I study the degradation behavior of lithium-ion cells used in an electric vehicle battery pack, with particular attention to how microscopic aging mechanisms can be linked to macroscopic electrical signatures. The central degradation modes I focus on are loss of lithium inventory and loss of active material. These modes determine how much usable capacity remains in an electric vehicle battery pack, how quickly power capability fades, and how safely the pack can be operated over repeated charge and discharge cycles. My objective is to connect destructive micro-scale characterization with non-destructive macro-scale diagnostics so that degradation modes in an electric vehicle battery pack can be quantified rather than only described qualitatively.
I begin from the observation that a commercial lithium iron phosphate cell, when aged under controlled conditions, shows changes in its open-circuit voltage, incremental capacity response, electrode half-cell capacity, diffraction peak intensity, and electrode surface morphology. Each of these observations contains information about loss of lithium inventory and loss of active material. However, a single observation is rarely sufficient. For example, a capacity fade measured at the full-cell level cannot by itself separate lithium loss from active material loss. Likewise, a scanning electron microscopy image can reveal a thicker solid electrolyte interphase film, but it does not directly give the ampere-hour capacity associated with that film growth. Therefore, I combine macro-level voltage-based diagnosis with micro-level material characterization to create a cross-scale description of degradation in an electric vehicle battery pack.
Experimental Platform and Cell-Level Testing
I selected a prismatic lithium iron phosphate cell with a nominal capacity of 20 Ah as the repeating unit for the study. The nominal voltage, internal resistance, mass, and dimensions are summarized in Table 1. The cell chemistry is relevant to many electric vehicle battery pack designs because lithium iron phosphate offers good thermal stability and long cycle life, even though its voltage curve is relatively flat. That flat voltage plateau makes degradation diagnosis more challenging, because small changes in electrode stoichiometry can produce subtle changes in the measured voltage. Consequently, I used both low-rate reference tests and micro-scale characterization to improve diagnostic confidence.
| Parameter | Value |
|---|---|
| Nominal capacity | 20 Ah |
| Nominal voltage | 3.2 V |
| Internal resistance | 7 mΩ |
| Mass | 485 ± 15 g |
| Dimensions | 130 × 70 × 27 mm |
| Chemistry | LiFePO4 / graphite |
I constructed a test platform consisting of a computer-controlled battery tester, a thermal chamber, a glove box for cell disassembly, a half-cell test station, an X-ray diffractometer, and a scanning electron microscope. The battery tester applied current and recorded voltage, current, and temperature. The thermal chamber held the cells at a controlled temperature so that external temperature variation would not dominate the degradation signal. I used the glove box to avoid air exposure during disassembly, because both the lithiated graphite anode and the delithiated cathode can react with oxygen and moisture. The half-cell test station allowed me to measure the capacity of individual electrode laminates against lithium metal. The diffractometer and microscope provided crystallographic and morphological evidence of aging.
I performed full-cell tests in several stages. First, I conducted capacity calibration to establish the reference capacity at the beginning of life and at selected aging checkpoints. Second, I ran cycle aging at a fixed charge and discharge rate. Third, I performed rate capability tests at C/25, C/10, C/5, C/3, C/2, and 1C. Fourth, I performed low-rate reference charge and discharge at C/25 so that the cell would reach a well-defined endpoint before disassembly. The low-rate reference step was especially important for an electric vehicle battery pack, because real packs rarely operate at C/25. A low-rate reference laboratory measurement provides a stable anchor for comparing macro-level diagnostic results with micro-level material measurements.
| Stage | Purpose | Rate or condition | Endpoint |
|---|---|---|---|
| Capacity calibration | Determine reference capacity | Multiple charge/discharge cycles | Discharge capacity variation below 2% |
| Cycle aging | Generate aged cells | 15 A charge and discharge | Voltage limits 3.65 V and 2.5 V |
| Rate test | Study polarization and rate dependence | C/25, C/10, C/5, C/3, C/2, 1C | Voltage limits with rest periods |
| Low-rate reference | Set consistent initial state before disassembly | C/25 | Full charge or full discharge |
| Disassembly | Extract electrode laminates | Glove box | Anode and cathode samples |
| Half-cell test | Measure electrode capacity | Low rate against lithium metal | Electrode-specific voltage limits |
| Material characterization | Identify crystal and surface changes | XRD and SEM | Diffraction patterns and morphology images |
The rate tests showed that the discharge capacity of the cell decreases as the current rate increases. This is a familiar consequence of polarization in an electric vehicle battery pack. At a higher rate, the terminal voltage reaches the discharge cutoff earlier, even though some lithium remains in the electrode. After rest, the voltage relaxes upward, indicating that the cell was not fully emptied at the cutoff. Therefore, if I disassemble a cell immediately after a high-rate discharge, the electrode state may not be the same as after a low-rate discharge. This is why I introduced a C/25 reference step before every destructive analysis. The reference step ensures that the anode and cathode are brought as close as possible to a common thermodynamic endpoint.
Degradation Modes in an Electric Vehicle Battery Pack
I classify the degradation of an electric vehicle battery pack into several coupled modes. The first is loss of lithium inventory. The second is loss of active material in the positive electrode. The third is loss of active material in the negative electrode. Each active material loss can be further divided into a lithium-containing fraction and a lithium-free fraction. These definitions are important because the same total active material loss can affect the full-cell voltage curve differently depending on whether the lost material contained lithium at the moment it became electrically isolated.
| Symbol | Meaning | Primary effect in an electric vehicle battery pack |
|---|---|---|
| LLI | Loss of lithium inventory | Reduces cyclable lithium; shifts electrode stoichiometry |
| LAMPE | Loss of positive active material | Reduces positive electrode capacity |
| LAMNE | Loss of negative active material | Reduces negative electrode capacity |
| LAMliPE | Lithium-containing positive active material loss | Shifts positive electrode stoichiometry |
| LAMdePE | Lithium-free positive active material loss | Changes positive electrode utilization window |
| LAMliNE | Lithium-containing negative active material loss | Shifts negative electrode stoichiometry |
| LAMdeNE | Lithium-free negative active material loss | Changes negative electrode utilization window |
The mechanisms that drive these modes are distributed across the cell. Solid electrolyte interphase growth consumes lithium and increases impedance. Graphite particle cracking and exfoliation reduce negative active material. Transition-metal dissolution and structural disorder reduce positive active material, although lithium iron phosphate is more structurally stable than many layered oxides. Electrolyte decomposition and gas generation can further increase polarization and reduce the accessible capacity of an electric vehicle battery pack. Temperature, charge rate, discharge rate, and depth of discharge all influence these mechanisms. For example, a high charge rate can promote lithium plating, which lowers lithium inventory and can also accelerate negative active material loss. A high temperature can accelerate solid electrolyte interphase growth and transition-metal dissolution. A low temperature can increase electrolyte viscosity, reduce ionic conductivity, and promote uneven lithium deposition.
The temperature dependence of ionic conductivity can be represented in an Arrhenius form:
$$\sigma = A \exp\left(-\frac{E_a}{RT}\right)$$
where σ is ionic conductivity, A is a pre-exponential factor, Ea is activation energy, R is the gas constant, and T is absolute temperature. This equation explains why low temperature can limit rate capability, and why high temperature can accelerate parasitic reactions. In an electric vehicle battery pack, the thermal management system therefore directly influences the trajectory of loss of lithium inventory and loss of active material.
Qualitative Micro–Macro Correlation
I first compared the qualitative signatures of aging across scales. At the full-cell level, I measured capacity fade and open-circuit voltage changes. At the electrode level, I measured half-cell capacity and diffraction patterns. At the surface level, I examined scanning electron microscopy images. The goal was to identify which micro-scale observations could be associated with which macro-scale degradation modes. This step is necessary before quantitative modeling, because it reduces the set of plausible explanations and helps avoid over-parameterized diagnostic models.
The diffraction patterns of the positive electrode contained many overlapping peaks. Because lithium iron phosphate and iron phosphate phases coexist over a two-phase region, the positive electrode pattern is not always easy to interpret as a simple mixture. The peaks are distributed over a range of angles, and some of them overlap. As a result, it is difficult to use positive electrode diffraction intensity alone to track positive active material loss in this chemistry. In contrast, the negative electrode patterns were more concentrated and easier to separate. I observed distinct peaks associated with lithium-carbon compounds and with carbon. As the cell aged, the intensity of the lithium-carbon peaks changed. In the fully charged state, the lithium-carbon compound peaks decreased with aging, indicating that the amount of lithium that could be stored in the negative electrode decreased. In the fully discharged state, the carbon peak also changed, indicating that the amount of accessible negative active material decreased.
The scanning electron microscopy images showed that the negative electrode surface became rougher as aging progressed. The edges of graphite particles became less distinct, and a covering layer became more apparent. I associate this covering layer with solid electrolyte interphase growth and with the accumulation of reaction products. The thicker the covering layer, the more lithium has been consumed in side reactions. Therefore, the surface morphology supports the interpretation that loss of lithium inventory is a major contributor to capacity fade in the studied electric vehicle battery pack. The morphology also supports the interpretation that negative active material loss occurs, because the accessible graphite surface changes and some particles appear to be isolated or covered.
| Observation scale | Observed change | Likely degradation mode |
|---|---|---|
| Full cell | Capacity decreases with aging | LLI and LAM combined |
| Full cell | Open-circuit voltage window shifts and compresses | LLI, LAMliNE, LAMdeNE |
| Positive electrode XRD | Overlapping peaks, weak separation | Difficult to quantify LAMPE directly |
| Negative electrode XRD | Lithium-carbon peak intensity decreases | LLI and LAMNE |
| Negative electrode SEM | Surface roughening and covering layer growth | SEI growth, LLI, LAMNE |
| Half-cell capacity | Positive capacity nearly constant, negative capacity decreases | Negligible LAMPE, significant LAMNE |
Open-Circuit-Voltage Diagnostic Framework
I built a macroscopic diagnostic model using the open-circuit voltage curve. The open-circuit voltage of a full cell is the difference between the positive electrode potential and the negative electrode potential. Each electrode potential is a function of its own state of lithiation. The positive electrode and negative electrode are therefore defined in separate coordinate systems. To compare them and to quantify degradation modes, I transform both into a common coordinate system.
I define the positive electrode coordinate as xPE and its potential as Up. I define the negative electrode coordinate as xNE and its potential as Un. The available positive electrode coordinate is xAPE, and the available negative electrode coordinate is xANE. The transformation from the pristine positive coordinate to the available positive coordinate can be written as:
$$
\begin{bmatrix}
x_{\mathrm{APE}} \\
y_{\mathrm{APE}}
\end{bmatrix}
=
\begin{bmatrix}
T_{x,\mathrm{APE-PE}} & 0 \\
0 & T_{y,\mathrm{APE-PE}}
\end{bmatrix}
\begin{bmatrix}
x_{\mathrm{PE}} \\
y_{\mathrm{PE}}
\end{bmatrix}
+
\begin{bmatrix}
R_{x,\mathrm{APE-PE}} \\
R_{y,\mathrm{APE-PE}}
\end{bmatrix}
$$
Because active material loss changes the amount of accessible material but not the electrode potential as a function of lithiation, the vertical scaling factor is unity. The horizontal scaling factor is the ratio of available positive capacity to pristine positive capacity:
$$
T_{x,\mathrm{APE-PE}} = \frac{C_{\mathrm{APE}}}{C_{\mathrm{PE}}}
= 1 – \frac{LAM_{\mathrm{liPE}} + LAM_{\mathrm{dePE}}}{C_{\mathrm{PE}}}
$$
The horizontal translation term accounts for the lithium-containing portion of the lost positive active material:
$$
R_{x,\mathrm{APE-PE}} = \frac{LAM_{\mathrm{liPE}}}{C_{\mathrm{PE}}}
$$
I apply the same logic to the negative electrode. The transformation from the pristine negative coordinate to the available negative coordinate is:
$$
\begin{bmatrix}
x_{\mathrm{ANE}} \\
y_{\mathrm{ANE}}
\end{bmatrix}
=
\begin{bmatrix}
T_{x,\mathrm{ANE-NE}} & 0 \\
0 & T_{y,\mathrm{ANE-NE}}
\end{bmatrix}
\begin{bmatrix}
x_{\mathrm{NE}} \\
y_{\mathrm{NE}}
\end{bmatrix}
+
\begin{bmatrix}
R_{x,\mathrm{ANE-NE}} \\
R_{y,\mathrm{ANE-NE}}
\end{bmatrix}
$$
with
$$
T_{x,\mathrm{ANE-NE}} = \frac{C_{\mathrm{ANE}}}{C_{\mathrm{NE}}}
= 1 – \frac{LAM_{\mathrm{liNE}} + LAM_{\mathrm{deNE}}}{C_{\mathrm{NE}}}
$$
$$
R_{x,\mathrm{ANE-NE}} = \frac{LAM_{\mathrm{liNE}}}{C_{\mathrm{NE}}}
$$
Loss of lithium inventory introduces a mismatch between the positive and negative stoichiometry windows. In an electric vehicle battery pack, this mismatch appears as a shift in the operating window of both electrodes. I represent it through the following relationship between the positive and negative coordinates:
$$
x_{\mathrm{NE}} C_{\mathrm{NE}} = x_{\mathrm{PE}} C_{\mathrm{PE}} – LLI
$$
Combining the transformations, I can express the full-cell open-circuit voltage as a function of the available negative coordinate:
$$
\mathrm{OCV}(x_{\mathrm{ANE}})
=
U_p\left(
\frac{x_{\mathrm{ANE}} C_{\mathrm{ANE}}
+ LAM_{\mathrm{liNE}} + LAM_{\mathrm{deNE}} + LLI}
{C_{\mathrm{PE}} – LAM_{\mathrm{liPE}} – LAM_{\mathrm{dePE}}}
\right)
–
U_n(x_{\mathrm{ANE}})
$$
This expression contains several combinations of parameters that cannot be uniquely separated from a single open-circuit voltage curve. I therefore re-parameterize the model into identifiable groups. I define:
$$
X_1 = C_{\mathrm{APE}} = C_{\mathrm{PE}} – LAM_{\mathrm{liPE}} – LAM_{\mathrm{dePE}}
$$
$$
X_2 = C_{\mathrm{ANE}} = C_{\mathrm{NE}} – LAM_{\mathrm{liNE}} – LAM_{\mathrm{deNE}}
$$
$$
X_3 = LAM_{\mathrm{liNE}} – LAM_{\mathrm{dePE}} + LLI
$$
$$
X_4 = x_{\mathrm{NE},0}
$$
With these definitions, the open-circuit voltage model becomes:
$$
\mathrm{OCV}(x_{\mathrm{ANE}})
=
U_p\left(\frac{x_{\mathrm{ANE}} X_2 + X_3}{X_1}\right)
–
U_n(1 – x_{\mathrm{ANE}})
$$
I map the measured capacity to the available negative coordinate using the following relation:
$$
x_{\mathrm{ANE}}(i) = \frac{\mathrm{Capacity}(i)}{X_2} + \frac{X_4}{X_2}
$$
where Capacity(i) is the charge or discharge capacity at measurement point i. I then fit the model to the measured low-rate open-circuit voltage curve. The objective is to minimize the root-mean-square error:
$$
\min \mathrm{RMSE}
=
\sqrt{
\frac{1}{n}
\sum_{i=1}^{n}
\left[
\mathrm{OCV}_i – \mathrm{OCV}_{\mathrm{ANE},i}
\right]^2
}
$$
I use particle swarm optimization to identify X1, X2, X3, and X4. Particle swarm optimization is well suited to this problem because it does not require a differentiable objective function and it can search a bounded parameter space efficiently. The fit quality is judged by the difference between the measured open-circuit voltage and the reconstructed open-circuit voltage over the full stoichiometry window.
The identified parameters show that the positive available capacity is nearly constant over the studied aging range, whereas the negative available capacity declines. The parameter associated with lithium loss and stoichiometry shift increases as state of health decreases. This already suggests that the dominant degradation modes in the electric vehicle battery pack are loss of lithium inventory and loss of negative active material, while loss of positive active material is comparatively small.
| Parameter | Physical meaning | Trend with aging | Interpretation |
|---|---|---|---|
| X1 | Available positive capacity | Nearly constant | LAMPE is small |
| X2 | Available negative capacity | Decreases | LAMNE increases |
| X3 | Stoichiometry shift and lithium loss | Increases | LLI and negative active material shift dominate |
| X4 | Initial negative stoichiometry | Slight change | Operating window shifts |
Quantitative Macroscopic Degradation Results
After identifying the grouped parameters, I separate the lithium-containing and lithium-free active material losses. I assume that when active particles become electrically isolated, the probability of isolation is similar across lithiation states. Under this assumption, the average lithiation of the lost material equals the average lithiation of the electrode over its operating window. This gives a way to estimate the lithium-containing fraction of active material loss. The average lithiation of the cracked positive and negative material is:
$$
x_{\mathrm{crk},p} = \frac{x_{\mathrm{APE}}^{\min} + x_{\mathrm{APE}}^{\max}}{2}
$$
$$
x_{\mathrm{crk},n} = \frac{x_{\mathrm{ANE}}^{\min} + x_{\mathrm{ANE}}^{\max}}{2}
$$
The lithium-containing positive and negative active material losses are then:
$$
LAM_{\mathrm{liPE}}
=
\frac{x_{\mathrm{crk},p} + 1}{2}
\left[
C_{\mathrm{APE},\mathrm{fresh}} – C_{\mathrm{APE},\mathrm{aging}}
\right]
$$
$$
LAM_{\mathrm{liNE}}
=
\frac{x_{\mathrm{crk},n} + 1}{2}
\left[
C_{\mathrm{ANE},\mathrm{fresh}} – C_{\mathrm{ANE},\mathrm{aging}}
\right]
$$
The lithium-free active material losses follow from the total available capacity changes:
$$
LAM_{\mathrm{deNE}} = LAM_{\mathrm{NE}} – LAM_{\mathrm{liNE}}
$$
$$
LAM_{\mathrm{dePE}} = LAM_{\mathrm{PE}} – LAM_{\mathrm{liPE}}
$$
Once the active material losses are separated, I recover loss of lithium inventory from the third grouped parameter:
$$
LLI = X_3 – LAM_{\mathrm{liNE}} + LAM_{\mathrm{dePE}}
$$
I applied this procedure to cells at different states of health. The positive active material losses remained very small and did not show a clear monotonic increase. The negative active material losses increased with aging. The loss of lithium inventory also increased with aging and was the largest single contributor in the early and middle stages of life. The maximum diagnosed loss of lithium inventory was 3.40 Ah, and the maximum diagnosed negative active material loss was 2.83 Ah. These values are significant for an electric vehicle battery pack because they represent a direct reduction in usable energy and available power.
| State of health range | LLI trend | LAMPE trend | LAMNE trend | Maximum diagnosed value |
|---|---|---|---|---|
| High SOH | Small but increasing | Negligible | Small | LLI: 3.40 Ah |
| Medium SOH | Dominant | Negligible | Increasing | LAMNE: 2.83 Ah |
| Lower SOH | Strongly increasing | Negligible | Strongly increasing | LLI and LAMNE both significant |
The macro-scale diagnosis is useful because it is non-destructive and can in principle be applied to an electric vehicle battery pack without taking the pack apart. However, it relies on assumptions. The most important assumption is that the electrode potential curves retain their shape and that the active material isolation process can be approximated by an average lithiation. To test whether the diagnosis is credible, I compared it with independent micro-scale measurements.
Micro-Scale Validation Using Half-Cell Capacity
I assembled half cells from the positive and negative electrode laminates extracted from aged full cells. In a half cell, lithium metal serves as the counter electrode, so the available lithium is not the limiting factor. The measured half-cell capacity therefore reflects the accessible active material capacity of the extracted laminate. If the positive half-cell capacity remains nearly constant while the negative half-cell capacity declines, then the micro-scale measurement supports the macro-scale conclusion that positive active material loss is small and negative active material loss is significant.
The positive half-cell capacities were nearly unchanged across the tested aging range. The negative half-cell capacities decreased as state of health decreased. This trend matches the open-circuit-voltage diagnosis. Because the units of half-cell capacity and full-cell diagnosis differ, I normalized both to a reference cell. I used the least aged cell in the negative half-cell group as the reference. The normalized capacity loss is:
$$
r_{\mathrm{loss,cap}} = \frac{Cap_0 – Cap_i}{Cap_0} \times 100\%
$$
The normalized open-circuit-voltage active material loss is:
$$
r_{\mathrm{loss,ocv}} = \frac{LAM_0 – LAM_i}{LAM_0} \times 100\%
$$
I compared these two normalized quantities for the negative electrode. The maximum difference between the half-cell capacity loss and the open-circuit-voltage-diagnosed active material loss was only 1.35%. This agreement is important because it provides independent support for the macro-scale diagnosis. It also confirms that the half-cell capacity change is not an artifact of cell assembly or measurement, but rather a real reflection of negative active material loss.
| Cell group | Half-cell capacity loss (%) | Diagnosed active material loss (%) | Difference (%) |
|---|---|---|---|
| Reference | 0 | 0 | 0 |
| Aged cell 1 | 4.55 | 3.20 | 1.35 |
| Aged cell 2 | 8.91 | 7.93 | 0.98 |
| Aged cell 3 | 11.54 | 10.40 | 1.14 |
Micro-Scale Validation Using Diffraction Peak Intensity
I also used X-ray diffraction to quantify the maximum lithium content in the negative electrode. In the fully charged state, the negative electrode contains lithium-carbon compounds. The two most useful reflections are associated with LiC6 and LiC12. I normalized the carbon reference and calculated the weighted lithium content from the two peak intensities:
$$
Li_xC_{\mathrm{aging}}
=
\frac{1}{6}
\frac{x_1}{x_1 + x_2}
+
\frac{1}{12}
\frac{x_2}{x_1 + x_2}
$$
where x1 is the LiC6 peak intensity and x2 is the LiC12 peak intensity. The percentage change in maximum lithium content is:
$$
LLI_{\mathrm{XRD}}
=
\frac{Li_xC_{\mathrm{fresh}} – Li_xC_{\mathrm{aging}}}
{Li_xC_{\mathrm{fresh}}}
\times 100\%
$$
Before correction, the maximum lithium content change reached 24.96%. This value is larger than the capacity fade of the full cell. The reason is that the calculation normalized the carbon signal, effectively assuming that the amount of accessible negative active material remained constant. However, the half-cell results show that negative active material is lost during aging. Therefore, the normalized lithium content overestimates the lithium inventory loss if it does not account for the reduction in accessible carbon.
I corrected the maximum lithium content calculation by including the negative active material loss measured from half-cell capacity. The corrected lithium-carbon content is:
$$
Li_xC’_{\mathrm{aging}}
=
\left[
\frac{1}{6}
\frac{x_1}{x_1 + x_2}
+
\frac{1}{12}
\frac{x_2}{x_1 + x_2}
\right]
\left[
1 – LAM_{\mathrm{NE}}
\right]
$$
where LAMNE is expressed as a fractional loss. The corrected percentage change is:
$$
LLI’ =
\frac{Li_xC_{\mathrm{fresh}} – Li_xC’_{\mathrm{aging}}}
{Li_xC_{\mathrm{fresh}}}
\times 100\%
$$
After correction, the diffraction-based maximum lithium content change agreed much better with the open-circuit-voltage-diagnosed loss of lithium inventory. The maximum error was only 1.68%. This result is significant because it connects a crystallographic measurement to an electrochemical degradation mode. It also demonstrates that the macro-scale open-circuit-voltage diagnosis does not merely fit the voltage curve; it produces a lithium loss value that is consistent with an independent material measurement.
| Aging level | OCV-diagnosed LLI (%) | Corrected XRD LLI (%) | Difference (%) |
|---|---|---|---|
| Low aging | 4.10 | 3.93 | 0.17 |
| Medium aging | 7.83 | 7.54 | 0.29 |
| High aging | 13.46 | 12.20 | 1.26 |
| Highest aging | 16.89 | 15.95 | 1.68 |
Incremental Capacity Curve Diagnostics
Although the open-circuit-voltage method is accurate, it is not convenient for online use in an electric vehicle battery pack. The open-circuit voltage must be measured or reconstructed, and the fitting procedure is relatively complex. The incremental capacity curve, defined as dQ/dV, is the derivative of the voltage curve. It amplifies small voltage changes and produces peaks that correspond to phase transitions and electrode reactions. Because the incremental capacity curve can be calculated from ordinary current and voltage data, it is attractive for battery management systems in an electric vehicle battery pack.
I examined the relationship between the open-circuit voltage curve and the incremental capacity curve. The plateau regions of the open-circuit voltage curve correspond to peaks in the incremental capacity curve. For the lithium iron phosphate cell, I identified three main peaks in the charging incremental capacity curve. I label them as the low-voltage peak, the middle peak, and the high-voltage peak, corresponding to the sequence of phase transitions during charging. The middle peak is sensitive to negative active material loss. The high-voltage peak is sensitive to loss of lithium inventory. The low-voltage peak is less useful for the present diagnosis because it can be influenced by multiple overlapping processes.
I first studied single degradation modes by constructing synthetic cells with controlled amounts of loss of lithium inventory, lithium-containing negative active material loss, and lithium-free negative active material loss. The single-mode simulations revealed several important effects:
| Degradation mode | Middle peak area | High-voltage peak area | High-voltage peak height |
|---|---|---|---|
| LLI increases | Nearly constant | Decreases | Decreases |
| LAMdeNE increases | Decreases | Increases | Increases |
| LAMliNE increases | Decreases | Decreases | Decreases |
| LAMdeNE + LAMliNE | Decreases | Approximately cancels | Approximately cancels |
The cancellation effect is important. In the studied cell, lithium-containing and lithium-free negative active material losses are comparable. Their effects on the high-voltage peak are opposite. As a result, the high-voltage peak area is mainly governed by loss of lithium inventory. The middle peak area decreases when either type of negative active material loss increases. The middle peak is therefore a useful indicator of total negative active material loss.
I then studied coupled degradation modes. When loss of lithium inventory and negative active material loss occur together, the high-voltage peak decreases strongly, and the middle peak also decreases. This matches the experimental incremental capacity curves from aged cells. The peak positions also shift slightly to higher voltage during charging as aging progresses. I attribute this shift mainly to polarization and impedance growth, which are not included in the ideal thermodynamic construction. Because the studied aging range is moderate, the shift does not prevent quantitative analysis, but it does increase the uncertainty of peak height calculations.
I derived quantitative relationships between peak area and degradation modes. For negative active material loss, I use the middle peak area:
$$
LAM_{\mathrm{NE}}
=
\frac{Area_{B,\mathrm{fresh}} – Area_{B,\mathrm{aging}}}
{Area_{B,\mathrm{fresh}}}
\times 100\%
$$
For loss of lithium inventory, the high-voltage peak area is initially normalized by the fresh high-voltage peak area. However, this introduces a bias because loss of lithium inventory shifts the entire operating window rather than only compressing a local peak. A better normalization uses the full fresh-cell capacity:
$$
LLI =
\frac{Area_{C,\mathrm{fresh}} – Area_{C,\mathrm{aging}}}
{Capacity_{\mathrm{fresh}}}
\times 100\%
$$
I compared the incremental-capacity-based diagnosis with the open-circuit-voltage-based diagnosis. When the peak area was used, the agreement was good. When the peak height was used, the scatter was larger. The reason is that peak height is sensitive to the exact shape of the peak and to the smoothing method, while peak area is more robust because it integrates over the peak. Using the corrected normalization, the maximum difference between the incremental-capacity method and the open-circuit-voltage method was 1.79% for loss of lithium inventory and 1.62% for negative active material loss.
| Degradation mode | Incremental-capacity feature | Maximum difference from OCV diagnosis | Preferred feature |
|---|---|---|---|
| LLI | High-voltage peak area | 1.79% | Peak area |
| LAMNE | Middle peak area | 1.62% | Peak area |
| LLI | High-voltage peak height | Larger scatter | Not preferred |
| LAMNE | Middle peak height | Larger scatter | Not preferred |
Rate Adaptability and Correction
An electric vehicle battery pack rarely operates at C/25. Therefore, I tested whether the incremental-capacity diagnostic method remains valid at higher rates. I calculated incremental capacity curves at C/25, C/10, C/5, C/3, C/2, and 1C. As the rate increased, the charging peaks shifted to higher voltage, and the discharge peaks shifted to lower voltage. The peak heights decreased. At C/2 and above, some peaks began to merge or disappear. These changes are caused by polarization, ohmic resistance, charge-transfer resistance, and diffusion limitations. They are not necessarily caused by degradation. Therefore, rate effects must be separated from aging effects.
I evaluated the diagnostic method at C/10, C/5, and C/3. The negative active material loss diagnosis remained broadly consistent with the C/25 reference. The scatter was larger because the middle peak is relatively small and asymmetric, and the smoothing method can affect its integrated area. The loss of lithium inventory diagnosis showed a systematic downward trend as the rate increased. The maximum absolute error was 3.25% at C/10, 4.77% at C/5, and 6.07% at C/3. This means that a rate-dependent correction is needed if the method is to be used online in an electric vehicle battery pack.
I introduced a rate correction factor for loss of lithium inventory:
$$
LLI_{\mathrm{corr}} = k_{\mathrm{rate}} \, LLI_{\mathrm{IC}}
$$
where krate depends on the current rate. I obtained the correction factors by comparing the incremental-capacity diagnosis at each rate with the C/25 reference diagnosis. The factors are listed in Table 11.
| Rate | C/25 | C/10 | C/5 | C/3 |
|---|---|---|---|---|
| Correction factor | 1.00 | 1.19 | 1.26 | 1.47 |
After correction, the loss of lithium inventory values at C/10, C/5, and C/3 were much closer to the C/25 reference. The maximum remaining error was 1.68%. This result indicates that the incremental-capacity method can be adapted to realistic operating rates with a simple offline or online correction function. For an electric vehicle battery pack, this is important because the battery management system can use the same peak-area logic across different driving and charging conditions, provided that the rate dependence is calibrated.
| State of health (%) | C/25 LLI (%) | C/10 corrected (%) | C/5 corrected (%) | C/3 corrected (%) |
|---|---|---|---|---|
| 96.54 | 1.08 | 1.21 | 1.28 | 1.49 |
| 93.47 | 4.10 | 3.93 | 4.47 | 2.77 |
| 90.61 | 5.05 | 6.33 | 5.77 | 5.39 |
| 89.12 | 7.83 | 7.32 | 7.54 | 6.84 |
| 86.77 | 10.99 | 10.57 | 10.84 | 10.96 |
| 83.63 | 13.46 | 12.20 | 11.87 | 13.11 |
| 79.76 | 16.43 | 14.91 | 14.75 | 15.26 |
| 79.41 | 16.89 | 16.60 | 16.29 | 15.95 |
I also considered how the method could be implemented online. A practical workflow for an electric vehicle battery pack would collect current and voltage data during normal operation. The battery management system would segment the data into charge and discharge events, smooth the voltage and capacity signals, calculate the incremental capacity curve, and extract the middle and high-voltage peak areas. The middle peak area would provide negative active material loss. The high-voltage peak area would provide loss of lithium inventory after rate correction. If the operating rate varies, the correction factor can be updated using a lookup table or an online calibration function. If the vehicle has enough rest time, an open-circuit-voltage reconstruction can provide a reference diagnosis for recalibration.
Practical Implications for an Electric Vehicle Battery Pack
The cross-scale results have several implications for the management of an electric vehicle battery pack. First, loss of lithium inventory is not the only degradation mode that matters. In the studied lithium iron phosphate cells, negative active material loss also becomes significant, especially as state of health falls. A battery management system that only tracks capacity fade may miss the distinction between lithium loss and active material loss. This distinction matters because the two modes affect the electrode stoichiometry differently and can influence the safe operating window.
Second, micro-scale measurements are valuable for validating macro-scale diagnostics. Without half-cell capacity and diffraction measurements, the open-circuit-voltage diagnosis would remain a curve-fitting exercise. With those measurements, I can show that the diagnosed negative active material loss is consistent with an independent electrode capacity measurement and that the diagnosed lithium loss is consistent with an independent crystallographic measurement. This validation increases confidence in the macro-scale method for an electric vehicle battery pack.
Third, the incremental capacity method is more suitable for online use than the full open-circuit-voltage fitting method. It requires only current and voltage data, and the key features are peak areas that can be computed with modest computational cost. The rate correction is essential because the peaks shift and shrink with current rate. In an electric vehicle battery pack, the current rate varies continuously, so the correction should be applied dynamically. If the rate is high enough that peaks merge, the method should either use a lower-rate window or rely on a reconstructed open-circuit voltage from low-current periods.
Fourth, the results suggest that the degradation trajectory of an electric vehicle battery pack can be represented by a small number of dominant modes. In the early stage, loss of lithium inventory dominates. In the later stage, negative active material loss becomes more important. Positive active material loss remains small in this chemistry. This trajectory can be used to design better charging strategies. For example, if loss of lithium inventory is accelerating because of lithium plating, the charging protocol can be modified to reduce plating. If negative active material loss is accelerating because of mechanical stress, the depth of discharge or the rate can be limited. If the pack is used in a hot environment, thermal management can be adjusted to slow solid electrolyte interphase growth.
Cross-Scale Diagnostic Workflow
I summarize the workflow that connects the macro and micro scales. The workflow begins with full-cell testing. Capacity calibration establishes the state of health. Low-rate reference tests establish a common thermodynamic endpoint. The open-circuit voltage curve is measured or reconstructed. The open-circuit-voltage model is fitted to identify available positive capacity, available negative capacity, and the stoichiometry shift parameter. The active material losses are separated into lithium-containing and lithium-free fractions using the average lithiation assumption. Loss of lithium inventory is recovered from the grouped parameters.
In parallel, selected cells are disassembled at known states of health. Half-cell tests measure the accessible capacity of the positive and negative electrodes. X-ray diffraction measures the lithium-carbon peak intensities in the negative electrode. Scanning electron microscopy observes surface morphology and solid electrolyte interphase growth. The half-cell capacity change provides an independent estimate of negative active material loss. The corrected diffraction intensity provides an independent estimate of loss of lithium inventory. The two macro-scale diagnostic outputs are then compared with the two micro-scale measurements.
For online application, the workflow shifts to the incremental capacity domain. The battery management system calculates the incremental capacity curve from ordinary operating data. The middle peak area gives negative active material loss. The high-voltage peak area, after normalization by fresh capacity and rate correction, gives loss of lithium inventory. The online results can be periodically recalibrated against a reconstructed open-circuit voltage or against a laboratory reference test. This hybrid approach allows the electric vehicle battery pack to maintain accurate degradation diagnostics without frequent destructive testing.
| Macro-scale quantity | Micro-scale measurement | Relationship | Validated error |
|---|---|---|---|
| LAMNE from OCV | Negative half-cell capacity loss | Both reflect accessible negative active material | 1.35% |
| LLI from OCV | Corrected lithium-carbon diffraction change | Both reflect cyclable lithium loss | 1.68% |
| LAMNE from IC middle peak | OCV-diagnosed LAMNE | Peak area compression | 1.62% |
| LLI from IC high-voltage peak | OCV-diagnosed LLI | Peak area reduction with capacity normalization | 1.79% |
Discussion of Assumptions and Uncertainty
The open-circuit-voltage method relies on the electrode potential curves remaining stable. In practice, electrode potential curves can change slightly with aging because of surface reconstruction, impedance growth, and active material isolation. I minimized this effect by using half-cell measurements from the same chemistry and by fitting the full voltage window rather than a single feature. The remaining uncertainty is small in the studied aging range, but it would increase if the cell underwent severe degradation, such as extensive lithium plating or major particle fracture.
The average lithiation assumption for active material loss is another source of uncertainty. If active material loss preferentially occurs at the end of charge or end of discharge, the lithium-containing fraction could differ from the average. The half-cell capacity comparison supports the assumption for the negative electrode, because the diagnosed and measured losses agreed within 1.35%. However, the assumption may be less accurate for other chemistries or for cells cycled under extreme conditions. Future work could combine post-mortem lithium mapping with the average lithiation model to refine the separation.
The incremental capacity method has its own uncertainties. Smoothing is necessary because numerical differentiation amplifies noise. I used a polynomial center smoothing method, which is computationally efficient and robust. However, it can distort asymmetric peaks. The middle peak in the incremental capacity curve is somewhat asymmetric, which explains part of the scatter in negative active material loss. A more advanced peak decomposition or a model-based incremental capacity method could reduce this scatter. Rate correction also introduces uncertainty because the correction factor depends on temperature, state of charge, and aging state. In an electric vehicle battery pack, the correction factor should be updated as more data become available.
Despite these uncertainties, the cross-scale agreement is strong. The macro-scale diagnosis does not simply produce a plausible number; it produces a number that matches an independent half-cell measurement and an independent diffraction measurement. This is the main contribution of the study. It shows that degradation modes in an electric vehicle battery pack can be quantified with a combination of voltage-based diagnostics and carefully designed material characterization.
Conclusions
I investigated degradation modes in a lithium iron phosphate cell intended for an electric vehicle battery pack. I combined full-cell testing, open-circuit-voltage modeling, half-cell capacity measurements, X-ray diffraction, scanning electron microscopy, and incremental capacity analysis. The following conclusions summarize the work.
First, the dominant degradation modes are loss of lithium inventory and loss of negative active material. Positive active material loss is negligible in the studied chemistry and aging range. The maximum diagnosed loss of lithium inventory was 3.40 Ah, and the maximum diagnosed negative active material loss was 2.83 Ah. These values show that both lithium loss and active material loss must be considered when assessing the state of health of an electric vehicle battery pack.
Second, the open-circuit-voltage diagnostic model can separate available positive capacity, available negative capacity, and stoichiometry shift. With an additional average lithiation assumption, the model separates lithium-containing and lithium-free active material losses. The resulting loss of lithium inventory agrees with an independent diffraction-based measurement after accounting for negative active material loss. The maximum error was 1.68%. The resulting negative active material loss agrees with negative half-cell capacity loss, with a maximum difference of 1.35%. These two comparisons validate the macro-scale diagnosis at the micro scale.
Third, the incremental capacity curve provides a practical route for online diagnosis in an electric vehicle battery pack. The middle peak area is sensitive to negative active material loss, while the high-voltage peak area is mainly governed by loss of lithium inventory. Peak area is more robust than peak height. After normalizing the high-voltage peak area by fresh capacity, the incremental-capacity method and the open-circuit-voltage method agree within 1.79% for loss of lithium inventory and 1.62% for negative active material loss.
Fourth, rate effects must be corrected for online use. As the current rate increases, the incremental capacity peaks shift and shrink. The loss of lithium inventory diagnosis decreases systematically with rate. I introduced a rate correction factor and reduced the maximum error to 1.68%. This makes the method more suitable for realistic operation of an electric vehicle battery pack, where the current rate is rarely constant.
Overall, I show that micro-scale material measurements and macro-scale electrical diagnostics can be connected in a quantitative way. The connection is not merely qualitative. It provides validated numbers for loss of lithium inventory and loss of active material. For an electric vehicle battery pack, this cross-scale framework can support better state estimation, more accurate remaining useful life prediction, and safer operating strategies. Future work should focus on reducing the uncertainty of incremental capacity peak decomposition, extending the method to real vehicle data, and incorporating temperature and rate dependence into online correction functions.