Solid State Communications, Vol. 78, No. 8, pp. 779-781, 1991. 003881098/91 $3.00 + .OO Printed in Great Britain. Pergamon Press plc COMMENTS ON CBR MODEL: PREDICTION OF COMPOSITION CORRESPONDING TO MAXIMUM CONDUCTIVITY IN MIXED CRYSTALS P. Manoravi and K. Shahi Department of Physics, Indian Institute of Technology, Kanpur 208 016, India (Received 10 January 1991 by C.N.R. Rao) The CBR model, which predicts the composition corresponding to the maximum ionic conductivity in homovalently doped mixed crystals, has been tested for many alkali halide mixed systems. The conditions for the validity of this model are analysed in view of the experimental observations. MIXED IONIC crystals, eg., KCl-KBr, KBr-NaI, etc., have attracted cons;.lerable attention in recent times [l-l 31. Many properties/parameters such as lattice constants (Vegard’s law), molar volume etc., are found to vary monotonically between the two end members. This is generally true, at least in case of mixed crystals of (homovalently doped) alkali halides. However, the ionic conductivity (6) and diffusion coefficient (D) show an unusual behaviour, viz., the existence of a well pronounced maximum in 0 (and 0) at certain intermediate composition. The value of 0 or D at this composition is often much larger than that of either end member. The composition corresponding to maximum d or D depends on the system under consideration, and the behaviour of the conductivity (or diffusion) in these cases cannot be explained on the basis of classical doping concept, nor any law of aver- ages. A few models [5-7, lo] have been proposed to explain the conduction properties of mixed crystals. One such model, called CBQ model, has been suggested by Varotsos [ 14, 151 to predict, among other things, the composition corresponding to the maximum g (or D) enhancement in mixed crystals. The aim of this short communication is to test the validity of this model in view of recent experimental results [9-131. According to the CBR model, the maximum con- ductivity composition x, (in molar fraction) in a mixed crystal system is given by [14, 151 where pd = k,/k, (k, being the compressibility of the defect volume and k, that of pure component) and (4 and h respectively being the molar volumes of the two end members such that I$ > I’,). The ratio pd is related to the pressure derivative of the isothermal bulk modulus (dB/dP) and the Born’s exponent (n) of the pure component through the relation 4(n + 3) ” = ’ + 9(dB/dP - 1)’ (3) Substituting the known values [ 17, 181 of n and dB/dP in equation (3), and v and VZ in equation (2). pd and A can be calculated for various mixed crystal systems. Equation (1) can then be used to calculate the values of the composition corresponding to maximum 0 or D (x,). The x, values obtained in this manner are listed in Table 1 for a number of mixed alkali halide crystals, along with the experimental values. It is readily noticed that the value of x,,, predicted by the CBhZ model [equation (1)] agrees with the experimental value to within f 0.05 for nearly half of the mixed crystal systems listed in Table 1. However, the agreement is poor for several other systems, and in a few cases the prediction of the CBR model is even absurd. For instance, in KBr-NaI (or NaI-KBr), the predicted value of x, exceeds unity which obviously is not poss- ible because x, [equation (1)] must lie within 0 and 1, i.e., zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJ Osr~lsl. As 1 is positive by definition [14, 151, the above inequality leads to the following conditions, zyxwvutsrqponmlkjih pd 2 2 (Or) pd d 0, (4) and pd d 2(1 - A))‘, (5) i.e., either pd is negative or greater than 2, and less than 2/(1 - A). The experimental values of the par- ameter appearing in the above +wo inequalities [equa- 779