Elastic constants of single crystals of the three phases of In---Pb alloys

In a study of the elastic behaviour of the InPb alloys, the elastic stiffness tensor components of crystals of each of the three phases (fct, $\text{c}\text{a}\text{> 1}$; fct, $\text{c}\text{a}\text{> 1}$; fcc) have been obtained as a function of temperature from pulse superposition measurements of ultrasonic wave velocities. Comparison of the elastic stiffness constants obtained for a fct ($\text{c}\text{a}\text{> 1}$) 5 atm.% Pb alloy with those of In itself and those of InTl and InCd alloys, establishes for this phase that alloying with Pb, as with TI and Cd, enhances the softening of the acoustic 110] phonon mode, polarization 1$\text{1}$0] near the Brillouin zone centre. The elastic properties of a 17 atm.% Pb crystal, which is in the fct ($\text{c}\text{a}\text{> 1}$) phase, are quite different from those shown by In alloys in the fct ($\text{c}\text{a}\text{> 1}$ phase; in particular the response to a shear stress is remarkably isotropie: there is no phonon mode softening in this alloy. Neither is there softening of this mode (which corresponds at the zone centre to the shear stiffness $\text{1}\text{2}$(C₁₁;C₁₂)) in crystals of the fee phase — in complete contrast to the dominating influence of the softening of $\text{1}\text{2}$(C₁₁;C₁₂) in the InTl and InCd fee alloys. In fact for a fcc In-75 atm.% Pb alloy the anistropy ratio for shear $\text{2C}{}_{44}\text{(C}{}_{11}\text{C}{}_{12}\text{)}$ is close to unity. The transitions between the three phases of the InPb alloys are markedly first order and acoustic mode softening has a much smaller influence on the elastic behaviour of the fct ($\text{c}\text{a}\text{< 1}$) and fcc InPb alloys than it has on the fct ($\text{c}\text{a}\text{< 1}$) InPb, InCd and InTl alloys.