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Evidence for Er3+⇌Tm3+ energy transfers in cadmium fluoride crystals
Journal of Luminescence 21(1980)153—164 © North-Holland Publishing Company
EVIDENCE FOR Er3~* Tm3~ENERGY TRANSFERS IN CADMIUM FLUORIDE CRYSTALS J.P. JOUART Laboratoire de Recherches Optiques, Faculté des Sciences, Université de Reims, Reims, France Received 10 July 1979
This paper describes the results of an investigation of energy transfers between Er3+ and Tm3+ ions in cadmium fluoride crystals. Four non-radiative transfers which play an important role in the infrared conversion processes are presented. For the first time, we report Er3+ —* Tm3+ —~ Er3+ transfers which explain how the Tm3+ acts as the sensitizer of the red fluorescence of Er3t The study of energy transfer by measurements of the anti-Stokes fluorescence intensity is shown to be a useful method to clarify the excitation mechanisms of rare-earth ions.
1. Introduction The purpose of the present paper is to study the processes of the infrared-tovisible conversion in cadmium fluoride crystals doped with Er3~and Tm3~ions and also to specify the excitation mechanisms of these ions. Of the various rare-earth activated materials, CdF 3~is particularly interest: Erbe easily converted from ing: it is an excellent red quantum counter [1} and it2 can a wide band insulator to an n-type semiconductorby heating in Cd vapour at around 500°C[2]. In this paper, we are principally concerned with the nonconducting form. When both Er3~and Tm3+ ions are present in the same crystal, the relative intensities of fluorescence are strongly influenced by the energy transfers. A detailed study of the intensities of the green, red and infrared emissions under Stokes and anti-Stokes excitation is described.
2. Samples preparation The crystal structure of CdF 2 is of2~ the type. The of fluorine ionscubes. are at When the ionsfluorite are at the centre altemate corners of cubic lattice and the Cd entering thea cadmium fluoride structure, a trivalent rare-earth ion replaces a divalent cadmium ion and charge compensation is necessary to maintain charge neutrality. 153
154
31
J.P. Jouart /Er
Tm3~energy transfers in CdF 2 (1,11)
~Ln
_
-~éIragonoIC4v-
t11O~
~rIgonoI(oxygen)C3v
-
-
-orrhorhombic C2v-
Fig. 1. Different models of centre.
2~sites is of cubic symmetry but charge compensaThe local crystal field at the Cd tion may modify it. Usually, different types of compensation are simultaneously present in the lattice and the resultant optical spectra are complex. Trivalent rare-earth fluorides introduce F— interstitial ions near the rare-earth ions producing centres with tetragonal symmetry (fig. 1). Without a charge compen. sator nearby, the site remains cubic. When the charge compensator is an oxygen ion, replacing one of the eight F nearest neighbours of the rare-earth ion, the local field is trigonal (fig. 1). The introduction of NaF in CdF 2 yields substitutional Na~ions and F vacancies which annihilate the F2~site interstitials. The charge compensator the and the perturbation of the cubic Na~ field occupies is orthorhombic nearest neighbour Cd (fig. 1). The emission of one of these types of centres may be considerably enhanced through appropriate preparation. The samples have been grown in our laboratory by the Bridgman technique. In each case, the concentration of Na~is twice that of the rare.earth ions. ErF 3 is introduced in concentrations of 10—2 and 4 10_2 mol/mol CdF2. The concentra34 (TmF tion of the Tm 3) ranges from 0.1 to 1%. By introducing NaF, a predominance of C2~symmetry centres is observed. A reduction of the intensity and a simplification of the spectra are noticed; the energies of the Stark levels of these orthorhombic centres can be experimentally determined from the absorption and emission spectra at 77 K (fig. 2) [3].
3#
J.P. Jouart / Er
Tm3~energy transfers in CdF 2
3cm~
22
155 4F
10
1
_______________
~
5/2-3/2
G 4
_____________
F7/2 20
18
3F
16
________________
2
3F 3
14 ‘~“f”(’(f”(”
___________________
‘19/2
12
10
4111/2 3H 5
~
13/2
3H
6
4
4
2 3H _______________
3~
6
_______________
Er3~
4115,2
Tm Fig. 2. Energy-level diagrams for Er3~and Tm3~ions with C
2.,, symmetry in the cadmium fluoride crystal lattice (compensation Nat). The widths of the levels correspond to the total Stark splittings.
An investigation of the energy mismatch between 3~and theTm3~ levels (table couples 1).of each ion allows to foresee the energy transfers between Er 3. Experimental methods The experimental apparatus used for the anti-Stokes fluorescence studies is shown in fig. 3. The size of the samples is about S X 5 X 5 mm3. Xenon and tungsten—
3~ Tm3~energy transfers in CdF
156
J.F. Jouart /Er
2
3+ and Tm3+ (the number in parentheses is the energy in cmt Table 1 Energythe transfers above groundbetween state) Er Initial levels
Final levels
4S
Energy mismatch i~E(cmt)
3H 312 (18611)
~I9/2 ~I9/2
(12667) (12667)
4s 4s312 (18601) 312 (18611)
+ + + + +
3H 6
3H 3H6 6 3H 3H 6 6 3H 3H6 3H6
(110)
—~
‘~l~I~ (12565)
+
(110) (110)
~I13/2 ~I13/2
(6624) (6896)
+
—~
~I11/2 (10405) ~l11/2 (10405)
+
~l13/2 ~I13/2
(6896) (6920)
+
~I13/2
(6939)
+
(110) (110)
-.
+
+
4F 4F912 (15456) 4F 912 (15469)
+
912 (15504)
+
3H 6
(0)
3/2 (6624)
+
3H6 3H 6
(110)
-.
~ 5/2
(557)
+
(110)
—~
~I15/2
(584)
+
(110) (110) (110) (110) (110) (110)
~I15/2 ~I1s,2 ~115/2 ~I15/2 ~I15/2 ~I15/2
(557) + (557)+ (557)+ (584) + (557) + (584) +
+
~l13/2
(6624)
~I13/2 ~I13/2 ~I13/2 ~L13/2 ~I13/2 ~I13/2 3H 3H4 3H4 3H 4 3H4 3H 4 3H4 3H 4 4
(6624) + (6633)+ (6633)+ (6633) + (6644) + (6644) +
3H6 3H 6 3H6 3H6 3H 6 6
(5871) (5865) (5865) (5871) (5865) (5871) (5865) (5871)
~I11/2 ~I11/2 ~I11/2 ~ 1/2 ~I11/2 ~‘11/2 ~I11/2 ~‘11/2
+
+ + + + + + + +
(0) (0)
(10405) (10405) (10405) (10405) (10350) (10350) (10350) (10350)
—~ —~
—~ —~
—~
— —~
—~ -. —, -. —~
— —~ -.
~ 3H 3H6 3H 6 3H 6 3H6 3H6 3H 6 6
+
4
4 3H 3H4 4 3H 5 3H 5 3H 3H5 3H 5
(6152)
+
(6152) (5871)
+
(8300) (8310)
+
6
+
6
(8550) (8550)
+10
3H5 3H4
(8550)
+15
(6170)
+
(6152) 3H4 (6179) 3H4 (6181) 3H 4 (6190) 3H4 (6152) 3H 4 (6197) 3H4 4 (6170) 4F (623) + 4F9/2(15654) (623) + 4F912(15654) (590) + 4F 912(15654) (590) + 4F912(15654) (500) + 4F 9/2(15654) (512) + 4F912(15654) (471) + 4F 912(15654) (471) + 912 (15654)
1 +10
—
— —
1
~
2 2
5 —4 +
+
7 0 0
—
1
—
7
+26 +32 +61 +55 +90 +96
halogen lamps are used for the infrared excitation. The infrared wavelengths are selected by interference filters (with bandwidths at half-maximum of about 30—40 nm). The infrared radiations are focussed onto opposite faces of the cube and adjusted until both beams overlap inside the crystal. The fluorescence from this part of the sample is focussed through a mechanical chopper and interference filters (pass band of about 10 nm) onto a photomultiplier or a PbS detector. The modulated signal is then detected by a PAR 121 lock-in amplifier. In the lifetime studies, the infrared excitation is modulated by a mechanical
3~
J.F. Jouart /Er
Tm3~energy transfers in CdF
157
2
~
~
L....J_mechanical chopper S1
XBO 75W xenon lamp
S2
100W tungsten-halogen filament lamp
F1,F2,F3
interfei~ncefilters
_________
F
I
•
_____________
PAR 121 lock—in amplifier and phasemeter
Fig. 3. Experimental apparatus for the anti-Stokes fluorescence studies.
chopper. The phase difference ~ between the excitation and the fluorescent signals gives the lifetime r through the relation: tg 0 = 2irfr where f is the frequency of the excitation signal. 3~and Er3~ absorption and emission shows thatmechanisms the Tm of the antiionsAnalysis presentof sixthe optical transitions which arespectra involved in the Stokes fluorescence (table 2).
Table 2 Optical transitions involved in the mechanisms of anti-Stokes fluorescence Ions
Optical transitions
Er3~ Tm3~ Er3~
~I15/2 ~Il1/2 3H 3H 6 — ~I13/2 5 ~‘15/2
Tm3~
3H6
34
Er
4
~3/2
Measured oscillator strengths
—3H —
4
115/2
Wavelengths (nm)
Interference filters (nm)
14 X108 X10 22.1
940— 980 1165—1225 1435—1540
955 ±24 1213±29 1490 ±35
35X108 -
1600—1660 1700—1750
1642±37 1721 ±32
1.6 X 10—8
8
535— 570
552± 3.5
ss~± 3.5
640± 5.5 Er3~
4F 9/2
—
~
5/2
640— 700 679± 6
3~ Tm3~energy transfers in CdF
/
158
J.P. Jouart Er
2
4. Experimental results and discussion 4.1. Study under 514.5 nm excitation 3~and Tm3~fluorescences on the conThe dependence of the intensities the Er centration of Tm3~ions (but invariantofconcentration of Er3~:10—2 mol/mol CdF 2) is measured at 77 K under 514.5 nm excitation (argon laser). The results are shown in fig. 4. 2H 3~centres do not Afterinexcitation byand 514.5 nmnon photons to the level (Tm absorb this region) rapid radiative decay1112 to the ~S3/2 state, Er3~shows fluorescence from 4S 3/2 to lowdependence lying levels of ~I15/2, ~I13/2, ‘11/2 ~~9/2. bands An analy3~concentration the intensity of theand emission at sis ofpm the (curve Tm 1); 0.83 pm (curve 2); 1.24 pm (curve 3) and 1.7 pm (curve 4) from 0.54 the 4S 3~centres to the 312 level, provides evidence of an energy transfer from the Er
\ X ~ \
:~
/
T~
~75
I
~
/~/
-~
6
/// /
I _Er3~: ~3i2 2-
: ‘~3/2
,,
3_
~)(~—4\~IN
/ /
5-
~
~2
)(~-~~
/
25
‘5~,’~_1~’~ -F
“
6-
i’
7-
“
1512
:‘111~
115,2
4113~~I15/2
~
0.54 urn 0.83urn 124 ~Lrn
i.~0’~im
41 912-—-.
3~3H 8-Trn
0,1
~I13/2
~‘111/2
~
‘
so f
115/2
0,66lLm
0.97urn 1.53urn
3H 4 —.
6
1,86~Lm
0,5 Thuflurn concenFroFion
(rnol 3+ •/.)and Tm3~luminescences on concentration of Tm3+ ions 77 K in CdF of intensities of Er 3~ions is fixed at Fig. 4.at Dependences 10—2 mol/mol CdF 2 for 514.5 nm excitation. The concentration of Er 2.
3~energy transfers in CdF
J.F. Jouart /Er~~ Tm
2
159
3~centres. The transfer is nonradiative as shown by an uniform quenching of the Tm spectrum. Consequently, the population of the 4S 312 state is markedly reduced by 3~-÷Tm3~which involve the probably multipolar interactions the transfers Er (table 1): Er3~:4S
3~:3H 312 -÷~I9/2
Tm
6 3~:3H Tm 6
,
3~:4S Er
312
-+
111/2
,
3H 4
-+
3H -4
5
The transfer probability coefficient isthe deduced from the lifetime measure of the 3~, 4S level. By introducing 0.5% Tm 312 lifetime from 3 ms to 3/s is obtained for the energy decreases transfer coefficient. 0.5 The ms. introduction A value of 10_17 cm of 0.5% Tm3~into 1% Er3~doped samples decreases the intensity of the fluorescences from the 4S 3/2 ~level, about 3-fold inten3~fluorescence due to the 1/2 but ~ ~increases 5/2 transition (fig. 4, the curve 6). sity of the Er This behaviour may be understood through the nonradiative transfer from the 4S 3~centres to the 3H 3~centres. 3/2 of Erof the fluorescence intensity 5 level ofof Tm Thelevel increase the ~ 3/2 ~ 5/2 transition (fig. 4, curve 7) can be explained by assuming that the ~ 1/2 ~I13/2 transition, succeeding to the precedent transfer, fills the ‘13/2 level. When only Tm3+ is present, the fluorescence in the 1.86 pm region (transition 3H 3H 3~)is absent, but occurs and increases with the Tm3+ concentra4 (fig. 4, 6 of Tm 8) as soon as Er3~is added. The sensitization by Er3~of the tion curve 3H 3F1 4S 43~to 3H6 fluorescence is due to the nonradiative the 312 levelfrom of 3H 3~(the Tm3~ion transfers relaxes byfrom multiphon decay Er 5 and 4 levels of 3H 3HTm 3~to 3H 5 3~ toby thethe metastable 4) and from the(table ~ 3/2 1): level of Er 4 level of followingstate multipolar interaction Tm Er3~: ~I13/2 ~ Tm3~: ~ —~
-+
-~
-+
-4
,
Measurements of the lifetime of the ~ 3/2 excited state under 1490 nm excitation (r 12 ms without Tm3~,r <0.1 ms with 0.5% Tm3~)allows one to determine the value of this energy transfer coefficient (1016, 10—15 cm3/s). Such an energy transfer has also been observed by other workers [41 in CaF 2. The7)enhance3~ion in the 1.53 pm region (fig. 4, curve shows mentthis of the fluorescence of Er than the transfers coming from ~S3/2. that transfer is less efficient The red emission of Er3~around 0.66 pm corresponding to the 4F 912 ~is found 5/2 3~under 514.5 nm excitation) transition (there is no visible emission of Tm to be constant by the addition of Tm3~(fig. 4, curve 5). This anomalous behaviour suggests the participation of two different excitation paths for the red emission: the first one is the nonradiative decay from ~S3/2and the second a process which does not imply the ~~3/2 level. This unknown process will be subsequently specify via measurement of the anti-Stokes fluorescence intensity. -+
/
160
3~ Tm3~energy transfers in CdF
JR Jouart Er
2
4.2. Study under 955 nm excitation 3+: There are twobypossible mechanisms for the green fluorescence of Er after excitation the 955excitation nm photons to the ~I11/2state, Er3~ ions are directly excited to 4F 3~:~I11/2 ~I1s/2, Er3~:~I11/2 or by absorption 712 level byofthe an upward additional transfer photon. Er From the 4F 712 4S level, the ions nonradiatively very short time to the fluorescent level 3/2. 3~indecay CdF in a 3~ markedly reduces this green anti-Stokes emission (fig. 5); Erpopulation of the 4S thisTm suggests that2:the state is very muchtransfers lowered between by the 3+. This result confirms the312 existence of energy presence Tm ions, from 4S Er3~and of Tm3~ 312 level. Like under 514.5 nm excitation, the red emission behaviour is different: 4F 3~is added and thethe intenpopulation of the 9/2 state does not decrease when Tm sity of the red anti-Stokes fluorescence is distinguishable by an increasing function up to a certain concentration of Tm3~(at about 0.3%). —~
—~
4.3. Study under 955 and 1213 nm excitations While the green emission is not influenced by the presence of 1.2 pm radiation, the superposition of both excitations 955 and 1213 nm intensifies the red anti-
-j 400 C
C.
77K
-~ -~
300
955 nm excilolion
~ 200 ‘I, C-
559nm La.
100
552nm I
0
0,1
0,2
~-i
.-
0.5 Thulium concenirolion (mol
I ‘/•
Fig. 5. Green emission intensity of Er3~(4%) versus Tm3~concentration in CdF 3~, Tm3~,Na~for infrared excitation (955 nm). 2 : Er
3~ Tm3’ energy transfers in CdF
J.P. Jouart / Er
2
161
4F 3~is present). This Stokes fluorescence from the 912 levelto(but only when additional emission cannot correspond the 1G 3H Tm 34, firstly 4 4 transition of Tm because the ‘G 4 level is not involved n the studied conversions, 3~ion is a quenching centreinfrared-to-visible of the blue fluorescence of secondly because the Er Tm3~[5]. The measurement of the red emission intensity as a function of the Tm3~concentration (fig. (6(a)) shows that the intensity increases up to about a 0.3% concentration of Tm3~.Beyond 0.3%, the red anti-Stokes fluorescence regularly decreases at the same time that the 4F 3~) 3F 3~)transfer begins. The involved 9/2(Erin fig. 7. 2,3(Tm processes are schematically shown The Tm3+ ions which strongly absorb in the 1.2 pm region, are raised from the ground level to the 3H 5 level state by the 3~ions relaxe to the metastable 3H1213 nm excitation. From this level, the Tm 3~ions are directly excited to the ~ 1/2 level by4 by the a multiphonon decay. 955 nm infrared light.The TheEr4F 912 level 3~ is then directly from ~I11/2by the Er3~ (table populated 1): following upward energy transfer Tm Tm3~:3H 3~:~I11/2 4F 4 Er 912 —~
—~
—~
—~
-4
,
-
This transfer is particularly important because it controls the red anti-Stokes
771<
771<
955nm and 1213nm E
so
~
~xcilafions
955nm and 1490nm ExcitaFions
679nm
fb
200~0:2
640
Thulium concenFrofion
~20o~:i:::o,is
~
Thulium concenlration
(mol ‘I.) (rnol %l 3~(4%) versus Tm3~concentration in CdF
Fig. 3~,Na~ 6. (a) Red for emission double infrared intensity excitation of Er (955 and 1213 nm). (b) Red emission intensity 2: of Er3~(1%) versus TmS+ concentration in CdF 3+, Tm3~,Na+ for double infrared excitaTm 2: Er tion (955 and 1490 nm).
162
3~ Tm3~energy transfers in CdF
J.F~Jouart / Er
2
Tm~ 3~)to activator Fig. 7. (Er3~). Schematic representation of energy transfer from sensitizer centre (Tm centre
fluorescence coming from 4F 912 level. We obtain an additional proof of the existence of this process by modulating the excitation instead of the emission. The continuous emission is not detected by the experimental apparatus, so the modulation of the 1213 nm infrared beam allows to eliminate the red anti-Stokes fluorescence coming from the single 955 nm excitation. When only one excitation is present, the fluorescence is negligible therefore this method presents the advantage of an observation with a dark background. In order to examine the occurrence of this energy transfer, we have the 3H measured 3H lifetime and the intensity of the fluorescence corresponding to the 4 6 transition. Unfortunately, no sensitive variation of the lifetime and 3H of the intensity has been detected under simultaneous excitation of ~I11/2and 5 levels. The transfer probability to the spontaneous emission proba3H is therefore negligible with respect 3H bility of 4 level. Because the lifetime of the 4 level is long (10—2 s), the transfer probability is probably less or equal to 1 ~ The probability of this energy transfer is given by C~i,where n is the population of ~ 1/2 level and C the transfer coeffi3~ions, to the absorpcient.probability The population n is proportional to thecoefficient number Nandp of Eris the spectral energy tion Bp (where B is the Einstein density of the xenon lamp at about 1000 nm)and to the lifetime r of the ~I11/2 level; with N = 2.5 X 1020 ions cm3, Bp = S X l0~s~(B = 5 X 1019 cm3/W is obtained from the oscillator strength and p 10—2 ~W s2/cm3 from the technical characteristics of the xenon lamp) and r = 102 s we find n = 1015 ions/cm3. Therefore, the coefficient of this Tm3 Er3~transfer is inferior or equal to 10_is cm3/s. At 77 K, though the energy matching is nearly perfect for the Tm3~ Er3~transfer (see table 1), this latter is nonresonant. The backtransfer is negligible for the following reasons: At 77 K, all the highest Stark levels of the 3H 4 state are not sufficiently popu-+
.
.
-*
-+
—
3”
Tm3~energy transfers in CdF
J.F. Jouart / Er
2
163
lated and so the energy 1). cannot flow back again to the thulium (the energy mismatch is of about 500 cm of both Er3~ Tm3~transfers coming from 4S In consequence 4F 3/2, the 912 level is insufficiently populated. 4F 3HThe measured radiative lifetime of the 912 state is ten times weaker than that of 4 and ~ 1/2 levels. The successive absorption of two photons by a single centre is generally the predominant mechanism for the infrared quai~tumcounters. Here, transfer 3H 3~and Er3~ ionsthe canenergy be used to betweenanthe 4 and ~I11/2excited levels of Tm achieve infrared quantum counter. To our knowledge, the only experiments of infrared quantum counter with energy transfer which have been realized up to now are those of Zalucha et al. [6}, and those of Pouradier and Auzel [7]. Zalucha et al. use the Nd3+ Pr~transfer in LaCl 3 which is based on the multipolar interaction: 3~: 111/2-4 ‘~I 3~~ 3P Nd 9/~ Pr 0 3~ Ho3~transfer in Ho~Y Pouradier and Auzel use the Ho 1_~F3 which is based on the multipolar interaction: 3~:~I~-÷~Is Ho3~:5F 5F Ho 5-+ 3. 3~ Er3~,Nd3~ Pr3~and Ho3~ Ho3~the spins these three Tm are For unchanged (iNStransfers = 0) and the variations of the total angular momentum are inferior or equal to two (iV ~ 2). In this case, Pouradier [8] has shown that the electrostatic dipole—dipole, dipole—quadrupole or quadrupole—dipole and quadrupole— quad rupole interactions have comparable probabilities. —
-*
—
~+
-4
-+
,
-+
-+
-+
4F 912
-
~i3/2___ -
3
Tm3
Er Fig. 8. Mechanism of the sensitization effect ofTm3+ ions on the red fluorescence of Er3+.
3~q’~ Tm3~energy transfers in CdF
J.P. Jouart / Er
164
2
4.4. Study under 955 and 1490 nm excitations Under double excitation (1490 and 955 nm) constant, the intensity of theby redabout emission of 3~ion of which the concentration is kept increases a facthe Er tor of 12 (fig. 6(b)), with the concentration of the Tm3~ions (up to 0.5% Tm3~). We propose a scheme for this two-photon excitation process. A check of the energy levels shows that the mechanism of the sensitization effect of Tm3~ions on Er3~red fluorescence includes two successive nonradiative energy transfers (fig. 8 gives the energy paths). After excitation by 1490 nm photons to the ~I13/2level, the Er3~(4Il 3+(~H 3/2)~÷ Tm 4)energy transfer occurs intensely because of suitable energy matching (table 1). Then, 955previously nm excitation, energy is transferred 3~ion accordingunder to the studiedthe transfer. back to the Er 5. Conclusion Direct evidence for new energy transfers between Er3~and Tm3+ ions has been established by measurement of the anti-Stokes fluorescence intensity. This is a useful method for observation and analysis of nonradiative energy transfers. We have shown that the Tm3+ behaves as a quenching centre of the green fluorescence of Er3+ and up to 0.3%, as the sensitizer of the red fluorescence of Er3t Under 955 nm excitation, the quenching of the green emission is attributed to two Er3~ Tm3~transfers coming from ~~3/2 level. Under 955 and 1213 nm excitations, 4F 3~:3H 3H 3~:~ 1/2 4F 9/2 is essentially populated by the transfer Tm 4 6, Er 9/2. 4F Under 955 and 1490 nm excitations, 9/2 is3~:~I principally populated by 3~:3two H suc3H cessive transfers: the first one is 3~: the 3H transfer3HEr 3~:13/2 ~Iis/2, 4 6, ~ 1/2~~ 4F Tm the other one is the transfer Tm Er sensitizer of the 9/2. 3+4 acts as6,the infrared fluoresLastly, have Er cence (1.86wepm) of shown Tm3t that Thisthe sensitization is due to the three studied energy transfers Er3+ —u~ Tm3~. -+
~4
—~
-4
—*
—4
References Ill L. Esterowitz, A. Schnitzler, J. Noonan and J. Bahler, Appi. Opt. 7 (1968) 2053. [21 J.S. Prener and J.D. Kingsley, J. Chem. Phys. 38 (1963) 667. 131 J.P. Jouart, These d’Etat, Reims (1977). [41 Yu.K. Voron’ko, M.V. Dniitruk, V.V. Osiko and V.T. Udovenchik, Soy. Phys. JETP (1968) 197. 151 F. Auzel, 0. Deutschbein, Z. Naturforsch. 24a (1969) 1562. [6] D.J. Zalucha, J.A. Sell and F.K. Fong, J. Chem. Phys. 60 (1974) 1660. [7] J.F. Pouradier and F. Auzel, J. do Phys. 37 (1976) 421. [81 J.F. Pouradier, These d’Etat, Paris 6 (1977).
27
EVIDENCE FOR Er3~* Tm3~ENERGY TRANSFERS IN CADMIUM FLUORIDE CRYSTALS J.P. JOUART Laboratoire de Recherches Optiques, Faculté des Sciences, Université de Reims, Reims, France Received 10 July 1979
This paper describes the results of an investigation of energy transfers between Er3+ and Tm3+ ions in cadmium fluoride crystals. Four non-radiative transfers which play an important role in the infrared conversion processes are presented. For the first time, we report Er3+ —* Tm3+ —~ Er3+ transfers which explain how the Tm3+ acts as the sensitizer of the red fluorescence of Er3t The study of energy transfer by measurements of the anti-Stokes fluorescence intensity is shown to be a useful method to clarify the excitation mechanisms of rare-earth ions.
1. Introduction The purpose of the present paper is to study the processes of the infrared-tovisible conversion in cadmium fluoride crystals doped with Er3~and Tm3~ions and also to specify the excitation mechanisms of these ions. Of the various rare-earth activated materials, CdF 3~is particularly interest: Erbe easily converted from ing: it is an excellent red quantum counter [1} and it2 can a wide band insulator to an n-type semiconductorby heating in Cd vapour at around 500°C[2]. In this paper, we are principally concerned with the nonconducting form. When both Er3~and Tm3+ ions are present in the same crystal, the relative intensities of fluorescence are strongly influenced by the energy transfers. A detailed study of the intensities of the green, red and infrared emissions under Stokes and anti-Stokes excitation is described.
2. Samples preparation The crystal structure of CdF 2 is of2~ the type. The of fluorine ionscubes. are at When the ionsfluorite are at the centre altemate corners of cubic lattice and the Cd entering thea cadmium fluoride structure, a trivalent rare-earth ion replaces a divalent cadmium ion and charge compensation is necessary to maintain charge neutrality. 153
154
31
J.P. Jouart /Er
Tm3~energy transfers in CdF 2 (1,11)
~Ln
_
-~éIragonoIC4v-
t11O~
~rIgonoI(oxygen)C3v
-
-
-orrhorhombic C2v-
Fig. 1. Different models of centre.
2~sites is of cubic symmetry but charge compensaThe local crystal field at the Cd tion may modify it. Usually, different types of compensation are simultaneously present in the lattice and the resultant optical spectra are complex. Trivalent rare-earth fluorides introduce F— interstitial ions near the rare-earth ions producing centres with tetragonal symmetry (fig. 1). Without a charge compen. sator nearby, the site remains cubic. When the charge compensator is an oxygen ion, replacing one of the eight F nearest neighbours of the rare-earth ion, the local field is trigonal (fig. 1). The introduction of NaF in CdF 2 yields substitutional Na~ions and F vacancies which annihilate the F2~site interstitials. The charge compensator the and the perturbation of the cubic Na~ field occupies is orthorhombic nearest neighbour Cd (fig. 1). The emission of one of these types of centres may be considerably enhanced through appropriate preparation. The samples have been grown in our laboratory by the Bridgman technique. In each case, the concentration of Na~is twice that of the rare.earth ions. ErF 3 is introduced in concentrations of 10—2 and 4 10_2 mol/mol CdF2. The concentra34 (TmF tion of the Tm 3) ranges from 0.1 to 1%. By introducing NaF, a predominance of C2~symmetry centres is observed. A reduction of the intensity and a simplification of the spectra are noticed; the energies of the Stark levels of these orthorhombic centres can be experimentally determined from the absorption and emission spectra at 77 K (fig. 2) [3].
3#
J.P. Jouart / Er
Tm3~energy transfers in CdF 2
3cm~
22
155 4F
10
1
_______________
~
5/2-3/2
G 4
_____________
F7/2 20
18
3F
16
________________
2
3F 3
14 ‘~“f”(’(f”(”
___________________
‘19/2
12
10
4111/2 3H 5
~
13/2
3H
6
4
4
2 3H _______________
3~
6
_______________
Er3~
4115,2
Tm Fig. 2. Energy-level diagrams for Er3~and Tm3~ions with C
2.,, symmetry in the cadmium fluoride crystal lattice (compensation Nat). The widths of the levels correspond to the total Stark splittings.
An investigation of the energy mismatch between 3~and theTm3~ levels (table couples 1).of each ion allows to foresee the energy transfers between Er 3. Experimental methods The experimental apparatus used for the anti-Stokes fluorescence studies is shown in fig. 3. The size of the samples is about S X 5 X 5 mm3. Xenon and tungsten—
3~ Tm3~energy transfers in CdF
156
J.F. Jouart /Er
2
3+ and Tm3+ (the number in parentheses is the energy in cmt Table 1 Energythe transfers above groundbetween state) Er Initial levels
Final levels
4S
Energy mismatch i~E(cmt)
3H 312 (18611)
~I9/2 ~I9/2
(12667) (12667)
4s 4s312 (18601) 312 (18611)
+ + + + +
3H 6
3H 3H6 6 3H 3H 6 6 3H 3H6 3H6
(110)
—~
‘~l~I~ (12565)
+
(110) (110)
~I13/2 ~I13/2
(6624) (6896)
+
—~
~I11/2 (10405) ~l11/2 (10405)
+
~l13/2 ~I13/2
(6896) (6920)
+
~I13/2
(6939)
+
(110) (110)
-.
+
+
4F 4F912 (15456) 4F 912 (15469)
+
912 (15504)
+
3H 6
(0)
3/2 (6624)
+
3H6 3H 6
(110)
-.
~ 5/2
(557)
+
(110)
—~
~I15/2
(584)
+
(110) (110) (110) (110) (110) (110)
~I15/2 ~I1s,2 ~115/2 ~I15/2 ~I15/2 ~I15/2
(557) + (557)+ (557)+ (584) + (557) + (584) +
+
~l13/2
(6624)
~I13/2 ~I13/2 ~I13/2 ~L13/2 ~I13/2 ~I13/2 3H 3H4 3H4 3H 4 3H4 3H 4 3H4 3H 4 4
(6624) + (6633)+ (6633)+ (6633) + (6644) + (6644) +
3H6 3H 6 3H6 3H6 3H 6 6
(5871) (5865) (5865) (5871) (5865) (5871) (5865) (5871)
~I11/2 ~I11/2 ~I11/2 ~ 1/2 ~I11/2 ~‘11/2 ~I11/2 ~‘11/2
+
+ + + + + + + +
(0) (0)
(10405) (10405) (10405) (10405) (10350) (10350) (10350) (10350)
—~ —~
—~ —~
—~
— —~
—~ -. —, -. —~
— —~ -.
~ 3H 3H6 3H 6 3H 6 3H6 3H6 3H 6 6
+
4
4 3H 3H4 4 3H 5 3H 5 3H 3H5 3H 5
(6152)
+
(6152) (5871)
+
(8300) (8310)
+
6
+
6
(8550) (8550)
+10
3H5 3H4
(8550)
+15
(6170)
+
(6152) 3H4 (6179) 3H4 (6181) 3H 4 (6190) 3H4 (6152) 3H 4 (6197) 3H4 4 (6170) 4F (623) + 4F9/2(15654) (623) + 4F912(15654) (590) + 4F 912(15654) (590) + 4F912(15654) (500) + 4F 9/2(15654) (512) + 4F912(15654) (471) + 4F 912(15654) (471) + 912 (15654)
1 +10
—
— —
1
~
2 2
5 —4 +
+
7 0 0
—
1
—
7
+26 +32 +61 +55 +90 +96
halogen lamps are used for the infrared excitation. The infrared wavelengths are selected by interference filters (with bandwidths at half-maximum of about 30—40 nm). The infrared radiations are focussed onto opposite faces of the cube and adjusted until both beams overlap inside the crystal. The fluorescence from this part of the sample is focussed through a mechanical chopper and interference filters (pass band of about 10 nm) onto a photomultiplier or a PbS detector. The modulated signal is then detected by a PAR 121 lock-in amplifier. In the lifetime studies, the infrared excitation is modulated by a mechanical
3~
J.F. Jouart /Er
Tm3~energy transfers in CdF
157
2
~
~
L....J_mechanical chopper S1
XBO 75W xenon lamp
S2
100W tungsten-halogen filament lamp
F1,F2,F3
interfei~ncefilters
_________
F
I
•
_____________
PAR 121 lock—in amplifier and phasemeter
Fig. 3. Experimental apparatus for the anti-Stokes fluorescence studies.
chopper. The phase difference ~ between the excitation and the fluorescent signals gives the lifetime r through the relation: tg 0 = 2irfr where f is the frequency of the excitation signal. 3~and Er3~ absorption and emission shows thatmechanisms the Tm of the antiionsAnalysis presentof sixthe optical transitions which arespectra involved in the Stokes fluorescence (table 2).
Table 2 Optical transitions involved in the mechanisms of anti-Stokes fluorescence Ions
Optical transitions
Er3~ Tm3~ Er3~
~I15/2 ~Il1/2 3H 3H 6 — ~I13/2 5 ~‘15/2
Tm3~
3H6
34
Er
4
~3/2
Measured oscillator strengths
—3H —
4
115/2
Wavelengths (nm)
Interference filters (nm)
14 X108 X10 22.1
940— 980 1165—1225 1435—1540
955 ±24 1213±29 1490 ±35
35X108 -
1600—1660 1700—1750
1642±37 1721 ±32
1.6 X 10—8
8
535— 570
552± 3.5
ss~± 3.5
640± 5.5 Er3~
4F 9/2
—
~
5/2
640— 700 679± 6
3~ Tm3~energy transfers in CdF
/
158
J.P. Jouart Er
2
4. Experimental results and discussion 4.1. Study under 514.5 nm excitation 3~and Tm3~fluorescences on the conThe dependence of the intensities the Er centration of Tm3~ions (but invariantofconcentration of Er3~:10—2 mol/mol CdF 2) is measured at 77 K under 514.5 nm excitation (argon laser). The results are shown in fig. 4. 2H 3~centres do not Afterinexcitation byand 514.5 nmnon photons to the level (Tm absorb this region) rapid radiative decay1112 to the ~S3/2 state, Er3~shows fluorescence from 4S 3/2 to lowdependence lying levels of ~I15/2, ~I13/2, ‘11/2 ~~9/2. bands An analy3~concentration the intensity of theand emission at sis ofpm the (curve Tm 1); 0.83 pm (curve 2); 1.24 pm (curve 3) and 1.7 pm (curve 4) from 0.54 the 4S 3~centres to the 312 level, provides evidence of an energy transfer from the Er
\ X ~ \
:~
/
T~
~75
I
~
/~/
-~
6
/// /
I _Er3~: ~3i2 2-
: ‘~3/2
,,
3_
~)(~—4\~IN
/ /
5-
~
~2
)(~-~~
/
25
‘5~,’~_1~’~ -F
“
6-
i’
7-
“
1512
:‘111~
115,2
4113~~I15/2
~
0.54 urn 0.83urn 124 ~Lrn
i.~0’~im
41 912-—-.
3~3H 8-Trn
0,1
~I13/2
~‘111/2
~
‘
so f
115/2
0,66lLm
0.97urn 1.53urn
3H 4 —.
6
1,86~Lm
0,5 Thuflurn concenFroFion
(rnol 3+ •/.)and Tm3~luminescences on concentration of Tm3+ ions 77 K in CdF of intensities of Er 3~ions is fixed at Fig. 4.at Dependences 10—2 mol/mol CdF 2 for 514.5 nm excitation. The concentration of Er 2.
3~energy transfers in CdF
J.F. Jouart /Er~~ Tm
2
159
3~centres. The transfer is nonradiative as shown by an uniform quenching of the Tm spectrum. Consequently, the population of the 4S 312 state is markedly reduced by 3~-÷Tm3~which involve the probably multipolar interactions the transfers Er (table 1): Er3~:4S
3~:3H 312 -÷~I9/2
Tm
6 3~:3H Tm 6
,
3~:4S Er
312
-+
111/2
,
3H 4
-+
3H -4
5
The transfer probability coefficient isthe deduced from the lifetime measure of the 3~, 4S level. By introducing 0.5% Tm 312 lifetime from 3 ms to 3/s is obtained for the energy decreases transfer coefficient. 0.5 The ms. introduction A value of 10_17 cm of 0.5% Tm3~into 1% Er3~doped samples decreases the intensity of the fluorescences from the 4S 3/2 ~level, about 3-fold inten3~fluorescence due to the 1/2 but ~ ~increases 5/2 transition (fig. 4, the curve 6). sity of the Er This behaviour may be understood through the nonradiative transfer from the 4S 3~centres to the 3H 3~centres. 3/2 of Erof the fluorescence intensity 5 level ofof Tm Thelevel increase the ~ 3/2 ~ 5/2 transition (fig. 4, curve 7) can be explained by assuming that the ~ 1/2 ~I13/2 transition, succeeding to the precedent transfer, fills the ‘13/2 level. When only Tm3+ is present, the fluorescence in the 1.86 pm region (transition 3H 3H 3~)is absent, but occurs and increases with the Tm3+ concentra4 (fig. 4, 6 of Tm 8) as soon as Er3~is added. The sensitization by Er3~of the tion curve 3H 3F1 4S 43~to 3H6 fluorescence is due to the nonradiative the 312 levelfrom of 3H 3~(the Tm3~ion transfers relaxes byfrom multiphon decay Er 5 and 4 levels of 3H 3HTm 3~to 3H 5 3~ toby thethe metastable 4) and from the(table ~ 3/2 1): level of Er 4 level of followingstate multipolar interaction Tm Er3~: ~I13/2 ~ Tm3~: ~ —~
-+
-~
-+
-4
,
Measurements of the lifetime of the ~ 3/2 excited state under 1490 nm excitation (r 12 ms without Tm3~,r <0.1 ms with 0.5% Tm3~)allows one to determine the value of this energy transfer coefficient (1016, 10—15 cm3/s). Such an energy transfer has also been observed by other workers [41 in CaF 2. The7)enhance3~ion in the 1.53 pm region (fig. 4, curve shows mentthis of the fluorescence of Er than the transfers coming from ~S3/2. that transfer is less efficient The red emission of Er3~around 0.66 pm corresponding to the 4F 912 ~is found 5/2 3~under 514.5 nm excitation) transition (there is no visible emission of Tm to be constant by the addition of Tm3~(fig. 4, curve 5). This anomalous behaviour suggests the participation of two different excitation paths for the red emission: the first one is the nonradiative decay from ~S3/2and the second a process which does not imply the ~~3/2 level. This unknown process will be subsequently specify via measurement of the anti-Stokes fluorescence intensity. -+
/
160
3~ Tm3~energy transfers in CdF
JR Jouart Er
2
4.2. Study under 955 nm excitation 3+: There are twobypossible mechanisms for the green fluorescence of Er after excitation the 955excitation nm photons to the ~I11/2state, Er3~ ions are directly excited to 4F 3~:~I11/2 ~I1s/2, Er3~:~I11/2 or by absorption 712 level byofthe an upward additional transfer photon. Er From the 4F 712 4S level, the ions nonradiatively very short time to the fluorescent level 3/2. 3~indecay CdF in a 3~ markedly reduces this green anti-Stokes emission (fig. 5); Erpopulation of the 4S thisTm suggests that2:the state is very muchtransfers lowered between by the 3+. This result confirms the312 existence of energy presence Tm ions, from 4S Er3~and of Tm3~ 312 level. Like under 514.5 nm excitation, the red emission behaviour is different: 4F 3~is added and thethe intenpopulation of the 9/2 state does not decrease when Tm sity of the red anti-Stokes fluorescence is distinguishable by an increasing function up to a certain concentration of Tm3~(at about 0.3%). —~
—~
4.3. Study under 955 and 1213 nm excitations While the green emission is not influenced by the presence of 1.2 pm radiation, the superposition of both excitations 955 and 1213 nm intensifies the red anti-
-j 400 C
C.
77K
-~ -~
300
955 nm excilolion
~ 200 ‘I, C-
559nm La.
100
552nm I
0
0,1
0,2
~-i
.-
0.5 Thulium concenirolion (mol
I ‘/•
Fig. 5. Green emission intensity of Er3~(4%) versus Tm3~concentration in CdF 3~, Tm3~,Na~for infrared excitation (955 nm). 2 : Er
3~ Tm3’ energy transfers in CdF
J.P. Jouart / Er
2
161
4F 3~is present). This Stokes fluorescence from the 912 levelto(but only when additional emission cannot correspond the 1G 3H Tm 34, firstly 4 4 transition of Tm because the ‘G 4 level is not involved n the studied conversions, 3~ion is a quenching centreinfrared-to-visible of the blue fluorescence of secondly because the Er Tm3~[5]. The measurement of the red emission intensity as a function of the Tm3~concentration (fig. (6(a)) shows that the intensity increases up to about a 0.3% concentration of Tm3~.Beyond 0.3%, the red anti-Stokes fluorescence regularly decreases at the same time that the 4F 3~) 3F 3~)transfer begins. The involved 9/2(Erin fig. 7. 2,3(Tm processes are schematically shown The Tm3+ ions which strongly absorb in the 1.2 pm region, are raised from the ground level to the 3H 5 level state by the 3~ions relaxe to the metastable 3H1213 nm excitation. From this level, the Tm 3~ions are directly excited to the ~ 1/2 level by4 by the a multiphonon decay. 955 nm infrared light.The TheEr4F 912 level 3~ is then directly from ~I11/2by the Er3~ (table populated 1): following upward energy transfer Tm Tm3~:3H 3~:~I11/2 4F 4 Er 912 —~
—~
—~
—~
-4
,
-
This transfer is particularly important because it controls the red anti-Stokes
771<
771<
955nm and 1213nm E
so
~
~xcilafions
955nm and 1490nm ExcitaFions
679nm
fb
200~0:2
640
Thulium concenFrofion
~20o~:i:::o,is
~
Thulium concenlration
(mol ‘I.) (rnol %l 3~(4%) versus Tm3~concentration in CdF
Fig. 3~,Na~ 6. (a) Red for emission double infrared intensity excitation of Er (955 and 1213 nm). (b) Red emission intensity 2: of Er3~(1%) versus TmS+ concentration in CdF 3+, Tm3~,Na+ for double infrared excitaTm 2: Er tion (955 and 1490 nm).
162
3~ Tm3~energy transfers in CdF
J.F~Jouart / Er
2
Tm~ 3~)to activator Fig. 7. (Er3~). Schematic representation of energy transfer from sensitizer centre (Tm centre
fluorescence coming from 4F 912 level. We obtain an additional proof of the existence of this process by modulating the excitation instead of the emission. The continuous emission is not detected by the experimental apparatus, so the modulation of the 1213 nm infrared beam allows to eliminate the red anti-Stokes fluorescence coming from the single 955 nm excitation. When only one excitation is present, the fluorescence is negligible therefore this method presents the advantage of an observation with a dark background. In order to examine the occurrence of this energy transfer, we have the 3H measured 3H lifetime and the intensity of the fluorescence corresponding to the 4 6 transition. Unfortunately, no sensitive variation of the lifetime and 3H of the intensity has been detected under simultaneous excitation of ~I11/2and 5 levels. The transfer probability to the spontaneous emission proba3H is therefore negligible with respect 3H bility of 4 level. Because the lifetime of the 4 level is long (10—2 s), the transfer probability is probably less or equal to 1 ~ The probability of this energy transfer is given by C~i,where n is the population of ~ 1/2 level and C the transfer coeffi3~ions, to the absorpcient.probability The population n is proportional to thecoefficient number Nandp of Eris the spectral energy tion Bp (where B is the Einstein density of the xenon lamp at about 1000 nm)and to the lifetime r of the ~I11/2 level; with N = 2.5 X 1020 ions cm3, Bp = S X l0~s~(B = 5 X 1019 cm3/W is obtained from the oscillator strength and p 10—2 ~W s2/cm3 from the technical characteristics of the xenon lamp) and r = 102 s we find n = 1015 ions/cm3. Therefore, the coefficient of this Tm3 Er3~transfer is inferior or equal to 10_is cm3/s. At 77 K, though the energy matching is nearly perfect for the Tm3~ Er3~transfer (see table 1), this latter is nonresonant. The backtransfer is negligible for the following reasons: At 77 K, all the highest Stark levels of the 3H 4 state are not sufficiently popu-+
.
.
-*
-+
—
3”
Tm3~energy transfers in CdF
J.F. Jouart / Er
2
163
lated and so the energy 1). cannot flow back again to the thulium (the energy mismatch is of about 500 cm of both Er3~ Tm3~transfers coming from 4S In consequence 4F 3/2, the 912 level is insufficiently populated. 4F 3HThe measured radiative lifetime of the 912 state is ten times weaker than that of 4 and ~ 1/2 levels. The successive absorption of two photons by a single centre is generally the predominant mechanism for the infrared quai~tumcounters. Here, transfer 3H 3~and Er3~ ionsthe canenergy be used to betweenanthe 4 and ~I11/2excited levels of Tm achieve infrared quantum counter. To our knowledge, the only experiments of infrared quantum counter with energy transfer which have been realized up to now are those of Zalucha et al. [6}, and those of Pouradier and Auzel [7]. Zalucha et al. use the Nd3+ Pr~transfer in LaCl 3 which is based on the multipolar interaction: 3~: 111/2-4 ‘~I 3~~ 3P Nd 9/~ Pr 0 3~ Ho3~transfer in Ho~Y Pouradier and Auzel use the Ho 1_~F3 which is based on the multipolar interaction: 3~:~I~-÷~Is Ho3~:5F 5F Ho 5-+ 3. 3~ Er3~,Nd3~ Pr3~and Ho3~ Ho3~the spins these three Tm are For unchanged (iNStransfers = 0) and the variations of the total angular momentum are inferior or equal to two (iV ~ 2). In this case, Pouradier [8] has shown that the electrostatic dipole—dipole, dipole—quadrupole or quadrupole—dipole and quadrupole— quad rupole interactions have comparable probabilities. —
-*
—
~+
-4
-+
,
-+
-+
-+
4F 912
-
~i3/2___ -
3
Tm3
Er Fig. 8. Mechanism of the sensitization effect ofTm3+ ions on the red fluorescence of Er3+.
3~q’~ Tm3~energy transfers in CdF
J.P. Jouart / Er
164
2
4.4. Study under 955 and 1490 nm excitations Under double excitation (1490 and 955 nm) constant, the intensity of theby redabout emission of 3~ion of which the concentration is kept increases a facthe Er tor of 12 (fig. 6(b)), with the concentration of the Tm3~ions (up to 0.5% Tm3~). We propose a scheme for this two-photon excitation process. A check of the energy levels shows that the mechanism of the sensitization effect of Tm3~ions on Er3~red fluorescence includes two successive nonradiative energy transfers (fig. 8 gives the energy paths). After excitation by 1490 nm photons to the ~I13/2level, the Er3~(4Il 3+(~H 3/2)~÷ Tm 4)energy transfer occurs intensely because of suitable energy matching (table 1). Then, 955previously nm excitation, energy is transferred 3~ion accordingunder to the studiedthe transfer. back to the Er 5. Conclusion Direct evidence for new energy transfers between Er3~and Tm3+ ions has been established by measurement of the anti-Stokes fluorescence intensity. This is a useful method for observation and analysis of nonradiative energy transfers. We have shown that the Tm3+ behaves as a quenching centre of the green fluorescence of Er3+ and up to 0.3%, as the sensitizer of the red fluorescence of Er3t Under 955 nm excitation, the quenching of the green emission is attributed to two Er3~ Tm3~transfers coming from ~~3/2 level. Under 955 and 1213 nm excitations, 4F 3~:3H 3H 3~:~ 1/2 4F 9/2 is essentially populated by the transfer Tm 4 6, Er 9/2. 4F Under 955 and 1490 nm excitations, 9/2 is3~:~I principally populated by 3~:3two H suc3H cessive transfers: the first one is 3~: the 3H transfer3HEr 3~:13/2 ~Iis/2, 4 6, ~ 1/2~~ 4F Tm the other one is the transfer Tm Er sensitizer of the 9/2. 3+4 acts as6,the infrared fluoresLastly, have Er cence (1.86wepm) of shown Tm3t that Thisthe sensitization is due to the three studied energy transfers Er3+ —u~ Tm3~. -+
~4
—~
-4
—*
—4
References Ill L. Esterowitz, A. Schnitzler, J. Noonan and J. Bahler, Appi. Opt. 7 (1968) 2053. [21 J.S. Prener and J.D. Kingsley, J. Chem. Phys. 38 (1963) 667. 131 J.P. Jouart, These d’Etat, Reims (1977). [41 Yu.K. Voron’ko, M.V. Dniitruk, V.V. Osiko and V.T. Udovenchik, Soy. Phys. JETP (1968) 197. 151 F. Auzel, 0. Deutschbein, Z. Naturforsch. 24a (1969) 1562. [6] D.J. Zalucha, J.A. Sell and F.K. Fong, J. Chem. Phys. 60 (1974) 1660. [7] J.F. Pouradier and F. Auzel, J. do Phys. 37 (1976) 421. [81 J.F. Pouradier, These d’Etat, Paris 6 (1977).
27