Metropolis algorithm grand canonical

The simulation is performed in a grand canonical ensemble (GCE) where all microstates have the same volume (V), temperature and chemical potential under the periodic boundary condition to minimize a finite size effect [30, 31]. For thermal equilibrium at a fixed pu, a standard Metropolis algorithm is repetitively employed with single spin-flip dynamics [30, 31]. When equilibrium has been achieved, the lithium content (1 — 5) in the Li, 3 11204 electrode at a given pu is determined from the fraction of occupied sites. The thermodynamic partial molar quantities oflithium ions are theoretically obtained by fluctuation method [32]. The partial molar internal energy Uu at constant Vand T in the GCE is readily given by [32, 33]... 

The parameter values we use here are g/R = 148.7K /mol, Ug = 3.79 A, Hs = 0.382 A , e JR = 72.2 K /mol, a = 3.92 A(taken from Aydt and Hentschke 1997). We will discuss computer simulation algorithms, especially the algorithm used in this example, in the next chapter. At this point we merely state that the following result is computed via grand-canonical Metropolis Monte Carlo using Eq. (5.128) as well as Eq. (5.129) for comparison. 

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