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A NEW INTERPRETATION OF ULTRASONIC ATTENUATION IN SUPERIONIC CONDUCTORS β
AND β”-ALUMINA
D. Almond, A. West
To cite this version:
D. Almond, A. West. A NEW INTERPRETATION OF ULTRASONIC ATTENUATION IN SU-
PERIONIC CONDUCTORS
βAND
β”-ALUMINA. Journal de Physique Colloques, 1981, 42 (C6),pp.C6-187-C6-189. �10.1051/jphyscol:1981655�. �jpa-00221591�
JOURNAL DE PHYSIQUE
CoZZoque C6, suppldment au n012, Tome 42, de'cembre 1981 page C6- 187
A NEW I N T E R P R E T A T I O N OF ULTRASONIC ATTENUATION I N S U P E R I O N I C CONDUCTORS B AND 6"-ALUMINA
D . P . A l m o n d a n d A . R . West *
SchooZ of MateriaZs Science, University of Bath, Bath, BA2 7AY, United Kingdom
* ~ e ~ a r t m e n t of Chemistry, University of Aberdeen, Aberdeen, AB9 2UE, United Kingdom
A b s t r a c t : Bmad asymnetrical attenuation peaks have been found i n t h e ionic conductors $ and $"-alumina which cannot be explained by Debye theory.
They axe interpreted a s being a consequence of non-exponential decay pro- cesses and are analysed using universal d i e l e c t r i c response theory.
Additional e f f e c t s associated with water contamination of t h e s m p l e s are discussed.
Measurernnts of the ultrasonic attenuation i n a s i n g l e c r y s t a l sanple of $-
alumina(') and a polycrystalline sample of predominantly $"-aluminaC2) reveal attenuation peaks a t low temperatures. The peaks are found t o be thermally acti- vated and have been associated with t h e hopping of Na
+
ions from site t o s i t e i n t h e i o n i c wnductors.Similar activation energies of 0.166 e V f o r B-alumina and 0.142 eV f o r B"- alumina were obtained from these rreasurewnts. These r e s u l t s =re obtained using Debye theory, i.e. assuming peaks occur where the product of angular
frequency w and relaxation time T equals one. The peaks were found, however, t o be much broader than e~spected f o r an interaction with ions which a l l have t h e sam relaxation t i m s . In the p a s t , broadened peaks of this type have been ex- plained by postulating a distribution of relaxation times, ~ C T ) . TZle attenuation a was then considered t o be foxmd from contributions corresponding t o a l l t h e relaxa- t i o n times i n the d i s t r i b u t i o n as i n equation 1.
a a J ~ c T ) l + D ~ T ~ d ~ w2T (1)
Examples of t h e attenuation peaks found in B-alumina and polycrystalline 8"- alumina are shown plotted against inverse temperature i n Figs.la and l b . The attenuation f o r an appropriate singlk relaxation time process is shown a s a dashed line i n each figure. The peaks
-
very similar i n shape and axe particularly asymnetrical. Qnventionally t h i s necessitates postulating a broad highly asym metrical distribution of relaxation times, and by inplication of b a r r i e r heights, i n these m t e r i a l s . Such a distribution s e e m t o be physically unreasonable i n cry- s t a l l i n e s o l i d s l i k e the $-aluminas. In t h i s paper v,e suggest an a l t e r n a t i v e interpretation of t h e data based on a re-nation of t h e relaxation process,similar t o t h a t h i c h has successfully explained a.namlaus featuxes of the d l e c t r i c a l
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981655
JOURNAL DE PHYSIQUE
response of dielectrics.
Fig.1. Attenuation of 240 MHz longitudinal waves i n single crystal 6-alumina, (Fig. l a ) and 55 MHz longitudinal waves in p l y c r y s t a l l i n e $"-alumina (Fig. lb)
versus inverse temperature. Fits of solid l i n e s use parameters shown as explained i n the text.
~ o n s c h e r ( ~ ) has shown that the dielectric loss in solids of a l l types cannot be explained using Debye theory and physicallyreasonable relaxation time distribu- tions. He has suggested that the data indicates that the fundmental Debye theory asslmption of pure exponential decay of dielectric perturbations is invalid. The
"universal d i e l e c t r i c response"C3) of mterials has been shown t o be a consequence of non-exponential decay processes. In d i e l e c t r i c solids strong my-body inter- actions betwan e l e c t r i c d i o p l e s cause non-exponential decay processes. Di- e l e c t r i c loss peaks axe found t o f i t functions of the form
Xf(w).. [&/wl )-m+(w/W2)1-n ] -l (2)
where the d i e l e c t r i c loss X'Cw) is related t o the thenrally activated parameters w l
and up the relaxation t h T has no meaning. The exponents m and (1-n) are related to the form of the decay process. In 8-al-a and mst other ionic conductors strong many-body interactions m y be e x p c t e d t o influence t h e decay of perturba- tions i n ionic concentration. The appropriateelectrical response of 6-alumina has been shownC4) t o be very non Debye-like and t o be f i t t e d by a function of the form of equation 2. A s both e l e c t r i c a l and mchanical relaxation phenamrla have been shownC1) t o be related to :N ion diffusion it is suggested that equation 2 might be used in place of the usual Debye expression t o account f o r mechanical relaxation peaks i n ionic conductors. The solid l i n e s in Figs.la and l b are f i t s of equation 3 below t o the data.
a a 1jT [ ~ w / w l ) ~ + c w / w ~ ) ~ - ~ l - ~ C3)
In these w l = up = wtexp(-Earn) has been used with the activation energies Ea mentioned above. The other p a m t e r s used i n the f i t s are shown i n the figures.
These are a l l similar t o those employed t o f i t the e l e c t r i c a l data(4) showing a detailed correspondence hewn e l e c t r i c a l and mechanical relaxations i n these mbrials. In t h i s interpretation tbe highly a s m t r i c a l loss peaks are a con-
sequence of the nonexponential decay of Ionic concentrations. The value of (1-n) which wntsols the f i t of the shallow gradient in attenuation on the low tenperature sides of the peaks is similar to the value obtained i n an AC conductivity study of 6-al-naC5). This study showd 6-alumina t o adhere t o Jonscher's universal law and t o be very non Debye-like. Although f o r a non-exponential decay T has no waning the par-ters w l and u p are thermally activated and can be used(4) t o obtain activation energies i n the usual way.
The high tenperature attenuation i n 6-alumina tends to deviate f r a n t h e f i t t e d curve. This is believed t o be a residual effect of water contamination of the sample. Samples of the type studied here have k e n reportedC6) t o contain absorbed water. This appears t o introduce a large additional contribution t o the attenuation.
The attenuation f-d before and a f t e r annealing(6) t o r-ve t h e water is shown in Fig. 2. Earlier r ~ ~ a s u r e ~ ~ ~ n t s ~ ~ ) w r e m a t e d by t h e effect of water and not the basic diffusion process. A similar phenorenon was found i n t h e polycrystalline 6"- alumina s a q l e s (2
.
Fig.2. Attenuation of 100 Wz longitudinal waves i n a single crystal sample of 6-alumina before and a f t e r annealing t o remove absorbed water.
References
1. D.P. Almond and A.R. West, Solid State Ionics (1981), in press.
2. D.P. A b n d , H. W l i c a a d A.R. West, Mat. Res. Bull. 16c1981) 117.
3. A.K. Jonscher, Nature, 287 (1977) 673.
4. D.P. Almnd and A.R. West, Phys. Rev. Letters 47 (1981) 431.
5. R. J. Grant, I .M. H o w , M.D. Ingram and A.R. West, Nature 266 (1977) 42.
6. T. Kaneda, J.B. Bates, J . C . Wang and H. Engstran, Mat. Fks. B u l l . 14 (1979) 1053.
7. D.P. Almond and A.R. West, phys. Lett. 69A C1918) 130.
