College Park, Maryland June 6 - 10 , 2004 |
M3-A3 (14:15): Vibrational Entropy of Dilute Alloying in Vanadium Studied by Inelastic Neutron Scattering
O. Delaire, T. L. Swan-Wood, M. G. Kresch, B. T. Fultz (California Institute of Technology)
Inelastic neutron scattering spectra were measured at room temperature on the LRMECS spectrometer for the dilute random substitutional alloys V(X) with X=Ni, Pd, Pt and Co, at impurity concentrations of 6 % to 7 %, and compared to that of pure vanadium. These spectra show a large stiffening of the phonon DOS when these impurities are introduced into the V host, even at these low concentrations. The experimental neutron-weighted DOS curves were inverted using a supercell Born-von Karman model coupled to an algorithm for optimizing the force-constants. From these calculations we obtained inter-atomic force-constants and DOS curves de-weighted from the different neutron cross-sections of V and impurities. The vibrational entropy of substitutional alloying in vanadium was calculated using these inverted DOS curves. We estimate the phonon entropy of alloying in vanadium for 6.25 % Ni, Pd, or Pt, and 7 % Co respectively to be: -0.093 ± 0.001 kB/atom, -0.136 ± 0.001 kB/atom, -0.188 ± 0.001 kB/atom, and -0.305 ± 0.003 kB/atom. The large negative vibrational entropy of alloying observed for the V-Pt and V-Co systems is comparable to or larger than the gain in configurational entropy for a 6 % to 7 % solute concentration. The source of this stiffening is primarily an increase in the 1NN longitudinal force-constants between the impurities and the host atoms. We show that the magnitude of this effect is in good agreement with the Rose universal equation of state and elastic relaxation theories. We expect to present additional results on V(Fe,Ti, Zr) alloys of similar compositions.
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