7Li MRI of Li batteries reveals location of ... · found that a duration of 500 μs for the phase...

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Supplementary Information

7Li MRI of Li-ion battery electrodes reveals microstructural lithium location

S Chandrashekar1,2, Nicole M Trease2, Hee Jung Chang2, Lin-Shu Du2,

Clare P Grey2,3* and Alexej Jerschow1*

1) Department of Chemistry, 100 Washington Square East, New York, NY 10003.

2) Department of Chemistry, Stony Brook University, Stony Brook, NY 11794. 3) Department of Chemistry, University of Cambridge, Lensfield Road,

Cambridge CB2 1EW, United Kingdom. * Correspondence and request for materials should be addressed to:: E-mail: Clare Grey, [email protected], Alexej Jerschow, [email protected]

Skin depth Radiofrequency penetrates conducting surfaces only up to a distance of the

order of the skin depth,

, (S1)

where μ0 is the permeability of the vacuum (4π x10-7 m kg A-2 s-2; ref. 1), μr is the

relative permeability of the medium (for lithium metal, μr=1.4; ref. 1), ρ is the

resistivity of the metal (92.8 nΩ m for Li metal; ref. 1) and ν is the frequency of

the applied rf field (194.4 MHz in this study).

δ =ρ

πμ0μrν

7Li MRI of Li batteries reveals location of microstructural Lithium

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Orientation-dependent rf penetration

The orientation of the conducting plates (electrodes) with respect to the incident

rf field has an influence on the overall rf field distribution within the coil volume. In

first approximation, following common boundary condition considerations,2 one

can assume that the rf field on the plate surface will become minimal when the

plates are oriented perpendicular to the incident field, and maximal, when they

are oriented in parallel. The consequence of this procedure is that the parallel

arrangement between rf field and conductor surface provides the maximum

signal, whereas the perpendicular arrangement gives zero signal in the center of

the plate. Figure S1 demonstrates that indeed the parallel orientation of the

electrodes with respect to the rf field gives maximum signal for the centers of the

electrodes, while the perpendicular orientation gives minimum signal, except at

the edges of the electrodes.

Signal-to-noise ratio (SNR) and factors affecting resolution in the images

Phase encoding gradients can only be applied for a limited duration in all

experiments, as rapid T2 decay quickly leads to significant SNR losses. We

found that a duration of 500 μs for the phase encoding gradients was a good

trade-off between adequate sensitivity and acceptable resolution. This constraint

also imposes a practical limit for the resolution in any phase encoding dimension.

For a maximum gradient strength of 500 mT/m (the case here) and a 500 μs

gradient duration, the best resolution achievable would be 121 μm. Although

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increasing the gradient duration can improve the resolution significantly, it comes

with the penalty of a large loss of sensitivity due to the rapid T2 decay. Higher

resolution could be achieved, however, more easily by the use of stronger

gradients. The SNR that was attained in the MRI experiments was more than

adequate as attested by the quality of the images. For example, in the 2D x-y

images of Figures 2a and 2b, SNR = 169 and 326 for the pristine and charged

states, respectively. Pulsed field gradients may induce currents in metals (Eddy

currents), such as the electrodes used in this work, affecting the apparent size of

the imaging window.3 Although the Eddy currents themselves are difficult to

calculate and predict, their scaling effect can be accounted for.3

In the directly observed (x) dimension, the dispersion of (Knight) shifts of the

metallic signals (up to 2200 Hz for the charged electrode) will lead to broadening

and/or shifting of image peaks on the order of 0.55 mm in the x-direction. Since

this direction is parallel to the electrode surface, any blurring in this dimension

does not affect the main conclusions of the above analysis, but will affect efforts

to locate the position of dendrites accurately within the battery. A discernible, and

as yet not fully understood, feature in these images is that the electrode signals

increase towards the edges of the electrodes. It is likely that this effect is due to rf

field distortions by the metal strips.





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SI References

1 Lide, D. R. & Frederikse, H. P. R. CRC Handbook of Chemistry and

Physics: A Ready-Reference Book of Chemical and Physical Data 78th

edn. CRC Press (1997).

2 Jackson, J. D. Classical Electrodynamics, 3rd edition. (John Wiley &

Sons, 1990).

3 Han, H., Green, D., Ouellette, M., MacGregor, R. & Balcom, B. J. Non-

Cartesian sampled centric scan SPRITE imaging with magnetic field

gradient and B0(t) field measurements for MRI in the vicinity of metal

structures. J. Magn. Reson. 206, 97-104 ( 2010).





a

b

Arb

. int

ensi

ty 2

1

0

Arb

. int

ensi

ty 2

1

0

0 -2 2 -2

2 0 x (mm) y (mm)

0 2 -2 1

-1 0

x (mm)

Fig. S1. Orientation dependence of the 7Li MRI. 2D images of the battery in its pristine state acquired in (a) parallel (same as in figure 1a of the main text), and (b) normal orientation of the electrode’s 2 mm side with respect to the rf field. The parallel arrangement corresponds to the schematic shown in figure 1a of the main text.





0

-1

1

y (m

m)

0 2 -2 x (mm)

Fig. S2. MRI reveals short-circuiting: Overlay of 7Li MRI x-y image contour plots of two different batteries: The red image is from the pristine state of the battery (same data as in figure 2a of the main text and figure S1a above). The black image is from a different bagcell which could not be charged properly due to a short circuit between the electrodes. The area of the short is clearly visible in the image.





1 0 -1 y (mm)

280

270

0 2

x (mm

)

-2 260 C

hem

ical

shi

ft (p

pm)

1 0 -1 y (mm)

280

270

0 2

x (mm

)

-2 260 C

hem

ical

shi

ft (p

pm)

b

a

Fig. S3. Comparison of 7Li CSI images at the 2nd orientation (figure 4) of the main text, after a 26° rotation, while the dashed red box indicates the location of the bulk metal. (a) in the pristine state, and (b) after applying a current (charged). This orientation clearly indicates a dendrite between electrodes. The large shift range of the microstructure closest to the inside of the Li metal anode is ascribed to the fact that the metallic lithium structures are disordered in their orientations with respect to B0, indicating that it is likely mossy lithium. The metallic lithium that is located clearly iwithin the electrolyte space is assigned to a dendrite growing on the lithium surface, towards the opposite electrode. Its smaller shift range is possibly due to the unique orientation of the dendrite's major axis relative to the bulk metal surface and B0.





Fig. S4. Slices through the CSI images for the pristine and charged battery. Apart from the chemical shift information available from CSI, this experiment further illustrates that additional features of the metal and microstructure signals become available due to the added frequency dispersion of CSI. The signals marked by a dashed rectangle are microstructures protruding further into the electrolyte space. These are not clearly visible in simple 2D or 3D MRI because there no chemical shift separation is seen. The chemical shift separation will become particularly important for the characterization of electrodes under different charging conditions, and the in situ capability of this technique is a major new step towards assessing new battery materials.

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