Phase stabilities structure maps

A quantum-mechanical interpretation of Miedema s parameters has already been proposed by Chelikowsky and Phillips (1978). Extensions of the model to complex alloy systems have been considered. As an interesting application we may mention the discussion on the stabilities of ternary compounds presented by de Boer et al. (1988). In the case of the Heusler-type alloys XY2Z, for instance, the stability conditions with respect to mechanical mixtures of the same nominal composition (XY2+Z, X+Y2Z, XY+YZ, etc.) have been systematically examined and presented by means of diagrams. The Miedema s parameters, A t>, A ws1/3, moreover, have been used as variables for the construction of structural maps of intermetallic phases (Zunger 1981, Rajasekharan and Girgis 1983). 

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. 

Watson RE, Bennet LH (1978) Transition-metals—d-band hybridization, electronegativities and structural stability of intermetaUic compounds. Phys Rev 818 6439-6449 Watson RE, Bennet LH (1982) Structural maps and parameters important to alloy phase stabUity. MRS Proceedings 19 99-104... 

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. 

Holmes 1983) states that when the above transversal homoclinic intersection occurs, that there is a structurally stable invariant Cantor set like the one for the Horseshoe map. It has also been shown by Holmes (1982) that this invariant set contains a countable, dense set of saddles of all periods, an uncountable set of non-periodic trajectories and a dense orbit. If nothing else is clear from the above, it is at least certain that homoclinic bifurcations for maps are accompanied by some very unusual phase portraits. Even if homoclinic bifurcations are not necessarily accompanied by the formation of stable chaotic attractors, they lend themselves to extremely long chaotic like transients before settling down to a periodic motion. Because there are large numbers of saddles present, their stable manifolds divide up the phase plane into tiny stability regions and extreme sensitivity to perturbations is expected. 

The phase behaviour of blends of PS-PI or PS-PB diblocks with PS homopolymer was summarized by Winey et al. (19926). Regions of stability of lamellar, bicontinuous cubic, hexagonal-packed cylindrical and cubic-packed spherical structures were mapped out as a function of homopolymer molecular weight, copolymer composition and homopolymer concentration. All blends were... 

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