1677
NOTES
Dee., 1957
TABLE I COMPARISON BETWEEN OBSERVED AND CALCULATED LATTICE PARAMETER VARIATIONS Oxide matrixa
Additive
Amount (atoms %)
Process
CdO6
hzoa
1.0
Cd2+-Cd’+
Ionic radiib
(A*)
Aa X Calcd.
+
lo4
(PI.)
Obsd.
+
Ratio calcd. obsd.
CdZf = 1.03 13 14 0.93 Cd’+ = 1.18 1n3+ = 0.92 Ni06.6 Liz0 1.0 Ni2 +-Ni3 + Ni2+ = .78 -25 30 0.83 Ni3+ = .35 Li1+ = .78 FesOP Liz0 1.0 FeZ+-Fe3+ Fez+ = .83 -32 27 1.18 Fe3+ = .67 Li‘+ = .78 Fe08 Fe3+(oxidation) 3.8 Fez+-Fe3+ As above -560 - 1900 0.30 Goldschmidt radii, except for Cd’+, for which a value estimated from trends in the periodic table a Reference (see text). is given, and for Ni3+, for which the value given in reference 5 is adopted. The last one however is probably rather small.
-
classical case of FeO oxidation is the example taken (Table 1): The effect of vacancies should make itself felt very strongly in this case, but the lattice actually shrinks even more than one would have anticipated without making allowance for this effe~t.~ The success achieved in describing the changes observed in the controlled valency process can be taken as giving further qualitative, if not quantitative, support to the simple ionic model of controlled valency. l o Alternatively, from the precision determination of lattice parameters for such systems, it is possible to throw some light on the ionic state of the components. For example, for CdO 0.5 GazOa,one would anticipate from the above scheme a net variaJion of the lattice parameter of -13 X lop4 A. Experimental X-ray observations, however, give a very slight increase, 4 4 the difference from the calculated value being A‘V = ny - T ( T ” ~- T ’ ~ ) n y - a(r3 - T ’ ~ ) 3 3 much l%rger than the experimental error of and y = 3(1 - a)/(l a), a being Poisson’s 0.0001 A. In this case the disagreement is large ratio. y is 1.5 for metals and 1.8 for alkali halides; enough to suggest that only a fraction of the Ga let us also assume 1.8for our metallic oxides. The ions (r = 0.62 8.)may have gone into solid solucell edge a will therefore change from a = N-’/a to tion inducing a change of valency. It has in fact a da = (1 AV)‘/a N-’/a, and since AV
