Free energy and vibrational entropy difference between ordered and disorderedNi3Al

Abstract

We have calculated free energy and vibrational entropy differences in Ni 3 Al between its equilibrium ordered structure and a disordered fcc solid solution. The free energy and entropy differences were calculated using the method of adiabatic switching in a molecular-dynamics formalism. The path chosen for the free-energy calculations directly connects the disordered with the ordered state. The atomic interactions are described by embedded-atom-method potentials. We find that the vibrational entropy difference increases with temperature from 0.14k B /atom at 300 K to 0.22k B /atom at 1200 K. We have calculated the density of states ͑DOS͒ of the disordered phase from the Fourier transform of the velocity-velocity autocorrelation function. The disordered DOS looks more like a broadened version of the ordered DOS. Analysis of the partial density of states shows that the Al atoms vibrations are most affected by the compositional disorder. The phonon partial spectral intensities along the ͗100͘ direction show that the vibrational spectrum of the disordered phase contains intensities at optical mode frequencies of the ordered alloy. We find that the volume difference between the ordered and disordered phases plays the most crucial role in the magnitude of the vibrational entropy difference. If the lattice constant of the two phases is set to the same value, the vibrational entropy difference decreases to zero. ͓S0163-1829͑98͒06202-X͔

Thermodynamic properties of average-atom interatomic potentials for alloys

“…Finally, the A-atom potential might be useful for thermodynamic calculations of phase behavior involving random solution phases, but in this case small difference in free energy may not be negligible. For instance, the order-disorder free energy for Ni 3 Al has been calculated by Ravelo et al [18] as 0.089-0.083 eV per atom in the range 200-700 K. The free energy difference between the true solid solution and the "average atom" solid solution that we compute here is ∆A~11-14% of the above value. This difference is not too large, and is much smaller than the configurational entropy difference, but might have small consequences for predicted phase behavior.…”

“…Specifically, the Hamiltonian H is parametrized by a scalar variable λ ∈ [0, 1] with H (0) being the system of interest and H (1) being the reference system. Following Skinner et al [17] and Ravelo et al [18], we use an "alchemical" transformation where atom types are transformed from the true elemental atoms to the A-atom at each atomic site via linear interpolation of the mass and the EAM potential. Specifically, for an atom site that is occupied by a type-X atom in the true random alloy, the mass and potential 0 100 200 300 400 500 600 700 3.52 functions are transformed as…”

First-Principles Computation of the Vibrational Entropy of Ordered and DisorderedNi3Al

“…In some studies [8,9], the complexity of the first-principles approach was tackled by using a simplified model for the vibrational entropy based on the Debye-Gruneisen approximation. All of these results seem to indicate that vibrational effects can be non-negligible.Calculations of the vibrational entropy difference between disordered and ordered Ni 3 Al (hereafter denoted DS o!d vib ) has so far been performed using only the semiempirical embedded atom method (EAM) [10][11][12]. Although the specific result seems to depend somewhat on the EAM potential used, all authors found values between 0.1k B and 0.3k B , which corresponds to the range of values found experimentally.…”

“…Calculations of the vibrational entropy difference between disordered and ordered Ni 3 Al (hereafter denoted DS o!d vib ) has so far been performed using only the semiempirical embedded atom method (EAM) [10][11][12]. Although the specific result seems to depend somewhat on the EAM potential used, all authors found values between 0.1k B and 0.3k B , which corresponds to the range of values found experimentally.…”

“…Surprisingly, the samples used to measure vibrational entropy differences even exhibited a decrease in lattice constant upon disordering, in contrast to the EAM results. Some EAM investigations [11] found that a large fraction of DS o!d vib is due to thermal expansion differences between the ordered and the disordered states, while experiments [3,4] The purpose of this paper is to attempt to reconcile some of these conflicting observations and to assess the importance of lattice vibrations in the Ni-Al system through a first-principles calculation of the difference in vibrational entropy between the ordered and disordered states for the Ni 3 Al compound. We find that this entropy difference is small [͑0.00 6 0.05͒k B ] and essentially temperature independent [͑0 6 1͒ 3 10 25 k B K 21 ].…”