Phase-field model of ion transport and intercalation in lithium-ion battery

Self-Organized Memristive Ensembles of Nanoparticles Below the Percolation Threshold: Switching Dynamics and Phase Field Description

“…Assuming that the parameters of interaction between atoms inside the particles and in the matrix are different, we can write the free energy density in the form: where W is the interaction parameter, and and are the free energy densities in particles and the matrix, which can be determined in the regular solution approximation: The interaction parameters , , and can be easily related to the interatomic interaction energies of solutions [ 36 , 37 ], is the Boltzmann constant, and T is the temperature. The approximating function can be chosen as follows: [ 38 , 39 ]. Taking into account expressions ( 8 ) and (9), the free energy density ( 7 ) is expressed as …”

“…The interaction parameters g P , g M , Ω P and Ω M can be easily related to the interatomic interaction energies of solutions [36,37], k B is the Boltzmann constant, and T is the temperature. The approximating function h(η) can be chosen as follows: [38,39]. Taking into account expressions ( 8) and ( 9), the free energy density ( 7) is expressed as…”