PRESSURE AND TEMPERATURE DEPENDENCE OF THE ELECTRICAL RESISTANCE OF THE f. c. c. AgI PHASE

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PRESSURE AND TEMPERATURE DEPENDENCE

OF THE ELECTRICAL RESISTANCE OF THE f. c. c.

AgI PHASE

B. Baranowski, J. Bowling, A. Lundén

To cite this version:

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JOURNAL DE PHYSIQUE ColloqUe C7, supplement ail n° 12, Tome 37, Decembre 1976, page C7-407

PRESSURE AND TEMPERATURE DEPENDENCE

OF THE ELECTRICAL RESISTANCE

OF THE f. c. c. Agl PHASE

B. BARANOWSKI, J. E. BOWLING (*) and A. LUNDEN

Department of Physics, Chalmers University of Technology, S-402 20 Gothenbusrg 5, Sweden

Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland

Résumé. — En commençant par des tablettes polycrystallines de y Agi, on a revu le diagramme des phases de Piodure d'argent, ainsi que les couches limites des phases y, a, c.f.c. et intermédiaire, au moyen de mesures de conductivité électrique effectuées dans des intervalles de temps étendus. On a mesuré la résistance électrique des tablettes de Agi, c.f.c. sur l'intervalle de température de 8 °C à 120 °C et sur l'intervalle de pression de 3 à 28 kbar, en employant l'argon comme moyen de transmission de la pression. On a calculé les valeurs des enthalpies d'activation pour diverses pressions, jusqu'à 7 kbar, et on les a partagées en trois parties.

Pour 25 et 70 °C, on a mesuré la résistance jusqu'à 28 kbar et on a obtenu la preuve que le volume d'activation dépend de la pression suivant une série entière jusqu'au terme quadratique. Les volumes d'activation effectifs sont positifs et ils deviennent moins élevés aux plus hautes pressions. On envisage la possibilité d'un changement du mécanisme de la conductivité ionique aux pressions hautes.

Abstract. — The phase diagram of silver iodide, starting with y phase polycrystalline samples, along with the y, a, f.c.c. and intermediate phase boundaries, was re-examined by electrical conduc-tance measurements carried out over long time intervals.

The electrical resistance of f.c.c. Agl polycrystalline pellets was measured in the temperature range 8 °C to 120 °C and the pressure range 3 to 28 kbar, using argon as the pressure transmitting medium. The values of the activation enthalpies were calculated for different pressures up to 7 kbar and were split into three parts.

For 25 and 70 °C, the resistance was measured up to 28 kbar, giving clear evidence of the pressure dependence of the volume of activation, expressed as a power series of pressure up to the quadratic

term. The effective volumes of activation are positive tending to lower values at higher pressures. A possible change in the mechanism of ionic conductivity at high pressures is considered.

1. Introduction. — Studies of how the electrical conductivity depends on temperature and pressure give information on the mechanisms of ion transport in solid salts, and, in addition, discontinuities in the electrical conductivity indicate phase transitions.

Silver iodide has been the object of a great number of investigations, but there is some disagreement in the literature regarding the phase diagram as well as on the electrical conductivity of some regions, specially concerning the pressure dependence. We considered it of interest to make a thorough study of the electrical conductivity with emphasis on the f. c. c. phase. Some preliminary results were published recently [1], and a more detailed account will appear elsewhere, including comparisons with previous investigations.

(*) Present address : Dept. of Metallurgy, University of Sheffield, St. George's Square, Sheffield, SI 3J D, England.

2. Experimental. — An impedance bridge was used to measure the electrical resistance at 1 kHz frequency of cylindrical samples, which were prepared in a press and which consisted of three layers. The central layer (1-10 mm thick) contained only polycrystalline silver iodide, while the two outer ones were made of a mixture of silver iodide and silver metal powder supporting a silver wire. The silver iodide sample was placed in a high pressure device, which had argon as the pressure transmitting medium. For the measurements made in Gothenburg a conventional two-step apparatus (Bas-set-Bretagne-Loire, France) capable of going up to 9 kbar was used, while in Warsaw measurements up to 28 kbar were made in a device described previously [2]. In both devices the temperature was controlled by a thermocouple placed near the sample, and manganin gauges allowed the pressure to be determined with an accuracy below 0.5 % of the measured value. The

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C7-408 B. BARANOWSKI, J. E. BOWLING A N D A . LUNDEN

resistance of the sample was measured with an accuracy that was mostly better than 1

%.

No attempt was made to evaluate the specific electrical conductivity, and we instead used the inverse value of the measured resistance in all interpretations.

3. Results and discussion. -3.1 THE PHASE DIAGRAM.

-

More than a dozen studies of the phase diagram of silver iodide have been reported in the literature. At room temperature and normal pressure two phases appear to co-exist, an hexagonal phase, P-AgI (B4), and a cubic phase, y-AgI (B3), of which the former is thermodynamically stable, but the latter may predominate under certain conditions. At normal pressure these two phases transform at 147 0C into a-AgI (B23) a phase with a high ionic conductivity. At pressures above some 3 kbar a f. c. c. phase is stable. At temperatures near ambient, there is also an intermediate phase, concerning which there is considerable controversy in the literature, both regarding the structure and the stability range.

When a sample undergoes a phase transition, there is a pronounced change in its resistance. Thus for measurements at constant pressure the discontinuities in the log R versus 1/T plots are well defined and consistent, reproducible from sample to sample and regardless of whether the sample is being heated of cooled. However, for measurements at constant temperature, there were several complications. When the pressure was raised and lowered the transitions showed marked hysteresis, and the pressure at which a phase change occurred also depended on the previous history of the sample. The transitions from

Ply

to intermediate and from f. c. c. to intermediate were found to be extremely time sensitive, while those from intermediate to f. c. c. and from intermediate to

Ply

occur on cue. Thus, unless the pressure is changed very slowly, the intermediate phase might not be obtained at all. This was the case in the work reported in our previous paper [I]. The phase diagram obtained from our resistance measurements is shown in figure 1. Our results agree better with those of Basset and Takahashi [3] than with those of Hinze 141.

FIG. 1 . - AgI phase diagram, squares (m) represent constant pressure measurement, open circles (0) represent constant

temperature measurements.

X-ray powder diffraction studies carried out on the samples used in our experiments indicate the presence of a cubic phase only (L. Nilsson, private communi- cation), and it is likely that most previous investigations also have been performed.under such conditions that transformations from the y phase were studied. Apparent discrepancies concerning the few investigations of the fl phase monocrystals [5-71 can be resolved by assuming that the structure of the intermediate phase as well as the pressure at which the transition takes place is different in the two cases. This would mean that at 25 O C the

P

phase is transferred at 1.1 kbar to a phase with an hexagonal structure, while the y phase goes over at 2.9 kbar to a tetragonal phase.

3.2 CONSTANT PRESSURE STUDIES OF ENTHALPIES OF ACTIVATION. - For the f.c.c. phase sample resistance was measured as a function of temperature at a number of pressures, such as from 8 OC to 120 O C at 4 kbar and 18 O C to 150 O C at 7 kbar. Although the resistance

is consistently higher when the measurement is done with increasing temperature than when the temperature is decreased, the slopes of a plot of log (R) against 1/T are the same in a given temperature range. Such plots show three distinct regions corresponding to low (I), intermediate (11) and high (111) temperatures. At 5 bar the transitions between these regions occur at approximately 35 O C and 85 OC. The interpretation is that extrinsic defects are predomiantly present in region I, in which conduction is assumed to take place primarily by an interstitial mechanism. In region I1 intrinsic Frenkel defects predominate, and in region I11 vacancies begin to contribute to the transport process.

Following standard procedure the slope of the plots of In a(=

-

In R) against 1/T give the experimental enthalpy AH,,, for the three regions, and from these the enthalpy of activation for interstitial migration, AHi,,, the enthalpy of formation of a Frenkel defect, AH,, and the excess enthalpy of activation, AH,,, are calculated :

AHi,,=AHI (1)

AHf =2(AHII

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AHi,,) (2) AH,, =AH,II-AHi,,-AHf/2=AH,IL-AHI,

.

(3) Table I also gives the volume of activation for interstitial migration, AV,,,, which is equal to the apparent volume of activation in region I, AT/,, cf the following section concerning how the activation volume is determined.

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ELECTRICAL RESISTANCE OF THE F. C. C . AgI PHASE

The enthalpies and volumes of activation for

f.

c. c. AgI at dzfferent pressures

AH,,,.

0

Region : AHi ,m AH, AH*, AVi,m

Pressure (kbar) I I1 111 (ev) (ev) (ev) cm2 mole-

'

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4 0.231 0.394 0.683 0.23 1 0.326 0.289 10.7 5 0.201 0.303 0.669 0.201 0.384 0.276 10.1

6

-

0.503

-

9 -6

7 0.289 0.617

-

0.289 0.656 - 9.0

3.3 VOLUMES OF ACTIVATION IN AN EXTENDED PRES- of activation A V is obtained. Thus for silver iodide we

SURE RANGE.

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The resistance measurements were find that this entity is dependent on the pressure :

extended up to 28 kbar at 70 O C and up to 25 kbar at

25 O C . The resistance increased with increasing pressure A V = A V o [ l - A ~ p ] = A V o ~ l - A ~ o ( l - a p ) p ] ( 5 )

Over the whole temperature range, see figure 2. This _where_/3 _{is the compressibility of activation.}_AVO and Ap, are to be understood as the low pressure limits

A of the two entities. An example of the pressure depen-

dence of the volume of activation is given in figure 3.

30

-

A 14

-

2 0

-

RlldLl lo- A V 1 ccmmle l 8 - C I 10 2 0 30 C 16 24 Plkbarl P / kbarf

Ro. 3. - The volume of activation calculated for a f. c. c. AgI RG. 2.

-

The electrical resistance of a f. c. c. AgI pellet as a _{pellet at}_{70 O C .}

function of pressure at 70 OC.

tendency is in agreement with three previous studies 18-

101, but it contradicts the earliest study [ll], according to which the conductivity of f. c. c. AgI should increase with increasing pressure, which was supposed to be due to an increasing contribution of electronic conductivity. We could not find any indication that this should be the case for f. c. c. AgI, and the observed decrease in electrical conductivity with increasing pressure seems to be normal behaviour, predicted by the macroscopic theory of electrical conductance and by simple physical reasoning.

By the least squares method we obtained the following correlation between the measured electrical resistance R of a pellet, and the pressure p :

From the slope of a plot of In (1/R) versusp the volume

The present study confirms our previous observation that the measured volume of activation increases for thicker pellets. Our measurements in the extended pressure range indicate a larger volume of activation when increasing the pressure than when decreasing it continuously. Both tendencies can be explained if grain boundaries play a role in the electrical conductance, which would be the case if Schottky defects are involved. The interpretation of our observation that the volume of activation decreases when the pressure is increased will be discussed in detail elsewhere. One possible explanation is that a continuous transition from one transport mechanism to another may occur on increasing the pressure, e. g. from a Frenkel to a Schottky mechanism.

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C7-410 B. BARANOWSKI, J. E. BOWLING AND A. LUNDBN

bromide the f. c. c. phase is stable at normal pressure For both of these salts two studies of the pressure dependence of the electrical conductivity are known [12-151. None of these indicate that the volume of activation should depend on the pressure for these two salts, but the pressure range covered was smaller than in our work. A comparison of the enthalpies of activation for AgI with those for AgCl and AgBr is complicated by the fact that the latter were obtained at normal pressure. However, it is obvious that the activation enthalpy for defect formation is much lower in AgI than in the other two silver halides. In general it

can be stated that the differences between AgI and the AgCl and AgBr are determined by the large iodide ions, which facilitate the formation of Frenkel defects and favour migration of interstitials over that of vacancies.

4. Acknowledgments. - This work has been supported by the Swedish National Science Research Council and the Royal Society of London, which provided an European Programme Research Fellow- ship (to J. E. B.). The authors would like to thank Dr. B. Heed for preparing samples and Mr. E. Kara- wacki for carrying out computer calculations.

References

[I] BARANOWSKI, B., LUNDEN, A., GUSTAFSSON, P. A., Phys. Status Solidi (a) 31 (1975) K61.

[2] BARANOWSKI, B., Ber. Bunsengens. Phys. Chem. 76 (1972) 714.

[3] BASSETT, W. A., TAKAHASHI, P., Am. Mineral. 50 (1965) 1576.

[4] HINZE, E., High Temp.-High Pressures 1 (1969) 53. [5] VEDAM, K., KIRK, J. L., SURI, S. K., Phase Transitions

(Pergamon Press) 1973, p. 91.

[6] SCHOCK, R. N., HINZE, E., J. Phys. & Chem. Solids 36

(1975) 713.

[7] FJELDLY, T. A., HANSON, R. C., Phys. Rev. B 10 (1974) 3569.

[8] NEUHAUS, A., HINZE, E., 2. Elektrochem. 70 (1966) 1073. [9] SCHOCK, R. N., KATZ, S., J. Chem. Phys. 48 (1968) 2094. [lo] SCHOCK, R. N., JAMIESON, J. C., J. Phys. & Chem. Solids

30 (1969) 1527.

111 ] WGGLEMAN, B. M., DRICKAMER, H. G., J. Chem. Phys. 38 (1963) 2721.

[12] EBERT, V. I., TELTOW, J., Ann. Phys. 15 (1955) 268. [13] ABEY, A. E., TOMIZUKA, C. T., J. Phys. & Chem. Solids 27

(1966) 1149.

[14] KURNICK, S. W., J. Chem. Phys. 20 (1952) 218.

1151 LANSIART, S., BEYELER, M., J. Phys. & Chem. Solids 36

(1975) 703.

DISCUSSION

S. FONTANELLA. - 1. Are there any effects due to the fact that the samples were pressed disks ?

2. What is the structure of the intermediate phase ?

A. LUNDBN.

-

1. The value of the activation volume should be different for a single crystal, but we expect that the pressure dependence of A V would be similar.

2. The intermediate phase obtained from y-AgI is tetragonal, while the intermediate phase obtained from P-AgI is hexagonal according to literature. A. B. LIDIARD.

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Your results on the f. c. c. phase of AgI are interesting because of the possible cornpari- son with AgCl and AgBr. The effects seen in AgCl and AgBr below their melting points are, I believe, under- standable in terms of the known thermal production of Ag+ Frenkel defects and their mutual interactions. The defects are more numerous in AgBr than in AgCI. The question therefore arises whether in f. c. c. AgI

they would be more numerous still and whether their interactions would then be sufficiently important to give rise to a disordering (but not melting) transition of the type envisaged in certain phenomenological models of such transitions (Rice, Haberman and others). Do you think it is possible to do more precise measurements on f. c. c. AgI (i. e. under pressure) to complete this picture ? Perhaps one could stabilize f. c. c. AgI to some extent by incorporating AgBr into it ?