Goldschmidt’s tolerance factor

Likewise, the TPO experiments showed that reoxidation of cobalt to form the perovskite structure is more favorable for larger lanthanides. Figure 5 shows a good correlation between the oxidation temperature obtained from the TPO profiles with the Goldschmidt s tolerance factor. Katsura et al. [18] studied the thermodynamics between 1473 and 1673 K of the oxidation of iron to the rare earth perovskites according to the reaction ... 

Figure 5. Goldschmidt s tolerance factor t versus (a) reduction and (b) oxidation temperatures obtained by TPR and TPO experiments for the perovskites LnCoO,.

Fig. 7.5 Behaviour of L11C0O3 perovskites (a) H2 ( ) and CO (O) yields from partial oxidation of methane as a function of the lanthanide ionic radii and (b)Goldschmidt s tolerance factor t and the oxidation temperature obtained from temperature-programmed oxidation experiments (after Ref. 108).

The stability of the perovskite structure depends on Goldschmidt s tolerance factor (rA +ro)/> (rB +ro), with 0.7 < t < 1.2. For tolerance factors outside this range nonperovskite structure are stable, including pyrochlore-type structures A2B2X6Z, AuriviUius phases (AuriviUius, 1949), or tetragonal tungsten bronze (TTB)-type structures Ba2MTi2X30i5 (M = Ln,Bi X = Nb,Ta) (Stennett et al., 2005). 

Although Goldschmidt s tolerance factor t is indeed very useful for the exploration of new compounds with perovskite structure, it is only a necessary condition but not the sufficient condition for the formation or the stability of perovskite structure [145]. Many systems having t in the range of 0.75—1.0 do not form perovskite-type compound. 

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