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The structural transformation from face-centered cubic (fcc) to body-centered cubic (bcc) is known as the Bain path. Both structures can be represented by a common tetragonal cell: bct (fct) with c/a = 2 and 1 (1 and 1/ 2) for bcc and fcc, respectively. Transitions between fcc and bcc occur in iron-carbon alloys by temperature quenching and in some metals upon heating and/or compression. Related to the Bain path tetragonal phases are shown to form in the epitaxial metal films in order to release the stress due to the size mismatch. The driving forces behind these transitions originate from an external force such as temperature, pressure or strain. In our work we consider a sequence of tetragonal phases in binary sp metal alloys that provides strong evidence for a correlation of c/a with an alloy composition or electron to atom ratio an internal parameter. A driving force behind the tetragonal distortion in these alloy phases is associated with the number of valence electrons per atom. Tetragonal structures of metallic phases are considered in In-Sn and related alloys including data on equilibrium ambient-pressure phases; metastable phases quenched from liquid and high-pressure phases obtained in our studies [1-6]. Degree of tetragonal distortion from fcc or bcc is related to the valence electron concentration (z) within a model of the Brillouin zone Fermi surface interaction (FSBZ). To analyse the features of the fcc bcc transformation path in sp metal alloys two contributions to crystal energy need to be considered: the electrostatic Ewald term and the electron contribution due to FSBZ. It was suggested that for In and In alloys it is favourable for BZ corners to touch the Fermi sphere. This results in the instability of fcc with respect to tetragonal distortion. According to this model the axial ratio adapts itself to maintain this contact following the expanded FS caused by alloying. Application of high pressure shifts the balance between the two terms of the crystal energy making the electronic contribution increasingly dominant. Our results on binary alloys under pressure correspond well this FSBZ model: (i) fcc fct transitions under pressure in the In-Pb alloys with 40 and 60 at.% Pb [4]; (ii) pressure-induced decomposition of the In5Bi3 compound into two tetragonal phases with different c/a [5]; (iii) a switch from c/a > 1 to c/a < 1 in the In-10 at.% Pb alloy on compression [6].

The fcc–bcc Bain path in binary alloys under high pressure: valence electrons as a driving force