Application of Lattice Gas Model with Monte Carlo Simulation

2 Application of Lattice Gas Model with Monte Carlo Simulation 

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 detailed simulation procedures and derivation of above thermodynamic quantities have been described elsewhere [16]. 

Another interesting thermodynamic phenomenon caused by the strong interaction of lithium ions is a two-phase coexistence during lithium intercalation and deintercalation that is, when intercalation/deintercalation proceeds in equilibrium between the Li-depleted and Li-rich phases (see Section 5.2.2). Pyun et al. also applied the Monte Carlo method to determine the mechanism of lithium intercalation into Lii I s[Ti5/3Li]y3 O4 in the two-phase domain [28]. For the cubic-spinel Lii+8 Ti5/3Lii/3]O4, both 8(a) and 16(c) sites are occupied by lithium ions each 8(a) site is adjacent to four first-nearest 16(c) and four second-nearest 8(a) sites, and each 16(c) site is surrounded by two first-nearest 8(a) and six second-nearest 16(c) sites. According to the model [28], the lattice Hamiltonian is defined as 

16(c) sites, so as to avoid the repulsive interaction between lithium ions that increases the ensemble energy of the lattice. 

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