Strain Derivatives for Practical Charge Rate Characterization of Lithium Ion Electrodes

During battery use, electrode materials are known to expand and contract in repeatable patterns, and this strain has been previously correlated with battery properties such as state of charge and state of health. In this study, we show that the second derivative of strain, d2e/dQ2, is mathematically proportional to dV/dQ within an electrode stage. We also experimentally quantify peaks in the strain curves for electrode stage transitions at practical charge rates of up to C/2 and confirm that transitions are visible in the practical scenario of discharging at the higher rate of 1C. Moreover, the location of the transition measured by d2e/dQ2 changes by less than 10% from 0.05 C to 0.5 C, but the transition measured with dV/dQ decreases by more than 15% from 0.05 C to 0.3 C, demonstrating the reliability of strain to measure electrode transitions at moderate charge rates. We also note that d 2 e/dQ 2 exhibits similar peak shifts as those expected in dV/dQ as the cell ages. Our derivations for the model system of graphite and lithium cobalt oxide can be generalized to other battery systems and used to characterize materials at practical charge rates impossible with only voltage. © The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any Lithium ion batteries are a popular choice for energy storage due to their high ratio of energy capacity to size and their low rate of self-discharge. 1 Unfortunately, batteries are difficult to characterize because they are essentially isolated systems with many reactions and processes occurring internally. Imaging the internal reactions and materials during battery operation is impractical, and very few tools exist that can provide information about material evolution during battery usage. Voltage is a common tool for characterizing battery materials duringoperation,particularlythederivativeofvoltagewithrespecttostate of charge, dV/dQ. A cell’s voltage is directly related to the chemistry of the materials, and many previous studies have investigated battery voltage and used it to identify phase transitions in materials, predict the effects of cell aging, and relate voltage to underlying chemical reactions. 2‐6 In addition, many of these studies have resulted in the development of models to help understand battery material evolution by predicting voltage curves based on the fundamental physics in the battery. dV/dQ has proven to be an extremely useful tool and an accurate predictor of cell aging, but it is limited by physical constraints. Notably, electrode phase transitions are most easily viewed at slow chargerates,andthedistinguishingfeaturesinadV/dQplotarenonexistent at high charge rates. Studies often cycle batteries at charge rates of C/20 or lower in order to glean information from dV/dQ curves. Recentbatteryresearchhasfocusedonmechanicalproperties,such as strain, e, as a novel tool to indicate underlying phenomena. 5,7‐12 This previous research relies on the fact that during battery operation, electrode materials are known to expand and contract in repeatable patterns. Strain has been correlated with important battery properties such as state of charge and state of health, and mechanical measurements can be used to identify capacity fade, lithium plating, and more. Batteries also produce repeatable plots of stress and strain versus state of charge during cycling, analogous to plots of voltage versus state of charge. Despite a surge in recent research on mechanical properties of batteries, battery strain remains underutilized as a tool to better understand electrode materials. A few studies have postulated that de/dQ bears a similarity to dV/dQ and might indicate phase transitions in electrode materials. 7,12,13 However, previous work does not fully explore how or why the derivatives of strain relate to dV/dQ or what advantages strain differentials have compared to voltage. In this paper, we specifically compare d 2 e/dQ 2 and dV/dQ, and we show that