An ultrasonic study of the elastic behaviour and phase stabilities of single crystals of In alloys - many grown and characterised for the first time - with Cd, T1 and Pb is presented. In both the fct and fee In-Cd alloys, the shear modulus ½ (C11 - C12) is much smaller than in In and tends to even smaller values as the fct-fcc structural transformation is approached from either the tetragonal or the cubic phase: the onset of instability is manifested as softening of the , q //  acoustic phonon mode near the Brillouin zone centre. However, in contrast to its behaviour in the In-rich, In-Tl alloys, ½(C11-C12) does not go to zero in the In-Cd alloys. This finding corresponds to the more recognisable first-order character of the transformation in the In-Cd compared to that in In-Tl alloys. Calorimetric measurements indicate enhancement of the fusion entropies due to the acoustic phonon mode softening. In the primary solid solution range (fct, c/a > 1), addition of tetravalent Pb to In (valency 3) also reduces the shear modulus ½ (C11 -C12) contrast to that of the divalent Cd and trivalent T1 alloys, this modulus is much larger than that of In in the other fct (c/a <1) phase; neither is mode softening evident in the Pb-rich fee phase - the anisotropy ratio A (= 2C44/(C11-C12)) close to unity and the elastic behaviour is isotropic. The shear constants of bee Tl-rich, In-Tl alloys are in agreement with Zener's prediction namely that ½(C11-C12) should be small compared with C44 for a closed ion shell bcc material. The alloy data has been used to obtain the first estimate of the elastic constants of the high temperature bcc polymorph of Tl. The. stability of this polymorph has been found to be - in accordance with Zener's arguments - due to its lower Debye temperature and consequently greater entropy than that of the normally occurring hcp form.
|Date of Award||1977|