Perovskite tolerance factor defined

Before dealing with these structure t es in detail, the clear-cut dependence of the occurence of these distorted perovskites on the radius ratio of the ions in question should be mentioned. The tolerance factor defined by Goldschmidt [115),... 

Several authors have pointed out that the enthalpy for the formation of perovskite-type oxides from the individual oxides exhibits a correlation with the perovskite tolerance factor, t, which is defined as ... 

Stability of the K2NiF4 structure in oxides. Just as for perovskite oxides, a tolerance factor t may be defined for A2B04 oxides as... 

The lower limits for cationic radii are rA > 0.09 nm, and rB > 0.051 nm in the case of oxides. Goldschmidt (79), on the basis of geometric considerations, defined the tolerance limits of the size of ions through a tolerance factor t = (rA + rx)l 2(rB + rx), where rA,rB, and rx are the radii of the respective ions t would be equal to one for the ideal cubic structure (Fig. 2). In fact, the perovskite structure exists in oxides only between the limits 0.75 < t < 1.0 with t between 0.8 and 0.9 in most cases. For t > 1 the calcite and aragonite structures are prevalent, whereas for t < 0.75 the stable structure is ilmenite. Roth (20) has classified the limits of the existence of these competing structures according to the ionic radii values. 

The tolerance factor (t), introduced by Goldschmidt (1926) is used to define the range of ionic radii of the A, B and X elements allowed by the perovskite structure ... 

Deviations from the ideal perovskite structure may better be described by the observed tolerance factors, fo, and the bond-length distortions of polyhedra, A. Such criteria were introduced by Sasaki et al. (1983) in order to describe structural deformations, arising from tilts and/or distortions of polyhedra in the perovskite-type structures. These parameters are defined as follows ... 

The structure stability of mixed conducting perovskite materials is usually defined in terms of the Goldschmidt tolerance factor t ... 

The deviation from the ideal structure in perovskite oxides can be expressed by the tolerance factor (t) defined as follows ... 

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