Thermodynamic Model for Substitutional Materials: Application to Lithiated Graphite, Spinel Manganese Oxide, Iron Phosphate, and Layered Nickel-Manganese-Cobalt Oxide

Abstract

We derive and implement a method to describe the thermodynamics of electrode materials based on a substitutional lattice model. To assess the utility and generality of the method, we compare model results with experimental data for a variety of electrode materials: lithiated graphite and layered nickel-manganese-cobalt oxide (Chevrolet Bolt Electric Vehicle negative and positive electrode materials, respectively), manganese oxide (in the positive electrodes of the Gen 1 and Gen 2 Chevrolet Volt Extended Range Electric Vehicle and the positive electrode of many high-power-density batteries), and iron phosphate (Gen 1 Chevrolet Spark Electric Vehicle positive electrode material and of immediate interest for 12 and 48 V applications). An early version of the model has been applied to lithiated silicon (Li-Si). As was found in the Li-Si study, the model enables one to quantitatively represent experimental data from these different electrode materials with a small number of parameters, and, in this sense, the approach is both general and efficient. An open question is the utility of controlled-potential vs. controlled-current experiments for the elucidation of the system thermodynamics. We provide commentary on this question, and we highlight other open questions throughout this work. Central to the modeling of electrochemical systems, particularly batteries relying on solid-state diffusion within the active materials, is an accurate description of the system thermodynamics.1-4 We describe and implement a thermodynamic model for substitutional electrode materials. At the heart of the model is a simple expression for the open-circuit potential U in terms of the fraction of filled sites x within a host material. To assess the value of the model, we apply it to four electrode materials of commercial interest today: lithiated graphite, spinel manganese oxide, iron phosphate, and nickel-manganese-cobalt oxide. The model is an expanded version of that described in Ref. 12. A slight alteration is needed to describe the nickel-manganese-cobalt oxide so that inaccessible lithium can be considered (giving rise to x 0 in Table I), and we also describe how reactions between sites within the electrode material can be addressed.This document is organized as follows. First, we provide an overview of the materials and instrumentation for the experimental characterization of the electrode materials. An introduction of the thermodynamic model is then presented, followed by a detailed description of the model. A discussion of results is then presented, followed by a brief Appendix devoted to the convergence properties of the series summation employed in the U(x) model. • C under about 0.01 Torr vacuum. Other materials were dried at 100 Experimental• C under vacuum of about 0.01 Torr. Cell assembly and cycling were performed under an inert argon atmosphere with O 2 and H 2 O concentrations < 1 ppm. Cycling was performed with a Princeton Applied Research PMC 2000 potentiostat/galvanostat. For the voltammetry work on the Ni 0.6 Mn 0.2 Co ...

The influence of surface inhomogeneity on the overcharge and lithium plating of graphite electrodes

“…The parameters and properties for the base case are provided in table 1, and table 3 provides the relevant dimensionless groups that govern the problem for the base case. The thermodynamic parameters for the MSMR model of lithiated graphite are identical to those of [21] with the exception of the LiC 12 to LiC 6 phase transition ( j=1): for this gallery, two percent of the capacity is split off to yield ideal, Nernstian behavior as the graphite completes lithiation (see j=7), consistent with the formation of an ideal solution as x 1  and x 0. H  The base case involves the charging of a large graphite particle at the 1 h rate (the 1C rate), which is known to be a challenge for lithium ion traction batteries today if a full charge is desired (i.e.…”

“…A practical aspect of the MSMR model is that, with few parameters that can be associated with the physical chemistry of the intercalation material, a quantitative fit of the open-circuit potential results, and this is key for the overall analysis. We refer the reader to [21] for a complete discussion on the application of the MSMR model to graphite.…”

“…The thermodynamics of lithiated graphite are modeled using the multi-site, multi-reaction (MSMR) model as described in [20][21][22][23]. A practical aspect of the MSMR model is that, with few parameters that can be associated with the physical chemistry of the intercalation material, a quantitative fit of the open-circuit potential results, and this is key for the overall analysis.…”

Quantifying structure dependent responses in Li-ion cells with excess Li spinel cathodes: matching voltage and entropy profiles through mean field models

“…To date, the information obtained from entropy profiling has been largely qualitative. Two approaches, which have already been applied to open circuit voltage (OCV) profiles 36,[39][40][41][42][43][44] could be considered to also understand entropy profiles at a more quantitative level. On the one hand, ab initio approaches based on effective cluster interactions (ECIs) could be applied within a density functional theory (DFT) framework.…”

“…On the other hand, parametric models can be directly fitted to experimental OCV profiles. [41][42][43][44] Although allowing rapid agreement between the models and experiment, the physical interpretation of the various parameters within the models, particularly the ones related to Li-Li interactions, is often unclear. Without an understanding of these parameters, it can be difficult to interpret the models when the cell chemistry is continuously changing, such as during cell aging.…”