Quantum magnetic imaging of current density in lithium-ion batteries

Abstract

The projected rapid growth of battery cell production over the next decade demands advanced diagnostic tools for quality control, ageing prediction, and recycling. Most existing techniques lack the spatial and temporal resolution required to capture internal electrochemical processes non-invasively. Here, we present magnetic imaging of current densities in battery cells, a sensitive quantum-magnetometry method that uses optically pumped magnetometers (OPMs) to perform real-time imaging of internal dynamics in open-circuit configuration. We demonstrate this approach for monitoring relaxation processes in 6000 mA h lithium-ion cells following pulsed discharges across a range of pulse durations and currents as well as states of charge. The measurement results are benchmarked against superconducting-quantum-interference-device (SQUID) magnetometry and validated with three-dimensional finite element simulations. Equivalent circuit models are employed to interpret the relaxation profiles, revealing spatially resolved features and transient magnetic-field signatures that are inaccessible with complementary non-invasive techniques such as electrochemical impedance spectroscopy (EIS). This work establishes OPM-based magnetic imaging of battery current density as a powerful diagnostic tool with potential impact on cell development, manufacturing quality assurance, and second-life assessment.

Figures (8)

• Figure 1: : (a) General scheme for non-invasive, non-contact magnetic imaging of a battery using an array of optically pumped magnetometers (OPMs, grey boxes). The exact configuration of the array, including sensor density and orientation, can be adjusted depending on specific experimental requirements (Table S1). Stand-off distance from the surface of the battery to the center of the atomic sensing volume (alkali vapour cell, depicted as a red cube) is less than 1 cm. (b) Snapshot of a typical vector magnetic image of a battery, with each pixel corresponding to the reading (here, magnetic field along the $z$-axis) from a single sensor of the OPM array. This spatially resolved method allows us to distinguish the magnitude and sign of the field due to differing current densities at different locations within the battery at any given point in time.
• Figure 2: : Time-series data from ambient measurements of a disconnected battery cell using a 1D $4\times1$ OPM array (top inset and Fig. S1(a)), showing an example of a 'jump' in the measured $B_x$ and $B_y$ magnetic fields within a period of 1h, out of a measurement over 32h. The background gradient depicts the cell temperature, as measured with a non-magnetic thermocouple mounted at the centre of the cell. Data were sampled at 2Hz, with moving averages of 20s and 1h used for magnetic field and temperature, respectively. See text for further details and discussion. Such data indicates that the OPM method is uniquely placed to detect localised phenomena of relatively small amplitude over longer timescales.
• Figure 3: : (a) Example of relaxation in the cell voltage (blue) immediately after a single 1, 0.5A (C/12) discharge pulse (orange), characterized by a relaxation time of 33.21±0.02s at which the voltage decays to $1/e$ of its initial value. The battery was fully charged and allowed to rest for 4h before the relaxation measurement was performed. The inset shows the full voltage measurement during and after the discharge pulse, with ($x$,$y$) indicating sensor positions in mm. (b) Measured magnetic field along the $x$-direction recorded with the 2D $2\times3$ OPM array (Fig. S1(b)) immediately after the discharge pulse---see legend inset for colour-coding. The magnetic fields at each pair of sensors located the same distance from the cell tabs ($y$-coordinate) approximately mirror each other---indicating a symmetry of current density amplitude about the $y$-axis---with the largest amplitudes farthest from the tabs (green and red curves). (c) Simulated electrolyte current density (see the section 'Finite-element simulations') along the $z$-direction in the positive electrode, 20µm from the electrode-separator boundary of a 62.4mAh-capacity single-layer cell following a discharge pulse. The current density is shown at eight points in the electrode, at positions directly below the sensors in the OPM array. As in the magnetic-field data, panel (b), the two locations farthest from the tabs show the largest amplitude. A peak in current density appears $\sim$30s after the pulse, followed by a decay from an average value of 5.24 ± 0.42mA□m to zero on timescales characterized primarily by an 'intermediate' relaxation time 50.92s and a 'slow' relaxation time 66.43s (as extracted from a tri-exponential fit, see the section 'Equivalent circuit models'), similar to the timescale of the magnetic-field response (b). (d) Example relaxation measurement of a battery cell at 100% SOC, recorded with an OPM at position (-13.5mm, 60mm, 8.2mm) from the midpoint of the cell tabs. Per Eq. \ref{['eqn:ECM']}, the sum of three exponential curves are fitted to the data---here with decay times $\tau_1 = 4.6 \pm 2.0s$, $\tau_2 = 20.3 \pm 3.5s$, and $\tau_3 = 95.5 \pm 6.3s$---which gives an $R^2$-value of 0.994.
• Figure 4: : Time-resolved magnetic images of relaxation after a 1 discharge of a fully charged cell with 0.1 C (0.6A), collected with the 2D $4\times4$ OPM array, Fig. \ref{['fig:Scheme']} and Fig. S1(c). The images, recorded at times of 10s, 150s, 300s, and 450s following the discharge pulse, track evolution of (a) the $y$-magnetic field and (b) the $z$-magnetic field as they decay to homogeneous equilibrium values. Red dashed lines demarcate the position of the cell beneath the sensors; the battery lies below the central $2\times4$ array of sensors, as indicated. Such images underscore the spatial and temporal variability which the OPM-based method is able to capture.
• Figure 5: : Comparison of equivalent OPM and SQUID recordings for method benchmarking and investigation of systematics. (a) Results of an OPM measurement in the $z$-direction above a battery after 0.6A (0.1 C) discharge of durations 15s, 30s, 60s, and 120s. The corresponding average magnetic fields at time $t=0$ are 142.8 ± 3.0pT, 215.2 ± 5.9pT, 283.6 ± 4.1pT, and 341.1 ± 5.6pT. The experiment was conducted three times for each discharge duration, with the mean field value plotted as a darker curve. Fitting monoexponential decays to the solid curves yields a characteristic average relaxation time of 20.5$\pm$0.9 s, where the error bar corresponds to standard deviation. (b) Results of an equivalent, simultaneous SQUID measurement recorded with the pick-up coil nearest to the OPM sensor and measuring the magnetic field along the same direction. The average fields at $t=0$ are 4.4 ± 1.2pT, 9.2 ± 0.3pT, 11.0 ± 0.4pT, and 18.8 ± 1.6pT. The greater variance in the 120s SQUID measurement (blue) is due to a systematic artefact in one trial, which has not been removed in order to keep the analysis of both datasets consistent. Fitting monoexponential decays to the solid curves yields a characteristic average relaxation time of 18.3$\pm$5.0 s, where the error bar corresponds to standard deviation.