POINT DEFECT PARAMETERS FOR NaClO3 CRYSTALS

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POINT DEFECT PARAMETERS FOR NaClO3 CRYSTALS

C. Ramasastry, K. Viswanatha Reddy

To cite this version:

C. Ramasastry, K. Viswanatha Reddy. POINT DEFECT PARAMETERS FOR NaClO3 CRYSTALS.

Journal de Physique Colloques, 1973, 34 (C9), pp.C9-431-C9-435. �10.1051/jphyscol:1973972�. �jpa-

00215448�

J O U R N A L DE PHYSIQUE Colloque C9, supp/kl)?e~lt ^ali no 1 1-1 2, Totue 34, Novembre-Dkcembre 1973, page C9-431

POINT DEFECT PARAMETERS FOR NaCIO, CRYSTALS

C. RAMASASTRY and K. VISWANATHA R E D D Y Solid State Physics Laboratory, Department of Physics Indian Institute of Technology, Madras-600036, India

RQume.

La conductivite electrique en courant continu d'un cristal ionique a bas point de fusion tel NaClOj a 6tC anaiysee et les paramktres de defauts ponctuels ont Cte evalues. Nous decrivons un procede pour determiner I'enthalpie de formation du defaut de Frenkel a partir des mesures de conductivite dans le domaine de temperature oh les contributions des defauts intrin- skques et extrinseques sont comparables. L'enthalpie obtenue est en bon accord avec la valeur obtenue par une experience independante sur la dilatation thermique de ces cristaux.

Abstract.

Tlie dc clcctrical conductivity data on a low melting ionic crystal such as NaC103 has been analysed and the point defect parameters have been evaluated. A procedure is described for determining the Frenkcl defect formation enthalpy from the conductivity data in the tempe- rature region where intrinsic and extrinsic defects contribution to conductivity are comparable in magnitude. The enthalpy so obtained is in good agreement with the value obtained from an independent experiment on tlie thermal expansion for these crystals.

1. Introduction. - The research work in our solid state physics laboratory is mainly centred round the study of defect controlled properties of low melting crystals such as NaNO,, NaCIO,. KCIO, NaBrO, and TI,SO,. The defect centres are investigated using the techniques of optical absorption, electron spin resonance, ionic conduction, dielectric constant, dielectric loss and a n o n ~ a l o u s thermal expansion.

The present paper reports the various phases of the analysis of tlie d. c. conductivity of pure and impurity doped NaClO, crystals. Almost all the parameters concerning the point defects in tlie crystal could be obtained from the conductivity data alone.

NaCIO, is a widely investigated crystal for its bulk properties but not from the point of view of the influence of point defects on these properties.

Its crystal structure [I]. optical activity [2]-[5]. piezo electricity [6]-[8], dielectric constant [7]-[9]. nuclear quadrupole resonance [I 01. thermal e\pansion [I I]-[[ 21 and optical absorption [I31 were all studied rather extensively. The radiation damage and colour centres due t o trapped niolecular species were published in a series of con~tnunications from tliis laboratory [14]- [18]. But only some preliminary work was reported on its electrical conductivity [7]. Our own work on the conductivity of NaCIO, was already partly published [19].

2. Experimental.

The crj,stals were grown by slow evaporation from s a t ~ ~ r a t e d solution in petri dishes. They were \viped clear of the l i q ~ ~ i d by filter paper, were heated at 130 "C for two hours and then slowly cooled. Only thosc crystals that remained

clear after tliis thermal treatment are selected for study. Tlie crystals are hard and could not be cleaved.

They can be ground and polished. However all the six faces have a high natural polish.

2 . 1 ANALYSIS.

The various steps in the analysis are : The log OT vs 1000/T plot does not show straight line regions. It is a curve with continuously changing slope. A simple graphical procedure is adopted to resolve tlie experimental curve into three straiglit line regions (Fig. 1) with the activation energies

Crystals doped with calcium impurity showed an increased conductivity indicating that cation vacancies are the dominant current carriers in the extrinsic region.

Tlie estimation of tlie impurity content in diffe- rently doped crystals was made using a mass-spectro- meter. The analysis of tlie conductivity isotherms (Fig. 2) within tlie frame work of the Stassiv-Teltow association theory required that a large part of the total cation impurities Ca, Ba, Mg, Tc, V, Cr, Fe ( 8 ppm) are perhaps charge compensated by divalent negative ion impurities such as SO;- and C O J - The impurity-vacancy :~ssociation energy is estimated

;IS E,, = 0.25 eV. This gives the jump activation energy of E , = 0.43 eV.

Tlie precxponential factor u,,, in tlie expression

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973972

C-9432 C. RAMASASTRY A N D K. VISWANATHA R E D D Y

FIG. 1. - Conductivity plot of an NaCIO3 crystal. Log o T v s 1 000/T. T h e straight line regions are not present. I t is broken up into three lines by a simple graphical procedure of fitting the experimental conductivity as a sum of exponential terms.

The activation energies are

= 0.55 + ^0.02 eV, El = 1.65 0.02 eV and E 3 = 3.5 5 0.5 eV. The conductivity changes at least by four orders of magnitude in a rather small

temperature range 100 OC t o 220 OC.

~ m p ~ r , ( ~ conceorraclon

c

FIG. 2.

Conductivity isotherms for NaCIO3 as a function of impurity content,

C D. If the total possible divalent impurity content is

C

we obtain the isotherms shown in the lower part of the figure. These are convex to the concentration axis, a feature which is against the Stassive-Teltow-Lidiard theory of association effects. However, the curves shown in the inset are of the right shape and we obtain by taking the Ca2'- and Ba'f impurities only for << C

The analysis of the isotherms gives a n association energy of Ea

0.25 eV for the impurity-

vacancy association.

In the extrinsic region, x, + x, and the electrical transport is predominantly by one type of defects, x,.

Also the mobility of the second carrier is low i. e.

p, 0, the single carrier approximation will hold even a t moderately higher temperatures, in spite of the fact x, is comparable t o x , . In both the cases we have

for cation vacancy mobility is obtained using the effective divalent impurity concentration C and an experimental conductivity a t any temperature in the extrinsic region of an impure crystal

where N is the number of lattice sites per unit volume, ^{X I} will consist of both the extrinsic and intrill~ic q the electronic charge and 12 the association factor defects,

which is calculated from the association equation.

X I = X l e + ^{X l i ( 6 )}

P ₌ 12 exp 0.25 eV

x1(l

P ) (3) and

The mobility of the cation vacancy can be calculated p, x l e and x l i can be calculated a t different tem- a t any other temperature using eq. (1). peratures using eq. ( 5 ) , (3), (7) and (6).

he experimental conductivity of the crystal in we should have ^{X ,} = x l i from the charge neutrality general may be due t o more than one defect. We condition

consider a two carrier model. x, = ( 1 - p) C + x , . (8)

(4) The mass action law applied t o the two defects gives where x,, x, are the mole fractions of the two defects, X 2 = = e s ~ l k e - E ~ / k T

say cation vacancies and interstitials and I ( , , 1.1, (9)

their mobilities. As we already have x, and x,, we plot log (x, xl)

POINT DEFECT PARAMETERS FOR NaCIO, CRYSTALS C9-433

vs 1000/T (Fig. 3). The slope of the line gives the enthalpy of formation per defect pair E, = 2.04 eV.

The intercept gave the preexponential entropy factor leading t o s, = 2.96 x eV/K.

200 150 roo "c

I I

2 0 2

2 2 2 3

2 5 2 6 2 7 2 8 1000 ,,I;<

FIG. 3. - Variation of the intrinsic carrier concentration with temperatures. The total cation vacancy concentration is calcu- lated from the observed experimental conductivity data using single carrier approximation. The extrinsic vacancy concentra- tion is obtained from the effective divalent impurity content and the association energy. The intrinsic vacancy concentration so obtained equals the intrinsic interstitial concentration for charge neutrality. The departure from the straight line occurs at a lower temperature for the purer crystals for which the single carrier approximation is not valid at these tenlperatures.

The enthalpy of formation of intrinsic defects is 2.04 eV.

There is a considerable departure of the experi- mental points at higher temperature from the extended straight line. 11 is perhaps due to the inadequacy of the single carrier approximation at these higher temperatures.

As expected, the temperature at which the deviation occurs is higher the greatel- is the divalent impurity content of the crystal. The single carrier model holds better for the impure crystals. In all cases. we need to bring in the contribution from the second defect also to account for the dcparturc from the straight line at the higher temperature.

The introduction of the second carrier is also necessary to account for thc f;lct that at temperatures

above 280 OC the conductivity of the impure crystal actually becomes less than that of the purer crystal while at lower temperatures, we have the opposite effect. The result is in a way similar to that observed in silver halide crystals. One can explain away the result if the mobility of the second carrier is higher than that of the first carrier above 180 OC.

Eq. (5) can no longer be used to obtain x , a t the higher temperatures if the second carrier also becomes mobile. One has to solve simultaneously the three eq. (3), (8) and (9) to get x , and x,. These give a cubic equation for x, o r x2, solving which one gets x , or x,. p2 can be obtained as a function of tern- perature from the observed conductivity data using eq. (4). The expression obtained is

Finally a computer least square fit is made for the data obtained on each crystal varying the several parameters. The computer refined values which agreed very well for the different crystals are not much different from the values obtained by the graphical analysis.

2 . 2 SUMMARY, OBSERVATIONS AND DISCUSSION. -

The various point defect parameters obtained by a step by step analysis of the conductivity data alone are contained in the equations :

The entire analysis is within the framework of the Stassiv-Teltow-Lidiard theory of the effects of asso- ciation of aliovalent impurities with the charge compensating defects.

The main difficulty in the analysis arises because there is a considerable overlapping of the extrinsic arid intrinsic regions in the rather relatively narrow temperature range available (700 t o 220 OC) for study. The first breukthrougli was the resolution of the conductivity curve into straight line regions purely by the empirical graphical method described earlier.

It can perhaps be profitably applied for other low melting ionic crystals.

Even tliough the graphical analysis of the conduc-

tivity data in the intrinsic region is represented by

a good straight line (Fig. 1 ) its slope does not refer

to any particular ;~ctiv:~tion energy. The complete

analysis described ;~bc>\lc shows that it represents

half the formation energy of the defect pair plus a

weighled average of the conlr.:~utions from the two

carriers.

C9-434 C. RAMASASTRY A N D K . VISWANATHA R E D D Y

We assumed in tlie above analysis that the entropy change is small when a vacancy migrates away from the first neighbour position of the divalent cation impurity. The other entropy terms both for formation and jump are rather large (eq. (I), (10). (9)). This seems to be a characteristic feature of the ionic crystals containing complex negative ions like NO;

and C10;.

Unlike in AgCl and AgBr, the jump activation energy of the interstitial is more than that of the vacancy. Even then, the interstitial is more mobile than the vacancy at higher temperatures. This is due to the large preexponential factor (contains entropy term) in the mobility of the interstitial. In fact the mobilities of the two defects become equal at a temperature given by

Above this temperature, the interstitials are more mobile than the vacancies. This could satisfactorily account for the observed lower conductivity of the impure crystal compared to that of the pure crystal above this temperature.

The mass spectrometer analysis revealed the pre- sence of several types of impurities Ca, Ba, Mg, Ti, V, Cr, Fe. But, a much smaller number, parti- cularly the C a 2 + and Ba2+ seem effective in producing vacancies and changing the conductivity. The rest might have been in the singly ionised state or preci- pitated in a separate phase or most probably charge compensated by anion impurities such as SO:- and CO:-.

The conductivity is rather low but it varies by several orders of magnitude even in the small tem- perature range of 70 OC to 220 "C. The crystal becomes cloudy if kept for several hours above 220 O C with the electric field on. Such an experiment was tried to obtain the transport numbers. But the changes in the masses of the end plates are imperceptible because of the very poor conductivity of the crystal.

The cloudiness of the crystal is obviously due to decomposition and the presence of trapped gases such as oxygen. If the electric field is not applied continuously, the crystals can be heated at 230 OC for several hours without any observable decompo- sition.

The large and highly polarisable negative ions are assumed to be rather immobile compared to the cations. The intrinsic defects are a s s ~ ~ m e d to be of Frenkel type consisting of cation vacancies and interstitials rather than of the Schottky type. The

analysis will be equally valid if the second defect is taken to be the negative ion vacancy. Only self- diffusion experiments using radioactive sodium and transport number measurements can possibly resolve the puzzle.

The computer fit of the conductivity data failed to give any additional information. It is our experience that the computer can be profitably employed only to refine the various parameters which are already obtained by graphical methods. Otherwise it will be a wild goose chase.

The thermal expansion of the crystal was also studied employing the capacitance change method.

One finds an anomalous increase of thermal expansion above 120 OC (Fig. 4). At these temperatures, the

FIG. 4.

Coefficient of thermal expansion of NaC10, crystal by the capacitance change method as a function of temperature.

The excess over the linear rate is analysed in the inset to give an activation energy of 2.1 eV. Thus the anomalous expansion o f the crystal above 120 O C (in the intrinsic region of conductivity)

can be attributed to the presence of intrinsic defects.

intrinsic defects also begin to increase exponentially

with temperature. In fact, tlie anomalous thermal

expansion, analysed after the manner of a similar

result in NaCI [21], gave an activation energy of

2.1 eV and this agrees reasonably with the formation

energy obtained from the electrical conductivity data.

POINT DEFECT PARAMETERS FOR NaCIO3 CRYSTALS C9-435

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