In the realm of energy storage, the li ion battery stands as a cornerstone technology, particularly for applications demanding high capacity and stability. The widespread adoption of li ion battery systems, especially lithium iron phosphate variants, necessitates robust and non-destructive diagnostic techniques to monitor internal states, such as state of charge (SOC) and state of health (SOH). While electrical and thermal parameters offer external insights, they often fall short in directly capturing the complex electrochemical and structural dynamics within a sealed li ion battery. Ultrasonic testing has emerged as a promising in-situ method due to its sensitivity, cost-effectiveness, and ability to probe internal material properties. However, most prior studies have focused on benign conditions—room temperature and low charge-discharge rates—neglecting the significant thermal effects and high-rate operations common in practical applications. The interplay between temperature, discharge current, and acoustic signals in a li ion battery remains poorly understood, limiting the technique’s reliability under strenuous conditions.
This study addresses these gaps by investigating the temperature-dependent mechanisms of ultrasonic propagation in a li ion battery. We develop an integrated electro-acoustic-thermal testing platform to systematically analyze how temperature variations, induced by different discharge rates, affect ultrasonic time-domain features. Crucially, we introduce a temperature coupling coefficient tied to SOC to decouple thermal influences from acoustic signatures, enabling a clearer interpretation of structural changes within the li ion battery. Our experiments encompass multiple cycles under varied temperatures and discharge rates, revealing that the decoupled acoustic characteristics can accurately track internal structural evolution. This work provides a methodological framework for applying ultrasonic diagnostics to li ion battery systems operating in high-demand scenarios, enhancing the fidelity of state assessment.
The operational principle of a li ion battery, particularly the lithium iron phosphate chemistry, hinges on the intercalation and deintercalation of lithium ions between electrodes. During charging, lithium ions extract from the cathode (LiFePO₄) and insert into the graphite anode, forming LiₓC₆, while the reverse occurs during discharge. This process alters the mechanical properties of the electrodes: the graphite anode experiences a substantial increase in Young’s modulus upon lithiation, whereas the cathode undergoes minimal volumetric change. Consequently, the effective Young’s modulus of the entire li ion battery is predominantly governed by the anode, making it sensitive to lithium concentration and, by extension, SOC. However, this relationship is further modulated by current density, as high rates induce lithium concentration gradients, leading to phase coexistence and reduced modulus. Establishing a robust electro-acoustic coupling requires accounting for these factors, alongside temperature effects that influence material elasticity and density.
Ultrasonic longitudinal waves propagating through a multilayered li ion battery carry information about the internal medium’s acoustic impedance, which depends on density (ρ) and Young’s modulus (E). The wave velocity (c) is given by:
$$ c = \sqrt{\frac{K + \frac{4}{3}G}{\rho}} $$
where K is the bulk modulus and G is the shear modulus, related to E and Poisson’s ratio (ν) via:
$$ K = \frac{E}{3(1 – 2\nu)} $$
$$ G = \frac{E}{2(1 + \nu)} $$
The acoustic impedance Z is:
$$ Z = \sqrt{\rho E} $$
For a li ion battery, ν remains relatively constant during cycling, so changes in c primarily reflect variations in E and ρ of the graphite anode and cathode. The time-of-flight (ToF) of an ultrasonic pulse through the battery thickness (l) is:
$$ \text{ToF} = \frac{l}{c} $$
and the signal amplitude (SA) correlates with impedance mismatches and attenuation. Typically, ToF and SA are extracted as time-domain features. Temperature fluctuations, however, introduce confounding effects: as temperature rises, materials expand (increasing l), and their elastic moduli and densities change (altering c), thereby affecting both ToF and SA. To isolate the structural changes due to electrochemistry, we must decouple these thermal contributions.
Our experimental setup comprises four modules: a battery cycling system, an ultrasonic measurement unit, a thermal control chamber, and a data acquisition suite. We utilize a commercial 20 Ah soft-pack lithium iron phosphate li ion battery, with a maximum recommended discharge rate of 3C. The ultrasonic module employs a pulse-receiver (CTS-8077PR) with 5 MHz piezoelectric transducers in a pitch-catch configuration, coupled to the battery surface using glycerol. A digital oscilloscope captures the ultrasonic signals synchronously with electrical parameters (voltage, current) and temperature data. To ensure consistent transducer pressure despite battery swelling, a custom 3D-printed fixture with a pressure sensor is employed. Temperature monitoring is critical; we measure surface temperatures and, under adiabatic conditions on one side, compute the internal average temperature (Tav) via a simplified one-dimensional heat transfer model:
$$ \rho C_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial z} \left( k_z \frac{\partial T}{\partial z} \right) + q_{\text{total}} $$
where ρ, Cp, and kz are the density, specific heat, and thermal conductivity of the li ion battery, respectively, and qtotal is the heat generation rate. This approach yields Tav with minimal error, essential for accurate decoupling.
Initial experiments characterize the temperature dependence of acoustic features in a li ion battery at open circuit. The battery is stabilized at various SOCs and subjected to a slow temperature ramp from 5°C to 45°C. The ToF and SA exhibit linear relationships with temperature, but the slopes vary with SOC. We define a temperature coupling coefficient kSOC as:
$$ k_{\text{SOC}} = \frac{\Delta \text{ToF}}{T_{\text{av}}} $$
where ΔToF is the ToF shift relative to a reference. The data across SOC levels are summarized in Table 1, showing that kSOC changes modestly with SOC, reflecting alterations in the thermal expansion coefficient due to lithiation state.
| SOC (%) | kSOC (ns/°C) | Amplitude Sensitivity (%/°C) |
|---|---|---|
| 100 | 2.1 | -0.15 |
| 80 | 2.3 | -0.18 |
| 60 | 2.5 | -0.22 |
| 40 | 2.7 | -0.25 |
| 20 | 2.9 | -0.28 |
| 0 | 3.1 | -0.31 |
The decoupled ToF, representing purely electrochemical-induced changes, is then computed as:
$$ \text{ToF}_{\text{decoupled}} = \text{ToF} – k_{\text{SOC}} \cdot T_{\text{av}} $$
We apply this to cycling data. For a 0.5C constant-current discharge followed by constant-current-constant-voltage charge, the raw ToF shows complex fluctuations with temperature swings, whereas ToFdecoupled reveals a smoother, more interpretable trend. During discharge, ToFdecoupled decreases gradually as lithium deintercalates from graphite, reducing anode modulus and thickness; near the end, a slight uptick occurs due to increased concentration polarization. The charge phase mirrors this pattern symmetrically, with a small hysteresis attributable to diffusion stresses. This decoupling effectively removes thermal artifacts, making the acoustic response directly correlate with SOC-driven structural changes in the li ion battery.
To assess reproducibility, we conduct six consecutive cycles under identical conditions. The decoupled ToF waveforms align closely across cycles, demonstrating that the method captures consistent electrochemical states without drift from temperature variations. This repeatability underscores the robustness of our temperature decoupling approach for monitoring a li ion battery over short-term usage.
We further explore the impact of discharge rate on the acoustic response of a li ion battery. Tests are performed at 0.25C, 0.5C, 1C, 2C, and 3C, all at an ambient temperature of 25°C. The results, summarized in Table 2, indicate that higher rates induce greater thermal effects, leading to larger raw ToF shifts. After decoupling, ToFdecoupled still shows rate-dependent characteristics: the amplitude of change increases with rate, and hysteresis becomes pronounced above 2C. This is attributed to enhanced concentration gradients and polarization at high currents, which alter the distribution of lithium ions and thus the effective modulus of the li ion battery. The decoupled signals remain sensitive to these phenomena, validating the method’s utility across operational intensities.
| Discharge Rate (C) | Max Raw ToF Shift (ns) | Max Decoupled ToF Shift (ns) | Hysteresis (ns) | Peak Temperature (°C) |
|---|---|---|---|---|
| 0.25 | 45 | 15 | 2 | 26.5 |
| 0.5 | 68 | 22 | 4 | 32.2 |
| 1 | 112 | 35 | 8 | 41.7 |
| 2 | 185 | 50 | 18 | 55.3 |
| 3 | 250 | 65 | 30 | 68.9 |
The underlying mechanism can be elucidated through the relationship between Young’s modulus and lithium content. For graphite, E varies approximately linearly with lithium concentration x, but at high rates, inhomogeneous lithiation reduces the effective modulus. Combining this with thermal expansion, the overall ToF response becomes a function of SOC, current density, and temperature. Our decoupling method simplifies this by subtracting the temperature component, leaving a signal primarily dependent on SOC and rate. This is crucial for practical BMS (Battery Management Systems) in a li ion battery pack, where real-time state estimation must account for dynamic thermal environments.
Moreover, the amplitude of ultrasonic signals also offers complementary insights. SA tends to decrease with temperature due to reduced impedance mismatch and increased attenuation, but after temperature compensation, residual variations correlate with electrode porosity and electrolyte degradation. Future work could integrate both ToF and SA decoupling for a multi-parameter health diagnosis of a li ion battery.
In summary, this study demonstrates a systematic method to decouple temperature effects from ultrasonic propagation characteristics in a li ion battery. By introducing a SOC-dependent temperature coupling coefficient and accurately measuring internal average temperature, we extract clean acoustic signatures that reflect intrinsic structural changes. Experiments across multiple temperatures and discharge rates confirm that the decoupled ToF reliably tracks electrochemical states, even under high-rate conditions where thermal interference is severe. The method enhances the applicability of ultrasonic testing for in-situ monitoring of li ion battery systems in electric vehicles, grid storage, and other demanding applications. Future directions include extending this approach to other battery chemistries, aging studies, and integrating machine learning for predictive analytics. Ultimately, advancing such non-destructive techniques will contribute to safer, longer-lasting, and more efficient li ion battery technologies.