Distortion-free inside-out imaging for rapid diagnostics of rechargeable Li-ion cells

Significance

Rechargeable batteries can pose severe risks due to their flammable components in combination with high energy density. These challenges motivate the development of advanced battery screening techniques capable of rapid battery assessment. MRI, a broadly accepted method in the healthcare industry, has been adapted for materials chemistry and energy storage research. A quantitative MRI approach based on 3D phase encoding bypasses the hurdles associated with strongly magnetic components that are common in modern batteries (e.g., iPhone models). The reported technology is virtually distortion-free and shows a high sensitivity to mechanical defects and the chemical state of the electrodes. This approach may enable industrial quality control applications with a high temporal resolution and may aid in battery development and monitoring.

Abstract

Safety risks associated with modern high energy-dense rechargeable cells highlight the need for advanced battery screening technologies. A common rechargeable cell exposed to a uniform magnetic field creates a characteristic field perturbation due to the inherent magnetism of electrochemical materials. The perturbation pattern depends on the design, state of charge, accumulated mechanical defects, and manufacturing flaws of the device. The quantification of the induced magnetic field with MRI provides a basis for noninvasive battery diagnostics. MRI distortions and rapid signal decay are the main challenges associated with strongly magnetic components present in most commercial cells. These can be avoided by using Single-Point Ramped Imaging with T₁ enhancement (SPRITE). The method is immune to image artifacts arising from strong background gradients and eddy currents. Due to its superior image quality, SPRITE is highly sensitive to defects and the state of charge distribution in commercial Li-ion cells.

The wide use of portable electronics and rapidly expanding market for electric vehicles have driven the demand for high capacity and safe rechargeable batteries. Challenges arise due to the presence of flammable materials in cells and their high energy densities. Noninvasive means of diagnostics can facilitate understanding of battery failure modes (1–4). MRI is a powerful tool for studying chemical, biological, and solid-state phenomena (5–8). Recently, in situ MRI of model electrochemical devices shed light on underlying physical and mechanistic processes (9–16). These techniques however could not be used to study commercial cells due to the conductive casings and small distances between electrodes, which hamper radiofrequency (RF) penetration. An inside-out MRI (ioMRI) approach that overcomes these limitations has been recently introduced (1). A magnetic field (MF) perturbation created by a cell depends on the magnetic susceptibility and morphology of its constituents. For example, the source of a strong induced magnetization in lithium-ion cells is often a lithium-intercalation compound. The magnetic susceptibility changes as a function of the amount of inserted lithium. Therefore Li intercalation and its state of charge (SOC) could be assessed in cells nondestructively and rapidly by ioMRI. Cells can also exhibit unique MF features characteristic of their defects.

Industrial-scale applications of such battery diagnostics could also employ rapid MRI methods (e.g., Fast Low Angle Shot – FLASH) (17). These techniques rely on either long evolution times and echo trains, frequency encoding, or slice-selective RF pulses. Conductive and magnetic materials are known to induce severe MRI artifacts (18–20). Several complications arise: a) The signals in the vicinity of such features can decay rapidly due to destructive interferences within voxels, and b) strong background gradients lead to image misregistration. These problems are resolved with fully phase-encoded MRI. Single-point ramped imaging with T₁ enhancement, SPRITE (21–24), has been successfully employed for imaging of challenging systems (14, 25–28) and is highly suitable for MF visualization in regions with strong local magnetism. This aspect is particularly important as incorporation of ferromagnetic materials into commercial batteries is a common practice.

Concepts of the Inside-Out SPRITE Method

MRI employs pulsed MF gradients to create a spatial variation of resonance frequencies based on the Zeeman splitting of nuclear spin energy levels. Conceptually, one may define a reciprocal k space, F(k), of spatial frequencies (29, 30), which represents the grid of raw data acquisition points, according to

$$\text{F}\left(\mathit{k}\right)={\displaystyle \sum _j}\text{A}\left({\mathit{r}}_j\right)\text{exp}\left(-i2\pi \mathit{k}{\mathit{r}}_j\right).$$ [1]

An image, A(r), is obtained via a Fourier transformation of F(k). An MR signal is acquired for discrete values of the vector k = γ g t (2π)⁻¹, where γ is the nuclear gyromagnetic ratio, g is the MF gradient, and t is time. K-space sampling may be performed by varying either time (frequency encoding) or the gradient magnitude (phase encoding). Single-point MRI relies exclusively on phase encoding (31).

Key parameters of the 3D centric-scan SPRITE pulse sequence (Fig. 1) are applied MF gradient g(g^X g^Y g^Z), gradient ramp time T_GR, gradient stabilization time T_GS, RF pulse flip angle α and pulse duration P_α, phase encoding time T_P, repetition period T_R, pulse train length N_TR, number of interleaves N_int, recovery delay between the pulse trains T₀. The sequence starts with a nonselective RF excitation at g = 0 followed by free precession during T_P and acquisition of a sample of free induction decay (FID). Note that T_P should exceed a probe “dead” time (10–100 µs). Then, the imaging gradient g is ramped to the next value over a period T_GR and is allowed to stabilize during T_GS. The following RF excitation, free precession (phase encoding), and single-point acquisition events take place in the presence of this gradient. P_α should excite the sample bandwidth for each g_k. Typically, α is a few degrees and P_α is a few microseconds long.

Fig. 1.

(A) Centric-scan SPRITE pulse sequence. (B) Sectoral k-space trajectories. In-plane sampling is repeated for a number of equally spaced k_Z values. (C) {x-y} and {x-z} views of the battery holder with respect to B₀ and B₁.

Although it is possible to execute the SPRITE loop continuously until the sampling process is complete, the gradient and RF hardware duty cycles can approach levels that cannot be sustained reliably by the equipment. The interleaved acquisition allows for control over the temperature inside the gradient coil system and RF circuit, and improves the image resolution (23, 24). The k space is divided into N_int interleaves. One interleaf is sampled with a train of N_TR “P_α - T_P - ACQ” blocks. After each train, a recovery delay T₀ ∼ 5 T₁ (spin-lattice relaxation time) is required.

Since F(k = 0) is a measure of the total spin density (Eq. 1), commencing k-space sampling at k = 0 enables quantitative measurement of the longitudinal magnetization and improved signal to noise (SNR) (22). Repetitive RF pulses modulate the longitudinal magnetization and the k-space envelope. Associated image blurring can be controlled by adjusting α (22–25).

Assigning gradient values to locations on the Cartesian grid is a robust and convenient sampling approach (23, 24). In this case, the image reconstruction consists of two simple steps: 1) reordering of the raw data into a complex array based on predetermined gradient tables (g_k^X g_k^Y g_k^Z), and 2) a fast discrete Fourier transformation.

Sectoral interleaves employed in this work result in isotropic in-plane blurring (11), Fig. 1B. The k-space matrix N^X × N^Y × N^Z is sampled plane-by-plane along Z. The in-plane trajectories (X-Y) are unwinding spirals confined within 8 sectors (N_int = 8).

T_R is limited by the hardware performance and safety requirements specific to RF and gradient duty cycles. The realistic range of T_R values is from 0.5 to 2 ms.

The image field of views (FOV) along the principal gradient axes (PGA) X, Y, and Z are

$$FO{V}^{XYZ}=\pi N{\left(\gamma G^{XYZ}{T}_P\right)}^{-1},$$ [2]

where G^XYZ are the maximum gradient values along PGAs.

The phase of the local transverse magnetization accumulated over the time T_P is

$$\phi \left(R\right)=\gamma \mathrm{\Delta }{B}_0\left(R\right)T_P,$$ [3]

where ΔB₀(R) = B(R)−B₀ is the local perturbation of static MF associated with the susceptibility contrast. The MR signal measured at location R at time T_P after the excitation pulse is described by

$$S\left(R,T_P\right)=I_Z\text{sin}\left(\alpha \right)\text{exp}\left(i\mathrm{\gamma }\mathrm{\Delta }{B}_0\left(R\right)T_P\right)\text{exp}\left(-T_P/T_2\ast \right),$$ [4]

where I_Z is the equilibrium magnetization. The time constant T₂* describing the rate of magnetization decay

$$T_2{\ast }^{-1}=T_2^{-1}+\gamma \mathrm{\Delta }B{\left(2\pi \right)}^{-1}$$ [5]

is determined via spin-spin relaxation rate (1/T₂) and MF inhomogeneity (ΔB) across a voxel. Thus, measuring the phase φ = arctan{Im(S)/Re(S)} as a function of T_P (Eq. 3) gives

$$\mathrm{\Delta }{B}_0\left(R\right)={\text{γ}}^{-1}d\phi /d{T}_P.$$ [6]

An MF map can be reconstructed from just 1 SPRITE scan (N_TP = 1). Acquiring several phase-encoded points per RF excitation in a single FID readout is a significant improvement in temporal resolution. Another benefit of this approach is a higher accuracy of the measured average phase due to reduced phase dispersion over the shorter delays. Note, since the acquisition occurs in the presence of an applied MF gradient, each point corresponds to a different FOV. The FOVs can be scaled using an established chirp Z-transform algorithm (23).

The duration of an io-SPRITE experiment is

$$\left(N^X{N}^Y{N}^Z{T}_R+N_{int}{T}_0\right)N_{TP}.$$ [7]

Two-dimensional (N ^X,Y = 64, N ^Z = 1, N_int = 8) and 3D acquisitions (N ^X,Y,Z = 64, N_int = 64 × 8) with T_R = 1 ms, T₀ = 1 s, and N_TP = 1 would consume 12 s and 13 min, respectively. The 3D experiments can be substantially accelerated, depending on T₀ and T_R (hardware limitations), and the k-space sampling strategy. For comparison, an io-FLASH MF map (128 × 128 × 128) requires 10 min with 4 echo times (TE).

The accuracy of io-MRI and characteristic MF perturbations are demonstrated for a cylindrical phantom comprising MnCl₂ solution (SI Appendix, Note S1 and Fig. S1). io-SPRITE provides excellent accuracy: + 4.5 ppm near the bottom and top of the capillary is in good agreement with the expected value (+4.59 ppm).

Following points highlight the benefits of the SPRITE design:

• 1)Immunity to susceptibility and chemical shift artifacts.
• 2)Highly quantitative measurements due to short T_P and centric ordering.
• 3)Flexibility in k-space sampling enables optimization of image resolution, contrast, measurement time, and gradient and RF duty cycles.
• 4)Active spoiling of transverse magnetization during T_GR and T_GS.
• 5)Acoustic noise is insignificant.
• 6)Accurate phase encoding is unaffected by the gradient pulse shape in the switching periods.

Results and Discussion

In the approach described previously by Ilott et al. (1), the cell is placed inside the dedicated battery holder, and a series of FLASH images is acquired with different TEs. Note that the ¹H MRI signal originates from the aqueous solution confined inside 2 detection volumes of the holder and not from the battery itself (thus the term inside-out was introduced). Fig. 1C shows the arrangement of the cell, the detection volumes, and the directions of the polarizing (B₀) and RF (B₁) magnetic fields. The orientation of the cell (Fig. 1C) was selected to minimize Faraday’s interaction of the oscillating B₁ field with electric circuits inside the battery and improve the B₁ homogeneity (9–11).

Below, we compare the results of FLASH and SPRITE-based ioMRI tests of iPhone-5 batteries.

These cells contain strongly paramagnetic as well as some ferromagnetic components. This situation could represent a “no go zone” for conventional MRI methods employing frequency encoding and slice-selective pulses. A 3D FLASH image of the holder containing an iPhone-5 battery illustrates this point (Fig. 2A). The positions and orientations of the image slices, {x-z} and {y-z}, with respect to the battery are indicated in Fig. 1C. Since the battery’s length exceeded the extent of the uniform spot of the RF resonator, the upper and lower halves of the battery were scanned separately, and 2 images were combined.

Fig. 2.

(A) {y-z} and {x-z} slices through the 3D FLASH image of the battery holder containing an intact iPhone-5 battery. (B) {y-z} and {x-z} slices through the 3D io-FLASH map; H₂O - containing regions. (C) The io-FLASH map with noisy data masked out.

The image regions near the center and the leads (bottom) of the cell were severely affected by MF inhomogeneity induced by the spatial variation in susceptibility. The corrupted domains occupied a significant part of the detection volume (Fig. 2A). The metal components present in the battery gave rise to 2 types of MRI artifacts: 1) complete loss of signal due to rapid dephasing of transverse magnetization (short T₂*) and 2) geometric distortions in the form of high-frequency ripples. A theoretical description of artifacts in gradient-echo MRI is provided by Reichenbach et al. (32).

The low-intensity voxels (SNR < 1) contained short-lived magnetization components with T₂* < 0.1 ms (Eq. 3). The spread of Larmor frequencies γΔB (2π)⁻¹ > 3 kHz on the length scale of voxel (∼ 0.4 mm) resulted in total dephasing of the transverse magnetization over the FLASH TE (2.5 ms). Significant signal loss can also be associated with the shifting of the gradient echo outside the acquisition window.

The source of the geometric distortions is the “contamination” of the applied frequency encoding gradient by “unaccounted for” background gradients. By design, frequency encoding is the detection of transverse magnetization in the presence of a constant and uniform MF gradient. Any arbitrary gradients added to this applied gradient will produce unwanted frequency shifts in k space thus assigning spins to false locations and altering true values.

Longitudinal slices through an io-FLASH MF map are shown in Fig. 2B. In order to remove MF components not associated with the battery, the MF map of the holder with the empty battery compartment was used as a reference image. The binary mask applied to this map was calculated from the reference image. It shows all voxels containing H₂O (i.e., space inside the holder excluding the battery compartment).

Phase data and local accuracy of the calculated MF field are compromised the most in these domains with the strongest background gradients. To further demonstrate the limited applicability of FLASH, Fig. 2C shows only voxels where the signal magnitude is above 20% of the overall density image maximum. Although the local SNR could be improved by signal averaging (at the expense of experiment time) the misregistration artifacts will remain. They can be mitigated to some degree by increasing the sampling bandwidth and frequency encoding gradient magnitude.

SPRITE images illustrate the method’s robustness against distortions (Fig. 3A). With T_P = 0.12 ms, a small T₂* - weighting effect was seen near the center. The MF map, Fig. 3B, shows well-defined patterns in the “difficult” regions. Note, io-SPRITE detected a frequency range almost 3 times larger than that of io-FLASH.

Fig. 3.

{y-z} and {x-z} slices through (A) 3D SPRITE image of the battery holder containing an intact iPhone-5 battery and (B) 3D io-SPRITE map (H₂O - containing regions; ROI [region of interest]: 53 × 90 mm²; N_TP = 1; n = 64, N_int = 64 × 8). (C) An iPhone-5 battery schematic, {y-z} and {x-z} views; the current collector and leads are shown in red.

The “8”-shaped feature near the center of FOV can be attributed to slightly ferromagnetic material inside the cell. Upon disassembly, this material was found to be a part of a Ni-plated tab. The extent of the arrangement is shown in Fig. 3C. Above and below the tip of the metal strip, the perturbations approached ±20 ppm. An MF variation of 40 ppm over a 5-mm distance is equivalent to an MF gradient of 75 mT m⁻¹. Temporal evolutions of the signal phase are illustrated for 2 representative locations (SI Appendix, Fig. S2).

Fig. 4 shows the MF maps of 2 damaged iPhone-5 batteries. Fig. 4A shows the effect of a 4-mm-diameter hole punched in the center of the lower half of the battery, as indicated on the right. The magnetic tab of this battery was cut and removed from that location. An effect of a 16-mm-diameter hole is demonstrated in Fig. 4B. The ferromagnetic metal strip was cut in half and the upper half was extracted. The image shows a striking MF pattern associated with the defect and the leads. Note that the 8-shaped MF pattern in Fig. 3B, observed near the center of the intact battery disappeared. Instead, the high MF field “cloud” emerged at the tip of the remaining half of the metal strip. Similar patterns were seen for the 2 leads at the bottom.

Fig. 4.

{x-z} and {y-z} slices through 3D io-SPRITE maps of two damaged iPhone-5 batteries: (A) 4 mm hole and leads removed; (B) 16 mm hole and the top half of the current collector removed. (H₂O - containing regions; ROI [region of interest]: 53 × 90 mm²; N_TP = 1; n = 64, N_int = 64 × 8).

MF can be inhomogeneous at the macroscopic level (larger than a voxel) or the microscopic (subvoxel) scale. In the latter case, small structures can be identified due to the partial volume effects even with relatively coarse resolution (1 mm) of SPRITE acquisition.

Next, we demonstrate the sensitivity of the method to certain defect features. Fig. 5 shows photographs of an intact PowerStream (PS) cell (A) and the same cell after introducing mechanical damage (B), Note, the damage did not affect the battery voltage. The defect at the center of the battery was produced by impacts with a metal cylinder of 10-mm diameter. Three impacts were applied to the same spot (0.79 cm²) with the energy of 1.2 J per impact and led to a highly visible imprint of a depth of ∼0.5 mm. A bulge was formed on the opposite side of the battery. The cell voltage, however, was not affected by this damage.

Fig. 5.

Photographs of (A) intact and (B) damaged PS batteries. {x-z} slices through io-FLASH (C and D) and io-SPRITE (E and F) maps. (H₂O - containing regions; ROI [region of interest]: 41 × 41 mm²; T_P range: 0.1–0.33 ms; N_TP = 1; n = 37, N_int = 37 × 4).

MF maps of the intact (Fig. 5C - FLASH, Fig. 5E - SPRITE) and damaged (Fig. 5D - FLASH, Fig. 5F - SPRITE) PS cells showed noticeable differences. The position and orientation of the {x-z} slice with respect to the cell are indicated in Fig. 1C. The MF perturbation by the intact cell was symmetrical and approached +25 ppm above and below (outside the FOV) the battery. The damaged battery (Fig. 5 D and F) exhibited noticeable asymmetry of MF. These changes are consistent with simulations of MF perturbations by “impressions” and “bulges” on the surface of paramagnetic objects (13).

MF perturbations observed by FLASH and SPRITE were different in magnitude and morphology. According to the SPRITE measurements (Fig. 5 E and F), MF increased by up to 6 ppm near the region of impact, while on the opposite side of the cell the field decreased by up to 2 ppm. Importantly, the FLASH MF values were found within a much narrower range of frequencies (from −4 to +8 ppm) as compared to the SPRITE data (from −10 to +25 ppm). The maximum change in MF detectable by FLASH was close to 1 ppm. FLASH images were also affected by ripple-like misregistration artifacts seen near the battery.

The discrepancy between io-SPRITE and io-FLASH measurements is partially attributed to the different extent of T₂* weighting, originating from a distribution of Larmor frequencies within the voxels. The most accurate MF measurement can be performed by collecting phase data immediately after the RF excitation pulse. This is the major technical limitation for all conventional MRI methods employing long evolution times. The high-frequency components are effectively filtered out by long TEs in the FLASH method. In voxels exhibiting a linewidth of γΔB (2π)⁻¹ >> 1/TE, the FLASH signal would be completely suppressed. Furthermore, once significant intravoxel averaging occurs, the field map derived from the overall phase measurement ceases to be accurate even before the signals decay. In addition, the high frequencies are suppressed by echo shifting and assigned to wrong locations as a result of misregistration (32). By contrast, SPRITE suffers only from a minimal T₂* weighting since its MF sensitizing period is much shorter (0.1 ms). Since SPRITE imaging is distortion-free, the main limitation for SPRITE-based ioMRI applications arises from T₂* times, short compared to T_P. A sensitivity limit can be established as T_P ∼ 5T₂*. Assuming T_P < 50 µs, the detectable range of frequencies Δν_1/2 = (πT₂*)⁻¹ is ∼30 kHz, i.e., 75 ppm in 9.4 T. A background gradient generating this linewidth over a 1-mm voxel (700 mT m⁻¹) is much greater than gradients produced by typical MRI systems (20–100 mT m⁻¹).

A relationship between SOC and susceptibility provides a mechanism of ioMRI contrast suitable for accurate battery diagnostics. In order to remove MF components independent of SOC, the fully charged iPhone-5 battery served as a reference sample. The reference MF map was subtracted from maps of the battery at different SOC. The histograms of MF perturbation variation (δΔB₀) due to SOC are shown in Fig. 6. This experiment demonstrates that despite the presence of large field distortions in these cells, the subtler changes in SOC distributions can easily be detected with the SPRITE approach.

Fig. 6.

Histograms of MF perturbation variation (δΔB₀) due to change in SOC of the iPhone-5 battery. The inserts show {x-z} slices through 3D io-SPRITE maps at two SOCs.

The cathode chemistry is responsible for the extent of the MF variations with SOC. Charging the PS cell (500 mA h) resulted in up to a 4-ppm change in the MF (SI Appendix, Fig. S3). A stronger effect was attributed to the overall higher content of magnetic elements, in particular Co. This consideration is in line with electron-dispersive X-ray spectroscopy (EDX) analysis (SI Appendix, Figs. S4 and S5).

In summary, we demonstrated a distortion-free ioMRI battery diagnostics method based on centric-scan SPRITE. Examples of practical relevance of the presented work are battery failures in popular smart phones (e.g., Samsung Galaxy Note 7). The major benefit of SPRITE is the ability to accurately visualize the magnetic field around devices containing strongly magnetic components, common ingredients of the battery manufacturing process. In addition to the superior image quality, a high temporal resolution can be achieved, which is suitable for in situ battery characterization and commercial quality control applications. The method is highly sensitive to mechanical defects and can distinguish fine changes in the electrode’s chemical states and composition.

Materials and Methods

Materials, MRI hardware and experiment parameters, software, image processing, and EDX equipment are described in SI Appendix, Note S2.