Gibbs-Duhem equation small system

This is the Gibbs-Duhem equation of the ensemble. When the extensive variables per small system are defined by X = X,/N, (5.8) and (5.9) are rewritten as... 

Let us consider a macroscopic system at T and P composed of N molecules that have chemical fj, , where the system contains no small system (or micelle). The Gibbs-Duhem equation for the system becomes... 

As shown by results for the Lu + H system from Subramanian and Smith (1982) in fig. 12, the metal-cubic hydride plateaus become very short for the later elements. Lu forms the smallest of all the rare-earth hydrides and has the highest solubility in the a-phase, as noted in section 3.2. Pressure-composition isotherms are reproducible between runs, with minimal hysteresis except at the lowest temperature of824°C. Phase boundaries and pressure equations thus determined are in excellent agreement with earlier work. Gibbs-Duhem integrations of the measured data and a small extrapolation to the LuHj composition give AH/ = — 204.8 + 1.9 kJ/mol and ASf = — 136 2J/molK. 

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