Karl S. Vorres' University of Miami
Coral Gables, Florida
Correlating AB04 Compound Structures
The term ABO~compounds is a general classification. A and B are two elements (not necessarily different) combined with oxygen. Examples would include KMn04, CaMoOP, GdAs04, ZrSiOa and TiTi04 (=Ti02). These may be grouped according to the valences of A and B as I-VII, 11-VI, 111-V and IV-IV compounds. The prediction of structures and compound formation has been the subject of thought and investigation for some time. A good knowledge of the subject is the best foundation for making structural predictions. A graphical representation of the data gives a large quantity of information in a manner that is readily grasped. One such approach has been used by Roth,= Keith and Roy,l and Wood4 with AB03 type compounds. The ionic radius of A is plotted against the ionic radius of B for these materials. The structure of each compound, if known, is plotted a t the appropriate intersection. The various structures fall into fairly definite regions. This illustrates the usefulness of the concept of ionic radius in correlating structures. Furthermore, if the structure of any particular AB03 compound of this type were not known, it could be predicted using this graphical correlation and the radii of the A and B ions. This technique is most effective when it is limited to given valence types such as the 11-IV AB03. A different type of diagram is obtained for the 111-111 type compounds. The perovskite structure is found in both diagrams in similar but not identical regions. There are other structures which are found in only one of the diagrame. In extending this approach to other stoichiometries such as ABOl it may be necessary t o differentiate further than valence types by aeparating ions into transition or non-transition metals. The figure shows a plot of Ahrens6 ionic radius of A versus the ionic radius of B for ABOn compounds in general. A and B are chosen such that the valence of A is always less than or equal to B. The structures of 154 compounds were found in a literature search. These structures are indicated at the intersections of the respective radii on 16 plots which were obtained by classification according t o valence types I-VII, 11-VI, 111-V, IV-IV with still further subdivision down to transition metals such as III(A)-V(A), III(A)-V(B), Presented at the 18th Congress of the International Union of Pure and Applied Chemistry, Montreal, August, 1961. This research was supported by the Institute of Gas Technology in Chicaeo and bv the Air Force Office of Scientific Research. ' present address, Department of Chemistry, Purdue University, Lafayette, Indiana. ROTE,R. S., J . Research Null. BUT.Standards, 58, 75 (1957). 'KEITH,M. L.ANDROY,R., Am. Min.,39, l(1954). ' WOOD,E. A,, Aeta Cryst., 4,353 (1951). A ~ R E N SL., H., Geoehim. Co~msmochim.A d a , 2 , 155 (1952).
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III(B)-V(A) or III(B)-V(B). (A) and (B) in these subdivisions refer to non-transition (A) and transition (B) metals respectively and are not t o be confused with the general expressions for cations A and B used in the designation AB04 compounds. To reproduce each structure, a sheet of tracing paper was laid over each chart, and then the compounds corresponding to that structure were drawn. Furthermore, compounds with different structures and adjacent to the desired one were also marked to establish boundaries. These tracings were then superimposed on one master chart. Boundary lines were then arbitrarily drawn
t o enclose only one structure type in an area and as far as possible to have only one area for each structure. This figure gives the proper structures for more than 90% of the compounds whose reported structures were found in the literature search. No solid solution studies have been made as yet to substantiate the boundaries-those were drawn solely t o get the best fit of the data. The dashed lines extending from the lower part of the CaFz area and the ZrOx area indicate a suggested boundary between extensions of the CaFz and SnOI structures. Dashed lines around the MgW04 area and part of the CaUOp area indicate areas of overlap, with SbTaOa and SnOl structures in the first case and CaF, in the latter case. The shading on the upper right and lower right side of the figure indicate areas in which no radii intersections, and therefore no compounds, exist. There are several reasons why a high percentage of compounds fit on a single chart, and some reasons why not all of the compounds will fit on it. One reason for the lack of fit on a single chart is that the range of radii covered by the diierent valence types is not the same. The I-VII group, for example, appears at the top of the chart and has no representatives in the lower third or right half. The IV-IV group is found extensively in the middle to the right side and has no representatives in the upper third. The net result is that a complete superposition of all valence types is not obtained over the entire chart, but rather a partial superposition over certain areas. It is in these areas of superposition of valence types that the exceptions to the structnral correlation are found. A reason why a high percentage will fit on single chart is that some structures seem t o he found over a range of valence types. For example the scheelite or CaWOI structure is found in all four valence types. The rutile structure (designated SnOz on the chart) is found in the 111-V as well as t,he IV-IV type. The BaSO, structure is found in the I-VII and 11-VI types. The anion type seems to determine the structure in several structure types such as VCrOl, CaWOn, and CePOd. The radii of the B ions are sufficiently different t o give a separation on these plots and thus yield areas elongated along the vertical axis. The radii of the A ions can vary relatively widely without changing the strncture. This is due to the large relative size and stability of the B o a " ion, as opposed to the existence of independent B and 0 ions. Thus the type of structure also depends on compound formation or solid solution of two mixed oxides, neither of which forms an anion in the presence of the other. The 45' line in the figure, represents the region in which the radii of A and B are equal. It can be seen that this line passes through the regions where random replacement of A and B takes place. The high symmetry of rntile, or fluorite, can be obtained for AB04 compounds only if A and B are equivalent in the lattice. The observed structures for a given stoichiometry apparent,ly depend on the magnitude of the radii and their ratio, the valence types, the coordination number of B and filling of the d and f shells. Since all of these variables come into play there are some
general exceptions to the chart. For this reason the form is not final but will be subject to revision as more structures are studied. Furthermore it will become more apparent that a single chart will not suffice t o show the structures for all valence types. The distribution within some of these areas will he described to indicate the manner in which they are filled. The VCrOI area has six compounds aligned along the vertical axis. The area for the scheelite or CaWOp structure includes 16 compounds primarily in the central area. Several exceptions to the over-all plot lie toward the lower left corner of the figure, and solid solution studies for the exceptions would not be expected to show the other structures on the over-all diagram for ABOa compounds. The upper area for the zircon (ZrSiO*) structure includes 13 compounds. The large zircon area to the lower right of the over-all diagram was tentatively labeled on the basis of only one reported structure (BTaO4). The upper area is broken up by the area occupied by the VCrO* structure. However, it would not be surprising to observe zircon solid solutions with this structure between compounds on both sides of the VCrOI area over all compositions. The area for the rutile structure includes 20 compounds. Not all of these are true rutile structures since a certain amount of distortion has been reported for them. It is interesting to note that if we can assume random placement of the A and B ions--even though the rutile lattice is distorted, we have some insight into the limits for isomorphous replacement. The discrepancy in size and charge is shown from the identification of the ions and the area involved. The cation to anion radius ratio given for the limit between the rntile and fluorite structures in AX2 compounds on geometric grounds is 0.73. It can be seen that the rutile type structure extends up to NbOz where the ratio is 0.53. ZrOl and HfOz, which have ratios (0.57 and 0.56) that lie within the limit for the rutile type, have monoclinic lattices a t room tempera ture. The structure reported for ZrOz seems to have features of both the rutile and the fluorite l a t t i ~ e . ~ Although ZrOz reportedly has a fluorite lattice, some impurity must be present to produce this. The area of the fluorite lattice includes 16 compounds. Except for the cases in which A and B are identical, these are usually solid solutions with a fluorite lattice. This also gives some insight into the requirements for isomorphous replacement in terms of size and valence differences. Further work needs to be done to determine some of these limits precisely. Frequently 15% differencesin ionic radii are used. Considerations must be given to the type of anion that is formed. The electronegativity of B decreases toward the right side of the plot, and that of A decreases toward the lower part of the chart, therefore the most covalent compounds would be found a t the lower right corner and the most ionic a t the upper left. The tendency to form stable polyatomic anions would increase toward the right side also, especially for B atoms with high charge. In summary, the chart here provided may be used to assist in general correlation of structures and even 6
MCCULLOUGE, J. D., Aclb Cryst., 12, 507 (1959). Volume 39, Number 1 7 , November 1962
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to predict structures of some compounds for which structure information is lacking. However the chart must he used with caution. A systematic study of these compounds may show still other structures which are not presently given here. This type of chart is also useful for the correlation of other properties, as Roth2 has shown. Certain electric properties of the ABOPcompounds studied are dependent on the structure. If a given property is dependent of the structure and can he associated with a given area, then this type of plot may be used as a
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general and powerful tool for correlating a large number of structure dependent properties. If one accepts the general validity of this approach, then conclusions may be reached in certain controversies. The compound VCrOl may also he written CrV04. The only difference lies in the valences of Cr(+ 6 or 3) and V(+ 2 or .5) respectively and thus the type of anion associated with it: either chromate or vanadate. On the basis of the reported structure it clearly seems to belong with the chromates and thus should be written VCr04 rather than CrV04.
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