Role of elasticity forces in thermodynamics of intercalation compounds: Self-consistent mean-field theory and Monte Carlo simulations

Abstract

We propose a self-consistent mean-field lattice-gas theory of intercalation compounds based on effective interactions between interstitials in the presence of the host atoms. In addition to short-range screened Coulomb repulsions, usually discussed in the lattice gas models, the present theory takes into account long-range effective attractions between intercalants due to elasticity of the host matrix. The mean-field phase diagram in the space of interaction parameters contains the domains of first-and second-order transitions of the order-disorder type, separated by a tricritical line, and the domain of the first-order transition of the gas-liquid-type separated from the homogeneous state by a critical line. Theoretical predictions are shown to be in qualitative agreement with the grand canonical Monte Carlo simulations. The peculiarities of the phase diagram give an insight into different types of behavior of the open circuit voltage observed in rechargeable batteries, in which an intercalation compound is used as an electrode material.

Correlation between the equilibrium and transport properties of intercalation systems

“…The chemical diffusion coefficient for crystalline LixW O3. The symbols (up triangles) correspond to the experimental data [24]. The parameters are the same as for the previous figure.…”

“…This involves at least two effects. First is a renormalization [2,24] of the net pair interaction between the intercalants due to their indirect interaction through the matrix. The second is a change of the host volume upon insertion of the guest species.…”

“…The term liner in the concentration can be viewed as an additional interaction which can be combined with cW x in µ 0 (x). Although this additional term is proportional to the elastic constant Λ, it is physically different from the interaction of elastic dipoles [2,24] which is already absorbed into W (see the discussion after equation ( 5)). This interaction takes place even if the sample is perfectly clamped (ε(x) = 0), while our term represents a cooperative effect due to ε(x) = 0.…”

Electrochemically driven first-order phase transitions caused by elastic responses of ion-insertion electrodes under external kinetic control

“…The concept of Frumkin-type intercalation isotherms, widely used in experimental studies of IIEs [3][4][5], ensures, basically, an equivalent approach to the thermodynamic characteristics of IIEs as compared to the LG models with interactions: the chemical potential of the guest ions includes, in addition to its standard value and entropic contribution, also an interaction term proportional to their bulk concentration. The concentration-independent proportionality factor, g, called also the interaction constant, has been interpreted within the LG model approach by Friedel oscillations in the density of screening electrons [1,2], and (or) by an interaction of the elastic dipoles through a strain-mediated field, appearing in the host matrix upon intercalation [1,2,6]. An important feature of the elastic model proposed in [1,2,6] is that as the net strain in the electrode becomes zero (e.g.…”

“…The concentration-independent proportionality factor, g, called also the interaction constant, has been interpreted within the LG model approach by Friedel oscillations in the density of screening electrons [1,2], and (or) by an interaction of the elastic dipoles through a strain-mediated field, appearing in the host matrix upon intercalation [1,2,6]. An important feature of the elastic model proposed in [1,2,6] is that as the net strain in the electrode becomes zero (e.g. in the case of the perfectly clamped electrode), the elastic dipole interactions do not disappear [7].…”