Magnetic Susceptibility and Internal Currents

Magnetic field alignment enables thicker-electrode batteries with higher energy density at a lower cost. Energy efficiency and reduction of CO2 emissions as modern trends rapidly to market introduce EV. The increasing demand for high capacity rechargeable batteries highlights the need for sensitive and accurate diagnostic technology for the state of a cell, for identifying and localizing defects or sensing capacity loss mechanisms. Both high and low temperature rangers have different effects on lithium-ion batteries. The use of magnetometry was then introduced to map the weak magnetic fields around LI-ion battery cell as a function of state of charge and upon introducing mechanical defects (Hu et al., 2019). The measurements provide maps of the magnetic susceptibility of the cell, which follow trends characteristic for the battery materials under study upon discharge.

The changes in magnetic susceptibility can be tracked across the charge dischargeable cycle. This follows an expected trend of lithiation state of the cathode material. For the measurement set up, the magnetic susceptibility measurements involve placing a sample in a magnetic field and measuring the smaller induced magnetic fields (Benšić et al., 2017). The magnetic sensors have a limited dynamic range which be located in a small magnetic field


a magnetic field to the cell. The magnetic field sensors are placed outside where the negligible magnetic field are found. Here there is a magnetic shield operate within a dynamic range. The magnetic field of a battery cell located inside the solenoid, however, is communicated to the sensor region without impediment. Apart from reducing environmental magnetic fields, the magnetic shield arrangement also ensures that magnetic lines emerging from the ends of the solenoid connect outside of the shield region. Moreover, the distribution of magnetic material inside the cell influences the spatial variation in the magnetic field. The MR methods provide the ability to measure tiny changes in magnetic field maps. This is through the use of phase map imaging or specific NMR probes. The MR shows how the magnetic field changes in a Li-ion cell. The MR method was developed to measure different cell properties (Ilott et al., 2018). When diagnosing state of charge in a Li-ion cell, the magnetic field in the plane perpendicular to the main face of the cell is displayed for clarity. The magnetic field can also be a diagnostic for a cell’s SOC and to measure defects in a cell’s a construction. Principal component analysis (PCA) shows clear grouping and separation using the second principal component. The PCA was performed on the 2D magnetic field maps which are themselves reconstructed from multiple phase –map images. This was performed on the magnetic field maps from the defected. The PCA is thus the oldest and widest used techniques since it is a smlple idea and reduce the dimensionality of dataset, while preserving as much ‘variability’ as possible.

Interpretation of Models

Battery cell models differ mostly in approach to compute lifetime for specific discharge profile in relation to the complexity of the drive model. The Shepard model is often used for precise calculation. The model determines total battery cell voltage using different parameters in relation to the battery current, polarization resistance, extracted capacity, maximum capacity and drop off exponential capacity. The parameters are obtained from the charging/discharging battery characteristics given by the manufacturer and in the end, this model calculates the voltage of the battery that depends on just one variable: State-Of – Charge (SOC). An upgrade of the Shepard model is proposed with an additional internal voltage source and parallel resists for modelling the magnetic effect on the battery cell as a result of the battery block design (Smyshlyaev, 2011).

As a result of Hall Effect, the electric field that has direction perpendicular to direction of ions it can be modeled as an additional parallel resistor to the Sheppard model of the cell. Lumped model also called lumped-parameter model, simplifies the description of the behavior of spatially distributed physical systems into a topology consisting of discrete entities that approximate the behavior of the distributed system under certain assumptions. It is useful in electrical systems, mechanical systems, heat transfer and acoustics. Lumped element model of electronic circuits makes the simplifying assumption that the attributes of the circuit, resistance, capacitance, inductance and gain are concentrated into idealized electrical components, resistors, capacitors and inductors (Ilott et al., 2018). The Finite Element Modeling (FEM) is the dominant discretization technique in structural mechanics. The basic concept in the physical interpretation of the FEM is the subdivision of the mathematical model into disjoint (non-overlapping) components of simple geometry called finite elements or elements for short. Objectives of FEM are;

  • Understand the fundamental ideas of the FEM ·
  • Know the behavior and usage of each type of elements covered in this course ·
  • Be able to prepare a suitable FE model for structural mechanical analysis problems ·
  • Can interpret and evaluate the quality of the results (know the physics of the problems) ·
  • Be aware of the limitations of the FEM (don't misuse the FEM - a numerical tool).

The three dimensional models above can resolve electrode structure at the submicron scale. Modelling magnetic field has the North Pole and the South Pole. This can be demonstrated by a bar magnet which when suspended align itself so that its north pole points to the geographic north of the earth. Magnetic fields in batteries helps in finding the current distribution within an electrochemical cell from magnetic field measurements (Concha et al., 2015). Current distribution is shown to be a useful measurement for diagnosis of cells and development of cell design. The magnetic field measurements can be obtained non-invasively and contain information about the current distribution. The electrode materials for Li-ion batteries should combine electronic and ionic conductivity, structural integrity, and safe operation over thousands of lithium insertion and removal cycles. A number of techniques have been used to characterize long-range and local structure, electronic and ionic transport in bulk of active materials and interfaces, with an ongoing move towards in situ techniques determining the changes as they happen. This reviews several representative examples of using magnetic properties toward understanding of Li-ion battery materials with a notion to highlight the intimate connection between the magnetism, electronic and atomic

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structure of solids and to demonstrate how this connection been used to reveal the fine electronic and atomic details related to the electrochemical performance of battery materials.

Chapter Summary

Inclusion, temperature impacts critically on the performance of lithium ion batteries and also limits the application of lithium ion batteries. Different temperatures conditions result in different adverse effects. Accurate measurement of temperature inside lithium ion batteries and understanding the temperature effects are important for the proper battery management. The current approaches in monitoring the internal temperature of Li-ion batteries are discussed in the models above.


  • Benšić, T., Hederić, Ž., Barukčić, M., Hadžiselimović, M., Cvetković, N. and Krstić, D., 2017. Battery pack design problems: Influence of the transverse magnetic field on internal battery resistance. Safety Engineering, 7(2), pp.49-53.
  • Concha, P.M.T., Velez, P., Lafoz, M. and Arribas, J.R., 2015. Passenger exposure to magnetic fields due to the batteries of an electric vehicle. IEEE Transactions on Vehicular Technology, 65(6), pp.4564-4571.
  • Hu, Y., Iwata, G.Z., Mohammadi, M., Silletta, E.V., Wickenbrock, A., Blanchard, J.W., Budker, D. and Jerschow, A., 2019. Battery Diagnostics with Sensitive Magnetometry. arXiv preprint arXiv:1905.12507.
  • Ilott, A.J., Mohammadi, M., Schauerman, C.M., Ganter, M.J. and Jerschow, A., 2018. Rechargeable lithium-ion cell state of charge and defect detection by in-situ inside-out magnetic resonance imaging. Nature communications, 9(1), pp.1-7.
  • resonance imaging. Nature communications, 9(1), pp.1-7. Liu, Y., Zhou, T., Zheng, Y., He, Z., Xiao, C., Pang, W.K., Tong, W., Zou, Y., Pan, B., Guo, Z. and Xie, Y., 2017. Local electric field facilitates high-performance Li-ion batteries. ACS nano, 11(8), pp.8519-8526.
  • Osaka, T. and Ogumi, Z. eds., 2014. Nanoscale technology for advanced lithium batteries (pp. 259-264). Berlin: Springer. Smyshlyaev, A., Krstic, M., Chaturvedi, N., Ahmed, J. and Kojic, A., 2011, June. PDE model for thermal dynamics of a large Li-ion battery pack. In Proceedings of the 2011 American Control Conference (pp. 959-964). IEEE.

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