Ragone Calculator: A Straightforward Tool to Determine Performance Metrics and Support Developments at an Application-Relevant Level

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Science and industry worldwide are conducting intensive research into various ways to improve existing battery concepts or transferring novel concepts to application. The development of materials and electrodes is an essential step in this process. However, the evaluation of the achievolumetric energy density performance parameters and the comparison of the different studies at this technological level with regard to practical applications is challenging, since special electrodes and cell concepts are typically used at laboratory scale. Here, a straightforward computational tool, the Ragone calculator, is provided to estimate performance data at the full cell level based on electrochemical measurements on electrodes.
The Ragone calculator requires the properties of the electrode, such as thickness, mass, composition and properties of the active material, as well as the results of the rate capability test. The mass and volume of the counter electrode are determined from the data entered and the N/P ratio. The masses and volumes of a hypotethic full cell are obtained from the data entered for the inactive components, such as the separator and current collector. These are then used to determine the energy and power densities from the results of the rate capability test.
To validate that the Ragone calculator estimates full-cell power with sufficient accuracy, half-cell tests were performed using NCM111 based cathodes. The obtained rate capability test results were entered into the Ragone calculator and the predicted performance at the full-cell level was compared to a practical full cell build from the same cathode and a graphite-based anode. The rate capabilities of the half-cell and the full cell with respect to the mass of the cathode material are in excellent agreement. When the obtained half-cell level results are projected to full cell level using the Ragone calculator, the obtained Ragone plots agree well with the practical full cell results. Accordingly, the Ragone calculator is suitable for estimating full cell performance based on half-cell data if the above assumptions hold.
To illustrate the applicability and functional scope of the Ragone calculator, some relevant examples are covered in the following. Figure 3a compares the rate capability of NMC111 electrodes of different electrode design and composition with respect to the mass of active material employed. The geometrical parameters of the electrodes were determined by thickness measurement and porosity calculations based on the composition. The thin electrode with high content of conductive carbon and binder, as typically used in laboratory studies, shows much higher specific capacity at high C-rates when compared to the thick electrode, whose composition is close to commercial electrodes for automotive batteries. This behavior is well-known and commonly related to enhanced Li-ion diffusion limitations in the electrolyte with increasing electrode thickness. Based on these results, it could be concluded that the thin electrode is very well suited for high performance requirements. However, extrapolation of the measurement results to the full-cell level using the Ragone calculator shows that not only gravimetric and volumetric energy density, but also gravimetric and volumetric power density are reduced compared to the thicker electrode. Even though there is hardly any capacity loss at higher C-rates for the thin electrode, the gravimetric and volumetric energy density are so low, due to the high proportion of inactive material in the cell (cf. bar charts in Figure 3b), that gravimetric and volumetric power density cannot surpass the thicker electrode even at high C-rates. Thus, the thicker electrode outperforms the thin one regarding both energy and power density. Such conclusions cannot be derivolumetric energy density directly from rate performance tests at the material and electrode level but are obtained straightforward by application of the Ragone calculator. Accordingly, an honest assessment of the electrode performance with respect to practical applications becomes possible.
Figure 3c shows some relevant examples to illustrate the functional scope of the Ragone calculator. Here, the impact of changing a graphite anode to materials with higher specific capacity can be evaluated using the Ragone calculator. For example, using Si or Li (N/P = 1.2) as the anode material instead of graphite increases the low rate volumetric energy density from 507 to 749 and 777 Wh L-1, respectively. In zero Li excess (anode-free) configuration, the low rate VED approach 920 Wh L-1, respectively. Sensitivity studies of this kind can be used to assess the usefulness of optimization approaches.

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