Negative Entropy of Mixing for Vanadium-Platinum Solutions

Abstract

The phonon densities of states for pure vanadium and the solid solutions V-6.25% Ni, Pd, Pt were determined from inelastic neutron scattering measurements. The solute atoms caused a large stiffening of the phonons, resulting in large, negative vibrational entropies of mixing. For V-6.25%Pt, the negative vibrational entropy of mixing exceeds the conventional positive chemical entropy of mixing. This negative total entropy of mixing should extend to lower concentrations of Pt, and the effect on the bcc solvus line is discussed. The experimental data were inverted to obtain interatomic force constants by using a Born-von Ká rmán model with an iterative optimization algorithm. The stiffening of bonds responsible for the decrease of entropy was found to occur mainly in first-nearest-neighbor solute-host bonds, and correlates in part with the solute metallic radius. DOI: 10.1103/PhysRevLett.93.185704 PACS numbers: 64.75.+g, 61.12.-q, 63.70.+h Mixing creates structural disorder, so the entropy of a mixed system is expected to be larger than an unmixed system. The well-known configurational entropy of mixing in the point approximationis always positive (c is concentration, 0 < c < 1). Its contribution to the free energy F E ÿ TS therefore promotes solubility at higher temperatures, and, in equilibrium with a second phase of lower entropy, the solubility limit of a solid solution should increase with temperature. This is typically observed, but exceptions are noteworthy, including unexplained cases where solid solubility decreases over a range of temperature, termed ''retrograde'' solubility. Experimental and theoretical investigations have shown that differences in vibrational entropy play an important role in the relative thermodynamic stabilities of solid phases [1][2][3][4][5]. There is now a widespread interest in better understanding the effects of vibrational entropy on phase diagrams, an active topic of ab initio investigations. Here we show, to our knowledge for the first time, a negative entropy of mixing at rather low solute concentrations, caused by the entropy of atomic vibrations. The thermal stability of structurally ordered states and disordered states is thereby reversed.Although the solubility of Ni in the body-centered cubic (bcc) V-rich phase is qualitatively consistent with the entropy of Eq. (1), the elements below Ni in the periodic table, Pd and especially Pt, have similar phase diagrams but show a much weaker temperature dependence of solubility in bcc V [6]. Owing to its incoherent neutron cross section and cubic crystal structure, vanadium is the ideal element for measuring a phonon densityof-states (DOS) by inelastic neutron scattering [7], as are V-rich bcc solid solutions. From the phonon DOS the vibrational entropy and other phonon thermodynamic functions can be obtained, at least at low temperatures. Previous studies of resonance modes of heavy solutes in vanadium suggest important effects on phonon thermodynamics [8][9][10][11].Alloys were prepared by arc melting under a highpurity ar...

Electron-phonon interactions and high-temperature thermodynamics of vanadium and its alloys

“…39,41 Figure 4 shows that the softening of the average phonon energy ͗E͘ for V-7%Co is in excellent agreement with the effect of thermal expansion predicted by the quasiharmonic model, ⌬͗E͘ / ͗E͘ =−␥ ⌬V / V. The V-6%Pt alloy follows a similar trend, although its ͗E͘ is suppressed at all temperatures by resonance modes of massive Pt atoms. 17 ͑An alloy of V-31%Cr, which has a similar electron-to-atom ratio to that of V-7%Co, also showed a similar behavior from 10 K to 300 K.͒ On the other hand, Fig. 4 shows that ͗E͘ for pure V and V-7%Nb deviate substantially from the thermal behavior predicted by the quasiharmonic model.…”

“…The rather small effect of the heavy Nb solutes ͑about two times heavier than the host V atoms͒ indicates that the effect of mass difference is not very important for 6% Nb solutes. In the case of Pt solutes ͑about four times heavier than V͒, a resonance mode occurs around 12 meV, 17 but the effect of 6% Pt solutes on the phonon DOS is overall very similar to that of 7% Co solutes, whose mass is similar to that of V atoms. This indicates that electronic and bonding effects dominate over mass effects, and this is compatible with the similar numbers of d electrons/atom in the V-6%Pt and V-7%Co alloys, 13 given as the electron/atom ratio in Table I.…”

“…This was explicitly shown for the case of V-6%Pt, in which the partial phonon DOS for Pt atoms is substantially different from the phonon DOS of the host vanadium lattice. 17 Besides, it is expected that the neutron weighting should be only mildly temperature dependent, thus having minimal effects on the temperature trends discussed here.…”

Heavy-impurity resonance, hybridization, and phonon spectral functions inFe1−xMxSi (M=Ir, Delaire1, Al-Qasir2, May3 et al. 2015Phys. Rev. BSelf Cite412190View full textAdd to dashboardCite

“…between 10 and 20 meV, an additional component is evident besides the shift, with an excess of spectral weight centered around 15 meV, which is most pronounced for the Ir-doped sample. Such enhancements have previously been observed for heavy impurities forming resonance modes, corresponding to local dynamics decoupled from that of the lattice 51,52 . We show in details below that both Os and Ir dopants lead to the formation of a resonance modes, for all the concentrations we investigated.…”

Vibrational thermodynamics of materials

“…Partial DOS curves for the solute atom and its V neighbors up to 3NN shell, obtained from the optimized supercell lattice dynamics. After [378].…”