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Energy transfer between Tm3+ and Er3+ in borate and phosphate glasses
JOURNAL OF NoN-CRYSTALLINE SOLIDS 11 (1973) 261-284 © North-Holland Publishing Co.
E N E R G Y T R A N S F E R B E T W E E N T m 3+ A N D Er 3+ I N BORATE AND PHOSPHATE
GLASSES*
RENATA RE1SFELD and YONA ECKSTEIN Department of Inorganic and Analytical Chemistry, The Hebrew University of Jerusalem, Israel Received 25 April 1972; revised manuscript received 30 August 1972 A study of the energy transfer process between thulium and erbium is presented. From our measurements of fluorescence emissions and decay times the energy transfer efficienciesand probabilities were calculated. In this work the energy transfer which occurs between the upper levels in the UV and VIS regions of the two ions was especially studied. In the Tm-Er system, a mutual migration of energy occurs. The energy transfer from thulium to erbium is a multichannel process in which the energy is transferred from all the metastable levels of thulium to the matching energy levels of erbium. In addition, backtransfer of energy from erbium to thulium occurs by crossrelaxation of respective erbium transitions. The efficiency of energy transfer from thulium to erbium is independent of the levels between which the transfer occurs, but is dependent on the matrix. It is concluded that the energy is transferred via the phonons of the host glass.
1. Introduction The m e c h a n i s m of the energy transfer process in trivalent rare earth ions has been the subject of several recent papers quoted in ref. 1 a n d also of our papers 2, 3) o n energy transfer between g a d o l i n i u m a n d terbium, a n d between e u r o p i u m a n d s a m a r i u m in borate a n d phosphate glasses respectively. The theory of a n o n r a d i a t i v e transfer of excitation energy from a rare earth ion acting as a d o n o r to a n o t h e r rare earth i o n acting as acceptor was developed in a classical p a p e r by Dexter4). Numerical calculation of the efficiency yield as a f u n c t i o n of the acceptor c o n c e n t r a t i o n were performed by I n o k u t i a n d HiroyamaS). The p u r p o s e of this work was to o b t a i n answers to the following questions: (1) Is the energy transfer between t h u l i u m a n d e r b i u m a radiative or a n o n radiative process ? (2) W h a t is the q u a n t u m efficiency of the energy transfer process? (3) W h a t are the transfer rates as a f u n c t i o n of c o n c e n t r a t i o n ? (4) W h a t is the m e c h a n i s m of the transfer? * This work was performed under NBS contract G-103. 261
262
R. REISFELD AND Y. ECKSTEIN
(5) Between which spectral levels does the energy transfer occur? Radiative transfer of energy occurs when an emission transition of one ion overlaps in energy an absorption transition of a second ion 6, 7). In such case, only the emission of the overlapping transition is affected. In contrast, when multipolar energy transfer occurs, all the emissions originating from a given level are equally quenched. The multipolar nonradiative transfer of excitation energy between rare earth ions in crystals can result from the process of resonant or nonresonant interaction. A specific case of resonant energy transfer is the resonant cooperation of ion pairs, first reported by Varsanyi and DiekeS), and later the mechanism and estimation of the probability of the process discussed by Dexter 9). The nonresonant energy transfer is always phonon-assisted, and as was shown by Miyakawa and Dexter 1o) and also by Reisfeld et al. 2, 8), the most important contribution to the probabilities of energy transfer comes from the dynamic part of the electron-phonon interaction. To our knowledge, the only energy transfer in the pair T m - E r reported as of today, was between 4113/2 level of Er and 3H 4 level of Tm12-16). In this paper it will be shown that energy transfer can occur also between the upper levels in the UV and VIS regions of the two ions. The energy transfer efficiencies and probabilities for energy transfer from Tm to Er were calculated using the same formulae as in the energy transfer study between Gd 3 + and Tb a + and between Eu 3+ and Sm 3+ systems 2 , 8 , 1 1 ) . Due to the inhomogeneous broadening of the spectral bands in glasses, the overlap between donor and acceptor levels is higher than it is in single crystals; also, the phonon spectra in glasses are broader. Both these facts should increase the efficiency of energy transfer, hence the importance of the study of energy transfer processes in glass media.
2. Theory Theories have been developed which give formulae for the rate of energy transfer by electric dipole~lipole interaction, electric dipole-quadrupole interaction and the exchange interaction 1, 4). While the two former interactions are electrostatic in origin, the last arises from the requirement of antisymmetry of the electronic wavefunction for the system consisting of both a donor and an acceptor molecule. Multipolar transfer can be responsible for remote interaction (e.g. 20,~) while exchange can be important for interaction involving near neighbors, but common to both is the condition that an overlap between the donor emission spectrum and the acceptor absorption spectrum is essential for the transfer to occur.
ENERGY TRANSFER BETWEEN T m 8+ AND E r 8+
263
The relevant formulae for the present case will now be presented. The probability of energy transfer by dipole-dipole interaction, assuming BornOppenheimer approximation, is
Pda --
4R6n4za g, ~e;
E4
dE,
(1)
where h is Planck's constant, c the velocity of light, R the separation of nuclei of donor and acceptor, e, e¢ the electric field in a vacuum and within the crystal respectively, ~c the dielectric constant, n the index of refraction of the medium, gl and gu the degeneracies of the ground and the excited states of the donor, f d ( E ) the observed shape of the emission band normalized to unity, i.e. ~fd(E)dE= 1. The quantity represented by F~(E) is the acceptor absorption, normalized so that a(E)=QFa(E ) and ~ F a ( E ) d E = I . The quantity a is the absorption cross-section, with Q=Sa(E)dE as the area measured under the absorption band. For the borate glasses used in this work, formula (l) may be written in a simplified form o):
IO'8 (g,)[, Aa(E)dE , A~(E)dE f fd(E)F~(E)dE] Paa= CdC.lal,~ gu HZR6 E2 ' 1.87x
(la) and for the phosphate glasses: 1.48 x 10 ~8 (g,)I~ Pda -CdCa/d/a
Ad(E)dE ~ Aa(E)dE f fd(E)Fa(E) dE] nER6 E2 , (lb)
where cd and c a are the donor and the acceptor concentrations in wt%, la, la are the thicknesses in mm of the glasses containing the rare earth, SAd(E)dE and SAa(E)dE are areas under the donor and acceptor absorption curves on a wavenumber scale, R is the interionic distance in/k, and n is the refractive index (n = 1.45 in borate and 1.48 in phosphate glass). In the factor appearing in eqs. (la) and (lb), the specific gravity of borate glasses was taken as 1.94, and that of phosphate glasses as 2.48 g/cm 3. For explanation of the formulae, see ref. 2. The c's and l's enter into the equations because they are needed in order to calculate the absorption cross-section Q from the experimentally obtained absorption spectra. The la and la, which represent the thickness of glass measured, containing the donor ions and acceptor ions respectively, are not necessarily equal, as the absorption spectra were obtained from two different glasses, containing donor only or acceptor only.
264
R. REISFELD AND Y. ECKSTEIN
The ratio between dipole-dipole and dipole-quadrupole transition probabilities is given in ref. 4 as: Pdq/Pdd = ( a o l R ) 2 ,
where ao is the atomic radius of the rare earth and R is the interionic distance. The quantum yield of energy transfer 17t is given 4) by: Pda'~d tlt - - 1
+
Pda't'd
(2)
where zd is the radiative lifetime of the pure donor level from which energy transfer takes place. The efficiency of energy transfer may also be expressed by: ~/t = 1 - r//~/o ,
(3)
where r/o and r/are the fluorescence yield of the donor alone and of the donor in the presence of an acceptor, respectively. It has been shown 11) that the last two expressions for ~/t are equivalent, provided that only one energy transfer channel is operative. Using eqs. (2) and (3) the rate constant of the energy transfer can be expressed as Pda = -
--
1 .
(4)
Zd In our experiments, energy transfer could be observed at concentrations of the acceptor as low as 0.25 wt% in borate glasses and in phosphate even lower. Those concentrations correspond to the distance of 23.9 A in borate and to a distance smaller than 22 A in phosphate glasses. The fact implies that the energy transfer observed in this work is of dipolar rather than exchange interaction type, the latter decreasing strongly with the interionic distance, which has never been less than about 14 A in the concentrations that we used z). It is true that some donor-acceptor distances would be much less than the average distances given (24 A and 22 A), however statistically the contribution to energy transfer of such donor should be negligible. 3. E x p e r i m e n t a l
3.1. REAGENTS For borate glasses: Riedel sodium tetraborate and Frutarom boric acid (2: 1), 99.9% purity were used. For phosphate glasses: Mallinckrodt sodium dihydrogen phosphate monohydrate, 99.5% purity were used. The sodium borate glass composition was (Na20).3.54(B203). The sodium metho-
ENERGY TRANSFER BETWEEN T m a+ AND E r a+
265
phosphate glass composition was N a 2 0 . P 2 0 ~. The rare earth oxides were Tm203 and Er203 Molycorp, 99.9~ purity. 3.2.
PREPARATION OF GLASSES
(a) Borate glasses: Dry thulium oxide was mixed with borax and boric acid in glass vials. Three series of mixtures were prepared, containing: (I) thulium only, with concentration ranging from 0.001 to 2.0 w t ~ ; (II) thulium at 1.0 wtg/o and erbium varying from 0.25 to 2.0 w t ~ ; (III) erbium only at 1.0 wt~. (b) Phosphate glasses: Dry sodium dihydrogen phosphate monohydrate was mixed with dry thulium oxide as described above for borate glasses. Four series of mixtures were prepared: (I) thulium only with concentration ranging from 0.0005 to 1.65 wtg/oo;(II) thulium at 1.0 Wt~o and erbium varying from 0.25 to 2.0 w t ~ ; (III) erbium only at 0.25 to 1.0 Wt~o; (IV) erbium at 1.0 w t ~ and thulium concentration varying from 0.01 to 1.0 wt~. More experimental details concerning the technique of preparation of the glasses can be found in one of our previous papers, e.g. ref. 17. Absorption spectra of the glasses were recorded on a Cary 14 spectrophotometer in the spectral region 2500/~ to 20000 ,~, using undoped glass as blank. Emission and excitation spectra were taken using a Turner Model 210 spectrofluorimeter or the spectrofluorimeter described earlierlS). In one case, namely in the excitation spectra of erbium, which could be measured only with the spectrofluorimeter built in our laboratory, the correction of excitation spectra was made by calibration with Rhodamine B. The decay times were measured using our spectrofluorimeter, where the light source was replaced by a flash unit with an EGG-FX-6AV flash lamp, having an average pulse duration of 3 Ixsec and energy of 0.4 joule per flash. The photomultiplier was connected directly to a Tektronix Type 502 A dual beam oscilloscope with an attached polaroid camera. All measurements were made at room temperature. 4. Results and discussion 4.1. OSCILLATOR STRENGTHS OF ERBIUM AND THULIUM
Tables 1 and 2 present the oscillator strengths (expressed as f numbers) calculated for Er 3+ and Tm a + respectively from the formula 19): f = 4.31S x 10 -9 I e(a) da, where e is the molar absorptivity at the energy a(cm-1). The oscillator strengths were calculated from the area under the absorption spectrum, using gaussian distribution analysis as described in detail in ref. 20.
266
R. REISFELDAND Y. ECKSTEIN TABLE 1 Oscillator strengths ( f ) of Er +3 in borate and phosphate glasses f ~ 4.318 × 10 9Se(a)da Borate glass
Energy level
4113/2 4Ii112
419/2 4F9/7 453/2 2Hii/2 4F7/s 4F5/2 1
Wave number (cm-i)
Wave length (nm)
6544 6697 7235 10256 12547 15349
1528.0 1493.0 1382.0 975.0 797.0 651.5
Phosphate glass f
( x 106)
4GII12 2K15/2
2G9/2 1 2G7/2 2p3/2
2D5/2 4G9/2 4D5/2 I 4D7/2
Wave length (nm)
6527
1532.0
6688 10256 12500 15209 15325
1495.0 975.0 800.0 657.5 652.5
3.19 1.2 1.2 3.2
1917518390
543.7 )I, 521.5
20470 22172 22573
488.5 451.0 443.0
2.76
24539 26176 26420
407.5 382.0 378.5
1.5
27322
f ( x 108)
2.31 1.09 0.5 2.8
30.61
18331 18921 19230 20470 21857 22148 22547 24539 26246 26420
544.5 528.5 1 520.0 488.5 457.5 451.5 443.5 407.5 381.0 378.5
366
4.7
27322
366.0
4.0
28011 31595 32200 32679 33361
357.0 316.5 310.5 306.0 299.7
1.2
293.5 288.0 281.0 275.0 257.5 255.5
357.7 320.5 317.2 312.7 306.7 301.7 296.7 293.5 287.7 283.0 274.7 256.5
1.44
34050 34722 35590 36363 38834 39138
28030 31207 31527 31986 32597 33147 33682 34071 34752 35345 36403 38989
16.28
1.19
4F3/2
2H9/2
Wave number (cm_i)
1.72
1.45 2.27 15.24
13.75 2.55 1.05 2.94 26.24
3.24
3.03 5.22 15.55
C o m p a r i s o n o f the a b s o r p t i o n spectrum o f a single rare e a r t h ion in a given glass to the s p e c t r u m o f the same glass in which b o t h t h u l i u m a n d erb i u m ions are present, reveals t h a t the a b s o r p t i o n s p e c t r u m o f the latter is a simple s u p e r p o s i t i o n o f the separate a b s o r p t i o n spectra for the two ions. Therefore, m a r k e d effects due to ion pairing, such as shifting o f lines o r
267
ENERGYTRANSFERBETWEENTm s+ AND Er a+ TABLE 2 Oscillator strengths ( f ) of Tm +3 in borate and phosphate glasses f = 4.318 × 10-9~e(cr) de Borate glass Energy level
Wave number (cm -a
Wave length (nm)
Phosphate glass f ( × 106)
Wave number (cm -1)
Wave length (nm)
f ( × 106)
aH4
5847 to 6134
1630.0 to 1710.0
3.94
5714
1750.0
-
aH5
8257
1211.0
2.09
8250
1212.0
1.82
aF4
12626 12903
4.39
12626
792.0
3.00
792.0 ~ 775.0 1
aF3
14619
684.0
4.02
14550
687.2
2.53
aF~
15100
662.0
0.70
15060
664.0
0.22
1G4
21231 21505
471.0 ! 465.0 ~
2.19
21052 21505
475.0 465.0
1.58
IDa
27855 28050
356.5 ) 355.0 ~
4.75
27855
359.0
3.06
aP1
34246 34662 35082 36363
292.0) 288.5 ~ 285.0~ 275.0 ]
33057 34364 35057 36166
302.5 I 291.0 286.0 i 276.5 )
aP2
37950 38387
262.51 260.5 ~
38095
262.5
116 I aPo
4.14
6.13
31.87
14.46
appearance of additional lines, do not exist. The assignments of the transitions in tables 1 and 2 are those given in the paper by Dieke and Crosswhite 21) (see fig. 1). 4.2. FLUORESCENCE AND EXCITATION SPECTRA OF ERBIUM AND ENERGY TRANSFER FROM ERBIUM TO THULIUM
Our previous paper 20) described in detail the emission transitions of thulium in glasses. Here we present the details on erbium (III). The UV and VIS fluorescence of erbium in our glasses was much weaker than that of thulium and only uncorrected spectra were measured. The fluorescence was observable only in phosphate glasses. The highest fluorescence intensity was obtained with 382 nm(4Glt/2) excitation (from a xenon source) and with 255nm(4D5/2, 4D7/2)22) excitation (from a low pressure Mercury source). The two excitations give rise to two different emission spectra. (a) The excitation into a 255 nm absorption band gives rise to a series of emissions which are summarized in table 3. This excitation results in a fast
268
R. REISFELD A N D Y. ECKSTEIN
xlO%ml
l
40
4D
-U
5/2 3p
38 :.56
4G
T
9/2
...............
zD "S
34 -R -Q
32
IS
_
zK
~/z z/z
"
3p, 3p
2 t]6 0
t3/2
Zp -p
31Z
.
30 ZG z/z 2Km/z "G 9/z
28 26
-M L
'D
2
11/2
.
2H "K
.
9/2
22 H
.
4F3/2 51z
-G
.
24 I
IG 4
4F
20
zH -F
18
7/2
E
.
D
~
-B
w
16
45
4F
11/2 3/z
3F
9/2
2
14 41 12
10 .~
9/8
11/2
3H 8 y
5
13/2
6 4 2 0
41m / z Er
Fig. 1.
3H6 Tm
Energy levels o f Er a+ and T m a+ according to Dieke and Crosswhite~l).
269
ENERGY TRANSFER BETWEEN T m 3+ AND Er 3+ TABLE 3
Emission spectrum of Er a+ at various excitation wavelengths Excitation (rim)
255.0a
382.0 b
Assigned transition 2p3/2 ~ 4115/2 2G7/2, 2G9/2, 2K15/2~ 4Gllf2 --~ 4115/2 2P3/~ -~ 4113/2 2p3/2 -+ 4Ill/2 2p3t2 --~ 419/2 2Hll/2-~'4115/2 2Ha/2~4113/2 "2S3/2 ~ 4h5/2
"1115/2
) i ) i
2Hll/2 ~ 4hs/z 2H9/2 -o- 4113/2 ) 453/2 ~ 4115/2 i
Wave length (nm) 310.0-320.0 360.0--370.0 388.0 404.0 473.0 530.0 540.0-550.0 524.0--530.0 548.0--557.0
a Excitation with mercury low pressure source. b Excitation with xenon source. and mostlikely radiationless relaxation to t h e 2p3/2 level (around 315 nm). From the 2p3/2 level the radiative transitions, which terminate on the multiplets of the ground 41 term, were detected. The radiative transitions from 2p3/2 to 4F9/2(15325cm-1), 4S3/2(18331 c m - ' ) and 2Hll/2(19230), as reported by Pollack23), which should occur in wavelengths longer than 620 nm, could not be observed because of the low sensitivity of the instrument in this region. The two last stages of relaxation, 453/2 a n d 2Hli/2 are also radiative, as seen from their fluorescence at 545.5 nm(4S3/2--.4115/2) and 528.5 nm(EHll/2---~4115/2). It should be noted that the band around 530 nm can also arise from the transition 2p3/2--~419/2 (see table 3.). (b) The excitation into the 382 nm(gG,,/2) level produces two bands, the first one peaking at 528.5 nm, which is probably due to the transition 2H 1U2---~4115/2, a n d the second and stronger band peaking at 547 nm, due to 4S3/2---~4I15/2 transition (see also table 3.). The excitation spectrum of erbium (1.0 w t ~ ) at the 547 nm emission, without and in the presence of thulium (1.0 wt~), is presented in fig. 2. It is evident that in the presence of thulium, quenching of erbium peaks around 310-320 nm(Ep3/2), 360-370 nm(2GT/2, 2G9/2, 2K15/2), 450-460 nm(4F3/2, 4F5/2) and 490 nm(¢FT/2) occurs. This change in spectral character of Er a + excitation spectrum, due to the presence of Tm 3 + ions, is observed even at a concentration of thulium as low as 0.01 Wt~o. Similar phenomena have been reported already by Varsanyi 2a) for Er a+ in LaCl3, who attributed the
270
R. R E I S F E L D A N D
|.0
r
~
i
i
i
i
i
r
i
Y. ECKSTEIN
f
i
i
i
t
i
i
i
i
i
i
09 I 0.8 4Gll ~
f%
0.7
////
/ i"',
//
'
Z
,,, >
~
15/2
0.5
l
i !
0.4
u.J n,0.3
/ /
0.2 // 0.1
I
sj /
/
//
f
/
II II
I
/
I
I
I
//
'~
f
//
I
300
550
400
450
,500
X (am} F i g . 2.
Excitation
spectrum dashed
of erbium curve:
at the
erbium
547
nm
in presence
emission.
Solid
curve:
erbium
alone;
of thulium.
absence of certain levels in the excitation spectrum of Er a+ to ion pair mechanism of energy transfer. The mechanism of ion pair resonance energy transfer is presented schematically in fig. 3. Assume two ions A and B. Ion A is initially in state 1, while B is in state 2. The two ions exchange energy nonradiatively by A going to level 3 while B goes to a higher excited state 4. This cross-relaxation will occur if the energy gap between levels 1 and 3 of ion A matches the energy difference from the ground state 2 to the higher lying level 4 of ion B. Peterson and Brindenbaugh 25) concluded from experimental data that the rate of energy transfer by double excitation is comparatively slow. They suggested, therefore, that in order for the probability of such a process to be appreciable, the energy should predominantly leave the long-lived (metastable) state of species A.
ENERGY TRANSFER BETWEEN T m a+ AND Er a+ A
271
B
\
Fig. 3.
Schema of ion pair resonance energy transfer.
In our case, the decrease of the intensities of the spectral bands in the excitation spectrum of erbium in the presence of thulium points to crossrelaxation of Er2P3/2---~4G11/2 and Er4G11/z--*4F7/2 transitions because of the matching of the energy gaps; the energy released in those transitions causes the excitation in the neighboring Tm 3+ ion. Symbolically: Er(2P3/2 ~ 4Gll/2 )
--*Tm(3H6 ~ 3 H 4 ) ,
Er (4G 11/2 --~ 4F7/2)
--.9Tm (3H 6 ~ 3H4).
This cross-relaxation of erbium transitions can be possible since the energy gap between Er2p3/2 and Er4G1u2 is 6000cm -1, while the energy gap between Tm3H6 and Tm 3H4 is 5714 cm-1 ; the energy gap between EraG11/2 and Er4FT/2 is 5950 cm -1. The absence of observable quenching from Er4G~ u2 level on excitation to this level can result from the high absorption coefficient of the 4115/2---~4G1~/2 transition (f=26.24) compared to 2p3/2 (f= 3.24) or 4F3/2 _ 7/2 ( f = 1.05-2.55), and a small ratio of Er (4G11/2---~ ----~4F7/2) ----~Tm(3H6---~3H4) transition compared to internal relaxation in erbium. 4.3. FLUORESCENCE AND CONCENTRATION DEPENDENCE OF THULIUM
The excitation spectra of thulium in borate and phosphate glasses are shown in fig. 4. The excitation spectrum of the 454 nm emission band of thulium consists of bands peaking at 262(3P2), 276(3pD, 287(3po, 116) and 358(1D2)nm. These bands correspond to the transition between the following levels of the thulium ion: 3H6----~ap2, 3H6----~ap1, 3H6----~3Po, lI 6 and 3H6---~lD 2. When thulium and erbium ions are present in the same glass, the spectral character of the excitation spectrum of thulium is unaffected by the presence of erbium; however, the intensities of the corresponding bands are weaker, due to energy transfer from thulium to erbium. Fig. 5 presents the corrected emission spectrum of thulium in borate and phosphate glasses excited t o 3 P 2 level. Table 4 gives the assignments of transitions for the various emission bands and their relative areas20).
272
R. REISFELD AND Y. ECKSTEIN
10
r
,
0.9
0.8
0.7 >I-Z I,d I--
Z w >
3~
0.6 0.5
I.-
0.4
0.3 i 3R 11 ' 113[~!![, ~ f~0' .X6t
I ,
0.2
0.1 25O
1 300
350
4OO
),. ( r i m )
Fig. 4. Excitation spectrum of thulium (1.0 wt ~) at the 454 nm emission. Solid curve: in borate glasses; dashed curve: in phosphate glasses. The intensities of the emission band around 454 nm(1D2---~aH,) as a function of thulium concentration in borate and phosphate glasses for series I and II, as observed by excitation into the 1D 2 (358 rim) level, are plotted in fig. 6. Linear dependence was observed over the concentration range of 0.0005--0.25 w t ~ thulium in phosphate and of 0.0014).1 w t ~ thulium in borate glasses. The concentration ranges of 0.25-1.1 wt~o in phosphate and 0.14).75 w t ~ in borate glasses also show linear dependence, but the slopes are smaller. At higher concentrations a strong quenching effect is observed (fig. 6). Presented also in fig. 6 is the effect of a decrease in intensity for 454 nm fluorescence versus erbium ion concentration (thulium concentration being constant at 1.0 wt~). Similar dependence of fluorescence on Er 3+ concentration was also obtained for the other emissions of thulium. Table 5 sum-
ENERGY
TRANSFER
BETWEEN
T m a+
AND
E r a+
273
merizes the ratio qofil of various thulium fluorescences in the presence of erbium, when the concentrations of both ions are 1.0 Wt~o. r/o represents the fluorescence of pure thulium, and t/ the fluorescence of thulium in the presence of erbium. 4.4. DECAY TIMESOF THULIUM The decay times of the 1D 2 level, observed when the excitation was into this level (385 nm) and the emission was at 454 nm(1DE---~3H4 transition) 1.0 - -
E
r
I
]
~
I
i
t
09 0.8
07 Z uJ
0
~- 04 _..I c~
/h
03
/;,,I
0.2
/i5
0.1
250 Fig. 5.
300
550
400
450
500 550 X Into)
600
650
700
750
Corrected emission spectrum of thulium (1.0 wt ~ ) excited to 3P2 (262 nm). Solid curve: in b o r a t e glasses; dashed curve: in p h o s p h a t e glasses
were simple exponentials with a decay constant of 13.5 p.sec in phosphate and 14.5 ~tsec in borate glasses. In the presence of Er 3 +, 1.0 wt~the decay times measured were 12.4 ~tsec and 10.0 lasec. With our apparatus, we could not measure the decay times for the other emitting levels of thulium, probably because of their very short lifetimes. 4.5. ENERGY TRANSFERRATESFROM THULIUMTO ERBIUM Using eq. (3) we have calculated the efficiency of energy transfer from thulium to erbium using the ratio of the aD2---*aH4 fluorescence (peaking at
274
R. REISFELD AND Y. ECKSTEIN TABLE 4 Emission spectrum of Tm a+ at various excitation wavelengths Emission Excitation (nm)
Assigned transition
Borate 2 (nm)
Phosphate R.A.*
2 (nm)
R.A.*
651.50 752.75 665.50 690.00
1.000 0.114 0.083 0.708
468.0 (1G4)
1G4 1G4 aFz 3Fz
~ 3H4 --+ all5 ~ 3H6 -+ all6
358.0 (1D~)
1D2 1D2 1D2 1G4 1G4 8Fz
-> all4 -~ all5 ~ 3F4 ~ 3H6 --~ 3H4 ~ 8H6
456.00 517.00 665.00 478.00 652.50 665.50
1.000 0.008 0.127 0.118 0.180 0.014
453.00 513.00 663.50 478.00 651.50 665.50
1.000 0.011 0.034 0.063 0.074 0.009
116 116 apo 116
~ all4 ~ all5 --~ 3F4 ) -+ aF4 t
355.00 385.00
0.446 0.125
350.00 383.00
1.000 0.094
465.00
0.155
463.00
0.200
500.00
0.110
498.00
0.060
530.00
0.061
521.50
0.094
ZPo ~ 1G4 ) 116 -+ 1G4 vt
705.00
0.754
701.00
1.000
1D~ -+ ZH6 1D2 --~ alia 1D2 ~ all5 1D2 ~ aF4 1G4 ~ all6 1G4 ~ all4 aF~ ~ all6 aF a -~ aH 6
367.50 456.00 517.00 . 480.00 . . .
0.275 1.000 0.067 . 0.190 . . .
365.00 453.00 513.00
0.133 0.455 0.044
478.00
0.105
aFa ap o -> aF a ) q6 ~ aF2 ~ 116 - +
288.0 (3Po)
. . . .
. . . .
* Relative areas; for each excitation the areas are given relatively to the strongest emission band which is taken as unity.
4 5 4 n m ) o f t h u l i u m i n t h e p r e s e n c e o f e r b i u m w h e n e x c i t e d i n t o 1D 2 level, t o t h e f l u o r e s c e n c e o f t h e t h u l i u m i o n a l o n e . T h e e n e r g y t r a n s f e r efficiencies, r/t, t h u s o b t a i n e d f o r v a r y i n g c o n c e n t r a t i o n s o f e r b i u m a r e p r e s e n t e d i n t a b l e 6 T h e v a l u e s o f P a , w e r e c a l c u l a t e d u s i n g eq. (4), w h e n t h e Zd f o r T m l D 2 level w a s t a k e n as 13.5 ~tsec i n p h o s p h a t e a n d 14.5 ~tsec i n b o r a t e glasses. T h e Pda values are presented in table 6 together with the average donor-acceptor distance calculated from the concentration r e s p e c t i v e glasses.
of the rare earth ions in the
ENERGY
TRANSFER
I
BETWEEN
I
T
,oL
Er a+
AND
I
r
275 ~
2a
/•/ /
0.9
\ 0.8
T m 3+
A// /
/
\
A
\
\ ig
r-o l
\
\
z i,i
0.6
"
~
_
~
o
'
~
j
I \
tsJ
\ laJ
m 0.4 0.3 0.2 0.1 II
0
I
I
l
I
0.5 1.0 CONCENTRATION wt %
I
I
1.5
Fig. 6. Fluorescence dependence of t h u l i u m on concentration at 358 n m excitation; fluorescence a b o u t 454 n m . Solid curves: (1) t h u l i u m in borate glass; dashed curves (2) t h u l i u m in p h o s p h a t e glass; (a) t h u l i u m alone; (b) t h u l i u m (1.0 wt ~ ) in presence o f varying concentrations o f erbium.
The donor acceptor distance R was calculated by use of formula R=
1 (na +nd) ~'
where nd and n a represent number of donor and acceptor ions in cm 3 respectively. For each series nd was kept constant and only the acceptor concentration was changed, therefore the Pda, calculated from our experimental results, can be examined as a function of the acceptor concentration. It should be realized that the donor acceptor distance obtained by the above calculation is related to the "real distance" which is the distance between the excited donor to the neighboring acceptor ion by some correction factor. This correction factor, which we could not calculate at present explicitly, is connected to the donor absorption cross-section and the photon flux of the
276
R. REISFELDAND Y. ECKSTEIN TABLE 5 Ratio of decrease of maximum fluorescence of thulium (r/0) to its fluorescence in the presence of erbium (v/) Emission transition Phosphate zp0---~3H6
Spo, q6-+ZH4
292 nm
350 nm
1D2-+3H 4 1Ga---~3H4 453 nm
Excited level 3P2 (262 nm) 8P0 (288 nm) 1D2 (358 nm) 1G4 (469 nm)
651.5nm
3P0,116---~1G4 701 nm
r/0/v/ 1.8
2.17 2.15
2.45 2.50 2.30
1.8 1.8 2.2 2.5
Borate aPo---~ZH6
3Po, 316---~ZH4
294 nm
355 nm
Excited level aP2 (262 nm) aPo (288 nm) ID2 (358 nm) 1G4 (469 nm)
1D2---~3H4 1G4--~3Ha 3p0,116-~1G4 456 nm
651.5nm
705 nm
v/0/q 1.6
1.6 1.4
1.7 1.6 1.6
1.6 1.6 1.5 1.8
t/0 = intensity of thulium fluorescence in glass containing 1.0 wt ~ of thulium only; rt = intensity of thulium fluorescence in presence of erbium, when the concentration of both ions in a glass is 1.0 wt ~.
light source which determine the n u m b e r of the excited d o n o r ions. I n a d d i t i o n it is quite likely that the distant d o n o r ions rapidly transfer the energy between them till the energy ends up o n a d o n o r i o n which is very near to a n acceptor ion. This d o n o r then transfers the energy to the acceptor. It should be noted that when excitation a n d emission are performed in the same level, only one c h a n n e l of energy is detected in the m e a s u r e m e n t s and, therefore, eqs. (2) a n d (3) are equivalent. 4.6. THE MECHANISM OF TRANSFER FROM THULIUM TO ERBIUM Here we shall discuss the opposite process to that given above, i.e. the energy transfer from t h u l i u m to erbium. As was m e n t i o n e d in the I n t r o d u c t i o n , various works have s h o w n that the presence o f Er a + can e n h a n c e the emission from the a l l , level of t h u l i u m by energy transfer f r o m the *I t 3/2 level of e r b i u m to the above level of thulium.
TABLE 6
23.9 21.1 20.5 19.5
0.25 0.50 0.75 1.00
0.065 0.125 0.265 0.398
Borate glasses Quantum efficiency o f transfer r/ tit ~ 1 - t/o
T m a+, donor, concentration constant 1.0 wt ~ .
R, d o n o r acceptor distance (A)
Concentration o f acceptor Er +a (wt %)
) -- 1
4.8 17.2 26.2 45.5
rd \r/ (sec-1 × 10~)
Paa =
1 (rt 0
22.0 19.6 18.5 17.7
R, d o n o r acceptor distance (/~)
0.195 0.296 0.430 0.556
Phosphate glasses Quantum efficiency o f transfer r/ r/t = 1 - V/o
Efficiency and probability o f energy transfer from T m 1D2* to Er (2G7/2, 2G9/2, 2K15/2)
-
1 (r/0 1) \r/ -Td
12.6 31.1 56.3 101.5
(sec 1 × 10 3)
-
Pda --
7'
-]
R. REISFELD AND Y. ECKSTEIN
278
Zverev et al. 15) observed also inverse transfer from the 3H 4 level of thulium to the 4113/2 level of erbium at room temperature in yttrium-erbium aluminium garnets. They showed that this energy transfer is due to the resonant interaction process and that the observed probabilities indicate a dipoledipole mechanism. In order to decide whether the energy transfer from thulium to erbium in our glasses between the higher, as yet unmeasured, levels of thulium and erbium, occurs by a dipole-dipole or dipole-quadrupole mechanism, we have applied our experimental data to formulae (1) and (4) and plotted t/o/t/versus C 6/3,'~ 1/R 6 and versus C s/3~ 1/R 8 (C being the sum of the donor and acceptor concentrations). It is difficult to conclude definitely from the graphs which is the mechanism of energy transfer, because both of the plots give almost linear dependence of t/o/t/ on concentration. However, the plot of t/o/t/ versus C s/a gives smaller deviation from the linearity. We should mention here that the two works which were published recently 26,87) indicate that a concentration dependence of fluorescent yield may reflect the dependence of the number of particles interacting in a given energy transfer process, and is not associated with the multipolar dependence of interaction. The usual two-particle process would be characterized by a C 2 dependence, and a general Q-particles process would be characterized by a C Q dependence. Inspection of table 5 brings us to the conclusion that energy is transferred already from the highest metastable excited state, from which also fluorescence is observed. This conclusion is drawn from the fact that on excitation into the 3p multiplet, all the intensities resulting from the transitions 3po, 116---~1G4, 3H4, 3H 6 decrease by a comparable amount of fluorescence. Similarly, on excitation into the 1D 2 level, all the transitions originating from this level decrease by the same factor. The same behavior was observed for excitation into the 1G4 level, as seen from table 5. This conclusion does not exclude the possibility of simultaneous energy transfer also from the levels lying under the 3po, 116 multiplet, i.e. 1D2, 1G 4 etc. when excited into the 3p multiplet since, as was mentioned above, energy transfer does occur from these levels. In a previous paper by Reisfeld et al. 14) the following expression was obtained for efficiency of the energy transfer process ~/oa/qd: ~ = r]
(1
+ ~'oPIc)
(
P2o ,
1 + t~2 P 2 1 / /
(5)
where P~c is the energy transfer probability from Tm XD2 to Er (2G7/2, 2G9/2, 2K~s/2 ) and P2D is the energy transfer probability from TmSPo, 'I6 to Er 2D5/2 at a given acceptor concentration; the quantity za= c~/UlO is the measured pure donor lifetime, ~bl the quantum yield of the TmlD2 level
ENERGY TRANSFER BETWEEN
279
T m 3+ AND Er 3+
excited at 1D 2 and ~b2 the q u a n t u m yield o f 3Po, II6---~tD2 transition; Pz 1 is the transition probability f r o m 3po, 1I 6 to 1D2 levels o f thulium and P l o is the radiative transition probability from the 1D 2 level to the ground state (see fig. 7). Tm 3+
Er +3 P2D
z
i P21 II
I I
I
('O~)
I
P~c
~A
~o
I
I
I
I
I I I I
r
%
• 2G 2 z , [ 7/2 G9/2 K 15/2)
A
(4115/2 )
r
I PBA ] I
P,or
C
nr
PBA
I I I
(3H6)
0 DONOR
ACCEPTOR
Fig. 7. Schematic energy level diagram for donor (Tma+)-acceptor (Er a+) system. Vertical wavy lines represent non-radiative transitions, broken lines: transitions via all processes, horizontal wavy lines: energy transfer transitions and vertical straight lines represent radiative transitions. The P-quantities represent the relevant transition probabilities between levels given in the subscrips of P. When subscripts "r" and "nr" appear they refer to radiative and non-radiative transition probabilities respectively, otherwise the transition is via all processes.
If the energy is transferred from the 3po, 116 level when excited into this multiplet, as observed by a decrease o f fluorescence from this level, then we can apply formula (5) in a following manner:
( o, 3Po ,,0 d/3po,l16
:
1 + ~'dP2D = 2.16,
(5a)
where z d is the decay time of 3po, 1I 6 level o f pure d o n o r and 2.16 is the obtained average experimental result for Tm 3 ÷ in phosphate glasses. W h e n the excitation is directly into I D 2 level we shall obtain:
y °2 ~ld ],o2 = 1 + "rdPlc = 2.3,
(5b)
where Zd is the decay time o f 1DE level o f pure d o n o r and 2.3 is also the ex-
R. REISFELDAND Y. ECKSTEIN
280
perimental result for Tm 3 + in phosphate glass (see table 5). The superscript after the parenthesis indicates the level from which the excitation was made and the subscript indicates the level from which emission was measured. If energy transfer occurs simultaneously from 3po, 1I 6 and 1D2 levels of thulium, then by measuring the relative quantum yield of the i D2 fluorescence on excitation to 3Po, 116, namely
by combination of (5a) and (5b) we should obtain dx~3P°'t 16 = (~] 0dx~3P°'q6 (~]dx~ 'D2 r/dj \r/d.,] X \~/d) = 2.16 × 2.3 = 4 . 9 7 , ID2
3Po,116
(5c)
ID2
the number 4.97 being the factor of decrease of intensity of 1D2 fluorescence when excited into 3p multiplet and when the double channel energy transfer occurs. However, the experimental value we obtained was 2.5. By similar fashion, by taking the ~]dx~1D2
/
for emission from ~G4 by excitation into ~D 2 we should obtain (~] 0dx~'D2
(~0dx~102
(y] 0dx~IG4
~)IG 4 = ~xr/d)ID 2 X ~x~d/IG4 = 2.3 X 2.5 = 5.75, whereas by direct measurement we obtained the value of 2.2. As can be seen, these calculated values do not match the obtained experimental results for decrease of 1D 2 or mG4 emission when excited at a higher state. The only possible explanation for such a discrepancy is the occurrence of a backtransfer of excitation energy from Er to Tm to the next lower electronic state. We propose the following explanation for this phenomenon. As can be seen from fig. 1 and tables 1 and 2, the following levels of thulium are close to the levels of erbium: Tm a+ levels 3Po, 116 1D2 1G4
Er a+ levels is close to is close to is close to
2D5/2 2G7/2, 2G9/2, 2K15/2 4F7/2
These pairs of levels can be operative in direct energy transfer between them. On excitation to Tm 3P o, 116 energy is transferred to the 2D5/2 level of
ENERGY TRANSFER BETWEEN T m 3+ AND E r 3+
281
erbium. This Er 3+ level relaxes to the (2G7/2, 2K15/2, 2G9/2, 4Gll/2 ) and the gained energy is backtransferred to the 1D 2 level of Tin. This assumption is justified by the facts that (a) erbium can be excited directly to the 2D5/2 and fluorescence is seen from the (2G7/2, 2K 15/2, 2G9/2, 4G11/2) multiplet (see section on erbium fluorescence); (b) the energy transfer takes place mainly from metastable levels, from which fluorescence is also observed. In a similar fashion, we can explain the small decrease of 1G, fluorescence when excitation is performed at a higher level. For example, on excitation to TmlD2 level, energy is transferred from TmtD2 to Er (2Gv/2, 2G9/2, 2K15/2), relaxation occurs to Er4F7/2, then energy is transferred back to TmlG4. Because of this effect, we did not observe an evident increase in 547 nm (4S3/2---, ---'41t 5/2) fluorescence of erbium in the presence of thulium when the excitatation of erbium was done through the thulium excitation level 1D 2. The energy transfer process from erbium to thulium does not have to be 100~o efficient, because the strong absorptions of Er at 2D5/2, (2G7/2, 2G9/2, 2K15/2, 4Gt 1/2) and (4F7/2, 2H 11/2) can provide other sources of excitation of thulium resonant level. The oscillator strengths of erbium are equal or larger than those of thulium and, hence, their contribution is significant compared with the energy transfer. From the experimental results on Tm 3 + and Tm 3 + + Er a + doped borate glasses, we can conclude that a similar mechanism of the mutual energy transfer process occurs in both glasses. In conclusion, there is a migration of energy between thulium and erbium in two directions. 4.7.
TRANSITION
PROBABILITIES FOR ENERGY TRANSFER FROM T H U L I U M
TO
ERBIUM
The transition probabilities for energy transfer from TmlD2 to Er a+ for given donor and acceptor concentrations may be obtained via eq. (4):
1{,o" 1).
P d a = .Cd ~,r/d - -
The theoretical dipole-dipole transition probabilities for energy transfer from 1D 2 to Er (2G~/2, 2G7/2, 2K 15/2) calculated from Dexter [formulae (la, lb)] are 13.6 sec - t and 27.42 sec - t in phosphate and borate glasses respectively, containing both thulium and erbium at concentrations of 1.0 wt~. By comparison of these results with experimentally-determined energy transfer probabilities, 101.5 x 103 sec -1 in phosphate and 45.5 x 103 sec -a in borate glasses (see table 6), we see that the experimental results are higher by three orders of magnitude than the theoretical results for dipole-dipole and by four to five orders for dipole-quadrupole interactions. Similar results
282
R. REISFELD AND Y. ECKSTEIN
were obtained for the Gd-Tb system2). It was suggested, therefore, that the energy transfer is a phonon-assisted transition 2, 3,11). According to the theory of Miyakawa and Dexter 1°) on phonon-assisted energy transfer in solids, the probability of this process depends on the energy gap, AE, between the levels of the donor and the acceptor in the form: W = W (0) exp ( -
flAE),
fl being a constant determined by the phonon nature of the host lattice and by the strength of electron-lattice coupling, and W(0) the energy transfer probability when zero phonon lines overlap, which is the rate at the temperature of absolute zero. The phonon-assisted energy transfer is governed by factors similar to those of the multipolar relaxation process. Moos 2s) and Weber 29) found that W(0) for the relaxation process is nearly independent of the individual nature of the rare earth ions and depends strongly on the host. This last conclusion has also been verified experimentally for energy transfer processes between pairs of rare earth ions in solids, by Yamada et al. 30). In resonant energy transfer, W= W(0); therefore, if the energy is transferred between various levels which are in resonance, the probability of phonon-assisted energy transfer should be independent of the specific levels involved. These expectations were confirmed by the similar factor of decrease of emission intensities from different levels of thulium in the presence of erbium (see table 5). Phonon-assisted energy transfer will have the effect of increasing the overlap integral of the absorption spectra of donor and acceptor as well as increasing the coupling between them. This follows from the fact that the probability of a phonon-assisted transfer depends on the difference between the matrix element of the dynamic part of the orbit-lattice interaction between the excited states of the acceptor ions and between the ground and excited states of the donor ion, in addition to the matrix elements of the multipole interaction, which are determined by eq. (1). The magnitude of these elements depends strongly on the extend to which the lattice is deformed. The rate of energy transfer is faster in phosphate than in borate glasses by a factor of about 2 (see table 5). In our previous paper2°), we found that the absorption and emission half-band widths of rare earths are larger in phosphate than in borate glasses. This was attributed to the fact that the cavity in which the rare earth ion can be situated is larger in phosphate glasses, thus permitting a larger variety of sites with slightly different crystal field parameters to exist, producing inhomogeneous broadening. From this we concluded that the large half-width in the emission spectrum of rare earth ions in glass is produced by inhomogeneous broadening rather than by
ENERGY TRANSFER BETWEEN T m 8+ AND E r 8+
283
crystal field-splitting (the glass host crystal field is stronger in borate than in phosphate glasses). The higher inhomogeneous broadening of the electronic levels of the rare earths, as a consequence of the stronger possibility of lattice deformation in phosphate than in borate glasses, in addition to broadening of the host vibrational bands, will increase the overlap integral of the absorption spectra of both donor and acceptor and will increase coupling between them. As a result, the probability of energy transfer from thulium to erbium should be higher in phosphate than in borate glasses, which was confirmed by our experimental results.
5. Conclusions (1) In the T m - E r system, a mutual migration of excitation energy occurs. The energy transfer from thulium to erbium is a multichannel process in which the energy is transferred from all the metastable levels of thulium to the matching energy levels of erbium. In addition, backtransfer of energy from erbium to thulium occurs by cross-relaxation of respective erbium transitions. (2) The efficiency of energy transfer from the 1D 2 level of erbium ranges between 0.14-0.60 in phosphate and 0.065-0.40 in borate glasses, for concentrations of 1.0 Wt~o thulium and 0.25-1.0 Wt~o erbium. (3) Energy transfer rates from the ~D 2 level of thulium to the respective level of erbium lie between 12.6 x 10 3 - 101.5 x 1 0 3 s e c - 1 for phosphate and between 4.8 x 103-45.5 x 10 3 sec -1 for borate glasses, for the ranges of concentration given in 2. (4) The efficiency of energy transfer from thulium to erbium is independent of the levels between which the transfer occurs, but is dependent on the matrix. Hence, it is concluded that the energy is transferred via the phonons of the host glass.
Acknowledgements The authors are grateful to Dr. B. Barnett for many fruitful discussions and to Dr. R. A. Velapoldi for his assistance in the measurements of corrected emission spectra.
References 1) E. Nakazawa and S. Shionoya, J. Chem. Phys. 47 (1967) 3211. 2) R. Reisfeld, E. Greenberg, R. Velapoldi and B. Barnett, J. Chem. Phys. 25 (1971) 1698. 3) R. Reisfeld and L. Boehm, J. Solid State Chem. 4 (1972) 417. 4) D. L. Dexter, J. Chem. Phys. 21 (1953) 836. 5) M. Inokuti and F. Hiroyama, J. Chem. Phys. 43 (1965) 1978.
284 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30)
R. REISFELDAND Y. ECKSTEIN L. G. Van Uitert, E. F. Dearborn and J. J. Rubin, J. Chem. Phys. 45 (1966) 1578. A. Y. Cabazas and L. G. DeShazer, Appl. Phys. Letters 4 (1964) 37. F. Varsanyi and G. 14. Dieke, Phys. Rev. Letters 7 (1961) 442. D. L. Dexter, Phys. Rev. 126 (1962) 1962. T. Miyakawa and D. L. Dexter, Phys. Rev. B1 (1970) 2961. R. Reisfeld, L. Boehm and B. Barnett, unpublished. L. G. Van Uitert and L. F. Johnson, J. Chem. Phys. 44 (1966) 3514. L. F. Johnson, J. E. Gausic and L. G. Van Uitert, Appl. Phys. Letters 7 (1965) 127. L. F. Johnson, L. G. Van Uitert, J. J. Rubin and R. A. Thomas, Phys. Rev. 133 (1964) A494. G. M. Zverev, G. Ya. Kolodnyi and A. M. Onishchenko, Soviet Phys.-JETP 30 (1970) 435. B. H. Softer and R. H. Hoskins, Appl. Phys. Letters 6 (1965) 200. R. Reisfeld and E. Greenberg, Anal. Chim. Acta 47 (1969) 155. R. Reisfeld, A. Honigbaum, G. Michaeli, C. Harel and M. Ish-Shalom, Israel J.Chem. 7 (1969) 613. W. T. Carnall, P. R. Fields and K. Rajnak, J. Chem. Phys. 49 (1968) 4412. R. Reisfeld and Y. Eckstein, J. Solid State Chem. 5 (1972) 174. G. H. Dieke and H. M. Crosswhite, Appl. Opt. 2 (1963) 675. M. J. Weber, Phys. Rev. 156 (1967) 231. S. A. Pollack, J. Chem. Phys. 38 (1963) 252. F. Varsanyi, in Quantum Electronics, Eds. P. Grivet and N. Bloembergen (Columbia Univ. Press, New York, 1964) p. 787. G. E. Peterson and P. M. Brindenbaugh, J. Opt. Soc. Am. 53 (1963) 1129. W. J. C. Grant, Phys. Rev. B4 (1971) 648. F. K. Fong and D. Y. Diestler, private communication. M. W. Moos, J. Luminescence 1,2 (1970) 406. M. J. Weber, Phys Rev. 157 (1967) 262; Phys Rev. 171 (1968) 283. N. Yamada, S. Shionoya and T. Kushida, J. Phys. Soc. Japan 30 (1971) 1507.
E N E R G Y T R A N S F E R B E T W E E N T m 3+ A N D Er 3+ I N BORATE AND PHOSPHATE
GLASSES*
RENATA RE1SFELD and YONA ECKSTEIN Department of Inorganic and Analytical Chemistry, The Hebrew University of Jerusalem, Israel Received 25 April 1972; revised manuscript received 30 August 1972 A study of the energy transfer process between thulium and erbium is presented. From our measurements of fluorescence emissions and decay times the energy transfer efficienciesand probabilities were calculated. In this work the energy transfer which occurs between the upper levels in the UV and VIS regions of the two ions was especially studied. In the Tm-Er system, a mutual migration of energy occurs. The energy transfer from thulium to erbium is a multichannel process in which the energy is transferred from all the metastable levels of thulium to the matching energy levels of erbium. In addition, backtransfer of energy from erbium to thulium occurs by crossrelaxation of respective erbium transitions. The efficiency of energy transfer from thulium to erbium is independent of the levels between which the transfer occurs, but is dependent on the matrix. It is concluded that the energy is transferred via the phonons of the host glass.
1. Introduction The m e c h a n i s m of the energy transfer process in trivalent rare earth ions has been the subject of several recent papers quoted in ref. 1 a n d also of our papers 2, 3) o n energy transfer between g a d o l i n i u m a n d terbium, a n d between e u r o p i u m a n d s a m a r i u m in borate a n d phosphate glasses respectively. The theory of a n o n r a d i a t i v e transfer of excitation energy from a rare earth ion acting as a d o n o r to a n o t h e r rare earth i o n acting as acceptor was developed in a classical p a p e r by Dexter4). Numerical calculation of the efficiency yield as a f u n c t i o n of the acceptor c o n c e n t r a t i o n were performed by I n o k u t i a n d HiroyamaS). The p u r p o s e of this work was to o b t a i n answers to the following questions: (1) Is the energy transfer between t h u l i u m a n d e r b i u m a radiative or a n o n radiative process ? (2) W h a t is the q u a n t u m efficiency of the energy transfer process? (3) W h a t are the transfer rates as a f u n c t i o n of c o n c e n t r a t i o n ? (4) W h a t is the m e c h a n i s m of the transfer? * This work was performed under NBS contract G-103. 261
262
R. REISFELD AND Y. ECKSTEIN
(5) Between which spectral levels does the energy transfer occur? Radiative transfer of energy occurs when an emission transition of one ion overlaps in energy an absorption transition of a second ion 6, 7). In such case, only the emission of the overlapping transition is affected. In contrast, when multipolar energy transfer occurs, all the emissions originating from a given level are equally quenched. The multipolar nonradiative transfer of excitation energy between rare earth ions in crystals can result from the process of resonant or nonresonant interaction. A specific case of resonant energy transfer is the resonant cooperation of ion pairs, first reported by Varsanyi and DiekeS), and later the mechanism and estimation of the probability of the process discussed by Dexter 9). The nonresonant energy transfer is always phonon-assisted, and as was shown by Miyakawa and Dexter 1o) and also by Reisfeld et al. 2, 8), the most important contribution to the probabilities of energy transfer comes from the dynamic part of the electron-phonon interaction. To our knowledge, the only energy transfer in the pair T m - E r reported as of today, was between 4113/2 level of Er and 3H 4 level of Tm12-16). In this paper it will be shown that energy transfer can occur also between the upper levels in the UV and VIS regions of the two ions. The energy transfer efficiencies and probabilities for energy transfer from Tm to Er were calculated using the same formulae as in the energy transfer study between Gd 3 + and Tb a + and between Eu 3+ and Sm 3+ systems 2 , 8 , 1 1 ) . Due to the inhomogeneous broadening of the spectral bands in glasses, the overlap between donor and acceptor levels is higher than it is in single crystals; also, the phonon spectra in glasses are broader. Both these facts should increase the efficiency of energy transfer, hence the importance of the study of energy transfer processes in glass media.
2. Theory Theories have been developed which give formulae for the rate of energy transfer by electric dipole~lipole interaction, electric dipole-quadrupole interaction and the exchange interaction 1, 4). While the two former interactions are electrostatic in origin, the last arises from the requirement of antisymmetry of the electronic wavefunction for the system consisting of both a donor and an acceptor molecule. Multipolar transfer can be responsible for remote interaction (e.g. 20,~) while exchange can be important for interaction involving near neighbors, but common to both is the condition that an overlap between the donor emission spectrum and the acceptor absorption spectrum is essential for the transfer to occur.
ENERGY TRANSFER BETWEEN T m 8+ AND E r 8+
263
The relevant formulae for the present case will now be presented. The probability of energy transfer by dipole-dipole interaction, assuming BornOppenheimer approximation, is
Pda --
4R6n4za g, ~e;
E4
dE,
(1)
where h is Planck's constant, c the velocity of light, R the separation of nuclei of donor and acceptor, e, e¢ the electric field in a vacuum and within the crystal respectively, ~c the dielectric constant, n the index of refraction of the medium, gl and gu the degeneracies of the ground and the excited states of the donor, f d ( E ) the observed shape of the emission band normalized to unity, i.e. ~fd(E)dE= 1. The quantity represented by F~(E) is the acceptor absorption, normalized so that a(E)=QFa(E ) and ~ F a ( E ) d E = I . The quantity a is the absorption cross-section, with Q=Sa(E)dE as the area measured under the absorption band. For the borate glasses used in this work, formula (l) may be written in a simplified form o):
IO'8 (g,)[, Aa(E)dE , A~(E)dE f fd(E)F~(E)dE] Paa= CdC.lal,~ gu HZR6 E2 ' 1.87x
(la) and for the phosphate glasses: 1.48 x 10 ~8 (g,)I~ Pda -CdCa/d/a
Ad(E)dE ~ Aa(E)dE f fd(E)Fa(E) dE] nER6 E2 , (lb)
where cd and c a are the donor and the acceptor concentrations in wt%, la, la are the thicknesses in mm of the glasses containing the rare earth, SAd(E)dE and SAa(E)dE are areas under the donor and acceptor absorption curves on a wavenumber scale, R is the interionic distance in/k, and n is the refractive index (n = 1.45 in borate and 1.48 in phosphate glass). In the factor appearing in eqs. (la) and (lb), the specific gravity of borate glasses was taken as 1.94, and that of phosphate glasses as 2.48 g/cm 3. For explanation of the formulae, see ref. 2. The c's and l's enter into the equations because they are needed in order to calculate the absorption cross-section Q from the experimentally obtained absorption spectra. The la and la, which represent the thickness of glass measured, containing the donor ions and acceptor ions respectively, are not necessarily equal, as the absorption spectra were obtained from two different glasses, containing donor only or acceptor only.
264
R. REISFELD AND Y. ECKSTEIN
The ratio between dipole-dipole and dipole-quadrupole transition probabilities is given in ref. 4 as: Pdq/Pdd = ( a o l R ) 2 ,
where ao is the atomic radius of the rare earth and R is the interionic distance. The quantum yield of energy transfer 17t is given 4) by: Pda'~d tlt - - 1
+
Pda't'd
(2)
where zd is the radiative lifetime of the pure donor level from which energy transfer takes place. The efficiency of energy transfer may also be expressed by: ~/t = 1 - r//~/o ,
(3)
where r/o and r/are the fluorescence yield of the donor alone and of the donor in the presence of an acceptor, respectively. It has been shown 11) that the last two expressions for ~/t are equivalent, provided that only one energy transfer channel is operative. Using eqs. (2) and (3) the rate constant of the energy transfer can be expressed as Pda = -
--
1 .
(4)
Zd In our experiments, energy transfer could be observed at concentrations of the acceptor as low as 0.25 wt% in borate glasses and in phosphate even lower. Those concentrations correspond to the distance of 23.9 A in borate and to a distance smaller than 22 A in phosphate glasses. The fact implies that the energy transfer observed in this work is of dipolar rather than exchange interaction type, the latter decreasing strongly with the interionic distance, which has never been less than about 14 A in the concentrations that we used z). It is true that some donor-acceptor distances would be much less than the average distances given (24 A and 22 A), however statistically the contribution to energy transfer of such donor should be negligible. 3. E x p e r i m e n t a l
3.1. REAGENTS For borate glasses: Riedel sodium tetraborate and Frutarom boric acid (2: 1), 99.9% purity were used. For phosphate glasses: Mallinckrodt sodium dihydrogen phosphate monohydrate, 99.5% purity were used. The sodium borate glass composition was (Na20).3.54(B203). The sodium metho-
ENERGY TRANSFER BETWEEN T m a+ AND E r a+
265
phosphate glass composition was N a 2 0 . P 2 0 ~. The rare earth oxides were Tm203 and Er203 Molycorp, 99.9~ purity. 3.2.
PREPARATION OF GLASSES
(a) Borate glasses: Dry thulium oxide was mixed with borax and boric acid in glass vials. Three series of mixtures were prepared, containing: (I) thulium only, with concentration ranging from 0.001 to 2.0 w t ~ ; (II) thulium at 1.0 wtg/o and erbium varying from 0.25 to 2.0 w t ~ ; (III) erbium only at 1.0 wt~. (b) Phosphate glasses: Dry sodium dihydrogen phosphate monohydrate was mixed with dry thulium oxide as described above for borate glasses. Four series of mixtures were prepared: (I) thulium only with concentration ranging from 0.0005 to 1.65 wtg/oo;(II) thulium at 1.0 Wt~o and erbium varying from 0.25 to 2.0 w t ~ ; (III) erbium only at 0.25 to 1.0 Wt~o; (IV) erbium at 1.0 w t ~ and thulium concentration varying from 0.01 to 1.0 wt~. More experimental details concerning the technique of preparation of the glasses can be found in one of our previous papers, e.g. ref. 17. Absorption spectra of the glasses were recorded on a Cary 14 spectrophotometer in the spectral region 2500/~ to 20000 ,~, using undoped glass as blank. Emission and excitation spectra were taken using a Turner Model 210 spectrofluorimeter or the spectrofluorimeter described earlierlS). In one case, namely in the excitation spectra of erbium, which could be measured only with the spectrofluorimeter built in our laboratory, the correction of excitation spectra was made by calibration with Rhodamine B. The decay times were measured using our spectrofluorimeter, where the light source was replaced by a flash unit with an EGG-FX-6AV flash lamp, having an average pulse duration of 3 Ixsec and energy of 0.4 joule per flash. The photomultiplier was connected directly to a Tektronix Type 502 A dual beam oscilloscope with an attached polaroid camera. All measurements were made at room temperature. 4. Results and discussion 4.1. OSCILLATOR STRENGTHS OF ERBIUM AND THULIUM
Tables 1 and 2 present the oscillator strengths (expressed as f numbers) calculated for Er 3+ and Tm a + respectively from the formula 19): f = 4.31S x 10 -9 I e(a) da, where e is the molar absorptivity at the energy a(cm-1). The oscillator strengths were calculated from the area under the absorption spectrum, using gaussian distribution analysis as described in detail in ref. 20.
266
R. REISFELDAND Y. ECKSTEIN TABLE 1 Oscillator strengths ( f ) of Er +3 in borate and phosphate glasses f ~ 4.318 × 10 9Se(a)da Borate glass
Energy level
4113/2 4Ii112
419/2 4F9/7 453/2 2Hii/2 4F7/s 4F5/2 1
Wave number (cm-i)
Wave length (nm)
6544 6697 7235 10256 12547 15349
1528.0 1493.0 1382.0 975.0 797.0 651.5
Phosphate glass f
( x 106)
4GII12 2K15/2
2G9/2 1 2G7/2 2p3/2
2D5/2 4G9/2 4D5/2 I 4D7/2
Wave length (nm)
6527
1532.0
6688 10256 12500 15209 15325
1495.0 975.0 800.0 657.5 652.5
3.19 1.2 1.2 3.2
1917518390
543.7 )I, 521.5
20470 22172 22573
488.5 451.0 443.0
2.76
24539 26176 26420
407.5 382.0 378.5
1.5
27322
f ( x 108)
2.31 1.09 0.5 2.8
30.61
18331 18921 19230 20470 21857 22148 22547 24539 26246 26420
544.5 528.5 1 520.0 488.5 457.5 451.5 443.5 407.5 381.0 378.5
366
4.7
27322
366.0
4.0
28011 31595 32200 32679 33361
357.0 316.5 310.5 306.0 299.7
1.2
293.5 288.0 281.0 275.0 257.5 255.5
357.7 320.5 317.2 312.7 306.7 301.7 296.7 293.5 287.7 283.0 274.7 256.5
1.44
34050 34722 35590 36363 38834 39138
28030 31207 31527 31986 32597 33147 33682 34071 34752 35345 36403 38989
16.28
1.19
4F3/2
2H9/2
Wave number (cm_i)
1.72
1.45 2.27 15.24
13.75 2.55 1.05 2.94 26.24
3.24
3.03 5.22 15.55
C o m p a r i s o n o f the a b s o r p t i o n spectrum o f a single rare e a r t h ion in a given glass to the s p e c t r u m o f the same glass in which b o t h t h u l i u m a n d erb i u m ions are present, reveals t h a t the a b s o r p t i o n s p e c t r u m o f the latter is a simple s u p e r p o s i t i o n o f the separate a b s o r p t i o n spectra for the two ions. Therefore, m a r k e d effects due to ion pairing, such as shifting o f lines o r
267
ENERGYTRANSFERBETWEENTm s+ AND Er a+ TABLE 2 Oscillator strengths ( f ) of Tm +3 in borate and phosphate glasses f = 4.318 × 10-9~e(cr) de Borate glass Energy level
Wave number (cm -a
Wave length (nm)
Phosphate glass f ( × 106)
Wave number (cm -1)
Wave length (nm)
f ( × 106)
aH4
5847 to 6134
1630.0 to 1710.0
3.94
5714
1750.0
-
aH5
8257
1211.0
2.09
8250
1212.0
1.82
aF4
12626 12903
4.39
12626
792.0
3.00
792.0 ~ 775.0 1
aF3
14619
684.0
4.02
14550
687.2
2.53
aF~
15100
662.0
0.70
15060
664.0
0.22
1G4
21231 21505
471.0 ! 465.0 ~
2.19
21052 21505
475.0 465.0
1.58
IDa
27855 28050
356.5 ) 355.0 ~
4.75
27855
359.0
3.06
aP1
34246 34662 35082 36363
292.0) 288.5 ~ 285.0~ 275.0 ]
33057 34364 35057 36166
302.5 I 291.0 286.0 i 276.5 )
aP2
37950 38387
262.51 260.5 ~
38095
262.5
116 I aPo
4.14
6.13
31.87
14.46
appearance of additional lines, do not exist. The assignments of the transitions in tables 1 and 2 are those given in the paper by Dieke and Crosswhite 21) (see fig. 1). 4.2. FLUORESCENCE AND EXCITATION SPECTRA OF ERBIUM AND ENERGY TRANSFER FROM ERBIUM TO THULIUM
Our previous paper 20) described in detail the emission transitions of thulium in glasses. Here we present the details on erbium (III). The UV and VIS fluorescence of erbium in our glasses was much weaker than that of thulium and only uncorrected spectra were measured. The fluorescence was observable only in phosphate glasses. The highest fluorescence intensity was obtained with 382 nm(4Glt/2) excitation (from a xenon source) and with 255nm(4D5/2, 4D7/2)22) excitation (from a low pressure Mercury source). The two excitations give rise to two different emission spectra. (a) The excitation into a 255 nm absorption band gives rise to a series of emissions which are summarized in table 3. This excitation results in a fast
268
R. REISFELD A N D Y. ECKSTEIN
xlO%ml
l
40
4D
-U
5/2 3p
38 :.56
4G
T
9/2
...............
zD "S
34 -R -Q
32
IS
_
zK
~/z z/z
"
3p, 3p
2 t]6 0
t3/2
Zp -p
31Z
.
30 ZG z/z 2Km/z "G 9/z
28 26
-M L
'D
2
11/2
.
2H "K
.
9/2
22 H
.
4F3/2 51z
-G
.
24 I
IG 4
4F
20
zH -F
18
7/2
E
.
D
~
-B
w
16
45
4F
11/2 3/z
3F
9/2
2
14 41 12
10 .~
9/8
11/2
3H 8 y
5
13/2
6 4 2 0
41m / z Er
Fig. 1.
3H6 Tm
Energy levels o f Er a+ and T m a+ according to Dieke and Crosswhite~l).
269
ENERGY TRANSFER BETWEEN T m 3+ AND Er 3+ TABLE 3
Emission spectrum of Er a+ at various excitation wavelengths Excitation (rim)
255.0a
382.0 b
Assigned transition 2p3/2 ~ 4115/2 2G7/2, 2G9/2, 2K15/2~ 4Gllf2 --~ 4115/2 2P3/~ -~ 4113/2 2p3/2 -+ 4Ill/2 2p3t2 --~ 419/2 2Hll/2-~'4115/2 2Ha/2~4113/2 "2S3/2 ~ 4h5/2
"1115/2
) i ) i
2Hll/2 ~ 4hs/z 2H9/2 -o- 4113/2 ) 453/2 ~ 4115/2 i
Wave length (nm) 310.0-320.0 360.0--370.0 388.0 404.0 473.0 530.0 540.0-550.0 524.0--530.0 548.0--557.0
a Excitation with mercury low pressure source. b Excitation with xenon source. and mostlikely radiationless relaxation to t h e 2p3/2 level (around 315 nm). From the 2p3/2 level the radiative transitions, which terminate on the multiplets of the ground 41 term, were detected. The radiative transitions from 2p3/2 to 4F9/2(15325cm-1), 4S3/2(18331 c m - ' ) and 2Hll/2(19230), as reported by Pollack23), which should occur in wavelengths longer than 620 nm, could not be observed because of the low sensitivity of the instrument in this region. The two last stages of relaxation, 453/2 a n d 2Hli/2 are also radiative, as seen from their fluorescence at 545.5 nm(4S3/2--.4115/2) and 528.5 nm(EHll/2---~4115/2). It should be noted that the band around 530 nm can also arise from the transition 2p3/2--~419/2 (see table 3.). (b) The excitation into the 382 nm(gG,,/2) level produces two bands, the first one peaking at 528.5 nm, which is probably due to the transition 2H 1U2---~4115/2, a n d the second and stronger band peaking at 547 nm, due to 4S3/2---~4I15/2 transition (see also table 3.). The excitation spectrum of erbium (1.0 w t ~ ) at the 547 nm emission, without and in the presence of thulium (1.0 wt~), is presented in fig. 2. It is evident that in the presence of thulium, quenching of erbium peaks around 310-320 nm(Ep3/2), 360-370 nm(2GT/2, 2G9/2, 2K15/2), 450-460 nm(4F3/2, 4F5/2) and 490 nm(¢FT/2) occurs. This change in spectral character of Er a + excitation spectrum, due to the presence of Tm 3 + ions, is observed even at a concentration of thulium as low as 0.01 Wt~o. Similar phenomena have been reported already by Varsanyi 2a) for Er a+ in LaCl3, who attributed the
270
R. R E I S F E L D A N D
|.0
r
~
i
i
i
i
i
r
i
Y. ECKSTEIN
f
i
i
i
t
i
i
i
i
i
i
09 I 0.8 4Gll ~
f%
0.7
////
/ i"',
//
'
Z
,,, >
~
15/2
0.5
l
i !
0.4
u.J n,0.3
/ /
0.2 // 0.1
I
sj /
/
//
f
/
II II
I
/
I
I
I
//
'~
f
//
I
300
550
400
450
,500
X (am} F i g . 2.
Excitation
spectrum dashed
of erbium curve:
at the
erbium
547
nm
in presence
emission.
Solid
curve:
erbium
alone;
of thulium.
absence of certain levels in the excitation spectrum of Er a+ to ion pair mechanism of energy transfer. The mechanism of ion pair resonance energy transfer is presented schematically in fig. 3. Assume two ions A and B. Ion A is initially in state 1, while B is in state 2. The two ions exchange energy nonradiatively by A going to level 3 while B goes to a higher excited state 4. This cross-relaxation will occur if the energy gap between levels 1 and 3 of ion A matches the energy difference from the ground state 2 to the higher lying level 4 of ion B. Peterson and Brindenbaugh 25) concluded from experimental data that the rate of energy transfer by double excitation is comparatively slow. They suggested, therefore, that in order for the probability of such a process to be appreciable, the energy should predominantly leave the long-lived (metastable) state of species A.
ENERGY TRANSFER BETWEEN T m a+ AND Er a+ A
271
B
\
Fig. 3.
Schema of ion pair resonance energy transfer.
In our case, the decrease of the intensities of the spectral bands in the excitation spectrum of erbium in the presence of thulium points to crossrelaxation of Er2P3/2---~4G11/2 and Er4G11/z--*4F7/2 transitions because of the matching of the energy gaps; the energy released in those transitions causes the excitation in the neighboring Tm 3+ ion. Symbolically: Er(2P3/2 ~ 4Gll/2 )
--*Tm(3H6 ~ 3 H 4 ) ,
Er (4G 11/2 --~ 4F7/2)
--.9Tm (3H 6 ~ 3H4).
This cross-relaxation of erbium transitions can be possible since the energy gap between Er2p3/2 and Er4G1u2 is 6000cm -1, while the energy gap between Tm3H6 and Tm 3H4 is 5714 cm-1 ; the energy gap between EraG11/2 and Er4FT/2 is 5950 cm -1. The absence of observable quenching from Er4G~ u2 level on excitation to this level can result from the high absorption coefficient of the 4115/2---~4G1~/2 transition (f=26.24) compared to 2p3/2 (f= 3.24) or 4F3/2 _ 7/2 ( f = 1.05-2.55), and a small ratio of Er (4G11/2---~ ----~4F7/2) ----~Tm(3H6---~3H4) transition compared to internal relaxation in erbium. 4.3. FLUORESCENCE AND CONCENTRATION DEPENDENCE OF THULIUM
The excitation spectra of thulium in borate and phosphate glasses are shown in fig. 4. The excitation spectrum of the 454 nm emission band of thulium consists of bands peaking at 262(3P2), 276(3pD, 287(3po, 116) and 358(1D2)nm. These bands correspond to the transition between the following levels of the thulium ion: 3H6----~ap2, 3H6----~ap1, 3H6----~3Po, lI 6 and 3H6---~lD 2. When thulium and erbium ions are present in the same glass, the spectral character of the excitation spectrum of thulium is unaffected by the presence of erbium; however, the intensities of the corresponding bands are weaker, due to energy transfer from thulium to erbium. Fig. 5 presents the corrected emission spectrum of thulium in borate and phosphate glasses excited t o 3 P 2 level. Table 4 gives the assignments of transitions for the various emission bands and their relative areas20).
272
R. REISFELD AND Y. ECKSTEIN
10
r
,
0.9
0.8
0.7 >I-Z I,d I--
Z w >
3~
0.6 0.5
I.-
0.4
0.3 i 3R 11 ' 113[~!![, ~ f~0' .X6t
I ,
0.2
0.1 25O
1 300
350
4OO
),. ( r i m )
Fig. 4. Excitation spectrum of thulium (1.0 wt ~) at the 454 nm emission. Solid curve: in borate glasses; dashed curve: in phosphate glasses. The intensities of the emission band around 454 nm(1D2---~aH,) as a function of thulium concentration in borate and phosphate glasses for series I and II, as observed by excitation into the 1D 2 (358 rim) level, are plotted in fig. 6. Linear dependence was observed over the concentration range of 0.0005--0.25 w t ~ thulium in phosphate and of 0.0014).1 w t ~ thulium in borate glasses. The concentration ranges of 0.25-1.1 wt~o in phosphate and 0.14).75 w t ~ in borate glasses also show linear dependence, but the slopes are smaller. At higher concentrations a strong quenching effect is observed (fig. 6). Presented also in fig. 6 is the effect of a decrease in intensity for 454 nm fluorescence versus erbium ion concentration (thulium concentration being constant at 1.0 wt~). Similar dependence of fluorescence on Er 3+ concentration was also obtained for the other emissions of thulium. Table 5 sum-
ENERGY
TRANSFER
BETWEEN
T m a+
AND
E r a+
273
merizes the ratio qofil of various thulium fluorescences in the presence of erbium, when the concentrations of both ions are 1.0 Wt~o. r/o represents the fluorescence of pure thulium, and t/ the fluorescence of thulium in the presence of erbium. 4.4. DECAY TIMESOF THULIUM The decay times of the 1D 2 level, observed when the excitation was into this level (385 nm) and the emission was at 454 nm(1DE---~3H4 transition) 1.0 - -
E
r
I
]
~
I
i
t
09 0.8
07 Z uJ
0
~- 04 _..I c~
/h
03
/;,,I
0.2
/i5
0.1
250 Fig. 5.
300
550
400
450
500 550 X Into)
600
650
700
750
Corrected emission spectrum of thulium (1.0 wt ~ ) excited to 3P2 (262 nm). Solid curve: in b o r a t e glasses; dashed curve: in p h o s p h a t e glasses
were simple exponentials with a decay constant of 13.5 p.sec in phosphate and 14.5 ~tsec in borate glasses. In the presence of Er 3 +, 1.0 wt~the decay times measured were 12.4 ~tsec and 10.0 lasec. With our apparatus, we could not measure the decay times for the other emitting levels of thulium, probably because of their very short lifetimes. 4.5. ENERGY TRANSFERRATESFROM THULIUMTO ERBIUM Using eq. (3) we have calculated the efficiency of energy transfer from thulium to erbium using the ratio of the aD2---*aH4 fluorescence (peaking at
274
R. REISFELD AND Y. ECKSTEIN TABLE 4 Emission spectrum of Tm a+ at various excitation wavelengths Emission Excitation (nm)
Assigned transition
Borate 2 (nm)
Phosphate R.A.*
2 (nm)
R.A.*
651.50 752.75 665.50 690.00
1.000 0.114 0.083 0.708
468.0 (1G4)
1G4 1G4 aFz 3Fz
~ 3H4 --+ all5 ~ 3H6 -+ all6
358.0 (1D~)
1D2 1D2 1D2 1G4 1G4 8Fz
-> all4 -~ all5 ~ 3F4 ~ 3H6 --~ 3H4 ~ 8H6
456.00 517.00 665.00 478.00 652.50 665.50
1.000 0.008 0.127 0.118 0.180 0.014
453.00 513.00 663.50 478.00 651.50 665.50
1.000 0.011 0.034 0.063 0.074 0.009
116 116 apo 116
~ all4 ~ all5 --~ 3F4 ) -+ aF4 t
355.00 385.00
0.446 0.125
350.00 383.00
1.000 0.094
465.00
0.155
463.00
0.200
500.00
0.110
498.00
0.060
530.00
0.061
521.50
0.094
ZPo ~ 1G4 ) 116 -+ 1G4 vt
705.00
0.754
701.00
1.000
1D~ -+ ZH6 1D2 --~ alia 1D2 ~ all5 1D2 ~ aF4 1G4 ~ all6 1G4 ~ all4 aF~ ~ all6 aF a -~ aH 6
367.50 456.00 517.00 . 480.00 . . .
0.275 1.000 0.067 . 0.190 . . .
365.00 453.00 513.00
0.133 0.455 0.044
478.00
0.105
aFa ap o -> aF a ) q6 ~ aF2 ~ 116 - +
288.0 (3Po)
. . . .
. . . .
* Relative areas; for each excitation the areas are given relatively to the strongest emission band which is taken as unity.
4 5 4 n m ) o f t h u l i u m i n t h e p r e s e n c e o f e r b i u m w h e n e x c i t e d i n t o 1D 2 level, t o t h e f l u o r e s c e n c e o f t h e t h u l i u m i o n a l o n e . T h e e n e r g y t r a n s f e r efficiencies, r/t, t h u s o b t a i n e d f o r v a r y i n g c o n c e n t r a t i o n s o f e r b i u m a r e p r e s e n t e d i n t a b l e 6 T h e v a l u e s o f P a , w e r e c a l c u l a t e d u s i n g eq. (4), w h e n t h e Zd f o r T m l D 2 level w a s t a k e n as 13.5 ~tsec i n p h o s p h a t e a n d 14.5 ~tsec i n b o r a t e glasses. T h e Pda values are presented in table 6 together with the average donor-acceptor distance calculated from the concentration r e s p e c t i v e glasses.
of the rare earth ions in the
ENERGY
TRANSFER
I
BETWEEN
I
T
,oL
Er a+
AND
I
r
275 ~
2a
/•/ /
0.9
\ 0.8
T m 3+
A// /
/
\
A
\
\ ig
r-o l
\
\
z i,i
0.6
"
~
_
~
o
'
~
j
I \
tsJ
\ laJ
m 0.4 0.3 0.2 0.1 II
0
I
I
l
I
0.5 1.0 CONCENTRATION wt %
I
I
1.5
Fig. 6. Fluorescence dependence of t h u l i u m on concentration at 358 n m excitation; fluorescence a b o u t 454 n m . Solid curves: (1) t h u l i u m in borate glass; dashed curves (2) t h u l i u m in p h o s p h a t e glass; (a) t h u l i u m alone; (b) t h u l i u m (1.0 wt ~ ) in presence o f varying concentrations o f erbium.
The donor acceptor distance R was calculated by use of formula R=
1 (na +nd) ~'
where nd and n a represent number of donor and acceptor ions in cm 3 respectively. For each series nd was kept constant and only the acceptor concentration was changed, therefore the Pda, calculated from our experimental results, can be examined as a function of the acceptor concentration. It should be realized that the donor acceptor distance obtained by the above calculation is related to the "real distance" which is the distance between the excited donor to the neighboring acceptor ion by some correction factor. This correction factor, which we could not calculate at present explicitly, is connected to the donor absorption cross-section and the photon flux of the
276
R. REISFELDAND Y. ECKSTEIN TABLE 5 Ratio of decrease of maximum fluorescence of thulium (r/0) to its fluorescence in the presence of erbium (v/) Emission transition Phosphate zp0---~3H6
Spo, q6-+ZH4
292 nm
350 nm
1D2-+3H 4 1Ga---~3H4 453 nm
Excited level 3P2 (262 nm) 8P0 (288 nm) 1D2 (358 nm) 1G4 (469 nm)
651.5nm
3P0,116---~1G4 701 nm
r/0/v/ 1.8
2.17 2.15
2.45 2.50 2.30
1.8 1.8 2.2 2.5
Borate aPo---~ZH6
3Po, 316---~ZH4
294 nm
355 nm
Excited level aP2 (262 nm) aPo (288 nm) ID2 (358 nm) 1G4 (469 nm)
1D2---~3H4 1G4--~3Ha 3p0,116-~1G4 456 nm
651.5nm
705 nm
v/0/q 1.6
1.6 1.4
1.7 1.6 1.6
1.6 1.6 1.5 1.8
t/0 = intensity of thulium fluorescence in glass containing 1.0 wt ~ of thulium only; rt = intensity of thulium fluorescence in presence of erbium, when the concentration of both ions in a glass is 1.0 wt ~.
light source which determine the n u m b e r of the excited d o n o r ions. I n a d d i t i o n it is quite likely that the distant d o n o r ions rapidly transfer the energy between them till the energy ends up o n a d o n o r i o n which is very near to a n acceptor ion. This d o n o r then transfers the energy to the acceptor. It should be noted that when excitation a n d emission are performed in the same level, only one c h a n n e l of energy is detected in the m e a s u r e m e n t s and, therefore, eqs. (2) a n d (3) are equivalent. 4.6. THE MECHANISM OF TRANSFER FROM THULIUM TO ERBIUM Here we shall discuss the opposite process to that given above, i.e. the energy transfer from t h u l i u m to erbium. As was m e n t i o n e d in the I n t r o d u c t i o n , various works have s h o w n that the presence o f Er a + can e n h a n c e the emission from the a l l , level of t h u l i u m by energy transfer f r o m the *I t 3/2 level of e r b i u m to the above level of thulium.
TABLE 6
23.9 21.1 20.5 19.5
0.25 0.50 0.75 1.00
0.065 0.125 0.265 0.398
Borate glasses Quantum efficiency o f transfer r/ tit ~ 1 - t/o
T m a+, donor, concentration constant 1.0 wt ~ .
R, d o n o r acceptor distance (A)
Concentration o f acceptor Er +a (wt %)
) -- 1
4.8 17.2 26.2 45.5
rd \r/ (sec-1 × 10~)
Paa =
1 (rt 0
22.0 19.6 18.5 17.7
R, d o n o r acceptor distance (/~)
0.195 0.296 0.430 0.556
Phosphate glasses Quantum efficiency o f transfer r/ r/t = 1 - V/o
Efficiency and probability o f energy transfer from T m 1D2* to Er (2G7/2, 2G9/2, 2K15/2)
-
1 (r/0 1) \r/ -Td
12.6 31.1 56.3 101.5
(sec 1 × 10 3)
-
Pda --
7'
-]
R. REISFELD AND Y. ECKSTEIN
278
Zverev et al. 15) observed also inverse transfer from the 3H 4 level of thulium to the 4113/2 level of erbium at room temperature in yttrium-erbium aluminium garnets. They showed that this energy transfer is due to the resonant interaction process and that the observed probabilities indicate a dipoledipole mechanism. In order to decide whether the energy transfer from thulium to erbium in our glasses between the higher, as yet unmeasured, levels of thulium and erbium, occurs by a dipole-dipole or dipole-quadrupole mechanism, we have applied our experimental data to formulae (1) and (4) and plotted t/o/t/versus C 6/3,'~ 1/R 6 and versus C s/3~ 1/R 8 (C being the sum of the donor and acceptor concentrations). It is difficult to conclude definitely from the graphs which is the mechanism of energy transfer, because both of the plots give almost linear dependence of t/o/t/ on concentration. However, the plot of t/o/t/ versus C s/a gives smaller deviation from the linearity. We should mention here that the two works which were published recently 26,87) indicate that a concentration dependence of fluorescent yield may reflect the dependence of the number of particles interacting in a given energy transfer process, and is not associated with the multipolar dependence of interaction. The usual two-particle process would be characterized by a C 2 dependence, and a general Q-particles process would be characterized by a C Q dependence. Inspection of table 5 brings us to the conclusion that energy is transferred already from the highest metastable excited state, from which also fluorescence is observed. This conclusion is drawn from the fact that on excitation into the 3p multiplet, all the intensities resulting from the transitions 3po, 116---~1G4, 3H4, 3H 6 decrease by a comparable amount of fluorescence. Similarly, on excitation into the 1D 2 level, all the transitions originating from this level decrease by the same factor. The same behavior was observed for excitation into the 1G4 level, as seen from table 5. This conclusion does not exclude the possibility of simultaneous energy transfer also from the levels lying under the 3po, 116 multiplet, i.e. 1D2, 1G 4 etc. when excited into the 3p multiplet since, as was mentioned above, energy transfer does occur from these levels. In a previous paper by Reisfeld et al. 14) the following expression was obtained for efficiency of the energy transfer process ~/oa/qd: ~ = r]
(1
+ ~'oPIc)
(
P2o ,
1 + t~2 P 2 1 / /
(5)
where P~c is the energy transfer probability from Tm XD2 to Er (2G7/2, 2G9/2, 2K~s/2 ) and P2D is the energy transfer probability from TmSPo, 'I6 to Er 2D5/2 at a given acceptor concentration; the quantity za= c~/UlO is the measured pure donor lifetime, ~bl the quantum yield of the TmlD2 level
ENERGY TRANSFER BETWEEN
279
T m 3+ AND Er 3+
excited at 1D 2 and ~b2 the q u a n t u m yield o f 3Po, II6---~tD2 transition; Pz 1 is the transition probability f r o m 3po, 1I 6 to 1D2 levels o f thulium and P l o is the radiative transition probability from the 1D 2 level to the ground state (see fig. 7). Tm 3+
Er +3 P2D
z
i P21 II
I I
I
('O~)
I
P~c
~A
~o
I
I
I
I
I I I I
r
%
• 2G 2 z , [ 7/2 G9/2 K 15/2)
A
(4115/2 )
r
I PBA ] I
P,or
C
nr
PBA
I I I
(3H6)
0 DONOR
ACCEPTOR
Fig. 7. Schematic energy level diagram for donor (Tma+)-acceptor (Er a+) system. Vertical wavy lines represent non-radiative transitions, broken lines: transitions via all processes, horizontal wavy lines: energy transfer transitions and vertical straight lines represent radiative transitions. The P-quantities represent the relevant transition probabilities between levels given in the subscrips of P. When subscripts "r" and "nr" appear they refer to radiative and non-radiative transition probabilities respectively, otherwise the transition is via all processes.
If the energy is transferred from the 3po, 116 level when excited into this multiplet, as observed by a decrease o f fluorescence from this level, then we can apply formula (5) in a following manner:
( o, 3Po ,,0 d/3po,l16
:
1 + ~'dP2D = 2.16,
(5a)
where z d is the decay time of 3po, 1I 6 level o f pure d o n o r and 2.16 is the obtained average experimental result for Tm 3 ÷ in phosphate glasses. W h e n the excitation is directly into I D 2 level we shall obtain:
y °2 ~ld ],o2 = 1 + "rdPlc = 2.3,
(5b)
where Zd is the decay time o f 1DE level o f pure d o n o r and 2.3 is also the ex-
R. REISFELDAND Y. ECKSTEIN
280
perimental result for Tm 3 + in phosphate glass (see table 5). The superscript after the parenthesis indicates the level from which the excitation was made and the subscript indicates the level from which emission was measured. If energy transfer occurs simultaneously from 3po, 1I 6 and 1D2 levels of thulium, then by measuring the relative quantum yield of the i D2 fluorescence on excitation to 3Po, 116, namely
by combination of (5a) and (5b) we should obtain dx~3P°'t 16 = (~] 0dx~3P°'q6 (~]dx~ 'D2 r/dj \r/d.,] X \~/d) = 2.16 × 2.3 = 4 . 9 7 , ID2
3Po,116
(5c)
ID2
the number 4.97 being the factor of decrease of intensity of 1D2 fluorescence when excited into 3p multiplet and when the double channel energy transfer occurs. However, the experimental value we obtained was 2.5. By similar fashion, by taking the ~]dx~1D2
/
for emission from ~G4 by excitation into ~D 2 we should obtain (~] 0dx~'D2
(~0dx~102
(y] 0dx~IG4
~)IG 4 = ~xr/d)ID 2 X ~x~d/IG4 = 2.3 X 2.5 = 5.75, whereas by direct measurement we obtained the value of 2.2. As can be seen, these calculated values do not match the obtained experimental results for decrease of 1D 2 or mG4 emission when excited at a higher state. The only possible explanation for such a discrepancy is the occurrence of a backtransfer of excitation energy from Er to Tm to the next lower electronic state. We propose the following explanation for this phenomenon. As can be seen from fig. 1 and tables 1 and 2, the following levels of thulium are close to the levels of erbium: Tm a+ levels 3Po, 116 1D2 1G4
Er a+ levels is close to is close to is close to
2D5/2 2G7/2, 2G9/2, 2K15/2 4F7/2
These pairs of levels can be operative in direct energy transfer between them. On excitation to Tm 3P o, 116 energy is transferred to the 2D5/2 level of
ENERGY TRANSFER BETWEEN T m 3+ AND E r 3+
281
erbium. This Er 3+ level relaxes to the (2G7/2, 2K15/2, 2G9/2, 4Gll/2 ) and the gained energy is backtransferred to the 1D 2 level of Tin. This assumption is justified by the facts that (a) erbium can be excited directly to the 2D5/2 and fluorescence is seen from the (2G7/2, 2K 15/2, 2G9/2, 4G11/2) multiplet (see section on erbium fluorescence); (b) the energy transfer takes place mainly from metastable levels, from which fluorescence is also observed. In a similar fashion, we can explain the small decrease of 1G, fluorescence when excitation is performed at a higher level. For example, on excitation to TmlD2 level, energy is transferred from TmtD2 to Er (2Gv/2, 2G9/2, 2K15/2), relaxation occurs to Er4F7/2, then energy is transferred back to TmlG4. Because of this effect, we did not observe an evident increase in 547 nm (4S3/2---, ---'41t 5/2) fluorescence of erbium in the presence of thulium when the excitatation of erbium was done through the thulium excitation level 1D 2. The energy transfer process from erbium to thulium does not have to be 100~o efficient, because the strong absorptions of Er at 2D5/2, (2G7/2, 2G9/2, 2K15/2, 4Gt 1/2) and (4F7/2, 2H 11/2) can provide other sources of excitation of thulium resonant level. The oscillator strengths of erbium are equal or larger than those of thulium and, hence, their contribution is significant compared with the energy transfer. From the experimental results on Tm 3 + and Tm 3 + + Er a + doped borate glasses, we can conclude that a similar mechanism of the mutual energy transfer process occurs in both glasses. In conclusion, there is a migration of energy between thulium and erbium in two directions. 4.7.
TRANSITION
PROBABILITIES FOR ENERGY TRANSFER FROM T H U L I U M
TO
ERBIUM
The transition probabilities for energy transfer from TmlD2 to Er a+ for given donor and acceptor concentrations may be obtained via eq. (4):
1{,o" 1).
P d a = .Cd ~,r/d - -
The theoretical dipole-dipole transition probabilities for energy transfer from 1D 2 to Er (2G~/2, 2G7/2, 2K 15/2) calculated from Dexter [formulae (la, lb)] are 13.6 sec - t and 27.42 sec - t in phosphate and borate glasses respectively, containing both thulium and erbium at concentrations of 1.0 wt~. By comparison of these results with experimentally-determined energy transfer probabilities, 101.5 x 103 sec -1 in phosphate and 45.5 x 103 sec -a in borate glasses (see table 6), we see that the experimental results are higher by three orders of magnitude than the theoretical results for dipole-dipole and by four to five orders for dipole-quadrupole interactions. Similar results
282
R. REISFELD AND Y. ECKSTEIN
were obtained for the Gd-Tb system2). It was suggested, therefore, that the energy transfer is a phonon-assisted transition 2, 3,11). According to the theory of Miyakawa and Dexter 1°) on phonon-assisted energy transfer in solids, the probability of this process depends on the energy gap, AE, between the levels of the donor and the acceptor in the form: W = W (0) exp ( -
flAE),
fl being a constant determined by the phonon nature of the host lattice and by the strength of electron-lattice coupling, and W(0) the energy transfer probability when zero phonon lines overlap, which is the rate at the temperature of absolute zero. The phonon-assisted energy transfer is governed by factors similar to those of the multipolar relaxation process. Moos 2s) and Weber 29) found that W(0) for the relaxation process is nearly independent of the individual nature of the rare earth ions and depends strongly on the host. This last conclusion has also been verified experimentally for energy transfer processes between pairs of rare earth ions in solids, by Yamada et al. 30). In resonant energy transfer, W= W(0); therefore, if the energy is transferred between various levels which are in resonance, the probability of phonon-assisted energy transfer should be independent of the specific levels involved. These expectations were confirmed by the similar factor of decrease of emission intensities from different levels of thulium in the presence of erbium (see table 5). Phonon-assisted energy transfer will have the effect of increasing the overlap integral of the absorption spectra of donor and acceptor as well as increasing the coupling between them. This follows from the fact that the probability of a phonon-assisted transfer depends on the difference between the matrix element of the dynamic part of the orbit-lattice interaction between the excited states of the acceptor ions and between the ground and excited states of the donor ion, in addition to the matrix elements of the multipole interaction, which are determined by eq. (1). The magnitude of these elements depends strongly on the extend to which the lattice is deformed. The rate of energy transfer is faster in phosphate than in borate glasses by a factor of about 2 (see table 5). In our previous paper2°), we found that the absorption and emission half-band widths of rare earths are larger in phosphate than in borate glasses. This was attributed to the fact that the cavity in which the rare earth ion can be situated is larger in phosphate glasses, thus permitting a larger variety of sites with slightly different crystal field parameters to exist, producing inhomogeneous broadening. From this we concluded that the large half-width in the emission spectrum of rare earth ions in glass is produced by inhomogeneous broadening rather than by
ENERGY TRANSFER BETWEEN T m 8+ AND E r 8+
283
crystal field-splitting (the glass host crystal field is stronger in borate than in phosphate glasses). The higher inhomogeneous broadening of the electronic levels of the rare earths, as a consequence of the stronger possibility of lattice deformation in phosphate than in borate glasses, in addition to broadening of the host vibrational bands, will increase the overlap integral of the absorption spectra of both donor and acceptor and will increase coupling between them. As a result, the probability of energy transfer from thulium to erbium should be higher in phosphate than in borate glasses, which was confirmed by our experimental results.
5. Conclusions (1) In the T m - E r system, a mutual migration of excitation energy occurs. The energy transfer from thulium to erbium is a multichannel process in which the energy is transferred from all the metastable levels of thulium to the matching energy levels of erbium. In addition, backtransfer of energy from erbium to thulium occurs by cross-relaxation of respective erbium transitions. (2) The efficiency of energy transfer from the 1D 2 level of erbium ranges between 0.14-0.60 in phosphate and 0.065-0.40 in borate glasses, for concentrations of 1.0 Wt~o thulium and 0.25-1.0 Wt~o erbium. (3) Energy transfer rates from the ~D 2 level of thulium to the respective level of erbium lie between 12.6 x 10 3 - 101.5 x 1 0 3 s e c - 1 for phosphate and between 4.8 x 103-45.5 x 10 3 sec -1 for borate glasses, for the ranges of concentration given in 2. (4) The efficiency of energy transfer from thulium to erbium is independent of the levels between which the transfer occurs, but is dependent on the matrix. Hence, it is concluded that the energy is transferred via the phonons of the host glass.
Acknowledgements The authors are grateful to Dr. B. Barnett for many fruitful discussions and to Dr. R. A. Velapoldi for his assistance in the measurements of corrected emission spectra.
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