Structure-field maps

BiFeOj is somewhat anomalous. (Most compounds adopt the pyrochlore stmc-ture under normal conditions of temperature and pressure, not a perovskite-related structure. However, high pressures tend to convert these pyrochlores to distorted perovskite phases.) 

These diagrams do not separate all phases precisely, and a number of efforts have been made to clarify the perovskite phase field more accurately. Recent efforts have used plots of the tolerance factor against the ratio of the radii of the B-site cation to the X-site anion as an octahedral factor  

Although stmcture-field maps do not predict the existence of the perovskite form with complete certainty, indicating that the factors that endow stability to this structure lie outside of simple radius correlations, the ease of the method makes it a simple and useful guide when unknown systems are being explored. 

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Fig. 7.4 Structure field map For A,BO< compounds as a function of cation size. Note that only the more common structures are plotted. Each point on this plot represents at least one compound having the indicated structure and size of cations A(rA) and B(ra). IFrom Muller, O. Roy, R. The Major Ternary Structural Families Springer-Verlag New York, 1974 Reproduced with permission. ...

Zircon, complete solid-solution behavior is observed, and a plot of the unit cell volume against x shows that Vdgard s Law is followed. When the end members are not is structural, a systematic change in the solubility range in both structures is found as A is varied, and the data have been systematized in terms of a simple, potentially predictive, structure-field map. The pervasive polymorphism of these ABO4 compounds, involving both reconstructive and displacive transformations and metastable structures produced by different sample preparation methods, indicates that the crystal structural stability of substituted compounds needs to be carefully evaluated as a function of temperature to assess the structural integrity of waste-form materials. 

The concept of a structure-field map (1) has proven useful in systematizing the occurrence of different structures among a range of fixed-stoichiometry compounds of the A yO type studied here. A binary phase diagram is constructed in which the axes represent the crystal radii (2) of the A and B ions, r and rg, for the appropriate near-neighbor configuration. 

The published (3) structure-field map (SFM) for the A B O compounds does shew regular regions of stability for the structures studied here, and it is evident that the rare-earth series provides a fine grid size in terms of variations of r. However, the lack of appropriately-sized B + ions produces wide gaps in the plot. In an attempt to remedy this, we have prepared and characterized a series of substituted compounds of the form A3+(Bi xB )5+04. If we presume that a compound of this form has a mean B-ion radius rB = (1 - x) r + x rfi , then we can produce a more detailed and precisely defined SFM. 

Figure 2. Left hand side Partial Structure field map for A +B +q compounds. Right hand side Corresponding variation of the cube root of the unit cell volume with the Size of the A ion 8rA.

Vdgard s Law is obeyed and that the concept of a mean radius of the B ion is a valid one. It thus provides additional justification for the use of the structure field map as shown in Figure 3 to predict structural existence and stability in a partially-substituted compound. 

In summary, we have demonstrated that the concept of a structure-field map is a useful one in systematizing the occurrence of crystal structures in a series of iso-stoichiometric compounds. In addition, the concept of a weighted mean radius of an ion at a particular site in a substituted compound has been found to be a valid one. The use of a SFM to predict structural stability and provide warnings about possible polymorphism (and so structural integrity) in a complex multicomponent substituted system could be a useful tool in assessing potential hosts for nuclear waste isolation. 

Fig. 7,5 Composite structure field map for ABXt struciures. X = F or O. (From Muller. O. Roy. R. The Mujor Tetnary SuucUmJ FimiSiesi Spnnger-Veriag New York. 1974. Reproduced with pemussion.l...

A structure field map is remarkably accurate. That exceptions do occur, usually on the borders of the fields, should not be surprising. Serious errors are relatively rare. 

Figure 1.19 Structure-field maps, schematic r versus r (a) (b) A B O ...

Figure 1.20 Structure-field maps, schematic tolerance factor t versus octahedral factor (a) ABO oxides (b) ABX halides (Original data in Li et al. (2008))...

Figure 31 (overleaf) summarizes the structures of the investigated AsRXg-type halides with A = Li, Na, Ag in form of a structure field map. 

Fig. 31. Structure field map for AjRX -type halides with A = Li,Na, Ag.

Because die ions remain in sixfold octahedral coordination in all of the compounds described, the different structures may be associated with the radii of the ions. Figure 42 summarizes the structures as mentioned above, including the AR2X5-type compoimds (see sect. 4.2.1), in form of a structure field map. 

Fig. 42. Structure field map of ARXj/ARjXj-type compounds.

Fig. 1. A structure-field map of the lanthanide and actinide trihalides. Packing efficiency, determined from the sum of the (assumed spherical) volume calculated from the anion and cation radii divided by the actual volume derived from the lattice parameters, is plotted against radius ratio. Only those trihalides that mark the limits of the structure field are indicated.

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