where αii denotes the chemical expansion coefficient, which represents the slope of the laoce constant of each direc-on (i = 1, 2, 3 corresponds to a, b, c-axis, respec-vely) with respect to the Li content in FMO (x in LixFe(MO4)1.5). x0 and aii 0 are the reference Li content and the reference laoce constant of each axis, respec-vely. According to Yue et al., the laoce constants of FMO along the a, b, and c axes exhibit anisotropic changes upon lithia-on, with maximum varia-ons of approximately -0.7, 2.0, and -0.3%, respec-vely . For simplicity, we neglect the chemo-mechanical strain along the a-axis, because our FMO thin film exhibited a localized a-axis orienta-on and are less likely to be constrained in this direc-on. Furthermore, we neglect the chemo-mechanical strain along the c-axis since it is much smaller compared to that along the b-axis. Therefore, we consider only the chemo-mechanical strain along the b-axis (i = 2). Using Eq. ( ) and under aforemen-oned assump-ons, the Gibbs free energy can be expressed as follows: