Charles T. Perrino
and Steven Peacock California State university Hayward, 94542
I I I
An Experiment in Solid State Chemistry The mobilities of ionic defecfs in silver bromide
Silver bromide and silver chloride have a lattice structure consisting of Frenkel-type defects (I). In the nomenclature of Honig (I), these are silver ion vacancies, Ago-, and silver ion interstitials, Ag+O. These charged defects provide mechanisms for ionic conduction in the silver halides where the transference number of silver ions is unity (2). In a previous paper (3)we described a method for determining the transference number in these compounds and briefly discussed Frenkel defects in thermal equilibrium. In this experiment we propose a procedure to separate the relative contributions of vacancies and interstitials to the ionic conduction. By determining the conductivity of AgBr doped with CdBrz and making comparisons with pure AgBr, it is possible to show that two defects are involved in ionic conduction and that the interstitial defect has the greater mobility. We intend only to review the salient features of the theory already presented in detail elsewhere (1, 4-6) and suggest that a reading of ( I ) and (3) is essential for a complete understanding of this paper.
crease the mole fraction of interstitial ions, X(Ag+o), relative to the pure crystal. This result is clearly indicated by the equations derived in (1) as follows 1) for silver ion vacancies
2) for silver ion interstitials
where X(CdBrz) is the mole fraction of cadmium bro-
Theory
Conduction in pure silver bromide is due to the migration of silver ions, vacancies and interstitials, under the influence of an electrical bias and can be given by the expression (2, 7) for the conductivity, oo,as
where N is the number of silver ions per cm3, e is the electronic charge, Xa is the mole fraction of Frenkel defects in pure AgBr, and w, and w, are the mobilities of the interstitial and vacancy, respectively. A measurement of the conductivity of pure AgBr does not permit separation of the mobilities of the defects. However, if CdBrz is added to AgBr, the conductivity will vary in a very unique way, first reported by Teltow (4) revealing a dual mechanism. More recent explanations of Teltow's results have appeared in several articles (6, 7). Cadmium bromide is incorporated into the silver bromide lattice by direct substitution of CdZ+ on Ag+ sites. This is accompanied by the formation of a silver ion vacancy, necessary for charge compensation, and a building up of a surface layer of AgBr. The surface layer is composed of the two bromide ions from the CdZ+ which pair up with a silver ion displaced by the cadmium ion and another from an interstitial site. The net result is to increase the mole fraction of vacancies, X(Ag0-) and de508 / Journal of Chemical Education
Conductivity ratio versus male fraction cadmium bromide. are the measured data points. The dashed lines indicate the shape of the isOthermS as found bvTeltow.
mide. Now we may write for the conductivity of the doped crystal (1, 71
and divide eqn. (4) by eqn. (1) to obtain the conductivity ratio a/ao. By substituting eqns. (2) and (3) into this ratio we obtain (I, 5)
where Xo = Xo(Ago-) = Xo(Ag+o) and @ is the ratio of the interstitial mobility to the vacancy mobility. @ is related to a minimum of the conductivity ratio which occurs in a plot of a/aa versus X(CdBr2) by the equation a/ao = 2 4 5 / ( 1 @) (5, 6). This is only physically significant when @ > 1. Since, a s the experiment will show, the conductivit~ of the doped crystal initially decreases and contains tewe-r interstitial defects, we can rt~ncludethar the intersritial defect has a greater mobility than the vacancy defect. This means that the first term in eqn. (1) is dominant in the pure crystal and for low dopant concentrations. The experimental results will give a value of o/ao a t the minimum from which @ can be calculated for a qualitative support of this conclusion. This is the interesting result first found by Teltow (4). The results will also show that beyond the minimum, the conductivity will vary linearly with dopant concentration as the vacancv mechanism becomes dominant. This is shown by eqn. (4) the interstitial term is negligible due to the increased concentration of CdBra. In this description we have made some simplifications. The theory does not fit experimental results for high dopant concentrations where association between the two charged defects becomes important. The interested reader can refer to the literature cited (5, 7) for satisfaction in these areas. We have restricted the experiment to low concentrations of CdBrz and modified the apparatus so that the technique is easily reproduced. These adjustments do not in any way detract from the important lessons of solid state chemistry to be learned from performing the experiment.
+
if
Experimental Approximately 10 samples of silver bromide doped with cadmium bromide ranging from 0 to 0.2 mole per cent are prepared. This is done by thoroughly mixing weighed amounts of the two compounds, to a total of 50 g each, and melting the mixture with a Fisher burner in a 50-mm porcelain crucible. Two platinum electrodes, approximately 1 cm square, with attached leads of platinum wire, are inserted into the melt and the crucible is cmled until the AgBr-CdBh mixture has solidified. The cooling process should be done hy slowly reducing the heat of the burner in order to prevent cracking of the solid. The leads are connected to two small bolts fixed into a circular transite cover which also serves to protect the sample from exposure to light during the experiment. The crucible is placed in a furnace where the temperature can vary from 220°C to 2509C. The resistance of each sample
is then measured at several temperatures according to the circuit described below. It is necessary to use an ac method (7, 8) far determining the resistance since the crystal will polarize and a steady current will not be sustained. It is from the current that the resistance and the conductivity are calculated. The only major instrument required to measure the current is a vacuum tuhe volt-meter, VTVM. The input of the VTVM is shunted with a resistor and the leads from the electrodes are connected in series with the shunt, an ac voltage supply, and a variable autotransformer or Variae. The voltage drop across the shunt is determined by the current through the circuit and is measured by the VTVM. If the shunt is a calibrated 1.000-ohm resistor, the VTVM will give a direct reading of the current. Application of high voltages will also lead to polarization of the crystal ( 8 ) so that it is best not to exceed 10V applied. Discussion We make the assumption that the conductivity can he calculated from the resistance, R, of polycrystalline material from the formula, a = LIRA, where A is the area of the electrodes and 1 the distance between them. It is possible to neglect the subtle frequency dependence of the conductivity found by Friauf (8) and we have found that 60 cps is sufficient to prevent polarization for a small duration of the applied voltage. The value of the conductivity found was approximately that reported in the literature (5). Specifically a value of 2.9 X ohm-' cm-I was measured a t 240°C for pure AgBr. Thus we may make a plot of c/o0 for the series of doped samples (see figure). The initial reduction of a due to the decrease in X ( A g + o ) is readily observed. The value of a/ao a t the minimum for 240°C is 0.63 and yields a value of 8 for 4. This is good agreement with Teltow's value of 3.74 since we only wish to prove that fii is greater than p,. At higher mole fractions of CdBrz a nearly linear dependence of a/ao on mole fraction of CdBrz is observed indicating that one vacancy contributes to the conductivity for each atom of CdZ+ that enters the lattice substitutionally. Under the conditions of our experiment we are not able to reproduce the smooth isotherms given by Teltow's data, nor can we compare our results to those found for the AgC1-CdClz system (7). Nevertheless our results exDose some verv interestine and subtle features of ionic r &lid state chemistry in general. conduction in k g ~ and In order to reproduce these results in a physical or advanced inorganic laboratory, a diligent effort will he required. Two students should he able to complete the experiment in 4 or 5 laboratory periods. Literature Cited (11 Honig, J . M..J.CHEM.EDDC..34.224 (1957). (21 M d t . N. F.. and Gurney. R. W.. "Electronic Pmcesres in lonie Cryrials." Dovv Publicationr. New York, 1964.Chspter2. (31 Perrim. C.. and Wentrmk.P.. J . CHEM.EDUC..49.543W731. 141 TPI~oY. J.,Ann. I'hm L D Z .5.63, 71.119d91. 15) Lidiard, A. B., "Handhuch der Physik." (Editor Flugge. 5.1 Val. XX Springer-Verlag, Berlin, IY57,Vol. XX, p.246. 161 Shermon, Paul G . . "OiCfu~ionin Solids." Mcl:raw~Hill, NewYoik. 1963. Chapter5. 171 Abbink, H. C., and Msrrm, D. S.. J. Phys Chpm Solids. 27,205 119861. (81 Friauf. R.. J. Chem. Phyx., 22,1329919944.
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