The formation volume in rare earth intermetallic systems: A representation by means of atomic physical quantities

The formation of the intermetallic phases is often accompanied by large volume effects, and several interpretations of this phenomenon have been proposed following different approaches, either from a simply empirical or purely theoretical point of view. In his pioneering work, Biltz (Biltz 1934) employed the experimental density values to list the molar volumes of the elements and of numerous inorganic and organic solids, including intermetallic phases. The systematic analysis of the data allowed the scientist to estimate the effective volumes of the atoms within the compounds, making possible the application of the volume additivity. Machlin studied the effects of electronegativity on energy and volume of formation, assuming that the volume corrections depend on the Gordy electronegativity difference (Machlin 1980). Watson and Bennett obtained 82a good correlation between the volume effects shown by the phases of the transition elements and a scale resembling the Gordy electronegativity, while a cellular method was applied to estimate the volume changes in phases with alkaline and alkaline earth metals (Watson and Bennett 1982, 1984). Alonso showed that a model of a disordered binary alloy of nontransition metals explains the tendency to a negative deviation from Vegard’s law as this lowers the energy of formation (Alonso et al. 1984). In the Miedema model (Miedema and Niessen 1982), the volume contraction in metallic systems can be ascribed to a charge transfer effect, described mainly by the differences both in an electronegativity-like scale (F*) and in the electron density parameter (nWS). Moreover, in systems with atoms of different radius, a further volume contraction may arise from elastic size mismatch energy. The differences in electronegativity are ignored in the Hafner approach, based on the lowest-order pseudopotential perturbation theory (Hafner 1985). This method provides good results for extended solid solutions of homovalent systems (intra-alkaline and intra-alkaline-earth alloys) and for some intermetallics of the cited elements. A phenomenological approach was used to describe the volume effects displayed by the intermetallic compounds formed by alkaline earths (Ca, Sr, Ba) and divalent rare earths (Eu, Yb) (Merlo 1988) and by the trivalent rare earths (Merlo and Fornasini 1993), introducing a charge transfer atomic parameter, correlated with Pauling’s electronegativity. More recently, the volume contractions of the binary phases of Ca, Sr, Ba, Eu and Yb were represented by a simple equation containing the electronegativity, the compressibility and the group number (Fornasini and Merlo 2006). The most advanced method is based on the calculation of partial atomic volumes and charges as a function of composition (Baranov et al. 2007).