AMIDR: A Complete Pulse Method for Measuring Cathode Solid-State Diffusivity
Authors: Ball Mitchell Afheldt , Cormier Marc M. E. , Zsoldos Eniko , Phattharasupakun Nutthaphon , Johnson Michel B. , Metzger Michael , Yang Chongyin , Dahn Jeff R. , Hamam Ines , Zhang Ning 
Published: February 2024

Lithium transport within cathode material is driven by diffusion. While fast cathode diffusion is desired, solid-state diffusivity is one of the most difficult cell material properties to measure. However, it is an important property to understand as cathode capacity is often limited by poor diffusivity. GITT (Galvanostatic Intermittent Titration Technique) is a common diffusivity measurement method. This technique is accomplished by applying a series of constant current pulses to a cell and analyzing the voltage response. While easy to use, this method only measures near the surface of the active material by assuming that it takes the geometry of a semi-infinite plane. This approximation means that GITT is only accurate when measuring the very initial voltage response. However, the voltage response cannot be analyzed too early as this may amplify error produced by CDL (double layer capacitance) and RI (interface resistance) found at the cathode-electrolyte interface which GITT does not account for. EIS (Electrochemical Impedance Spectroscopy), an AC method, is better suited for distinguishing CDL/RI from diffusivity but also struggles to evaluate diffusivity beyond the surface of active material within a reasonable time frame1. In addition, instruments capable of quality EIS are often cost prohibitive compared to DC cell testers.
The voltage responses after the first few moments of a pulse are relevant when evaluating cell behaviour in real-world applications and should be considered to produce comprehensive measurements of diffusivity and its performance impact. AMID (Atlung Method for Intercalant Diffusion) is a multi-rate pulse method produced by this lab which uses a series of pulses, both short/fast and long/slow, and an approximation-free analytical model (developed by Sven Atlung) for diffusion in a spherical particle, not a semi-infinite plane2. However, AMID cannot differentiate diffusion impedance from resistance and therefore requires that resistance be considered negligible. In addition, while AMID mathematics are free of approximations, the typical multi-rate pulse protocol does require that series of pulses be approximated as singular pulses3. Lastly, the multi-rate pulse protocol limits the state-of-charge resolution of diffusivity measurements.
AMIDR (Atlung Method for Intercalant Diffusion and Resistance) incorporates a GITT-style single pulse protocol with AMID-style mathematics modified to account for resistance as shown in Figure 1b). AMIDR collects pulse data with a pseudo-logarithmic time distribution. This means that the same number of data points is collected in 0.1-1.0 seconds, 1.0-10 seconds, 10-100 seconds and so on. Unlike GITT which measures diffusivity at an early arbitrary point in a pulse, AMIDR considers the entire length of a pulse comprehensively. Fractional capacity is calculated for each datapoint by dividing the actual capacity with the ideal “impedance-free” capacity expected at that voltage as shown in Fig 1c). These fractional capacity values, normalized from 0-1, are fitted to the modified Atlung model. This modified Atlung model is nearly the same as the original Atlung model except an additional term is added for capacity limited by resistance. Unlike AMID, AMIDR measures both diffusivity and resistance simultaneously by using both as fitting parameters. Lastly, while CDL is usually small enough for RI to behave simply like ohmic resistance on relatively short time scales (>0.1 seconds), AMIDR has the option to account for CDL/RI when relevant such as near the bottom of a complete discharge.
AMIDR is a new diffusivity measurement method tailored for cathode material in Li-ion batteries. By combining the advantages of various previous diffusivity methods, AMIDR eliminates many of their concerns and sources of error such as sampling of only the material surface, alternate confounding sources of impedance, and expensive equipment as seen in Figure 1a). When paired with proper cell design (i.e. ultra-low single layer cathode loading to remove pore impedance and reference electrodes to remove anode impedance), AMIDR can produce high resolution diffusivity measurements with improved accuracy and applicability to real-world cell performance.
References

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Figure 1. (a) Comparison of various Diffusivity measurements. (b) The modified Atlung model for diffusion in a spherical particle. (c) How pulse data is converted to the unitless Atlung model.

Figure 1