Pettifor structure maps

Fig. 1.13 The Pettifor structure map for sp-valent AB2 triatomic molecules with N 16 where N is the total number of valence electrons. The full triangles and circles correspond to bent and linear molecules respectively whose shape is well established from experiment or self-consistent quantum mechanical calculations. The open symbols correspond to ambiguous evidence. The data base has been taken from Andreoni et a/. (1985).

Pettifor s structure maps additional remarks. We have seen that in a phenomenological approach to the systematics of the crystal structures (and of other phase properties) several types of coordinates, derived from physical atomic properties, have been used for the preparation of (two-, three-dimensional) stability maps. Differences, sums, ratios of properties such as electronegativities, atomic radii and valence-electron numbers have been used. These variables, however, as stressed, for instance, by Villars et al. (1989) do not always clearly differentiate between chemically different atoms. 

Pettifor, D.G.(1995) Structure mapping. In Intermetallic Compounds-Principles and Practice, eds. Westbrook, J.H. and Fleischer, R.L. (John Wiley Sons Ltd., Chichester), Vol. 1, pp. 419-438. 

Fig. 8.16 (The upper panel shows the structure map (xp, Xd) for 169 pd bonded AB compounds, where xp and Xd are values for the A and constituents of a certain chemical scale x which orders the elements in a similar way to the relative ordering number, M. The lower panel shows the theoretical structure map (NptNd), where Np and Nd are the number of p and d electrons respectively. (From Pettifor and Podloucky (1984).)...

An attractive, semiempirical application of physical insight into alloy formation is found in classifications of alloy phase data into structure maps, quantum diagrams, and so on (see Structure Property Maps for Inorganic Solids) where a necessarily limited number of coordinates (one to three) must reflect the physical parameters determining the property of interest. An example is given below in the Pettifor map for Ti-Al intermetallics. Further developments in the mapping of intermetallics are due to Ceder. ... 

Figure 7 A structure map for the AB binaries using the Pettifor index. (Ref 7. Reproduced by permission of Institute of Physics)...

D.G. Pettifor, Crystal Structures of Intermetallic Compounds, Structure Mapping, in J.H. Westbrook, R.L. Fleischer (Eds.), Wiley, Chichester, 2000, p. 195. 

Pettifor, D.G. (1984). A Chemical Scale for Crystal-Structure Maps. Solid State Commun. 51, 31-34. 

Pettifor DG (1984) A chemical scale for crystal-structure maps. Solid State Commun 51 31-34... 

Pettifor DG (2003) Structure maps revisited. J Phys Cond Matter 15 V13-V16... 

Pettifor DG (1986) The structures of binary compounds phenomenological structure maps. J Phys 019 285-313... 

Villars, P., Mathis, K. and Hulliger, F. (1989) Environment classification and structural stability maps. In The Structures of Binary Compounds, eds. de Boer, F. and Pettifor, D. (North-Holland, Amsterdam), Vol. 2, p. 1. 

Some aspects of the mentioned relationships have been presented in previous chapters while discussing special characteristics of the alloying behaviour. The reader is especially directed to Chapter 2 for the role played by some factors in the definition of phase equilibria aspects, such as compound formation capability, solid solution formation and their relationships with the Mendeleev Number and Pettifor and Villars maps. Stability and enthalpy of formation of alloys and Miedema s model and parameters have also been briefly commented on. In Chapter 3, mainly dedicated to the structural characteristics of the intermetallic phases, a number of comments have been reported about the effects of different factors, such as geometrical factor, atomic dimension factor, etc. on these characteristics. 

An extension of the application of these maps to the systematic description of certain groups of ternary alloys has been presented also by Pettifor (1988a, b). Composition averaged Mendeleev numbers can be used, for instance, in the description of pseudo-binary, ternary or quaternary alloys. All these maps show well-defined domains of structural stability for a given stoichiometry, thus making the search easier for new ternary or quaternary alloys with a particular structure type (and which, as a consequence, may have the potential of interesting properties and applications (Pettifor 1988a, b)). 

Figure 3. Distribution map of the coordination types of the partner atoms In the binary Ca phases. Vertically Is reported the atomic percentage of the calcium atom In the phase, and horizontally the partner elements ordered according to the scale proposed by Pettifor (1984). Each symbol reters to an Intermediate phase with known structure. Small Ml circles represent phases with unknown structure.

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