dQ/dV plot from Galvanostatic Charge Discharge Data

dQ/dV plot from Galvanostatic Charge Discharge Data

dQ/dV is known for differential capacity plot. It makes us understand better about the electrodes characteristics of lithium ion batteries. This article will help you plot a dQ/dV curve from Charge-Discharge statistics data of the battery.

Background

The applications of secondary batteries ranging from consumer electronics to electric vehicles has a common requirement of high performance, low cost, durable and reliable batteries. Out of many secondary energy storage devices, lithium ion batteries are able to meet the growing demand of energy storage due to its high energy density and ease for rechargeability. However, with current technology, the lifetime of the battery is often less than the desired product lifetime and tends for the repetitive replacement.

A popular way to improve the life time and device safety of the battery is through analysing its state of health (SOH) and managing its degradation rates. Due to its complex mechanism the direct estimation of SOH is not possible. Hence for this, the analysis through charge/discharge during its lifetime will be interpreted {1}.

One most popular method called differential capacity (dQ/dV) was widely used for characterizing SOH of secondary batteries. Differential capacity (dQ/dV) analysis can be used to measure the alignment of electrodes within a full Li-ion cell without the use of a 3-electrode cell.  This allows cell degradation mechanisms to be understood.

Figure1(a,b) is source credited from Croy, J. & Kim et.al work {2}. The team has analyzed the behavior of  Li2MnO3 against lithium in a coin cell. Figure 1(a) shows the charge/discharge plot with corresponding differential capacity dQ/dV plot (shown in Figure 1(b) ).

Figure(1) : Shows the plot of dQ/dV of  Li2MnO3 against lithium in a coin cell

Introduction : dQ/dV plot

dQ/dV plot is an electrochemical analysis that estimates the performance of the battery. It
 provides fingerprint of battery life, degradation capability, which is plotted against differential capacity Vs Voltage. It is mainly used as a method of characterizing state of health (SOH) in secondary batteries through the identification of peaks that correspond to active material phase transformations. For reliable analysis, cells are cycled under low constant currents to minimize resistance and diffusion effects, making deployment into applications such as electric vehicle charging unfeasible.

Here, is an example article for better understanding :
S Pathan et al., reported the estimation of the process involved in the battery while charging and discharging. Following figure(2) shows the dQ/dV plot of NMC (nickel manganese cobalt oxide) Vs graphite in a lithium coin cell {3}.

                         Figure(2) : dQ/dV plot between NMC vs Graphite in coin cell

           Noticeably, there are three different peaks in the above plot stating as 1.Electrolyte decomposition, 2.Graphite intercalation and 3. Phase transition. Usually an irreversible capacity loss will happen between 1.25–0.5 V versus Li/Li+ on the graphite anode, whereas for the lithium NMC vs graphite it appears at between 2.25–3 V in a full-cell configuration. There is a crystal structure change in the graphite  C6 → LiCx at 3.5 V peak. Similarly peak 3.6V represents the phase change from original layered structure (H1) to monoclinic phase (M) of NMC. The irreversible capacity loss in the battery indicates the formation of the solid electrolyte layer

Steps for Plotting the dQ/dV curve:

Basically dQ/dV plot is the product of constant current with slope of the voltage curve.

dQ/dV = i*dV/dt

Here are the steps describing the procedure for plotting dQ/dV in two methods.

This method is differentiated with respect to :
1) For a electrochemical system that records slope of the voltage curve( labelled as dV/dt) and 2) For a electrochemical system which records only Step time (t) and Voltage (V)

Method 1 : For dV/dt available data

1. Acquire the battery data of the respective C-rate  with respect to its step time and  voltage during charge/discharge process.
2. Select the slope of the voltage curve (dV/dt) and copy it to a new excel sheet.
3. To this dV/dt, multiply with constant current i (current applied) and let’s name it as dQ/dV
4. With dQ/dV as y-axis and voltage as x-axis plot the graph. It is preferable to use line plot type.
5. If required smooth the data using Adjacent Averaging filter in Origin software or any other software can be used for this purpose


Method 2 : For Voltage and Step Time available data

1. Acquire the battery data of the respective C-rate with respect to its step time and voltage during charge/discharge process.
2. Copy the entire step time and voltage in a new excel sheet
3. Initially multiply the constant current (i) with step time. This is done because   Q=i*t. Let's name it as Q
4. For the above Q data, apply the differentiation in the excel sheet as :
Formula for (dQ/dV) = { =(Qn -(Qn-1) )/(Vn -(Vn-1) ) }
Where n = refers the row number in excel, and n-1 = refers the previous row number in excel
5. With the calculated dQ/dV and voltage, plot a line graph (dQ/dV as y-axis and Voltage(V) as x-axis).
6. If required, smooth the graph using Adjacent Averaging filter in Origin software or any other software can be used for this purpose.

Conclusion

A numerous studies has been conducted for understanding the degradation and loss of capacity of lithium ion batteries over decades. Through these dQ/dV electrochemical studies the health of the battery will be estimated in terms of its electrode degradation, mechanical, chemical and structure modification during the charge-discharge process.

References

A. Fly, R. Chen,Rate dependency of incremental capacity analysis (dQ/dV) as a diagnostic tool for lithium-ion batteries,Journal of Energy Storage,Volume 29,2020,
101329,10.1016/j.est.2020.101329.
Croy, J. & Kim, Dae-Hyun & Balasubramanian, Mahalingam & Gallagher, Kevin & Kang, Sun-Ho & Thackeray, Michael. (2012). Countering the Voltage Decay in High Capacity xLi(2)MnO(3)center dot(1-x)LiMO2 Electrodes (M=Mn, Ni, Co) for Li+-Ion Batteries. Journal of The Electrochemical Society. 159. A781. 10.1149/2.080206jes.
Tanveerkhan S Pathan and Muhammad Rashid and Marc Walker and W D Widanage and Emma Kendrick (2019). Active formation of Li-ion batteries and its effect on cycle life. Journal of Physics: Energy. 10.1088/2515-7655/ab2e92
Marzocca, Lauren M and Terrill B. Atwater. “Differential Capacity-Based Modeling for In-Use Battery Diagnostics, Prognostics, and Quality Assurance.” (2014).


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