperature
T(K) 10 20 30 40 60 80 100 140 170 200 240 300
k, (s- ‘)
kCR(s- ‘)
58.4 58.5
832 870
61.8 65.2 66.3 70.3 77.9 84.1
1050 1160 1270 1370 1590 1700
71 (1997) 313-319
315
in
kET (s- ‘) 5.5 5.7
109
2120
1.2 8.2 10.0 13.0 15.3 30.0 49.9
10K 50 K 80 K
Sm3 + as a significant contributor to the decay kinetics. The variation of the intrinsic decay rate k. of the isolated Sm3+ donor ion and the Sm3+ + Sm3’ cross-relaxation rate kCR with temperature is shown in Fig. 2 as curves (a) and (b), respectively. Comparison with emission spectra in the 4Gs,2 + ‘jHsj2, (jH?,l and “H 9,2 regions at 10 and 300 K [7] show that the temperature dependence of k. is entirely
170K
300 K
0
5
10
IS
Time / I 0-3s Fig. 1. Time Cs,NaSma
evolution of the 4G5,2 emission of Sm’ zsYo ,s Cl, as a function of temperature.
’ in
10 C
0,Ol
dependence normalised
k”‘Sm_Eu
-
k,Sm
-
k“‘Sm-Sm
0,1 Temperature-‘/
Fig. 2. Temperature ‘Gs,* state of Sm3’
v
Km’
of the intrinsic decay rate k. (a), cross-relaxation rate kCR(b), and energy-transfer to the values k,, = 58.4 s-r, kCR= 832 ss’, and kET = 5.5 ss’ at 10 K.
rate kFT (c) of the
316
T. Luxbacher
et al. /Journal
of Luminescence
71 (1997) 313-319
consistent with the relaxation mechanism being due to the sum of magnetic-dipole-allowed electronic transitions and electric-dipole-allowed vibronic transitions. Below 100 K the dependence of k0 on temperature is well described using the coth law for vibronic transitions [13, 141, k,(T) = ko(O)CpiCoth i
~
(2) B
(
)
with the sum running over all enabling modes of the lattice, and the amount of their contribution is determined by pi. As the temperature is increased, additional radiative and non-radiative processes involving the thermally populated (4G5j2)r7 level contribute to the intrinsic decay rate. The temperature dependence of the cross-relaxation rate of Sm3+ acceptor ions is slightly stronger but again entirely consistent with an electric dipole vibronic-electric dipole vibronic (EDV-EDV) cross-relaxation mechanism. The stronger temperature dependence of kCR is due to this quantity being proportional to the product of two vibronic mechanisms involving v6 and v4 as well as v3 and a minimal contribution of magnetic-dipole processes. The most-probable phonon-assisted mechanisms for cross relaxation having the smallest energy mismatch between the donor emission and the acceptor absorption transitions are [S] (4Gs,z)T-s + (6H~,z)L --) PFI
1,2Ws
+
(6Fs,2P-s, (34
(4G5i2)r8
+ (%z)b
+ Ah
+
m
1/2r6
+ (6Fs,2)r7g (3b)
(4G5,2)rS
+ ?Hs,2)L + @I
(4G5,2P-8
+
+
Av2
---) (6F5,2)r7
(3c)
l,2w-8,
PH5,2P-7
--) PFs,2&3
+
?h
l,2w-8r
where AvI = 71 cm-’ in Eq. (3b) corresponds to the v6 normal mode of the [SmC16]+ entity, and Av2 = 32 cm-’ in Eq. (3~) may be bridged by the creation of a lattice-phonon mode. The pairs of donor and acceptor transitions in Eqs. (3a) and (3d) are almost resonant within the uncertainty in the positions of the ‘jF, 1,2 crystal-field levels.
0
5
IO
I5
20
25
Time / 10m3s Fig. 3. Temperature dependence of luminescence the 4Gs,z state of Sm3+ in CszNaSmo.01Eu0.99C16.
decay
from
Fig. 3 shows luminescence decay curves from the 4G 5,2 State Of sm3+ in CS2NaSIIIo.olEUo.99C16 at various temperatures. Note that the main contribution to the temperature dependence is due to the energy transfer from Sm3+ donor ions to Eu3+ acceptors. The temperature dependence of the energy-transfer rate kETis shown as curve (c) in Fig. 2. The rapid increase of kET above 80 K indicates that two different mechanisms are involved. At low temperature the most-probable mechanism for energy transfer from Sm3+ donor ions to Eu3+ acceptors in the crystals Cs2NaSm,Eu,Y, _X_,C16 involves the EDV transitions Sm3+:(4G5,2)Ts + Eu3+ :(7F0)L’I + Sm3+ :(6Hs,Jrs
+ Eu3+ :(5Do)T1 + AV,ib,
(4)
where the energy mismatch AV,i, = 395 cm-’ can be bridged by coupling to two odd-parity
T. Lubacher
vibrational modes of the [LnC1J3- ions. This energy-transfer mechanism becomes more efficient as the tem~rature is increased due to the phonon with [exp(hv/kaT) - l]-‘, density increasing where hv is the phonon energy and is again consistent with a squared coth law. At temperatures above 80 K the resonant energy-transfer pathway Sm” ’ : (4G512)r7 + Eu3 + : (7FI)lY4+ Sm” )-:(6H7j2)r7, Ts + Eu3+ :(‘Da)rr
317
et al. j Journal of Luminescence 71 (1997) 313.--319
(5)
becomes important where both transitions are of magnetic-dipole-allowed electronic origin.
overlap integral in Eq. (6) gives
2 d&y f AE,,+ -7r4(E,j’d- E,,,)2 + (A.&j + AE,,,)2.
The temperature dependence of the resonant energy-transfer process of Eq. (5) is introduced by the Boltzmann factors of Eq. (7) and the normalised line shape functions of Eq. (8) which depend on the position and width of the donor emission and acceptor absorption lines. The homogeneous width of a transition line is given by the sum of homogeneous widths of the initial and final energy levels which may be written as Cl73 AE(T) = AEM”“’+ AEDi’(T) + AERaman( T),
5. Discussion In our shell model, we assume Fiirster-Dexter multipole-multipole interaction [15,16] between statistically distributed donor and acceptor ions where the rate of resonant energy transfer from a donor D to an acceptor A may be written as
(8)
(9)
where AEMuitiis due to multiphonon emission processes being essentially temperature-independent. The second contribution to the transition line width, AED”, results from the absorption or emission of a single phonon and is represented by the coth law [14]. The last term in Eq. (9),
XL>
9 wW
(6) The probability of resonant energy transfer involving the donor emission transition d’ -+ d and the acceptor absorption transition a -+ a’ is introduced by the squared matrix eiement of the interaction Hamiltonian I?,,. pds is the thermal population of the n’th state which is go-fold-degenerate and separated by the energy Ed‘ from the lowestlying state of the initial donor multiplet and is calculated as
VI
with a similar notation for the acceptor. Taking Lorentzian line shape functions of half-widths AEdsd and A&,, centred at energies Ed,d and E,,, the
dx
[exp(x) - 11’
’
is due to two-phonon Raman scattering processes where AMdP and AMd contain the second-order matrix elements of the electron-phonon coupling Hamiltonian for initial and final states of the transition cl -+ d’, x = ko/kBT, and wb is the phonon cut-off frequency assuming a Debye distribution. pcrystis the mass density of the crystal and v is the average phonon velocity. Similarly, the change in the position of a spectral line with temperature is given by the difference of the positions of the two relevant energy levels which show approximately a T4 dependence according to [17] &r&(T) = (AMd, - AMd)
3?i 2R2Pcrystvs
XII
x3
expfx) - 1
dx .
(11)
318
T. Luxbacher
et al. /Journal
of Luminescence
71 (1997) 313-319
Table 2 Boltzmann factors of thermally populated states involved in the resonant mechanism of energy transfer between Sm3+ donor ions and Eu3+ acceptors as a function of temperature
x lo2 10 30 80 100 140 170 200 240 300
300K 0
5
10
15
4 20
energy gap / cti’ Fig. 4. Overlap integral of Eq. (8) as a function of width and position of donor and acceptor transitions. The arrow indicates the change of the overlap integral with temperature.
To model the temperature dependence of a resonant energy-transfer process, Eqs. (10) and (11) have to be introduced in Eq. (8) for both donor and acceptor transitions. A simpler approach to estimate the increase of the resonant energy-transfer rate with temperature is shown in Fig. 4 where the overlap integral of Eq. (8) has been plotted as a function of both positions and widths of donor and acceptor transition lines. Comparison with absorption and excitation spectra shows an increase of the width of the Sm3+ (6Hs,2)17 + (4Gs,2)Is and the Eu3+(‘F,)I, + (5D1)14 magnetic-dipole transitionsfrom2cm-‘at80Kto5cm-‘at300Kand an increase of the energy mismatch from 6 cm- ’ at lOK[6,12]to15cm-’ at 300 K which is indicated by the arrow in Fig. 4. The effect of the changes in the transition line widths and the energy mismatch on the rate of energy transfer is negligibly small for this particular system. The overlap integral of Eq. (8) is almost independent of temperature in the range 80-300 K.
0 0 0.1 0.3 1.4 2.6 4.0 5.9 8.7
x lo* 0 0 0.5 1.8 7.4 13.2 19.2 26.6 35.6
x 102 0 0 5 x 1om4 6x 1O-3 0.1 0.3 0.8 1.6 3.1
Therefore, the temperature dependence of the energy-transfer rate is introduced only by the thermal populations of the Sm3+(4G5,2)17 and Eu3+(‘F1)r4 states and are given in Table 2. The energy gaps between the Ts and I7 crystalfield levels of the Sm3+ 4G5,2 multiplet as well as between the ‘FO and ‘Fi states of Eu3’ are about 350 cm-‘. Since the initial states of both donor and acceptor ions are separated from the low-lying states by one phonon, thermal equilibrium is reached within the nanosecond time scale. The thermal populations of these states become 0.1% for Sm3 + and 0.5% for Eu3 + at 80 K, increasing to 9% for Sm3+ and 36% for Eu3+ at 300 K. In Eq. (6) the product of these Boltzman factors, p[(4GS,2)r7] xp[(‘F,)I,], determines the contribution of the resonant process to the total energytransfer rate. The increase of the thermal population of both donor and acceptors states is constant in the temperature range 200 K-300 K. We therefore expect a linear increase of kET with ln(l/T) which is in agreement with curve (c) in Fig. 2.
6. Conclusions The temperature decay from the Cs,NaSm,Y 1_,J& for energy migration a rate comparable
dependence of luminescence 4G5,2 state of Sm3+ in (x = 0.05-l) gives no evidence among Sm3+ donor ions with to the cross-relaxation and
T. Luxbacher
et al. /Journal
energy-transfer rates. The assumption of the crossrelaxation processes occurring by electric dipole vibronic-electric dipole vibronic interaction is manifested by the observed temperature dependence of kCR. For energy transfer from Sm3+ donor ions to the ‘D, state of Eu3+ acceptors in Cs2NaSmo.olEu,Yo.99_,C1, (y = 0.05-0.99) two mechanisms are involved. Below 80 K the temperature dependence of the energy-transfer rate is entirely consistent with a phonon-assisted process following a squared coth law, while resonant magnetic dipole-magnetic dipole interaction between the Sm3’ donor and Eu3+ acceptor ions becomes dominant as the temperature is increased. The temperature dependence of the latter process is well understood in terms of the thermal populations of the donor and acceptor states involved.
Acknowledgements We thank The British Council for financial support under their ARC scheme. TL thanks the Bundesministerium fur Wissenschaft, Verkehr und Kunst and the Technische Universitat Graz for a travel grant.
of Luminescence
71 (1997) 313-319
319
References [l] [2] [3] [4] [5] [6] [7] [S] [9] [lo] [l l] [12] [13] [14]
[15] [16] [17]
S.O. Vasquez and C.D. Flint, Chem. Phys. Lett. 238 (1995) 378. T. Luxbacher, H.P. Fritzer, R. Sabry-Grant and CD. Flint, Chem. Phys. Lett. 241 (1995) 103. T. Luxbacher, H.P. Fritzer. K. Gatterer and C.D. Flint, .I. Appl. Spectr. 62 (1995) 27. T. Luxbacher, H.P. Fritzer and C.D. Flint, _I. Phys.: Condens. Matter 7 (1995) 9683. T. Luxbacher, H.P. Fritzer and CD. Flint, J. Lumin., accepted. A.K. Banerjee and R.W. Schwartz, Chem. Phys. 58 (1981) 255. D.R. Foster, F.S. Richardson and R.W. Schwartz. J. Chem. Phys. 82 (1985) 618. F.S. Richardson, M.F. Reid, J.J. Dallara and R.D. Smith, J. Chem. Phys. 83 (1985) 3813. P.A. Tanner, Chem. Phys. Lett. 155 (1989) 59. R.W. Schwartz, Mol. Phys. 30 (1975) 81. O.A. Serra and L.C. Thompson, lnorg. Chem. 15 (1976) 504. C.D. Flint and F.L. Stewart-Darling, Mol. Phys. 44 (1981) 61. A.D. Liehr and C.J. Ballhausen, Phys. Rev. 106(1957) 1161. C.J. Ballhausen, Molecular Electronic Structure of Transition Metal Compounds (McGraw-Hill. London, 1979). T. Forster, Ann. Phys. 2 (1948) 55. D.L. Dexter, J. Chem. Phys. 21 (1953) 836. D.E. McCumber and M.D. Sturge, J. Appl. Phys. 34 (1963) 1682.
LUMINESCENCE ELSEVIER
Journal
of Luminescence
71 (1997) 313-319
Temperature dependence of luminescence decay from the 4G5j2 state of Sm3+ in Cs,NaSm,Y 1 _ $1, and Cs,NaSm,Eu,Y 1_ x_ ,C16 Thomas Luxbachera,*, Harald P. Fritzef,
Colin D. Flintb
“Institut,fiir Physikalische und Theoretische Chemie, Technische Universitiit Graz, Rechhauerstraje 12, 8010 Graz. Austria bLaser Laboratory. Department of Chemistry, Birkheck College, 29, Gordon Square, London WCIH OPP, UK Received
29 October
1996; accepted
15 January
1997
Abstract Luminescence decay curves for the 4Gsiz + 6H712 emission of Sm 3+ in the cubic hexachloroelpasolite crystals Cs2NaSm,Y1 -+C16 (X = 0.005-l) and CszNaSm,Eu,YI -X-yC16 (X = 0.01P0.95, y = 0.05-0.99) have been measured over the temperature range lo-300 K using pulsed laser excitation into the (6H5j2)r7 + (4Gs,z)rs magnetic-dipole-allowed electronic transition of Sm3’. The luminescence from the 4G 512state is strongly quenched by both cross relaxation to nearby Sm”’ ions and energy transfer to the 5D~ state of Eu3+ acceptors. The temperature dependence of cross relaxation and energy transfer is discussed in terms of the involved mechanisms. Keywords:
Cross
relaxation;
crystals; CszNaSm,Eu,Y
Energy
transfer;
Shell model;
Luminescence
1. Introduction
the temperature range lo-300 K. The intrinsic decay rate k, of the isolated Sm3’ donor ion is measured as the exponential decay rate of the Cs2NaSmo.oosYo,995C16 crystal which is k. = 58.4 s-l at 10 K increasing to k0 = 109 S-I at 300 K [2]. According to our shell model the crossrelaxation rate kCR to a single Sm3 ’ acceptor in the first shell is determined from the measured exponential decay constant for Cs,NaSmCl,[ 1) which is 11 600 s- ’ at 10 K increasing by a factor of 2.7 at 300 K. In the elpasolite crystals it is sufficient to include only acceptors of shells n = l-3 and within this three-shell model for dipole-dipole interaction the cross-relaxation rate kCR = 832 s- 1 at 10 K increasing to kCR = 2120 s-’ at 300 K [2]. The energy-transfer rate is determined from results obtained for Cs,NaSm,.01Euo.9&16 with a small concentration of donor ions and almost
In a series of papers a recently developed shell model for energy transfer [l] has been applied to understand the luminescence decay curves for the emission from the 4G5,2 state of Sm3+ in the hexachloroelpasolite crystals Cs,NaSm,Y 1_J&, (x = 0.005 to x = 1) [2-41 and Cs2NaSm,Euy Y, _x_yClh (X = 0.01-0.95, y = 0.05-0.99) [S]. In the latter material the emission from the 4Gs,2 state of Sm3+ is strongly quenched by both cross relaxation to nearby Sm 3+ ions and energy transfer to the ‘D 0 state of Eu3+. In this paper, attention is focused on the crystals Cs,NaSm,Y 1_,Cls (x = 0.005-l) and CszNaSmo.olEu,Yo.99_,C1, (y = 0.05-0.99) over *Corresponding
author.
decay curves; Cubic hexachloroelpasolite
1-xm,c16
Fax:
+ 43 316 8738225.
0022-23131971S17.00 m$>1997 Elsevier Science B.V. All rights PII SOO22-23 13(97)00097-5
reserved
314
T. Luxbacher et al. 1 Journal of Luminescence
100 mol% of the acceptor as kET = 5.5 s-l at 10 K increasing to 49.9 s-’ at 300 K. The stronger temperature dependence of kET indicates that two different mechanisms for energy transfer are involved. The temperature dependencies of ko, kCR, and kET are discussed in terms of resonant and phonon-assisted relaxation and energy-transfer processes.
2. The shell model for cross relaxation and energy transfer Within the shell model for simultaneous treatment of cross-relaxation and energy-transfer processes, luminescence decay curves following a 6function excitation pulse take the form [S] shells r(t)
=
I(Wv(
x
-bt)
N.
N. -rn
n
1
1
n=l
r,=O
q.=o
- G;(rnkCR + qnkET)
exp C
O~,n(x,
Y)
71 (1997) 313-319
and energy transfer. In the particular system Cs,NaSm,Eu,Y 1-X-J& there is no evidence to include higher-order multipole-multipole interaction with s > 6. For dipole-dipole interaction the geometric factor, G,“, is independent of the shell number IZ[S] and will therefore be included in the definitions of kCR and kET. As discussed in a previous paper [4] the expansion in Eq. (1) may be truncated at n = 3 for the elpasolite lattice.
3. Experimental Crystals of high optical quality were grown using a vertical Bridgman technique [a]. Luminescence curves were measured for the decay (4GS,z)Ts -+ (6H7,2)r,, Ts emission of Sm3+ at 16 500 cm-’ after pulsed laser excitation into the (6Hs,2)r, + (4Gs,z)rs transition at 17 760 cm-’ as described in detail previously [2].
(1)
4. Results
k. is the intrinsic decay rate of the isolated donor
ion including radiative and non-radiative relaxation processes, k CR is the cross-relaxation rate from the donor to a chemically identical acceptor ion in the first shell, and kET is the rate of energy transfer to a n = 1 acceptor chemically different from the donor. The distance dependence of the multipolar interaction between donor and-acceptor ions which is assumed in our model is introduced by the ratio (RJR,)S where R, is the distance between the donor and an acceptor in the nth shell and s = 6, 8, or 10 for electric dipole vibronicelectric dipole vibronic (EDV-EDV) or magnetic dipole-magnetic dipole (MD-MD), electric dipole vibronic-electric quadrupole (EDV-EQ), and electric quadrupole-electric quadrupole (EQ-EQ) interaction, respectively. The occupancy factor O[:,“((x, y) is the probability of finding I, acceptor ions chemically identical to the donor and q,, chemically different acceptors in the nth shell which has a capacity to contain N, acceptors [S]. G”, is a geometric factor containing the angular dependence of cross-relaxation and energy-transfer processes. In Eq. (1) we have assumed the same mechanisms to occur for both cross relaxation
The spectroscopic and vibrational properties of Cs,NaSmC16 and CspNaEuC16 have been investigated both experimentally and theoretically [6-121. The electronic spectra are dominated by magnetic dipole allowed electronic origins and electric-dipole-allowed vibronic origins. In the Cs,NaSm,Eu,Y I _ x j& crystals a variety of cross-relaxation and energy-transfer pathways exist involving the 6F, (J = 3, $, $,y) intermediate states of Sm3+ and the 7F1 and 5D0 states of Eu3+ [4]. The kinetic data for the relaxation of the 4Gs,2 state of Sm3 + in Cs,NaSm,Eu,Y, _*_ $16 is given in Table 1. Fig. 1 shows the temperature dependence of luminescence decay from the 4Gs,2 state of Sm3+ in Cs,NaSm 0.25Y0.75c16. At all temperatures the decay curves consist of an initial non-exponential fast process followed by a slightly non-exponential slower region. The proportion of the fast process increases with increasing temperature. There is no evidence for a change in the mechanism occurring in this compound over the whole temperature and concentration ranges studied. This would appear to exclude energy migration among the 4G5,z state of
T. Luxbacher et al. 1 Journal of Luminescence
Table 1 Kinetic data for the relaxation of the 4Gs,2 state of Sm3’ Cs,NaSm,Eu,.Y, _X_,Cl, as a function of temperature
T(K) 10 20 30 40 60 80 100 140 170 200 240 300
k, (s- ‘)
kCR(s- ‘)
58.4 58.5
832 870
61.8 65.2 66.3 70.3 77.9 84.1
1050 1160 1270 1370 1590 1700
71 (1997) 313-319
315
in
kET (s- ‘) 5.5 5.7
109
2120
1.2 8.2 10.0 13.0 15.3 30.0 49.9
10K 50 K 80 K
Sm3 + as a significant contributor to the decay kinetics. The variation of the intrinsic decay rate k. of the isolated Sm3+ donor ion and the Sm3+ + Sm3’ cross-relaxation rate kCR with temperature is shown in Fig. 2 as curves (a) and (b), respectively. Comparison with emission spectra in the 4Gs,2 + ‘jHsj2, (jH?,l and “H 9,2 regions at 10 and 300 K [7] show that the temperature dependence of k. is entirely
170K
300 K
0
5
10
IS
Time / I 0-3s Fig. 1. Time Cs,NaSma
evolution of the 4G5,2 emission of Sm’ zsYo ,s Cl, as a function of temperature.
’ in
10 C
0,Ol
dependence normalised
k”‘Sm_Eu
-
k,Sm
-
k“‘Sm-Sm
0,1 Temperature-‘/
Fig. 2. Temperature ‘Gs,* state of Sm3’
v
Km’
of the intrinsic decay rate k. (a), cross-relaxation rate kCR(b), and energy-transfer to the values k,, = 58.4 s-r, kCR= 832 ss’, and kET = 5.5 ss’ at 10 K.
rate kFT (c) of the
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71 (1997) 313-319
consistent with the relaxation mechanism being due to the sum of magnetic-dipole-allowed electronic transitions and electric-dipole-allowed vibronic transitions. Below 100 K the dependence of k0 on temperature is well described using the coth law for vibronic transitions [13, 141, k,(T) = ko(O)CpiCoth i
~
(2) B
(
)
with the sum running over all enabling modes of the lattice, and the amount of their contribution is determined by pi. As the temperature is increased, additional radiative and non-radiative processes involving the thermally populated (4G5j2)r7 level contribute to the intrinsic decay rate. The temperature dependence of the cross-relaxation rate of Sm3+ acceptor ions is slightly stronger but again entirely consistent with an electric dipole vibronic-electric dipole vibronic (EDV-EDV) cross-relaxation mechanism. The stronger temperature dependence of kCR is due to this quantity being proportional to the product of two vibronic mechanisms involving v6 and v4 as well as v3 and a minimal contribution of magnetic-dipole processes. The most-probable phonon-assisted mechanisms for cross relaxation having the smallest energy mismatch between the donor emission and the acceptor absorption transitions are [S] (4Gs,z)T-s + (6H~,z)L --) PFI
1,2Ws
+
(6Fs,2P-s, (34
(4G5i2)r8
+ (%z)b
+ Ah
+
m
1/2r6
+ (6Fs,2)r7g (3b)
(4G5,2)rS
+ ?Hs,2)L + @I
(4G5,2P-8
+
+
Av2
---) (6F5,2)r7
(3c)
l,2w-8,
PH5,2P-7
--) PFs,2&3
+
?h
l,2w-8r
where AvI = 71 cm-’ in Eq. (3b) corresponds to the v6 normal mode of the [SmC16]+ entity, and Av2 = 32 cm-’ in Eq. (3~) may be bridged by the creation of a lattice-phonon mode. The pairs of donor and acceptor transitions in Eqs. (3a) and (3d) are almost resonant within the uncertainty in the positions of the ‘jF, 1,2 crystal-field levels.
0
5
IO
I5
20
25
Time / 10m3s Fig. 3. Temperature dependence of luminescence the 4Gs,z state of Sm3+ in CszNaSmo.01Eu0.99C16.
decay
from
Fig. 3 shows luminescence decay curves from the 4G 5,2 State Of sm3+ in CS2NaSIIIo.olEUo.99C16 at various temperatures. Note that the main contribution to the temperature dependence is due to the energy transfer from Sm3+ donor ions to Eu3+ acceptors. The temperature dependence of the energy-transfer rate kETis shown as curve (c) in Fig. 2. The rapid increase of kET above 80 K indicates that two different mechanisms are involved. At low temperature the most-probable mechanism for energy transfer from Sm3+ donor ions to Eu3+ acceptors in the crystals Cs2NaSm,Eu,Y, _X_,C16 involves the EDV transitions Sm3+:(4G5,2)Ts + Eu3+ :(7F0)L’I + Sm3+ :(6Hs,Jrs
+ Eu3+ :(5Do)T1 + AV,ib,
(4)
where the energy mismatch AV,i, = 395 cm-’ can be bridged by coupling to two odd-parity
T. Lubacher
vibrational modes of the [LnC1J3- ions. This energy-transfer mechanism becomes more efficient as the tem~rature is increased due to the phonon with [exp(hv/kaT) - l]-‘, density increasing where hv is the phonon energy and is again consistent with a squared coth law. At temperatures above 80 K the resonant energy-transfer pathway Sm” ’ : (4G512)r7 + Eu3 + : (7FI)lY4+ Sm” )-:(6H7j2)r7, Ts + Eu3+ :(‘Da)rr
317
et al. j Journal of Luminescence 71 (1997) 313.--319
(5)
becomes important where both transitions are of magnetic-dipole-allowed electronic origin.
overlap integral in Eq. (6) gives
2 d&y f AE,,+ -7r4(E,j’d- E,,,)2 + (A.&j + AE,,,)2.
The temperature dependence of the resonant energy-transfer process of Eq. (5) is introduced by the Boltzmann factors of Eq. (7) and the normalised line shape functions of Eq. (8) which depend on the position and width of the donor emission and acceptor absorption lines. The homogeneous width of a transition line is given by the sum of homogeneous widths of the initial and final energy levels which may be written as Cl73 AE(T) = AEM”“’+ AEDi’(T) + AERaman( T),
5. Discussion In our shell model, we assume Fiirster-Dexter multipole-multipole interaction [15,16] between statistically distributed donor and acceptor ions where the rate of resonant energy transfer from a donor D to an acceptor A may be written as
(8)
(9)
where AEMuitiis due to multiphonon emission processes being essentially temperature-independent. The second contribution to the transition line width, AED”, results from the absorption or emission of a single phonon and is represented by the coth law [14]. The last term in Eq. (9),
XL>
9 wW
(6) The probability of resonant energy transfer involving the donor emission transition d’ -+ d and the acceptor absorption transition a -+ a’ is introduced by the squared matrix eiement of the interaction Hamiltonian I?,,. pds is the thermal population of the n’th state which is go-fold-degenerate and separated by the energy Ed‘ from the lowestlying state of the initial donor multiplet and is calculated as
VI
with a similar notation for the acceptor. Taking Lorentzian line shape functions of half-widths AEdsd and A&,, centred at energies Ed,d and E,,, the
dx
[exp(x) - 11’
’
is due to two-phonon Raman scattering processes where AMdP and AMd contain the second-order matrix elements of the electron-phonon coupling Hamiltonian for initial and final states of the transition cl -+ d’, x = ko/kBT, and wb is the phonon cut-off frequency assuming a Debye distribution. pcrystis the mass density of the crystal and v is the average phonon velocity. Similarly, the change in the position of a spectral line with temperature is given by the difference of the positions of the two relevant energy levels which show approximately a T4 dependence according to [17] &r&(T) = (AMd, - AMd)
3?i 2R2Pcrystvs
XII
x3
expfx) - 1
dx .
(11)
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71 (1997) 313-319
Table 2 Boltzmann factors of thermally populated states involved in the resonant mechanism of energy transfer between Sm3+ donor ions and Eu3+ acceptors as a function of temperature
x lo2 10 30 80 100 140 170 200 240 300
300K 0
5
10
15
4 20
energy gap / cti’ Fig. 4. Overlap integral of Eq. (8) as a function of width and position of donor and acceptor transitions. The arrow indicates the change of the overlap integral with temperature.
To model the temperature dependence of a resonant energy-transfer process, Eqs. (10) and (11) have to be introduced in Eq. (8) for both donor and acceptor transitions. A simpler approach to estimate the increase of the resonant energy-transfer rate with temperature is shown in Fig. 4 where the overlap integral of Eq. (8) has been plotted as a function of both positions and widths of donor and acceptor transition lines. Comparison with absorption and excitation spectra shows an increase of the width of the Sm3+ (6Hs,2)17 + (4Gs,2)Is and the Eu3+(‘F,)I, + (5D1)14 magnetic-dipole transitionsfrom2cm-‘at80Kto5cm-‘at300Kand an increase of the energy mismatch from 6 cm- ’ at lOK[6,12]to15cm-’ at 300 K which is indicated by the arrow in Fig. 4. The effect of the changes in the transition line widths and the energy mismatch on the rate of energy transfer is negligibly small for this particular system. The overlap integral of Eq. (8) is almost independent of temperature in the range 80-300 K.
0 0 0.1 0.3 1.4 2.6 4.0 5.9 8.7
x lo* 0 0 0.5 1.8 7.4 13.2 19.2 26.6 35.6
x 102 0 0 5 x 1om4 6x 1O-3 0.1 0.3 0.8 1.6 3.1
Therefore, the temperature dependence of the energy-transfer rate is introduced only by the thermal populations of the Sm3+(4G5,2)17 and Eu3+(‘F1)r4 states and are given in Table 2. The energy gaps between the Ts and I7 crystalfield levels of the Sm3+ 4G5,2 multiplet as well as between the ‘FO and ‘Fi states of Eu3’ are about 350 cm-‘. Since the initial states of both donor and acceptor ions are separated from the low-lying states by one phonon, thermal equilibrium is reached within the nanosecond time scale. The thermal populations of these states become 0.1% for Sm3 + and 0.5% for Eu3 + at 80 K, increasing to 9% for Sm3+ and 36% for Eu3+ at 300 K. In Eq. (6) the product of these Boltzman factors, p[(4GS,2)r7] xp[(‘F,)I,], determines the contribution of the resonant process to the total energytransfer rate. The increase of the thermal population of both donor and acceptors states is constant in the temperature range 200 K-300 K. We therefore expect a linear increase of kET with ln(l/T) which is in agreement with curve (c) in Fig. 2.
6. Conclusions The temperature decay from the Cs,NaSm,Y 1_,J& for energy migration a rate comparable
dependence of luminescence 4G5,2 state of Sm3+ in (x = 0.05-l) gives no evidence among Sm3+ donor ions with to the cross-relaxation and
T. Luxbacher
et al. /Journal
energy-transfer rates. The assumption of the crossrelaxation processes occurring by electric dipole vibronic-electric dipole vibronic interaction is manifested by the observed temperature dependence of kCR. For energy transfer from Sm3+ donor ions to the ‘D, state of Eu3+ acceptors in Cs2NaSmo.olEu,Yo.99_,C1, (y = 0.05-0.99) two mechanisms are involved. Below 80 K the temperature dependence of the energy-transfer rate is entirely consistent with a phonon-assisted process following a squared coth law, while resonant magnetic dipole-magnetic dipole interaction between the Sm3’ donor and Eu3+ acceptor ions becomes dominant as the temperature is increased. The temperature dependence of the latter process is well understood in terms of the thermal populations of the donor and acceptor states involved.
Acknowledgements We thank The British Council for financial support under their ARC scheme. TL thanks the Bundesministerium fur Wissenschaft, Verkehr und Kunst and the Technische Universitat Graz for a travel grant.
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71 (1997) 313-319
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References [l] [2] [3] [4] [5] [6] [7] [S] [9] [lo] [l l] [12] [13] [14]
[15] [16] [17]
S.O. Vasquez and C.D. Flint, Chem. Phys. Lett. 238 (1995) 378. T. Luxbacher, H.P. Fritzer, R. Sabry-Grant and CD. Flint, Chem. Phys. Lett. 241 (1995) 103. T. Luxbacher, H.P. Fritzer. K. Gatterer and C.D. Flint, .I. Appl. Spectr. 62 (1995) 27. T. Luxbacher, H.P. Fritzer and C.D. Flint, _I. Phys.: Condens. Matter 7 (1995) 9683. T. Luxbacher, H.P. Fritzer and CD. Flint, J. Lumin., accepted. A.K. Banerjee and R.W. Schwartz, Chem. Phys. 58 (1981) 255. D.R. Foster, F.S. Richardson and R.W. Schwartz. J. Chem. Phys. 82 (1985) 618. F.S. Richardson, M.F. Reid, J.J. Dallara and R.D. Smith, J. Chem. Phys. 83 (1985) 3813. P.A. Tanner, Chem. Phys. Lett. 155 (1989) 59. R.W. Schwartz, Mol. Phys. 30 (1975) 81. O.A. Serra and L.C. Thompson, lnorg. Chem. 15 (1976) 504. C.D. Flint and F.L. Stewart-Darling, Mol. Phys. 44 (1981) 61. A.D. Liehr and C.J. Ballhausen, Phys. Rev. 106(1957) 1161. C.J. Ballhausen, Molecular Electronic Structure of Transition Metal Compounds (McGraw-Hill. London, 1979). T. Forster, Ann. Phys. 2 (1948) 55. D.L. Dexter, J. Chem. Phys. 21 (1953) 836. D.E. McCumber and M.D. Sturge, J. Appl. Phys. 34 (1963) 1682.