Ionic conductivity of mixed silver halide crystals

Ionic conductivity of mixed silver halide crystals

J. Phys. Chew. Solids Vol. II. pp. 173 -178 Pergamon Press Ltd., 1980. Printed in Great Britain IONIC CONDUCTIVITY OF MIXED SILVER HALIDE CRYSTALS? L...

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J. Phys. Chew. Solids Vol. II. pp. 173 -178 Pergamon Press Ltd., 1980. Printed in Great Britain

IONIC CONDUCTIVITY OF MIXED SILVER HALIDE CRYSTALS? L. S. CAINI and L. M. SLIFKIN Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27514, U.S.A. (Received 14 August 1978; accepted 20 July 1979)

Abstract-Toevaluate theeffectsofmixed halides on the lattice defectparameters of the silver halides, we have measured theionicconductivity both oftheentire range ofmixed AgBr- AgCl single crystals, and also of several iodide-doped crystals. For the AgBr-AgC1 system, the intrinsic conductivity at a given temperature decreases monotonically from pure AgBr to pure AgCI. The deduced Frenkel defect formation energy varies only a little from 0 to 50 mole % AgCl, and then increases rapidly with further increase in AgCl content, closely paralleling the ratio of bulk modulus to dielectric constant. The defect formation energy in these crystals hence reflects the average macroscopic properties of the solid solution. For the iodide-doped crystals, however, the results are quite different. Small amounts.of iodide cause large increases in the conductivity of AgBr and AgCI, especially in the latter. These results suggest that the elastic strain introduced by the oversized iodide ion exerts an appreciable local effect on the Frenkel defect formation, in contrast to the crystal-averaged response found for the AgBr-AgC1 solid solutions. Furthermore, the Arrhenius plots for the conductivities of the AgBr:I specimens show curvature which suggests a temperature-dependent pairing of the solute.

INTRODUCTION Ionic conductivity measurements on ionic solids provide information about the thermodynamic and kinetic parameters which govern the number, mobility, and interactions of point defects, i.e. the enthalpies and entropies of defect formation, migration, and interaction. Simple ionic solids, such as the alkali and silver halides, have been extensively studied in recent years in order to determine their point defect properties, as well as to provide a model for application to more complex solid state systems. In particular, there have been several measurements ofthe temperaturedependence of the ionic conductivity of nominally pure silver chloride and silver bromide, as well as of crystals intentionally doped with aliovalent cationic impurities [l-6]. The results of these studies have usually been analyzed by a non-linear leastsquares computer-fitting to yield the required thermodynamic parameters. Attempts have also been made to relate solute transport parameters to both the size and the electronic structure of the solute ion [6,7]. To our knowledge, there has been no prior study of the ionic conductivity of solid solutions of AgBr/AgCl, which are completely miscible over the entire range of composition. In the case of iodide-doped crystals, however, for which the solute is only slightly soluble at temperatures well below the melting point, there have been several earlier qualitative reports, by Teltow [S]

TSupported by UNC Materials Research Center through NSF Grant No. DMR-7500806, and by NSF Grant No. DMR-76-18862. IPresent address: Department of Physics, Davidson College, Davidson, NC 28036, U.S.A.

and Matejec[9], on polycrystalline material. There have also been studies of iodide-doped silver halide microcrystals [ 101, but the distribution of composition throughout the microcrystals was not known. All of these previous reports agree that the addition of iodide causes an increase in the ionic conductivity of the silver halides. It is the intent of the present work to extend these studies to well-defined, large single crystals, and to attemptamorequantitativeanalysisofthe halidesolute effects. We therefore report measurements of the ionic conductivity of a range of mixed AgBr-AgCl single crystals, and of five iodide-doped crystals. The primary goal was to determine the dependence on composition oftheintrinsicconductivityand theenergyofformation of the Frenkel defects (although the conductivity also depends on the activation energy for migration of the interstitial silver ion, this energy is so small that its compositional variations are essentially invisible in an experiment such as the present one). Of particular interest is the question as to whether the mixed halide crystal has properties reflecting some average medium or whether, instead, the conductivity will reflect effects of local lattice strains introduced by the different sized ions in the solid solution. EXPERIMENTAL PROCEDURE The single crystals were prepared by Mr. Charles B. Childs of the Crystal Growth Facility of the University of North Carolina. Except for the two AgCl-rich mixed AgBr/AgCl crystals, which were pulled from the melt, the crystals were grown by the Bridgman technique. The boules, typically 2.5 cm in diameter and 15-20 cm long, were single crystals in the case of the AgBr/AgCl 173

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specimens. The iodide-doped boules contained extensive polycrystalline portions, but there were regions which were both transparent and had no observable grain boundaries. Monocrystal samples were cut from these boules by means of a jeweler’s saw, after which they were handpolished on graded silicon carbide papers to the form of a flat rectangular parallelepiped about 0.5-l cm’ in cross-section and 0.4 cm thick. They were then etched lightly in a sodium thiosulfate solution and annealed in an atmosphere of 30mm of helium for two weeks. During the sample preparation, extreme care was taken to prevent contamination by divalent cation impurities. All handling was done with finger cots and all glass apparatus and surfaces were previously cleaned with a solution of sulfuric acid and sodium dichromate, and then rinsed thoroughly. All treatments of the silver halides were carried out under safelight. Measurements were made on nominally pure AgBr, pure AgCl, four mixed AgBr/AgCl crystals (at composition intervals of approximately 20 mole %), three iodide-doped crystals of AgBr, and two iodidedoped AgCl crystals. Halide compositions were determined by chemical analysis, performed by Johnson-Matthey Chemicals Ltd. No analyses were made for uncontrolled divalent cation impurity, since crystals produced by the UNC Crystal Growth Facility typically have less than 1 ppm aliovalent impurity; this was confirmed for the present specimens by the low values of the ionic conductivity in the extrinsic region. The compositions of all of the specimens used are listed in Table 1. For the iodide-doped material, no results are Table 1. Basic data for the mixed silver halides at 295 K (A)





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presented for crystals of higher solute content because, contrary to suggestions often encountered in the literature dealing with photographic silver halide microcrystals, the real solubility of iodide is not much above the maximum values shown in Table 1. For the purposes of data reduction, it was also necessary to know the mass densities of the specimens. For the AgBr/AgCl crystals, these were determined by hydrostatic weighing; the lattice constants thereby calculated from the known compositions and densities were found to be in excellent agreement with those measured directly by Chlteau[ll]. For the iodidedoped crystals, the densities were calculated from the known compositions andCh&teau’svaluesofthelattice constants. These densities are also displayed in Table 1. Electrodes were painted on using Dag Dispersion No. 154, primarily a suspension of graphite in methanol. The conductivity measurements were made in an apparatus described by Gerlach[3]. Measurements were taken at 10 kHz in a helium atmosphere on two different bridges, a General Radio 1615-A and a 716-C capacitance bridge, depending on the value of conductance being measured. At the beginning of a measurement, the temperature was raised slowly to the highest temperature used, approximately 3W315”C. No data were taken at higher temperatures than this because oftheonset ofthe well-known anomalous conductivity increase, which sets in around 325”C, and which precludes the use of high-temperature conductivity in the determination of low-temperature defect energies. Several data points were taken during this initial warm-up for comparison with later, more detailed measurements during the stepwise cool-down. These latter data were taken at 3-5” intervals while cooling down to room temperature. Sufhcient time was allowed for thermal equilibrium to occur at each temperature. For the AgBr/AgCl samples, measurements were also made below room temperature in an effort to extend the extrinsic region far enough so that a detailed computer analysis of vacancy migration and association energies might also be possible. These measurements were made separately in a heated liquid nitrogen cryostat, at 5” intervals during cool-down from 100°C to -50°C. This temperature range allowed enough overlap with the high temperature range so that the two sets of data could be superimposed. In all cases the agreement was excellent between the two sets, for a given specimen. It was not feasible to extend the data below - 50°C because of the very low conductivity at these temperatures.



The conductivity curves for all six crystals are shown in Fig. 1. The curves are numbered in order of increasing AgClcontent, with pure AgBr represented by No. 1 and pure AgCl by No. 6. Each curve is composed ofapproximately 80 data points and extends from about 300 to - 50°C.


Ionic conductivity of mixed silver halide crystals are currently

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Fig. 1. Ionic~ndu~vityofAgBr-AgCl~~sin~e~s~~ Curve 1: AgBr; 2: AgBr-2Omole % AgCI; 3: AgBr-39 % AgCl; 4: AgBr-57% AgCI; 5: AgBr-79 % AgCl; 6: AgCL

As can be seen from the figure, at any given temperature in the intrinsic region (1000/T > 2.5), the conductivity decreases monotoni~lly with increasing content of AgCl, falling especially rapidly from the 50 - 50 composition to pure AgCl. In the region of the knee and in the extrinsic region, however, where the conductivity is dominated by the uncontrolled small amount of divalent cation impurity, the curves cross and it is not possible to say ~ythingq~ntitative. It can also be seen that this ~pu~ty content is sufficiently small that even upon extending the range of measurement down to -50°C the extrinsic slope in these nominally pure crystals is still not well-defined. The usual model for the analysis of ionic conductivity data in the silver halides assumes Frenkel defects in the silver sublattice, the o~upation ofsubstitutional lattice sites by any divalent cation impurity ions that may be present, and the partial association of these divalent cation impurities with cation vacancies to form neutral complexes. Long range interactions between charged defects are allowed for by using the Debye-HtickelLidiard approxima~on. Equations are developed to describe the mass-action equilibria between the concentrations of the various defects, and the conductivity is then writtenas thesumofthe products of the concentration, charge, and mobility of each mobile defect. The experimental data for conductivity versus temperature are then fit by means of this theory which, in general, contains a total of 11 adjustable parameters. The difficulty of obtaining a unique and unambiguous set of parameters, in the absence of other data, such as tracer diffusivities, has recently been emphasized by Murthy and Pratt[lZ]. In the present research, the unavailability of a prolonged range of extrinsic conductivity (a result of the high purity of the material) renders such a goal virtually impossible. We therefore

engaged in doping these crystals with several parts per million ofa divalent cation, Mn' +, in order to obtain the necessary extrinsic data to supplement the present results. This will hopefully make possible the determination of relatively unambiguous values for the cation vacancy parameters as a function of composition of the mixed crystals. Meanwhile, in the absence of the possibility of a unique computer fit, one can still obtain semiquantitative comparisons for some of the important defect parameters, particularly for the formation enthalpy of the Frenkel defect. In the intrinsic region, the majority of the current is carried by the interstitial silver ions, especially at temperaturesnot too near to the meltingpoint. Ifone thusneglects thecontribution from vacancy motion, then the slope of ln(rrT) vs l/T should have the value [h,/2 + hi]/k, where cr is the conductivity, T the absolute temperature, hf the Frenkel defect formation enthalpy, hi the effective enthalpy of motion for the interstitial, and k is Boltzmann’s constant. Since it has been found[2,4] that hi is only a few percent of h, in the silver halides, the variation with composition of the slope of the intrinsic region of the plot of In (aT) vs l/Tshould give a good measure of the composition dependence of h,/2. Straight lines have therefore been drawn through the intrinsic regions of the curves in Fig. 1. The values of these slopes have then been normalized to the value for pure AgBr, and these normalized values are plotted as a function of composition in Fig. 2. The trend seen in this figure is similar to the trend earlier reported for the bulk modulus for these same mixed crystals [ 133. In this connection, a proportionality between bulk modulus and the various defect energies is also a feature of the simple, semi-empirical theoretical treatment of VarotSOSand Alexopoulos [14]. They suggest that the Gibbs

1 0.9 0


’ ’ ’ 40 60 Mole % Ag Cl


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Fig. 2. Comparison of the slope of the intrinsic region of the conductivity plots (open cirdes) with the product of bulk mod&s and inverse dielectric constant (filled cirdes) at 500 K, as a function ofcomposition. All values are normal&d to the value of AgBr. The solid iii are drawn only as an aid to the eye.




free energy of defect formation can be represented as a local elastic work,and hence is proportional to the bulk modulus times the atomic volume. They thereby obtain defect parameters which have been found to agree well with experiment. The defect formation enthalpies should also depend on the inverse of the dielectric constant of the medium. Thus, we are led to compare the compositional variation of/r/ with that of the ratio of the bulk modulus to the dielectric constant. This ratio, again normalized to the value for pure AgBr, is also shown in Fig. 2 as a function of composition. The data shown are for 500 K, which lies within the measured intrinsic region; they are calculatedfrom theelasticdataofCainC131 andalinear interpolation of the dielectric constants determined for pure silver halides by Smith [lS]. Comparison of the two curves demonstrates a striking qualitative agreement, indicating that this simple model does indeed satisfactorily account for the main dependence of h, on composition for the AgBr/AgCl system. Any additional effect attributable to localized elastic strains, which should be most evident at compositions near the middle of the range, is not apparent in these experimental results. The effective Frenkel defect formation energy for the AgBr/AgCl system thus seems to respond primarily to bulk-averaged physical properties, rather than to the detailed local atomic configurations. In this sense, these results differ greatly from those obtained with iodide-doped crystals, and which are described below. RESULTS: THE IODIDE-DOPED


The ionic conductivities of the AgBr-AgI mixed crystals are shown in Fig. 3. One sees relatively large increases in conductivity upon the addition of small percentages of iodide. (The crossings of several of the 4.0

L. M.


curves at lower temperatures is probably simply due to variations in extrinsic impurity content). These increases are in qualitative agreement with the previously reported measurements on polycrystals. At 28o”C, for example, the 2.1 % iodide sample has a 55 y{ larger conductivity than pure AgBr, the 3.7 :/, iodide sample has an 81% larger conductivity, and the 4.9 % iodide sample has a 116 “/, larger conductivity. At any particular temperature in the intrinsic region, the conductivity increases monotonically (although not always linearly) with increasing iodide content. Moreover, in comparison with the AgBr/Cl system, the addition of iodide to AgBr produces increases that are approximately ten times greater than the decreases produced by a comparable addition to AgBr of chloride. This undoubtedly is a reflection of the greater local strain about an iodide ion. Besides the large increases in conductivity, the most striking feature of these curves, which is not readily apparent on the coarse scale of Fig. 3, is the continuous upward curvature in the intrinsic region for all the iodide-doped AgBr samples. This is seen more clearly in Fig. 4, which shows an expanded plot of the conductivity in the intrinsic region. The curvature is readily apparent on these plots, especially when compared to the linear AgBr plot. Because of this curvature, it is not possible to make use of standard conductivity theory in order to analyze these plots for changes in the enthalpies of Frenkel defect formation and migration. It appears likely that this curvature is due to a temperature-dependent aggregation of iodide ions. To test this, we performed quenching experiments and temperature cycling experiments, but found no hysteresis effects nor other dependence of conductivity on thermal history or time. Previous luminescence ex4.0







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Fig. 3. Ionic conductivity of AgBr-AgI mixed single crystals Curve 1: AgBr; 2: AgBr-2.1 mole % AgI; 3: AgBr-3.7% AgI; 4: AgBr-4.9 “/, AgI.

















Fig. 4. Ionic conductivity of AgBr-AgI mixed single crystals in the intrinsic region. Curves same as Fig. 3, but on expanded scale.

Ionic conductivity of mixed silver halide crystals periments [16], moreover, have shown that in AgBr/I samples with comparable iodide contents, a nonnegligible fraction of the iodide ions may be present as close pairs. We suggest, therefore, that the conductivity curvature may be caused by the temperature dependence of the concentration of pairs or other small aggregates of1 -, but not by larger precipitates, since we would have seen the hysteretic effects of any larger precipitates in the quenching experiments. The strain fields of pairs and small aggregates may well produce effects on the concentration of Frenkel defects which are different from those of the isolated iodide ions, and hence which would be temperature dependent as the aggregates grow and shrink. Moreover, a simple estimate of the anion jump frequencies, based on extrapolation of self-diffusion data [ 171, indicates that the equilibrium between single iodide ions and pairs could be established too rapidly, at these iodide concentrations, to be quenched in; this is thus consistent with the fact that our quenching experiments revealed no hysteresis effects. The ionic conductivities of the AgCl-AgI system are shown in Fig. 5. We see that the conductivity increases substantially in the intrinsic region with the addition of even these very small amounts of iodide. The changes per unit iodide addition are much greater than the corresponding effects in the AgBr-AgI system. The increase in conductivity is, again, in qualitative agreement with the earlier, qualitative investigations of others. Considering the small amounts of iodide present, these increases are striking. At 28O”C, for example, addition of only 5 x lOA mole fraction iodide produces a 22 ‘A increase in conductivity, while the increase for the 0.4 % AgI sample is 37 %. Thus, the addition of only 0.05 ‘Aiodide to AgCl causes as large a fractional increase in conductivity as does addition of 1% iodide to AgBr, or the addition of 4 % bromide to AgCl. This effect is not surprising, in that iodide is more


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oversized in AgCl than in AgBr, or than bromide is in AgCl. Another difference between the iodide-doped AgBr and AgCl is the lack of noticeable curvature in the intrinsic region of the iodide-doped AgCl. Presumably, this curvature would appear if one could introduce a highenoughconcentrationofiodide.Becauseofthelow solubility in AgCl, however, there may not be enough solute to form pairs. On the other hand, since the intrinsic regions of the plots of Fig. 5 are rather linear, one might hope to analyze their slopes to obtain a measure ofthe change in the Frenkel defect formation energy as a function of iodide content (the migration activation energy of the interstitial silver is already so small that any effect on it of the addition of iodide would be invisible). Unfortunately, the extent of this linear region is rather small, being limited at low temperatures by the curvature that precedes the intrinsic-extrinsic knee and at high temperatures by the early onset of the wellknown anomalous conductivity excess (which, interestingly, was found to set in at significantly lower temperatures in the iodide-doped AgCl than in pure material, and which thereby defeated our efforts to extend the linear region up to about 350°C). Therefore, instead of attempting to deduce defect parameters by means of computer fitting, we have simply made a comparison of the slopes of the linear intrinsic regions ofthe curves of Fig. 5. We find that the effective values of h, for the two iodide-doped samples are both approximately 7 % less than that for pure AgCl, but we cannot, by this crude analysis, distinguish a dependence of h, on the concentration of iodide. We thus see that the addition of iodide to both AgBr and AgCl causes large increases in the intrinsic conductivity. These increases are much more dramatic than the corresponding changes found for AgBr-AgCl crystals. The data thus indicate that the elastic strain introduced by the oversized iodide ion causes a significant decrease in the formation energy of the Frenkel defect, probably by lowering the energy of a cation vacancy at adjacent sites. This is not surprising, since on a hard-sphere model, the iodide ion is so large that it overlaps neighboring halide ions in both AgBr and AgCl. This mode1 is, of course, consistent with the observation that the effect of iodide solute in AgCl is much greater than in AgBr. On the other hand, in mixed AgBr/AgCl crystals, a hard-sphere model does not predict any overlap of the bromide ion onto neighboring ions; this can thus explain why these materials do not show the dramatic effects found with iodide-doped crystals, but instead respond simply in terms of the bulk-averaged macroscopic properties. wish to thank Charles B. Childs for growing the crystals, and Herbert Manning and Daniel Bourland for help with the experiments.

Acknowledgement-We 1.5


2.5 1000/T




Fig. 5. Ionic conductivity of AgCI-AgI mixed single crystals. Curve 1: AgCl; 2: AgCI--0.05 mole % AgI; 3: AgCI-0.4 % Agl.

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