HAL Id: jpa-00215378
https://hal.archives-ouvertes.fr/jpa-00215378
Submitted on 1 Jan 1973
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
STUDIES OF SELF-DIFFUSION IN POTASSIUM FLUORIDE BY NUCLEAR MAGNETIC
RESONANCE TECHNIQUES
I. Hoodless, J. Strange, L. Wylde
To cite this version:
I. Hoodless, J. Strange, L. Wylde. STUDIES OF SELF-DIFFUSION IN POTASSIUM FLUORIDE BY NUCLEAR MAGNETIC RESONANCE TECHNIQUES. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-21-C9-24. �10.1051/jphyscol:1973903�. �jpa-00215378�
JOURNAL DE PHYSIQUE Colloque C9, supplkmenf au no 11-12, T o ~ n e 34, Novembre-DPcembre 1973, page C9-21
STUDIES OF SELF-DIFFU SION IN POTASSIUM FLUORIDE BY NUCLEAR MAGNETIC RESONANCE TECHNIQUES
I. M. HOODLESS ('7, J. H. S T R A N G E a n d L. E. WYLDE (**) Faculty o f Natural Sciences, The University, Canterbury, Kent, U. K.
RtLsumC. - La mesure des temps de relaxation TI et TI,, de resonance magnktique nucleaire a CtC effectuee dans K F pur et dope par C a ' . entre 470 et 1090 K. Le processus responsable de la relaxation est I'auto-diffusion. A partir de I'influence de la temperaturz sur T I et TI,, I'enthalpie de migration du cation est trouvee Cgale a 0,83 eV et celle de I'anion a 1,35 eV.
La comparaison des frequences de saut de K . et F calculCs par rmn et conductivitk montre que la diffusion extrinseque a lieu par lacunes cationiques libres et par complexes impurete-lacune.
La dernikre contribue au processus de relaxation ; les lacunes libres et les lacunes associees ont des vitesses de diffusion semblables. A plus haute temperature, i l apparait une contribution apprkciable des lacunes anioniques.
Abstract. - Nuclear magnetic resonance relaxation time measurements of TI and TI, have been made on pure and Ca"-doped single crystals of K F over the temperature range 470 to 1090 K. The process responsible for relaxation is self-diffusion. From the temperature depen- dence of TI and TI,,, the cation migration enthalpy is found to be 0.83eVand theanionmigration enthalpy is found to be 1.35 eV.
Comparison of the jump frequencies for potassium and fluoride ions calculated from the relaxa- tion times and from conductivity measurements shows that extrinsic diffusion takes place via cation single vacancies and impurity-vacancy conlplexes. The latter contribute to the relaxation process, indicating that, in KF, free and complexed vacancies have similar diffusion rates. At higher temperatures there is a significant contribution from anion vacancies to the diffusion process.
1. Introduction. - Schottky defects are normally considered t o be the predominant point defect in the alkali halides with NaCl structure. Ionic self- diffusion a t high temperatures occurs via such defects a n d two techniques are co111111only employed to study this process, namely ionic conductivity and radiotracer diffusion. The latter technique is very inconvenient for the study of fluorides due t o tlie short half-life of the only suitable tracer 18F. Mea- surements arc limited to short diffusion anneal times and observations are restricted t o the high tempe- rature, rapid difrusion region [I]. I t has recently been shown [2] that, in N a l , nuclear magnetic resonance (nmr) relaxation time measurements can provide reliable information on self-diffusion. In particular.
the measurement of the '%a spin-lattice relaxation time in the rotating frame, T,,,, was shown to be useful, in that it permitted the sodium ion jump frequency to be measured over five orders of magni- tude. Since I 9 F has a large nucleilr- mngnetic dipole moment, nuclear spin I = i and has 100 ",, natural abundance, it is very convenient for nmr studies.
( * ) Prcscnt address : Chemistry Dcpartmcnt. Lnhehcad
University, Thunder Bay, Ontario. Canada.
(**) Present addrcss : Building Research Station. Garston.
Watford, U K .
I n order t o investigate ionic motion in K F we have measured the temperature dependence of both ionic conductivity a n d "F nmr relaxation times for single crystals of KF. The conductivity measurements alone arc insufficient t o establish the diffusion process.
The spin-lattice relaxation time. T I , is sensitive to ionic diffusion only a t the higller temperatures and i t is difficult t o interpret the d a t a in terms of absolute values of the ionic j u m p frequency since no minimum in T, is I-eached below the melting point. The measu- rements of TI,,, the relaxation time in the presence of a resonant rf magnetic field, provide considerably more information. As with Nal, it is possible to study cation dilT~ision well into the extrinsic region. Since the self-diffusion rate in this region depends on the concentration of aliovalcnt impurities in the crystal, i t is possible to produce a known concentration of cation vacancies by selective doping. C a F , was used as a dopant for both conductivity and nmr measurements and a value for tlie enthalpy of cntior~
migration. All,, obtained. At temperatures above about 900 K , TI,, is determined by anion diffusion.
I t is interesting t o observc that in samples doped
\+it11 d i ~ u l e n t cations (in which cation diffusion is increased) the anion contribution to 7',,, i n this upper temperature range is more clcarly rcsol\cd
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973903
C9-22 I. M. HOODLESS, J. H. STRANGE A N D L. E. WYLDE since the relaxation rate due to faster cation motion
is here reduced.
2. Experimental. - Single crystals of K F and KF + CaF, were grown by the Czochralski teclini- que [3] from Optran grade, zone refined KF. The calcium content of the crystals was determined by atomic absorption spectrophotometry.
Nmr measurements were made using a pulsed spectrometer operating at 13.5 MHz. T, was measured using a 900-r-90° pulse sequence. T,,, mensurements were made by applying a 90" pulse followed by a much longer pulse whose rf phase was shifted by ,900 from that of tlie first pulse. All nmr measurements were made with the crystal (100) axis parallel to B,.
3. Results and Discussion. - 3 . 1 CONDUCTIVLTY. -
The results of conductivity measurements on p~i1.e crystals of KF are shown in figure 1 as a plot of
FIG. I . - Intrinsic conductivity of KF.
log oT versus reciprocal temperature. The intrinsic region appears in the temperature range 865 to I100 K and extends over only three orders of magni- tude in log oT. Pronounced curvature is observed at temperatures above I036 K ( 1 0 3 / ~ = 0.965 K - I ) .
The curvature could indicate a significant anionic contribution to conduction as in KC1 [4], [5], [6], [7].
KBr [8], K I [9] and RbCl [lo], or it may be caused by Debye-Hiickel interactions. This latter effect is not normally so large and allowance for Debye- Hiickel effects in the conductivity data interpretation produces relatively small changes in the values of the diffusion parameters. These results will be discussed in more detail in a later publication.
3 . 2 NUCLEAR MAGNETIC RESONANCE. - The rela-
tive motion of nuclei which have magnetic moments results in fluctuations of the local dipole magnetic field, B,,,, at these nuclei. If tlie nuclei are in a large steady magnetic field B,, these fluctuations can cause spin-lattice relaxation of the nuclear magnetic dipoles, whereby the nuclear dipoles assume a Boltz- mann distribution over the energy levels corresponding to the allowed orientations of tlie dipoles in B,.
The energy level separation is hw, = fiyB,, where y is the gyromagnetic ratio of tlie nucleus and o, is the frequency of tlie Larmor precession. The relaxa- tion process is ch~uacterized by the spin-lattice relaxation time. T , , which can best be measured by p ~ ~ l s e d nmr tecliniqucs. The relaxation rate is greatest, i. e. T, is a ~ n i n i m ~ ~ m , when tlie average frequency,
to,, of the fluctuating magnetic field, B,,,, is approxi- mately equal to tlie Lurmol- frequency, to,. If in addition to B,, a resonant rotating sf magnetic field (frequency to,) with magnitude B,, where B, $ B , 9 B ,,,. is applied perpendicular to B, then a nucleiu- spin-lattice relaxation time can be defined along the direction of B , , denoted T,,, [I I].
This is a minimum when to, -. co, where w , = pBl.
In the sample considered here, KF, the resonant nucleus is I9F. However, the potassium nucleus also has a magnetic moment and the local magnetic field at the fluorine nuclei is duc to both fluorine and potassium nuclei. Since these ions diffuse at different rates they contribute separately to tlie fluorine spin relaxation.
The ionic jump frequencies do not reach the Larmor frequency to,
-
lo8 s - ' even at the highest tenipe- ratures of tlie measurements. Thesefore, no minimum in T, is reached. Since c r l , -. 10' s - ' for tlie B , fields used Rere, both K f and F jump frequencies might be expected to pass through this frequency range as the sample temperature is raised. but each at different temperatures. Minima might therefore be expected which correspond to modulation of B,,,, by both K f and F- diffusion. We follow the procedure [I21 outlined in a PI-evious paper [ I ] to relate the measure~ilents of TI,, for ' " F to the average ionic jump frequencies of K f . V, and F - , 11,. Thc relaxation process is ~ ~ s s ~ ~ m e d to bc modulation by self-diffusion of the tlipolar coupling between like spins (fluorine with fluorine) and unlike spins (potas- siunl with fluorine).Results obtained from riiens~irements of 7-, and T,,, i n doped sa~nples of KF are shown in figure 2.
The lower dashed lines refer to measurements at two different B , ficld strengths of ' " F relaxation in KFdoped with 12. x 1 0 " mfol'CaF,. As predicted, no minimum i n 7 , is found. T,,, is seen to decrease with increasing temperature and at temperatures 700 to 800 K u kink is apparent which is suggestive of the onset of a niinimi~m in T,,,. However, as the temperature is raised fi~rther, T , , continues to decrease more rapidly than before. We can attribute this beliaviour to tlie K + diffusion controlling T I , , at
STUDIES O F SELF-DIFFUSION I N POTASSIUM FLUORIDE C9-23
FIG. 3. - K1- and F- jump frequency I? versus lO3/T. irli
and 0 0 0 V P for Ca2+ 12 x 10-6 mf. The dashed linc indi- FIG. 2. - Nmr 19F relaxation time measLlr-ements T I and cates the jump freq~~encies calculated from the conductivity TI,. The line - - - indicates T I meaSurements : - - - - - T I P data obtained for the same sample, following the procedure measurements at BI of 7.35 G (upper) and 3.2 G (lower) for described in reference [2]. f -:- f v K and x ., >: in1: for Cai+ 12 x 10-6 m f ; 0-0-0 TI, at B I of 6.6 G for Ca2+ 79 \, 10-6 mf. The solid line again refers to the cor-1.e~-
Cai 79 ;,, 10-6 m f . ponding conductivity results.
low temperatures. A minimum due to this process
There is good agreement between the data obtained would occur when (I,, + 11,)
-
o, = 2 1 , B , where by conductivity and nnir measurements. Diffusion 21, is the gyromagnetic ratio of I9F. A second mini-parameters are compared in the table. The major mum, arising frotn niodulation of tlie dipolar inter-
action between I 9 F spins is possible wlien \,,, = o,.
The decrease in TI,, - ,. above 800 K is tliought to be due to tlie approach to this second minimum. This interpretation is clearly confirmed by experiments on the more heavily doped sample, which contains 79 x 10-(' mf CaF,. The T I , , results for this sample (full line) are also shown in figure 2. If self-diffusion proceeds via lattice vacancies, increased doping with divalent cations increases K + and decreases F - diffusion rates. Consequently for this sample, tlie condition for the minimum due to K' motion (relative to F - ) should be niet at lowet- temperatures, while that for the F - motion alone should shift to liiglier temperatures. As seen from figure 2, this does occur and results in 11101-e clearly defined minima.
Full analysis of tlie nmr data according to the procedure in reference [2] allows calculntion of the F and K f jump frequencies. The values obtained for these two samples are sliown in figure 3. Also shown on this figure are tlie j u ~ i i p frequencies calcu- lated from conductivity measurements on tlie same samples.
Drffirsior~ parameters for K F obtained jTon1 conc/uc8- /iuitj9 aricl nliir data. 11, is the ent1ialp.v of Schottkj.
pair fo/.iliation, All, and Ah, are actiuatio~z erlthalp~es o f cotion aritl ariion L1acancy nzigrntion respectirelj', ant/ 1 is tlie entlialpj~ o f association of the inzprwity- 11aca11c.1' cotnplex.
Conductivity nmr
Parameter (eV)
- - ( e v )
-
11, 2.72 -
Ailc 0.84 0.83
All., 1.65 1.35
7. 0.17 -
Activation energy for low temperature intrinsic
diffusion 1.98 2.0
discrepancy is in the entlialpy of motion of anion vacancies, A h , : we would suggest that the nmr
C9-24 I. M. HOODLESS, J . H. STRANGE A N D L. E. WYLDE value is more reliable since it is obtained from v,
data extending over four orders of magnitude, whereas the conductivity is mainly controlled by K + diffusion over the entire temperature range.
It can be seen that, for the extrinsic range (600 to 800 K), the K + jump frequencies calculated from the nmr measurements are slightly lower than those calculated from conductivity data. This demonstrates the correlation effect which is analogous to the Haven ratios observed for radiotracer measurements. The effect observed in nmr has been discussed previously [2]
and for single vacancy diffusion on a NaC1-type lattice the theoretical value v,,,/l~ ,,,,,,, i , i , , = 0.67 [I 21.
The value observed for K F is 0.68, confirming that K + diffusion occurs via single vacancies.
At temperatures below about 600 K, the slope of the conductivity results (Fig. 3) increases due to impurity-vacancy complex formation. No change in slope is observed for the nmr results, suggesting that the associated vacancies diffuse through the
lattice at a similar rate to the free vacancies. A similar behaviour was noted with NaI [2].
4. Conclusions. - The conductivity results for K F suggested an anionic contribution to the conduc- tion process at the highest temperatures. Nmr relaxa- tion studies not only confirm this but allow a more detailed study of anion diffusion. At lower temperatures nmr measurements are consistent with conductivity measurements and indicate that diffusion occurs via cation single vacancies. Impurity-vacancy coniplexes appear to diffuse through the lattice at a rate close to that of free vacancies. The detailed comparison of conductivity which is a bulk property, and nmr relaxation which is sensitive to the details of motion on the microscopic scale, when carried out on samples of well-defined purity (the same sam- ples in this case), can provide significant information on diffusion and a stringent test of the proposed model for self-diffusion.
References
[I] MATZKE, H. J., J. Phys. Chern. Solids 32 (1971) 437. [7] JACOBS, P. W. M . and PANTELIS, P., Phys. Rev. B 4 (1971 [2] HOODLESS, I. M., STRANGE, J. H. and WYLDE, L. E.. J. 3757.
Phys. C 4 (1971) 2742. [8] CHANDRA, S. and ROLFE, J., C L I I ~ . J. Phys. 49 (1971) 2098.
[3] CZOCHRALSKI, J. Z., Z. Phys. Chem. 92 (191 8) 21 9. [9] CHANDRA, S. and ROLFE, J., Catr. J. Phys. 48 (1970) 397.
[lo] FULLER, R. G . and REILLY, M., PIzys. Rev. Lett. 19 (1967) [4] ALLNATT, A. R . and JACOBS, P. W. M., Trans. Farado), 113.
SOC. 58 (1962) 116. [I I] LOOK, D. C. and LOWE, 1. J., J. Chem. Phys. 44 (1966) [5] FULLER, R. G., MARQUARDT, C. L., REILLY, M . H . and 2995.
WELLS, J. C., Phys. Rev. 176 (1968) 1036. [IZ] WYLDE, L. E., Ph. D. thesis (unpi~blished). University of [6] CHANDRA, S. and ROLFE, J., Can. J. Phys. 48 (1970) 412. Kent, U K 1972.
DISCUSSION J. S. DRYDEN. - When Meakins and I published,
several years ago, our enthalpies of dipole rotation in doped lithium, sodium and potassium halides there were few reliable enthalpies for the motion of cation vacancies obtained from electrical conductivity or diffusion measurements with which to compare our results. What data there was suggested that (as in the results for K F reported in this paper) the energy opposing the motion of a cation vacancy was lower when the vacancy was in the vicinity of a diva- lent impurity ion. However over the years the values
obtained from electrical conductivity or diffusion have been decreasing and are now, in many cases, the same or only a few percent larger than our values ; with one exception. The exception is NaI where work by the same authors (Hoodless, Strange and Wylde) using the same methods as in this paper, gave a value lower than the dielectric relaxation result. We have therefore repeated recently our measurements on Nal taking more care over purity and temperature stability but I have to report that our value (0.53 eV) is still 14 % higher than theirs (0.46 eV).
