Evidence for highly anharmonic low-frequency vibrational modes in bulk amorphous Pd40Cu40P20

We have measured the elastic constants of amorphous Pd40Cu40P20 (isotropic, two independent elastic constants), single crystal Pd40Cu40P20 (tetragonal, six elastic constants), and single crystal Pd50Cu50 (fcc, three elastic constants) over the range 3.9 < T < 300 K. The temperature dependences of the shear moduli of crystalline Pd40Cu40P20 and Pd50Cu50 are well described by C(T)=C(0)-BT2+Delta C-Lat(T), where BT2 gives the electronic contribution and Delta C-Lat(T) is the contribution due to the anharmonicity of the lattice vibrations. The temperature dependence of the shear modulus of amorphous Pd40Cu40P20 includes an additional contribution, Delta C-E(T), which becomes dominant for T < 20 K: C(T)=C(0)-BT2+Delta C-Lat(T)+Delta C-E(T). The Delta C-E(T) contribution can be explained by the presence of a small number of low-frequency, highly anharmonic vibrational modes, which we characterize as Einstein oscillators with temperature theta(E)approximate to 12 K and Gruumlneisen parameter gamma(C')(E)2. Theory and computer modeling suggest that these modes involve the collective vibration of stringlike arrays of atoms.