DIRECT MEASUREMENT OF 19F- SELF DIFFUSION IN BARIUM FLUORIDE CRYSTALS BY NMR

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DIRECT MEASUREMENT OF 19F- SELF

DIFFUSION IN BARIUM FLUORIDE CRYSTALS BY

NMR

R. Gordon, J. Strange

To cite this version:

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C7-476 JOURNAL DE PHYSIQUE Colloque C7, suppliment au no 12, Tome 37, De'cembre 1976

DIRECT MEASUREMENT OF ''F- SELF DIFFUSION IN BARIUM

FLUORIDE CRYSTALS BY NMR

R. E. GORDON and .J. H. STRANGE

Physics Laboratory, The University, Canterbury, Kent, U. K.

Rksum6. - La mesure directe de l'auto-diffusion de l9F- dans les cristaux de BaF2 a et6 effec- t u k au moyen de la technique de gradieat de champ en impulsions (PFG). Le coefficient d'auto- diffusion a et6 mesure sur trois ordres de grandeur entre 1 000 K to 1 300 K. Ces mesures dkmon- trent la viabilit6 de cette technique pour obtenir les donnkes d'auto-diffusion quand il n'y a pas de traceur convenable.

Abstract.

-

The direct measurement of 19F- self-diffusion in BaFz crystals has been carried

out using the pulsed field gradient (PFG) technique. The self-diffusion coefficient has been measured over three orders of magnitude in the temperature range 1 000 K-l 300 K. These measurements demonstrate the viability of this technique as an alternative means of obtaining self-diffusion data when there is no suitable radiotracer available.

1. Introduction.

-

At present only limited data is available on ''F- self-diffusion in alkaline earth fluorides. The only available radioisotope, ''F, has such a short half-life that the direct measurement of self-diffusion by a radiotracer experiment is very difficult to perform. Only one such study has been reported [l] and the data cover a limited temperature range.

Anion diffusion in alkaline earth fluorides can be deduced from conductivity measurements by assuming the validity of the Nernst-Einstein relationship or by measuring the effect of self-diffusion on NMR spin relaxation. Both of these indirect techniques have been used in a recent comprehensive study (Figueroa, D. R., Chadwick, A. V. and Strangz, J. H. to be published) of 19F- self-diffusion in BaF, single crystals. The conductivity data were analysed assuming that Frenkel pairs are the dominant intrinsic defect in the BaF, fluorite lattice. Self-diffusion coefficients were evaluated over eight orders of magnitude. An even greater range was covered by the NMR relaxation time measurements where, by using the encounter model [2] for nuclear spin relaxation due to 19F- self-diffusion in fluorite lattices, the mean residence time of ''F- ions on the lattice was evaluated. The self-diffusion coefficient was then calculated from the Einstein diffusion equation. Good agreement was obtained between the results of these two different techniques but a direct measurement of self-diffusion is desirable since the results would not then depend on the interpretation of the data according to a parti- cular model. A direct measurement of self-diffusion has the advantages of testing the validity of the Nernst-Einstein relationship in fluorite lattices and of providing a stringent test of the encounter model

interpretation of nuclear spin relaxation in the presence of self-diffusion.

Using the measurement of NMR spin echoes and a pulsed magnetic field gradient, direct measurement of self-diffusion in suitable systems may be achieved. The nuclear spin state of the diffusing species serves as a label for each ion and the effect of ionic motion is to modify the apparent spin-spin relaxation time, T,,

and permits a convenient and direct measurement of self-diffusion. This technique has hitherto been restricted in its application to liquids, adsorbed gases and a few molecular solids just below their melting point.

2. Experimental.

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Since detailed discussions of the pulsed field gradient (PFG) technique are available in the literature [3-51 only a summary will be present- z d here. T+e PFG technique consists of -measuring

FIG. 1.

-

The pulse sequence used to measure self-diffusion by

the pulsed field gradient (PFG) method.

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19F- SELF-DIFFUSION IN BaFz BY NMR C7-477

the amplitude of a spin-echo created by two rf pulses of magnetic field strength B, which are separated by a time z. The rf frequency is the Larmor frequency,

w,, of the nuclear spins and is determined by the applied magnetic field B,(z) and the gyromagnetic ratio, y, of the nucleus studied. The width and amplitude of the rf pulses are adjusted such that the nuclear magnetization, MO, when viewed in a reference frame (X', y', 2') rotating at oo about the Bo(z) direction, rotates first of all through 900 and then through 1800. The spin-echo is measured in the presence of two rectangular pulses of a linear, homogeneous magnetic field gradient of duration 6 and magnitude g. The pulse sequence is illustrated in figure 1.

The 900 pulse rotates MO into the x'y' plane, as shown in figure 2, and the precession of MO about the

Y'

X I

FIG. 2. - Rotation of the nuclear magnetization, MO, through 900 by Bl(o.10) viewed in a reference frame ( X ' , y', z') rotating

about B. with frequency WO.

z'-axis induces an NMR signal which decays away due to the individual component vectors of MO accumulating a phase difference while precessing in the X' y' plane. The effect of the first gradient pulse is to introduce a phase angle shift in the precession of the spins that depends on the position of the spin along the direction of the field gradient. The 1 SO0 pulse rotates each component of MO through 1800 about the B, direction after which a second field gradient pulse, identical to the first, is applied. Since the components of MO have been rotated through 1800 the phase angle shift is exactly the reverse of that produced by the first field gradient pulse and the components of MO come into phase again at time 2 2 to produce a spin-

echo. The echo height will be smaller than the initial height of the NMR signal immediately following the 90° pulse because of spin-spin relaxation which can be described by a relaxation time T,. If the spins diffuse to new positions along the field gradient direc- Lion during the interval A then the phase shifts produ-

ced by the field gradient pulses will not be equal and opposite and as a result there will be incomplete rephasing at 2 z. The echo height will be attenuated. For spins undergoing unrestricted diffusion it has been shown [4] that

where A(2 .c)* is the echo height in the presence of the gradient pulses, A(2 z) is the echo height in the absence of the gradient pulses and D is the diffusion coefficient.

The measurements were made using a Polaron SE180 pulse spectrometer operating at 10 MHz. Field gradient pulses of 100 G cm-' were generated by a specially constructed PFG unit. Details of this unit and of the high temperature NMR probe will be described elsewhere. All the measurements were made on single crystals grown from the melt using the Stockbarger [6] technique.

FIG. 3.

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Fluorine self-diffusion measurements in BaF2. 0

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C7-478 R. E. GORDON AND J. H. STRANGE

3. Results and discussion.

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The results of the self-diffusion coefficient measurements in BaF, are shown in figure 3. Also shown are the data in the common temperature range of the previous radiotracer study [l] and that of the most recent conductivity study [7] carried out on BaF,. The results from these three studies are in fair agreement except at the highest temperatures. The self-diffusion coefficient, D', as measured by this technique should agree with the diffusion coefficient, D,,, measured in the radiotracer study but since there are so few data points available from the latter it is difficult to make a valid comparison between the two sets of data. Application of the Nernst-Einstein equation to the conductivity data yields a self-diffusion coefficient, D,, which for an interstitialcy mechanism should have the value D' = 0.74 D,. This relationship does not appear to be obeyed according to our data. The discrepancy may indicate that an additional diffusion mechanism is present which provides no contribution to ionic conductivity, although an undetected systematic experimental error cannot be discounted.

One important feature of the PFG data that should be noted is the decreasing temperature dependence

of D' as the temperature approaches 1 300 K. This behaviour is consistent with the presence of an order- disorder transition taking place in the fluorine sub- lattice as observed by Thomas [g] at 1 300 K in BaF, in a neutron powder diffraction study.

These measurements have demonstrated the viability of using th%-PFG method to study self-diffusion in solids with suitable nuclei and serves as the only alternative means of obtaining direct self-diffusion data when there is no suitable radiotracer isotope available. "F- diffusion in alkaline earth fluorides is a particularly good example. In table I the main features of the four methods of measuring self-diffusion in fluorites have been compared.

Acknowledgments.

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The authors are grateful to the Science Research Council for an equipment grant and a fellowship for one of us (R. E. G.). They wish to thank Drs. A. V. Chadwick, D. R. Figueroa and Mr. V. M. Carr for helpful discussions and for providing the crystal samples, Mr. P. 5. Freeman and Mr.

J.

B. W. Webber for help in constructing the equipment and Mr. D.

I.

Rayers for carrying out some of the measurements.

Comparison of techniques for measurement of ''F- dijiusion in fluorite crystals

Feature PFG Tracer Conductivity Spin relaxation

-

Type Direct measurement Measurement of "F- self-diffusion ''F- self-diffusion of "F- self-diffu- "F- self-diffusion measured indirectly measured indirectly

sion by interpretation of by interpretation of

charge transport data nuclear spin relaxation data

Label 1 9nucleus ~ nucleus, very dif- Ionic charge ''F nucleus

ficult, half life is 1 .l

hours

Re-use of Non-destructive Destructive Non-destructive Non-destructive

sample

Range (cm2

S-l) 10-'O -, 10-l' -+ I O - ~ 10-l4

'

10-6 10-'6 -+ I O - ~

References

111 MATZKE, Hj., J. Mat. Sci. 5 (1970) 831. 151 PACKER, K. J., REES, C. and TOMLINSON, D. J., in Dzl%usio~

. . . .

[2] WOLF, D., Phys. Rev. B 10 (1974) 2710. Processes, 1 (1971) 101, editor J. N. Sherwood et al. (Gordon and Breach).

[3] ST~SKAL, E. 0. and TANNER, 1. E., J. Chem. Phys. 42 (1965) [6] STOCKBARGER, D. C., Rev. Sci. Instrum. 7 (1936) 133. 288. _{[7] CARR, V. M., CHADWICK,}_A._{V. and FIGUEROA,}_{D. R.,}

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19F- SELF-DIFFUSION IN BaFz BY NMR

DISCUSSION C. R. A. CATLOW. - Regarding the discrepancy you

observe between your measured 19F self diffusion coefficients, and those calculated from conductivity measurements via the Nernst-Einstein relationships. I think that this could be explicable in terms of a non- defect assisted diffusion mechanism in which fluorine atoms exchange position via interstitial sites ; such a process would contribute to diffusion, but not to conductivity as it does not effect transport of charge. I have performed calculations on the saddle point for this mechanism which indeed suggest that it should be competitive with the vacancy mechanism that is normally assumed to be predominant.