Elastic behavior and vibrational anharmonicity of a bulk ${\mathrm{Pd}}_{40}$${\mathrm{Ni}}_{40}$${\mathrm{P}}_{20}$ metallic glass

The elastic behavior has been studied of a bulk metallic glass of composition ${\mathrm{Pd}}_{40}$ ${\mathrm{Ni}}_{40}$ ${\mathrm{P}}_{20}$, prepared by the recently developed technique of slow cooling from a dehydrated flux of boric oxide in an ultraclean environment. A large ratio ($B^S$/μ=4.56) of the bulk to shear moduli and a large Poisson’s ratio (0.40) at room temperature indicate intrinsic softening of transverse acoustic phonons. Pulse-echo-overlap measurements have been made of both ultrasonic modes between 4.2 and 293 K. Both $C_{11}$ and $C_{44}$ decrease with temperature and show enhanced stiffening at low temperatures which can be associated with two-level systems. To examine nonlinear acoustic properties of a metallic glass the hydrostatic pressure dependence of the ultrasonic wave velocities has been measured. Both ${\mathrm{dB}}^S$/dP (=7.52) and ${\mathrm{dC}}_{44}$/dP (=1.0) are positive, showing that the modes stiffen under hydrostatic pressure in the normal way. The results are used to examine quantitatively the vibrational anharmonicity of a metallic glass by recourse to the mode Grüneisen parameters (${\gamma }_l$=3.20, ${\gamma }_t$=2.23). The mean long-wavelength acoustic mode Grüneisen parameter γ¯ ${}_H{}^{\mathrm{el}(=2.59\mathrm{}}{}_{}{}^{}$) at room temperature is comparable with the thermal Grüneisen parameter ${\gamma }_H^{\mathrm{th}(=2.24\mathrm{}}$). In general, the temperature and pressure dependences of the elastic constants show that metallic glasses, unlike many ${\mathrm{SiO}}_2$-based insulating glasses, have elastic and anharmonic properties similar in kind to the crystalline state (in this case to the component transition metals nickel and palladium). An equation of state for a metallic glass is presented for the first time: The compression is found to be small, being similar to that of nickel.