Stability limits on the Poisson ratio: application to a martensitic transformation

The directional dependence of the Poisson ratio has been calculated from elastic constant data for indium and indium-thallium alloys. In the composition range 16-31 at. % thallium these alloys undergo a martensitic phase transformation from the higher temperature face-centred cubic form to the lower temperature face-centred tetragonal one. The onset of instability of crystals of both phases is associated with softening of the [110], [110] polarized acoustic phonon mode; the effect of this mode softening on the Poisson ratio is studied here. One of the alloys investigated (27 at. % thallium) transforms at 125 K; the Poisson ratio variation with temperature near this transformation point is considered in the facecentred cubic phase. A study of the approach to the transition from the face-centred tetragonal side is made possible by room temperature elastic constant measurements through the series indium, indium-1 1.5 at. % thallium and indium-15 at. % thallium. From whichever side the phase boundary is approached, an increase in anisotropy results in the curve showing the Poisson ratio variation in the plane perpendicular to the [110] direction of strain. The limits on the Poisson ratio have been derived from crystal stability criteria based on the requirement that the strain energy remains positive. A comparison between the actual and limiting values shows that in the direction corresponding to the shear by which the transformation proceeds, and only in that direction, the actual Poisson ratio tends towards its lower limit (set by the Born stability criteria) as the phase boundary is approached. In the other directions considered the actual value tends towards only its upper bound, set by the condition that the volume compressibility is positive.