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EQUILIBRIUM BETWEEN TYPE I AND TYPE II
M3+-F-i COMPLEXES IN ALKALINE EARTH
FLUORIDES
J. Crawford, Jr, G. Matthews
To cite this version:
JOURNAL DE PHYSIQUE Colloque C7, supplkment au no 12, Tome 37, Dkcembre 1976, page C7-297
EQUILIBRIUM BETWEEN TYPE I
AND
TYPE
II
M3
+-F;
COMPLEXES
IN ALKALINE EARTH FLUORIDES
(*)
J. H. CRAWFORD, Jr. and G. E. MATTHEWS Department of Physics e t Astronomy, University of North Carolina,
Chapel Hill, N. C . 27514, U. S. A.
Rksumk.
-
Nous avons examine le modkle accept6 de la structure de la rhrientation des dip6les de la fluorure aux interstices impurs dans CaFz et SrF2 auxquelles nous avons ajoutk une impuretk de terre rare trivalente ; nous avons fait ces experiences en utilisant les techniques de YITC. Nous avons examine la dependance de la temperature des concentrations du type I1 (dipBle trigone) relatives au type I (dip6le tetragone) dans la region renfermke par I'apogCe de I'ITC qu'on croit associe avec le mouvement vers l'kquilibre du dip6le de type 11. Quant B SrFz : Gd3+, nous avons observe un accord excellent avec le comportement anticipk et nous avons trouve que la difference d'enthalpie entre les deux especes de dip6les etait 0,046 eV. Nous avons trouvk aussi que la propor- tion du type 11 au type I augmente en raison de la decroissance de M3+ ; ce rQultat s'accorde avec des recherches d6jk faites. Le wmportement des dipBles dans CaFz : Gd3+ et CaF2 : Tm3+ n'ktait pas compatible avec 1'6quilibre simple : ce qui suggkre soit que Ies dipBles du type I1 dans CaF2 approchent de Ykquilibre par un chemin qui ne comprend pas les positions des dipBles du type I ;soit que I'apogee de I'ITC est occasionne par la reorientation d'une structure dipolaire qu'on n'a pas encore identifiee.
Abstract.
-
The model for the structure of impurity-interstitial fluoride dipoles in CaF2 $ SrF2 doped with trivalent rare earth impurity has been investigated using ionic thermocurrent (ITC) techniques. The temperature dependence of the relative concentrations of type I1 (next-nearest neighbour M3+-Fi- dipoles which have trigonal symmetry) to type I (nearest-neighbour M3+-Fr dipoles with tetragonal symmetry) was examined over the region spanned by the upper ITC peak thought to be associated with type I1 dipole relaxation. For SrFz : Gd3+ excellent agreement with expected behaviour was observed and the enthalpy difference between the two dipole species was found to be 0.046 eV. The ratio of type I1 to type I was also found to increase with decreasing size of M3+ in agreement with previous reports. The behaviour of dipoles in CaF : Gd3+ and CaFz : Tm3+ was not consistent with simple equilibrium suggesting that either type I1 dipoles in CaFz relax by some path which does not involve type I sites or the upper temperature relaxation peak is caused by an as yet unidentified dipolar structure. The effect of ion size in CaF2 : M 3+ on therelative amplitudes of type I and type I1 peaks showed no systematic variation.
1. Introduction.
-
Introduction of aliovalent impu- rities into ionic crystals creates a charge imbalance which is usually compensated by the introduction of point defects whose net charge balance the deficit or excess introduced by the impurity. I n alkaline earth fluorides which crystallize in the fluorite structure, namely CaF,, SrF, and BaF,, trivalent cation impurity M 3 + is compensated by an equal concentration of interstitial fluoride ions FF provided there is no compensating impurity such as O = present [I]. Because of coulombic interaction between the impurity and its compensator, M3+-F; complexes tend t o form. These complexes are dipolar in character and, if there is adequate thermal activation, they may partially orient in an applied electric field. Therefore,(*) Supported by ERDAunder Contract E 40-1-3766.
their reorientation kinetics may be studied by means of either ac (dielectric absorption) [2] or d c (ionic thermoconductivity or ITC) [3-81 polarization methods and the concentrations of these complexes are reflected by the strength of the relaxation signal. From ESR and ENDOR studies of paramagnetic M 3 + ions the structure of the complexes can also be determined. I t is found that in CaF, the tetragonal (C,,) type I
complex in which the F; compensator is in the nearest neighbouring interstitial position is dominant [9, 101. In BaF, the next-nearest interstitial site domi- nates [ll, 121 and this produces the trigonal (C,,) or type I1 complex. The intermediate member of the series, SrF,, shows a mixture of the two types [ l l , 121 and the ratio of their concentrations is sensitive to the size of the impurity ion [13].
In this paper we report a study of the equilibrium
C7-298 J. H. CRAWFORD, JR. AND G . E. MATTHEWS between type I and type I1 complexes in SrF, and CaF,.
The temperature dependence of the population of the two types of dipoles has been investigated and the impurity ion size has been studied. The experimental method used in the investigation was thermal depola- rization or ITC [14]. From the fact that two peaks are observed and thermal equilibrium can be accomplished by annealing over the temperature interval (180-230 K) of the upper ITC peak, henceforth referred to as the type I1 peak, it can be concluded that the accepted model for the relaxation modes governing reorienta- tion of these two coupled complexes is correct for SrF,. By contrast, the behaviour of CaF, is anoma- lous. The experimentally indicated enthalpy difference between the two forms is much too small to account for the large difference in their populations. This anomalous behaviour parallels other inconsistencies in equilibrium between the isolated components and the tetragonal dipolar complexes uncovered by Franklin and Marzullo [I51 in their study of CaF, : Gd3+.
2. Experimental details.
-
The crystals used in this study were obtained from Optovac, Inc. with a nominal M3 + impurity concentration of 0.05 and 0.1 mole percent. They were virtually oxygen free as evi- denced by the very small amplitude of the [M3+ OqF] ITC relaxation peak [16]. Thermal depolarization was carried out by the usual method first developed by Bucci et al. [14], [17]. Individual specimens up to 1 mm thick with powdered silver electrodes applied to opposite faces were mounted in the high impedance chamber of a nitrogen cryostat. Polarizing fields of--
5 000 V/cm were used. Depolarization currents were measured with a Cary 401 vibrating reed electrometer. Peak currents were of the order of lo-'' A with a back- ground noise of-
10-l5 A. The heating rates were 3 K min.-I at low temperature (type I peak region) and 5 K min.-' at higher temperatures. Linear heating rates were maintained by monitoring the output of the copper-constantan thermocouple emf and nulling this against a reference voltage supplied by an on-line PDP-12 computer according to a second degree polynomial approximation to the thermocouple emf us T curve. The imbalance signal controlled the spe- cimen heater current. The specimen chamber was filled with 1 atm. helium exchange gas to minimize temperature gradients across the specimen.In studies of the temperature dependence of equili- brium between type I and type I1 dipoles the specimen was annealed in a polarizing field at some temperature in the range spanning the type I1 ITC peak. The period of the anneal was greater than six type I1 relaxation times as calculated from the reorientation activation energy E, and the reciprocal relaxation time applicable to the type I1 peak as determined from the ITC equa- tion. The specimen was cooled rapidly under applied field to a temperature near the maximum of the type I peak, held there for a short time to estblish a fixed
type I polarization and then cooled further to immobi- lize type I dipoles.
3. The reorientation model. - Lidiard (1) has recently reviewed the relaxation kinetics of M3+-F;
dipoles. The interstitial is considered to be bound to the M 3 + by coulomb and elastic interactions. Since type I and type I1 are in equilibrium with each other, they form a coupled system and relaxation is governed by normal relaxation modes [18, 191. Perturbation by an applied field excites the triply-degenerate TI, mode whose reciprocal relaxation time is two valued and given by
z-' = 2 W,,
+
2 W,,+
q
w,,
+
[(2 W,,+
2 W,,-
3
W21)2+
4 W1,w,,]~'~
.
(1) The Wi;s represent the frequency of interstitial trans- fer from site i to site j and subscripts 1 and 2 refer to nn and nnn sites respectively. Because of the structure, a direct transfer from one nnn site to another seems unlikely ; hence Wz2 is usually assumed to be zero.FIG. 1. - TWO possible saddle point configuration for the coupled type I-type I1 dipole system which yield two ITC relaxation peaks. In (a) type I is more stable and in (b) type I1
is more stable.
M~+-F; COMPLEXES I N ALKALINE EARTH FLUORIDES C7-299 complexes. The two approximate solutions of eq. (1)
are
It is interesting to note that the lower temperature peak is always associated with type I dipoles and the relative stability of the two types is reflected in the relative amplitudes of the two peaks. Any other confi- guration would produce a single peak.
At equilibrium
where N , and N,, represent the concentration of dipo- les of the two types. Since W i j = W$ exp[- E,,/kT],
where the entropy difference between the two types AS,, = In [4 wf2/3 w;~] and the enthalpy difference 4E12 =
E 1 2
-
E,,.The concentrations of the two dipolar species in equilibrium with each other at the anneal temperature TI, can be obtained from the areas under their respec- tive ITC peaks i. e. the total polarization P, accor- ding to
where for the ith dipole pi is the dipole moment, Ni the concentration, Ep the polarizing field and Ti is the polarization temperature. The value of the dipole moment is usually taken to be the unrelaxed point ion (UPI) value .which is expected to be a reasonable approximation. It is also possible in principle to deter- mine the ratio of dipole moments by invoking dipole conservation, i. e. the total number of dipoles remains fixed. Hence,
By taking measurements of P i after annealing at widely different values of TI,, p, can be eliminated from eq. (6) and I ~ I / p I I can be readily determined by numerical analysis.
Results.
-
4.1 DIPOLE BEHAVIOUR IN SrF, : M3'.-
4.1 .1 Effect of temperature. - The temperature dependence of the equilibrium ratio N,,/N, was mea- sured for SrF, doped with nominally 0.1 mole percent of GdF, over the range 185 K to 215 K. Figure 2 (open circles) shows a plot of In NI,/N, vs the recipro- cal of the temperature TI, of equilibration. The fit to a straight line is better than 1%
which is considered to be excellent. The slope of this curve corresponds toDl,
= 0.046 eV. From the intercept at 1/T,, = 0 it was found that AS,, = 1.0 k which appears to be a reasonable value. The values of N , and N,, were obtained using the UP1 dipole moments for both dipoles. An error in the dipole moment ratio wouldFIG. 2. - A plot of In [NII/NI] vs the reciprocal of the upper polarization temperature for SrF2 : Gd3+ (open circles), CaFz :
Gd3+ (open squares) and CaF2 : Tm3+ (open triangles).
have no effect upon the value of AE,, but could shift AS,, significantly. Consequently, eq. (6) was employed and ,uII/pI was calculated by successive approximation. The best value was found to be 2.4 which is 50
%
larger than the J3 UP1 value. Using this value in cal- culating N,,/NI reduces AS,, to 0.04 k which again is quite reasonable. In support of this large dipole moment ratio is recent work of Sherstkov et al. [20] who find from studies of the effect of electric field on the ESR spectrum of CaF, : Gd3 + that p, is 0.77 of theUP1 value. This implies a strong inward relaxation around the Gd3+ as well as a possible shift of the charge distribution around the type I dipole. In SrF, with its larger host cationic radius as compared to CaF,, an even greater reduction might be expected for type I. On the other hand, relaxation in the type I1 complex is not expected to be as extensive in either CaF, or SrF, because F i is outside the first F- coordina- tion shell. Hence the disparity between the experi- mental and UP1 dipole moment ratios is not unrea- sonable.
C7-300 J. H. CRAWFORD, JR. AND G. E. MATTHEWS earths decreases with increasing atomic number
through the series (the lanthanide contraction), a shift of the dominant complex type might be expected from one end of the series to the other. Their ESR measurements bear out this model since SrF, : Ce3+ was observed to contain mainly type I and SrF, : Yb3 +
was observed to contain mainly type 11.
We have checked this site preference for various dopants with ITC. The ratio N , , / N , was indeed found
to increase with decreasing ion size for the impurities available. In SrF, : Ce3+ the type I relaxation peak was scarcely detectable whereas for Er3+, an impurity near the upper end of the lanthanide series, type I1 was clearly dominant. These results are consistent with the ESR measurements [13] and are tabulated in table I.
Intfuence of rare earth ion size upon
the population of type I and type II dipoles in SrF,
Dopant Ion Size (A) T I (K) T I , NI,/N,
- -
-
-Y3+ 0.893 154 215 95
Gd3 + 0.938 146 208 0.21
Ce3 I. 1.034 149 197 0.008
4.2 DIPOLE BEHAVIOUR IN CaF, : M3
+.
- 4 . 2 . 1 Effect of temperature. - Studies similar to those described above for SrF, : Gd3+ were performed to determine the effect of annealing in the region of the type I1 ITC peak on N,,/N, in CaF, : Gd3 + and CaF, : Tm3+. The results shown in figure 2 (open squares and triangles, respectively) do not accord nearly so well with the relaxation model as do those for SrF, : Gd3+. There is much scatter. Values ofAE,, are 0.005 f 0.004 eV and 0.012 f 0.001 eV for CaF, : Gd3" and CaF, : T:+ respectively. This is much too small a temperature dependence to account for the small values of the ratios unless an unreaso- nably large entropy change is involved. Hence it appears questionable whether the relaxation in the type I1 peak region leads to equilibrium between type I and type 11. Another such indication is the fact that room temperature irradiation with 137Cs y-rays (0.67 MeV) causes the type I1 peak of CaF, : Gd3 + to decrease by
--
36%
whereas type I decreases by only 7.5%.
If the two species were in thermal equilibrium in the type I1 peak region each peak would exhibit the same relative decrease. Anneals above 100 OC were necessary to restore the initial population.4 . 2 . 2 The effect of ion size.
-
As in the case of SrF,, the effect of the nature of the impurity onN , , / N , was explored using a number of lanthanide
ions. The results are tabulated in table 11. One effect of changing the impurity was the often substantial shift of the temperature T , of the maximum of the type 11
Type I and type I1 ITC peak characteristics for various dopants in CaF,
Dopant - Yb5+ Tm3 + Er3 + Dy3 + Tb3 + Gd3+ Eu3 + Sm3 + Nd3 + Ce3 +
Ion Size (A)
-
0.858 0.867 0.881 0.905 0.923 0.938 0.950 0.964 0.995 1.034ITC peak. The value of T, is also tabulated. By compa- rison there was only a small shift of T , for the type I1
peak in SrF,. It is evident from these data that ion size has no systematic effect in CaF,.
5. Discussion.
-
The results obtained with SrF, : Gd3 strongly support the accepted model for relaxation of type I and type I1 dipoles in this material. Moreover, the difference in binding of-
0.046 eV of the two species for this impurity is in keeping with expectation in view of the reported [21] total binding energy of--
0.2 eV. The reasonable experimental value of dipole moment ratios of the two complexes gives further support to the correctness of the model. Finally, the ITC results support the ESR study [13] of the effect of ion size upon N , , / N , in SrF,.The situation in CaF, : M 3 + is not nearly so satis- factory. The lack of convincing evidence of thermal equilibrium between the two dipolar types upon annealing in the type 11 peak region must indicate one of the following : a) the type 11 dipole is isolated from type I by a potential barrier which can be surmounted only above room temperature and hence the type I1 relaxes by an alternative path, i. e. W,, 9 W,,. b) The type I1 peak is not caused by nnn dipole rela- xation but some other dipolar species associated with the M3 + in question. c) The type I1 peak is associated with some unknown and uncontrolled impurity introduced accidentially during crystal growth. Possi- bility (c) can be ruled out on the basis of our observa- tions that the amplitude of the type I1 peak scales with M3 + concentration for small impurity concentra- tions and T , is dependent upon the identity of M3+.
M~'-F; COMPLEXES IN ALKALINE EARTH FLUORIDES C7-301 this path is favored for BaF, rather than CaF,, phase aggregates in the alkali halides and optical Possibility b) must be considered a likely one. The dipo- evidence for higher order aggregates in CaF, : M3 +
le may be some metastable form frozen in upon has been reported [23], 1241. Clearly additional work cooling or a complex aggregate which acts like a is needed to identify conclusively the dipoles respon- composite dipole with a small total dipole moment. sible for the so called type I1 peak in CaF, : M3'. It Evidence of an aggregate connected dipolar relaxation can no longer be attributed to a type I1 dipole in has been reported by Cappelletti et a2. [26] for Suzuki- equilibrium with a type I as previously proposed [S].
References
[I] For a review see LIDIARD, A. B., Crystals with the Fluorite Structure, Hayes, W., ed. (Oxford University Press) 1974. C h a ~ t e r 3.
[2] FRANKLIN, A.-D. and MARZULLO, S., J. Phys. C 3 (1970) L 239.
[3] ROYCE, B. S. H. and MASCARENHAS, S., Phys. Rev. Lett.
24(1970) 98.
[4] STOTT, 3. P. and CRAWFORD, J. H., Phys. Rev. Lett. 26 (1971) 384.
[5] KUNZE, I. and MiiLLER, P., Phys. Starus Solidi (a) (1972) 197.
[6] STIEFBOLD, D. R. and HUGGINS, R. A., J. Solid State
Chem. 5 (1 972) 15.
[7] KITTS, E. L., IKEYA, M. and CRAWFORD, J. H., Phys. Rev. B 8 (1973) 5840.
[8] Krrrs, E. L. and CRAWFORD, J. H., Phys. Rev. B 9 (1974) 5264.
[9] WEBER, M. J. and BIERIG, R. W. Phys. Rev. 134 (1964) A 1492.
[lo] BAKER, J. M., DAVIES, E. R. and HURRELL, J. P., Proc.
Soc. London A 308.
[11] SIERRO, J., Phys. Rev. Lett. 4 (1963) 178. [12] RANON, U. and YARIV, A., Phys. Lett. 9 (1964) 17.
[13] BROWN, M. R., ROOTS, K. G., WILLIAMS, J. M., SHAND, W. A., GROTER, G. and KAY, H. F., J. Chem. Phys. 50
(1 969) 891.
[14] B u c c ~ , C. and FIESCHI, R., Phys. Rev. Lett. 12 (1964) 16. [15] FRANKLIN, A. D. and MARZULLO, S., Proc. Brit. Ceram.
Soc. 19 (1971) 135.
[16] KITTS, E. L. and CRAWFORD, J. H., Phys. Rev. Lett. 30
(1973) 443.
[17] B u c c ~ , C., FIESCHI, R. and GUIDI, G., Phys. Rev. 148
(1966) 816.
[I81 FRANKLIN, A. D., SHORB, A. and WACHTMAN, J. B., J.
Research NBS 68A (1964) 425.
[19] NOWICK, A. S., J. Phys. & Chem. Solids 31 (1970) 1819. 1201 SHERSTKOV, Yu. A., VAZHENIN, V. A. and ZOLOTAREVA, K.
M., Sov. Phys. Solid State 17 (1976) 1830.
[21] BOLLAMNN, W., GORLICH, P., HAUK, W. and MOTHES, H.,
Phys. Stat. Sol. (a) 2 (1970) 157.
1221 KORNIENKO, L. S. and RYBALTOVSKI, A. O., SOV. Phys. Solid State 15 (1974) 1322.
[23] FENN, J. B., WRIGHT, J. C. and FONG, F. K., J. Chem.
Phys. 59 (1 973) 559.
1241 TALLANT, D. R. and WRIGHT, J. C., J. Chem. Phys. 63 (1975) 2074.
[25] CATLOW, C. R. A., J. Phys. C 9 (1976) 1845.
I261 CAPPELLETTI, R., FERMI, F., LEONI, F. and OKUNO, E., Proceedings of the International Symposium on Electrats and Dielectrics, STio Carlos, Brasil, Sept. 1975 (in Press).
DISCUSSION R. CAPELLETTI. - If you change the overall con-
centration of the trivalent rare erath in the crystal, what does happen to the ratio between the concen- tration of type I1 and that of type I dipoles ?
J. H. CRAWFORD. - The ratio of concentrations of type I1 to type I dipoles increases with increasing impurity concentration.
J. FONTANELLA. - HOW might (or will) the exis- tence of low temperature relaxations (cluster, etc.) affect the equilibration arguments in CaF, ?
Type I1 dipoles increase with concentration (0.1- 1.0
%)
in the samples of CaF, : Eu studied (Andeenet Font.), however, they increase by about the same factor in BaF, : Er. They also increase in SrF, : Er but not so fast. Clusters (very L. T. relax.) are forming in SrF, : Er but not BaF, : Er. Type I1 dipoles were very weak in the samples of CaF, : Er studied.
