Goldschmidt tolerance factor

ABOs compounds containing lanthanum are closer to the ideal perovskite than those containing smaller rare earth ions. Compounds of the smaller rare earth ions appear to have a distorted perovskite structure of lower symmetry. When, however, the relationship between the radii is very far from being ideal (eq. 31), strong distortion may result giving an entirely different structure. The Goldschmidt tolerance factor, t, for the perovskite structure is related to the ionic radii by... 

A useful parameter by which the stability of perovskites can be judged is the Goldschmidt tolerance factor t (25). In a study of the thermochemistry of the lanthanide (IV) perovskites... 

Goldschmidt tolerance factor perovskites Gokhshtein, Yakov Peysachovich... 

For the ideal cubic lattice of ABO3 perovskite, A is the larger cation surrounded by eight BC>6 octahedra. In order to estimate the general possibility of perovskite lattice formation from ionic radii, the Goldschmidt tolerance factor (ts) can be used [i] ... 

As observed by TPR, the nature of the Ln affects the reducibility of Co in the perovskites LnCoO,. The Goldschmidt tolerance factor t = (r, + r )/[V 2 (r( +r(,)j obtained for the structures of LaCoO, PrCoOi, NdCoO, SmCoO,and GdCoO,were 0.899, 0.885, 0.878, 0.867 and 0.857, respectively. These tolerance factors indicate that considering solely geometric factors lanthanum, the largest ion in the series, forms the most stable perovskite structure. This trend is reflected in the TPR results where the perovskite LaCoO, the most stable structure, is reduced at the higher temperatures, 844 K (Fig. 5). 

An interesting feature of these structures is the degree of mismatch between the set of layers of different types. Geometrical considerations (see Fig. 9c) suggest that the size match will be perfect if the so-called Goldschmidt tolerance factor t = rf o)Nl r Q) =. Since V2(r(. Q) ... 

The data obtained allowed us to verily that the Goldschmidt tolerance factor t, used to predict the oxide-based perovskites stability [11] could also be utilized to correlate the stability of fluoiinated ternary compounds. The t value is a lunction of the anionic and cationic radii, the closer the t factor is to unity, the greater is the perovskite stability. 

Similar reaction sequences can probably be established for compositions with other cation combinations as well. However, it is not clear whether a generalized reaction sequence can be established for complex Pb compositions. There have been other attempts to generalize the tendency to form the py-rochlore phase in complex Pb compositions through correlations in ionic size, ionic bonding, and so on [31,32]. Two parameters were used the Goldschmidt tolerance factor [33], defined as... 

Cf compounds have been acquired recently (Fuger et al. 1993). A linear relationship exists between the heat of formation of these perovskite-type oxide systems and the Goldschmidt tolerance factor, which permits estimations for the enthalpies of formation of a number of homologous compounds of this type. From data of such Cf compounds, the enthalpy of formation of CfOj was estimated to be - 854-1- lOkJ mol in good agreement with a value of — 858 kJ mol derived from interrelationships between the molar volumes of dioxides and their standard enthalpies of solution (Morss 1986). It has not been feasible to carry out such direct experimental measurements with CfOj and these indirect approaches have provided the only data of this type. Data for other actinide oxides can similarly be obtained by these indirect approaches. 

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

The perovskite stracture is illustrated in Figure 6.10(b). The ideal stoichiometry of a perovskite is ABX3, where X is an anion, B is a cation with octahedral coordination, and A is a large cation with cuboctahedral coordinatioa The two cation sites are cormnordy referred to as the B-site (coordination number = 6) and the A-site (coordination number = 12). In order for the ideal cubic stracture to be realized the size of the A- and B-site cations mnst be well matched. The size match or lack thereof between the two cations is given by the Goldschmidt tolerance factor, t ... 

Structure). One expects the descent in symmetry to be a function of a modified Goldschmidt tolerance factor,... 

It should be noted that the new compounds prepared by Berndt et al. (1975) only appear to be stable at lower temperatures at higher temperatures they decompose into one or more solid-solution phases, and it is therefore interesting to speculate on the possibility of the stable existence of other such compounds at even lower temperatures. The lower limit of 0.77-0.79 for the Goldschmidt tolerance factor is, of course, derived empirically from experimental observation... 

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