Thermodynamics of the solid Ni-S system
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e three nickel sulfides (Ni36xS2, Ni1–xS, and NiS2) known to exist above 800 K.[1,2,3] The compositional range of nonstoichiometry is relatively wide in Ni36xS2 and Ni1–xS. As for the former phase, Lin et al.[4] measured the chemical potential of sulfur, concluding that two phases should exist. Yagi and Wagner[5] supported such a phase separation by measuring the chemical diffusivity and electrical conductivity besides the chemical potential. Stølen et al.[6] measured the heat capacity of the low- and hightemperature phases of Ni3S2, giving no definite conclusion about the existence of two phases. Fjellva˚g and Andersen[7] conducted numerous high-temperature diffraction experiments to determine the lattice constant of Ni36xS2 between x 5 –0.4 to 10.4 in a temperature range from 800 to 1100 K. They confirmed no possible indication of phase separation. Cemic and Kleppa[8] made a calorimetric study of lowtemperature Ni3S2, low-temperature NiS, high-temperature NiS, and NiS2 to estimate the formation heats, which were close to those calculated from the equilibrium sulfur pressure measurements by Lin et al.,[4] Rosenqvist,[9] and Rau.[10,11] Schiffman and Miller[12] applied the Knudsen effusion technique to calculate the S vapor pressure and the heat of formation for the three phases, which differed substantially from the preceding measurements and calculations. The primary objective of the present work is to find how atoms should be arranged and how vacancies should be distributed in high-temperature compounds of Ni36xS2 and Ni1–xS by applying statistical thermodynamics to published chemical potential measurements.[10,11] This was possible owing to the strong dependence of thermodynamic properties on the crystallographic arrangement of atoms. II.
THERMODYNAMIC ACTIVITY OF Ni AND ENTHALPY OF FORMATION OF NI3S2
Figure 1 shows a phase diagram of the Ni-S system between XS 5 0.3 and 0.7 in a temperature range from 473 to 1333 K. It is a part of the diagram given by Okamoto,[3] except that the regions of b (or high-T Ni3S2) and Ni7S6 agree in shape with those by Kullerud MINORU ARITA, Research Assistant, is with the Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8550, Japan. Contact e-mail: aritamin@ minarita.net Manuscript submitted December 9, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A
and Yund[1] and except that the transition temperatures are in accordance with those given by Rau.[10,11] The two broken lines in the b phase were originally suggested as phase separation by Lin et al.[4] In the embedded figure as an enlarged view of a lower portion of the b phase, the shaded area represents a path of Gibbs–Duhem integration to calculate the activity of Ni at three temperatures. To integrate the measured activity of S, we need to know the activity of Ni at one or more points of composition. In the Ni-S system, the only known value exists as the definition of one for pure Ni. Rau measured the equilibrium pressure of disulfide gas through the entire region of Ni36xS2.[11] According to the phase diagram of Figure 1, the t
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