1. Introduction

2. Expansion Mechanisms in Battery Cells

3. Measurement of Expansion in Lithium-Ion Battery Cells

3.1. Contact Approaches

Contact measurements can be carried out both outside the housing on entire battery cells and on individual components within disassembled battery cells. Contact measuring principles vary in terms of sensor contact area and the pressure applied between the sensor and object to be measured. Contact approaches can be divided into dilatometer, strain, and buoyancy measurements.

3.1.1. Dilatometer

Mechanical dilatometry is one of the oldest and most frequently used methods for measuring the expansion of different materials on a macroscopic level [76]. Primarily used to determine the specific temperature coefficient, this method has now become established for measuring the expansion of battery cells. The typical design of a dilatometer is comprised of a sensor that is positioned away from the heat source. As a result, it is possible to calculate the coefficient of thermal expansion (CTE) of the material or device by characterizing expansion [76].

Depending on the sensor design, dilatometers can be of various types, such as push piston, push rod, capacitance, high resolution-laser, and optical [77]. One of the advantages of dilatometer measurements is the possibility to measure the entire battery cell as well as single components individually. The advantage of dilatometry lies in its non-destructive nature and simplicity. The most common system, especially to measure the expansion of battery cells and electrochemical devices are push piston dilatometers [76,77]. The measuring object is placed between two plates, one fixed and one with the possibility to move parallel in the direction of the swelling.

Dilatometers can be used to make ex situ measurements to assess the expansion and the intercalation of guest ions into a host structure [78]. In this case, the battery cell must be disassembled and the thickness of individual components can be measured. For a good estimation of expansion in the battery cells, the post mortem analyses should be done for unaged and aged samples. In 1982 Biberacher et al. [79] presented a method for measuring the electrochemical intercalation of HSO₄⁻/H₂SO₄ in graphite using a high-resolution push piston dilatometer. They observed a maximum dilation of 140% for graphite during intercalation. Figure 3 shows two typical apparatuses for dilatometry measurements of electrochemical devices. Figure 3(a) shows the setup for the thickness measurement of single working electrodes. The working and counter electrodes are separated by a rigid separator, which is in modern dilatometer setups, typically made out of a stiff, but porous and permeable glass frit [80,81]. The push piston sensor is placed above the working electrode to measure the horizontal displacement from intercalation into, and deintercalation out of this electrode. The dilatometer illustrated in Figure 3 (b) has the ability to measure the swelling of whole battery cells. The displacement sensor is typically placed in the center of the battery cell.

Moyssari et al. [78] used an electrochemical dilatometer to measure the change in thickness of anode materials with different SiG compositions, one with a ratio of 0/95, and one with a ratio of 20/75. Two coin cells were made using each anode composition. The working electrode was SiG and the counter electrode was made of lithium metal. After a 6 $\mathrm{h}$ rest period, eight cycles were performed with a C-rate between $0.033$ C and $0.1$ C. The electrochemical dilatometer used contains a separator made of porous borosilicate glass between the two electrodes. This separator mechanically decouples the two electrodes. The expansion sensor applies a force of 1 $\mathrm{N}$ to ensure a permanent contact. It was found that the specific capacitance and the capacitance loss increase with higher silicon content. The hysteresis between lithiation and delithiation also increases with enlarged silicon content. During normal use, an expansion of $5.2$% occurs. Among other causes, this can be attributed to the continuous formation of SEI. In the formation cycles, the expansion behavior increased from about $5.5$% for the 0/95 electrode to about 47% for the 20/75 electrode. For later cycles, the expansion behavior for the 0/95 electrode remains the same. For the next largest SiG ratio of 3/92, the expansion decreased from 14% during formation to 7% for further cycles. For the SiG ratio of 20/75 to a relative expansion of 20% after the initial formation cycles. This expansion behavior remains constant during the further cycles, with little deviation. The specific capacity increases from a ratio of 0/95 to 20/75 from $326.55$ $\mathrm{m}$$\mathrm{Ah}$/$\mathrm{g}$AM to $925.62$ $\mathrm{m}$$\mathrm{Ah}$/$\mathrm{g}$AM. The authors also show that the lithiation of silicon takes place after the graphite lithiation is completed.

Rieger et al. [82] use dilatometry to investigate the expansion of commercially available LCO/G cells. For this purpose, one dilatometer was used for the graphite anode and one for the LCO cathode. The setup is similar to that shown in Figure 3 (a). Here, an expansion of the LCO cathode of about 2% and of the graphite anode of about 7% with complete lithiation were measured. During normal use, as specified by the manufacturer, there is an expansion of 5%.

When the expansion of the entire battery cell is investigated, in operando measurements can be performed. The expansion of the complete battery cell is measured during charging and discharging cycles. The in operando measurement is included in the classification in situ measurements. The direct expansion at one point of the battery cell or at multiple points can be measured with linear displacement sensors as shown in Figure 3. The pressure that is built up due to the expansion inside the battery cell can also be measured with pressure sensors and load cells [83,84,85,86].

In Figure 3 (b) a common test stand for measuring the complete thickness change of battery cells is shown. Most of these setups consist of frames above and below the battery cell(3) held together by parallel screws (6). The battery cell (7) is typically placed on the bottom frame (3). A pressure plate (5) is placed on top of the cell, to create a constant pressure over the entire surface. The swelling over the complete surface of the battery cell is measured. The screws also constrain the springs (2), which exert force on the pressure plate. The dial gauge (4) is located in the middle of the top frame. The electrical contact (1) is directly connected to a battery cell testing device. [20] Apparatuses similar to that in Figure 3 (b) were also used to investigate expansion in pouch cells in several references [20,48,52,69,87,88,89,90,91,92,93,94,95]. Some apparatuses exclude the springs (2) and pressure plate (5). In such cases, the expansion of a single point of an uncompressed battery cell is measured [96,97].

This apparatus allows for the measurement of the complete cell. The measurement of the complete battery cell gives information about all electroactive layers, separators and the electrolyte. In 2003, Lee et al. demonstrated one of the first test stands for the measurement of 1D battery expansion [98]. A data logger with a dial gauge was equipped to a constant load of 300 $\mathrm{g}$. The dial gauge was connected to a data logger system and the complete rig was placed inside a climate chamber. The formation of the SEI layer in the initial charge was shown. The irreversible swelling was reported to account for up to 2% of the initial thickness and the overall expansion was up to 4% of the initial thickness of the cell.

Rieger et al. [82] investigated the expansion of $2.3$ $\mathrm{Ah}$ LCO/G cells with two opposing contact displacement sensors, each located at the center of the cell. The measurements made are compared with the mean values of a 3D structured light camera system. Rieger et al. concluded that 1D-dilatometry can be used to calculate the SoC-dependent electrode swelling for electrochemically and mechanically coupled models for battery cells.

Louli et al. [99] used a 1D-dilatometer setup to investigate the volume change of NCA/SiO-G cell with a capacity of 260 $\mathrm{m}$$\mathrm{Ah}$. The cathode material had x and y values of the single components between $0.05<x<0.15$ and $0.02<y<0.10$. A single stacked battery cell consisting of only one positive and one negative electrode was built for this measurement. The displacement sensor was located in the middle of the cell. A spring was installed to exclude local expansion due to gas formation. The applied pressure was limited to 30 $\mathrm{k}$$\mathrm{Pa}$, which has no impact on the cell behavior. The result, shown in Figure 4 (b), showing an asymmetric behavior for charge and discharge. This asymmetry is a sign of hysteresis between the charge and discharge cycles. It is also shown, that the thickness change is not linear with the SoC for this battery cell.

Vorwerk et al. [52] used 1D-dilatometry measurements to log the cell expansion during abuse testing. They performed tests under critical cell conditions with overcharging, reaching a SoC over 100%. The investigated cells were NMC/G cells with a capacity of 75 $\mathrm{Ah}$. The measurement setup was similar to the one shown in Figure 3 (b). It was discovered that there was a significant increase in cell expansion at a SoC of 112% up to $2.2$ $\mathrm{m}$$\mathrm{m}$ (17% of initial cell thickness). This expansion could be explained by gas production due to decomposition reactions of the active material. After the cycle was stopped, the cell was allowed to relax for 45 $\mathrm{h}$ to ensure that no cell bursting or fire occurred. In this time, the expansion increased by further 5%. As a result, they concluded that the expansion of the cell starts far ahead of events like cell bursting. Expansion of battery cells could be an indicator for monitoring the safety of battery cells.

Berckmans et al. [100] investigated the influence of external pressure on battery cells with two different chemistry types. One cell is constructed with a NMC532 cathode, and the other with a NMC622 cathode. The anode material was a silicon-graphite alloy. The measurement apparatus used is similar to the one demonstrated in Figure 3 (b). The dial gauge was replaced with a force sensor between the top mounted plate and the pressure plate on top of the battery cell. In this study, the force exerted due to the cell expansion is measured, instead of the expansion itself. Figure 5 shows the voltage and current in the top graph from the OCV test, whereas the lower graph shows the exerted force. The force could be divided into three main stages. The first red stage shows nearly constant behavior, which could be explained by the quantity of graphite in the anode alloy, which experiences less volume expansion than silicon during intercalation [101]. Delithiation in graphite occurs at potentials of 0.1-$0.2$ $\mathrm{V}$ vs. Li/Li⁺, whereas in silicon deintercalates at potentials of 0.3- $0.5$ $\mathrm{V}$ vs. Li/Li⁺ [27,102,103,104]. This is one possible reason for constant force readings at the beginning. Further tests demonstrated that there is no C-rate dependency on the induced force due to intercalation.

Jin et al. [105] performed tests to evaluate the stress from battery cells cycled under constant thickness and the thickness evolution of battery cells under constant force. For the stress measurement, a similar setup to Berckmans et al. [100] was used. The thickness measurement was performed with constant load applied to the top of the cell, and was made with a high-speed camera. A NMC532/G cell with a nominal capacity of $1.6$ $\mathrm{Ah}$ was chosen for these measurements. The applied stresses were $34.5$ $\mathrm{k}$$\mathrm{Pa}$ and $172.4$ $\mathrm{k}$$\mathrm{Pa}$. For the thickness measurement the applied stress was $103.4$ $\mathrm{k}$$\mathrm{Pa}$, as determined from previous experiments. The cells were charged at different C-rates and upper cut-off voltages. As a result, for the stress measurement, it was concluded that the stress increased with a higher upper cut-off voltage, but decreased if the initial stress or the C-rate are increased. The thickness on the other hand increases if the C-rate of the upper cut-off voltage are increased, but the thickness evolution is decreased if the initial stress is increased.

Louli et al. [99] investigated both 1D-dilatometer measurements and the force exerted by an NCA cell. Two additional chemistries were also investigated: LCO/Si and NCA/nano SiC with capacities of 230 $\mathrm{m}$$\mathrm{Ah}$ and 165 $\mathrm{m}$$\mathrm{Ah}$ respectively. The NCA cathode material had x and y values of the single components between $0.05<x<0.15$ and $0.02<y<0.10$. For this measurement a setup with two enclosure walls was used, in which a defined pressure through a screw with one adjustable enclosure wall can be generated. Between this casing, the pouch cell is placed with a pressure plate and the pressure sensor. The cells were cycled for more than 1,000 $\mathrm{h}$ at 40 °C and charged with a C-rate of C/3. An irreversible increase in pressure was observed over the time. The LCO/SiG-alloy battery cell had a much higher irreversible volume expansion. The reversible pressure for two different cycles is shown in Figure 8 (b) in orange and violet. The pressure measured has a similar asymmetric behavior as the measurement with the 1D-displacement sensor mentioned earlier.

Stock et al. [95] used a setup to measure the gas production and the swelling of the cell with a 1D-dilatometer. An adjustable pressure plate was fixed by four springs onto the surface of the cell with a pressure of 200 $\mathrm{k}$$\mathrm{Pa}$. A tactile displacement sensor was located at the center of the plate to measure the swelling behavior of the cell. A second plate was placed on the gas bag which was attached to the cell without any extra pressure applied. This plate is free to move in one direction and a second tactile sensor is placed in the center of the cell. Through the applied pressure on the cell, the gas is forced to move into the attached gas bag. Through calibration, the accuracy of the volume measurement is $0.6$ $\mathsf{\mu }$$\mathrm{l}$. The authors showed that the main gas production and the expansion in acnmc622/G cells and NCA/SiC cells occur during the formation cycles. Another result was that the gas production with respect to the cell voltage in NMC/G cells diminishes when the dilation begins to increase. This is explained by the fact that the formation of the SEI layer begins before the lithiation of the graphite anode.

Bitzer and Gruhle [69] used 1D-dilatometry to detect lithium plating in-operando in NMC pouch cells. The state of the art to detect lithium plating was to measure the negative anode potential vs. Li/Li⁺ with a reference electrode or in a half cell configuration. Initially, they started with calculating the molar masses of the transferred charge. They found that plating should lead to an increase in volume expansion, since the intercalation of lithium ions in graphite results in a lower expansion than the deposition of metallic lithium on the anode surface.

Figure 6 shows the expansion behavior of the transferred charge with and without plating measured with the 1D-dilatometer. It could be seen, that the absolute expansion with high current (red) is much higher than with a low current (blue). The peak arises at the constant voltage phase and decreases when the charge is stopped. Through decomposition of electrolyte, gas is produced. The presence of gas can introduce errors on the measurement of the expansion of electrodes. In order to differentiate the swelling of the pouch cell caused through gas production or electrode expansion. Bitzer and Gruhle [69] proposed a method including a spring directly coupled to the dial gauge. The spring adds a defined force against the battery cell and any gas will move sideways and only solid expansion will add enough force to contract the spring.

Grimsmann et al. [106] performed 1D-expansion measurements with a setup similar to the one in Figure 3 (b). They compared the expansion of calendaric and cycle aged cells, as well as cells with provoked lithium plating. To induce lithium plating, 22 $\mathrm{Ah}$ NMC cells were placed in a climate chamber at 0 °C and were charged with high currents. As a result, they confirmed and expanded on the findings of Bitzer and Gruhle [69]. The expansion of the cells with lithium plating is higher than the expansion from cycle aging under normal condition. There is also a difference in the expansion behavior based on the dominant degradation mechanism in the cell. The three tested mechanisms showed different swelling behavior.

Oh et al. [107] studied the expansion of a 5 $\mathrm{Ah}$ prismatic NMC/G cell. Five contact displacement sensors were mounted on the surface of the cell. One was placed at the center of the surface and the other four were located in a cross pattern on the top, the bottom, left and right of the center probe. On the opposing side, one extra displacement sensor was located on the center of the surface. They came to the conclusion that the greatest expansion takes place in the center of the cell with $1.5$% expansion with respect to the initial thickness and around $0.75$% for the other positions. The measured expansion on the left and right side was smaller than on the upper and lower sensor. Also, the expansion decreases towards the edges with a maximum expansion of $0.55$% on the right and left side and around $0.3$% for the top and bottom. This difference could be caused by the mechanical constraints of the cell housing. The variation of the ratio between the center and the other locations are similar. Therefore it was concluded that one sensor in the center can accurately quantify the cell swelling.

3.1.2. Buoyancy Measurements

Aiken et al. [108] were the first to use the Archimedes principle to measure the amount of produced gas in the formation cycling of battery cells. The purpose of this measurement was to understand the behavior of gas production during formation cycling and in undefined conditions, such as electrode / electrolyte redox reactions. They made use of an apparatus resembling the the left image in Figure 7. They immersed a cell in a non-conductive fluid and hung it from a balance on the top of the apparatus. By placing the cell into liquid, a buoyant force $F_b$ acts on the cell.

$$F_b={\rho }_{Fluid}·g·V_{Cell}$$

(1)

where ${\rho }_{Fluid}$ describes the mass density of the fluid, g defines the acceleration due to gravity and $V_{Cell}$ is the volume of the cell. In Figure 7, the right side displays the active forces acting on the cell. In stationary conditions, the balance of forces is, according to Ref [95], as follows:

$$F_g=F_b+F_t+F_{w,\left|\right|}$$

(2)

where $F_g$ is the measured force, $F_t$ is the tension force by the hook and $F_{w,\left|\right|}$ is the force due to the connection wires. Since the measured force and the wire force remain constant due to the same mass, changes in the measured force are only a function of the volume of the cell. This leads to changes in the buoyant force and therefore in the tension force. $F_t$ can be represented as:

$$\Delta F_t=\Delta m_{balance}·g=-{\rho }_{Fluid}·g·\Delta V_{Cell}=-\Delta F_b$$

(3)

Rearranging Equation (3) according to the change in volume gives:

$$\Delta V_{Cell}=-{\displaystyle \frac{\Delta m_{balance}}{{\rho }_{Fluid}}}$$

(4)

With this equation, the volume change of the cell can be derived from the mass measurement registered on the balance.

Aiken et al. [108] investigated gas formation with different kinds of electrolyte with the apparatus shown in Figure 7. They used NMC111/G cells with a capacity of 225 $\mathrm{m}$$\mathrm{Ah}$. Nine cells were investigated. Five cells were clamped between pressure plates to ensure a constant force on the cells surface, and the remaining four cells were cycled unconstrained. During formation, the immersion bath was placed inside a climate chamber and heated up to 40 °C. In the first cycle, the clamped cells produced a large amount of gas in a short time and then remained constant. The unrestrained cells, on the other hand, form an initially higher quantity of gas, which then decreases very quickly. This is explained by the fact that the gas is diverted into the gas pocket in the clamped condition and has little time to react with the electrodes. In a second test, formation cycles with different currents were performed. They concluded that during the formation cycle, the composition and the quantity of the gas produced is similar, as long as currents remain below C/3.

Stock et al. [95] used both the Archimedes principle, and 1D-dilatometry to compare the gas production of two different cells in the formation cycle. One cell had a NCA cathode with a SiC anode and the other had a NMC cathode and a graphite anode. Similar to the Aiken study, the authors investigated gas formation in both compressed and uncompressed cells. Measurements on the compressed cells were made using 1D-dilatometry with a pressure plate on the cell surface to apply pressure. Measurements on uncompressed cells where made using the Archimedes principle, as was done in the Aiken study. Figure 8 shows the expansion measured for both measurement techniques with the NCA/SiC cell on the left-hand side and the NMC/G cell on the right-hand side. For the NCA cell, both measurements provide similar results, for the NMC, however, the two measurements provide different results. This is explained by the fact that the unstressed cell initially produces a large amount of gas in the liquid phase of the graphite intercalation, which later reacts to form liquid or solid components in the graphite structure. In the tensioned structure, no reduction reaction can take place due to the applied pressure. Cell dilation is described as the main expansion influence.

Figure 8. Comparison between 1D-dilatation measuring of gas production through pressure plate and immersion bath. Normalized volume for NCA/SiC cells (a). Normalized volume for NMC/G cells (b); Reproduced under Creative Commons License without any changes (CC BY 4.0 by Stock et al. [95]).

Figure 8. Comparison between 1D-dilatation measuring of gas production through pressure plate and immersion bath. Normalized volume for NCA/SiC cells (a). Normalized volume for NMC/G cells (b); Reproduced under Creative Commons License without any changes (CC BY 4.0 by Stock et al. [95]).

Leißing et al. [109] investigated the influence of the C-rate on the gassing behavior of NMC622/graphite cells with nominal capacity of 5 $\mathrm{Ah}$. To determine the amount of gas which is produced on formation cycles, the same apparatus as Aiken et al. is used [108]. They charged the cells at different C-rates and measured the volume differences due to gas production directly after reaching the lower cutoff voltage. The most gas is produced ($7.7$ $\mathrm{m}$$\mathrm{l}$) with a C-rate of 2C and the least amount of gas ($1.6$ $\mathrm{m}$$\mathrm{l}$) is produced with a C-rate of 0.1C. The lowest C-rate of 0.05C produces, in contrast, a comparatively high amount of gas ($4.2$ $\mathrm{m}$$\mathrm{l}$). This is explained due to the long time spent at lower potentials. The extended formation time leads to an increase of electrolyte reduction and more parasitic reactions.

Louli et al. [99] used the principle of buoyancy force, in addition to pressure measurements and the 1D dilatometry measurement to measure the volume change of battery cells during charge and discharge cycles after formation. They compared all three measurement techniques, shown in Figure 4. All three techniques demonstrated similar behavior in volume expansion, leading to the conclusion that all techniques are suitable for this type of measurement.

Many of the proposed methods for applying Archimedes’ principle use the technique to measure gas evolution in battery cells during the formation cycles with different electrolyte compositions [110,111,112,113,114,115,116] or with electrodes with different chemical compositions [117].

3.1.3. Strain Measurement

To establish reliable condition monitoring for lithium-ion batteries, it is advantageous to integrate strain measurement into the classical electrical measurements of battery cells [118]. The expansion of the cell induces deformation in the housing due to strain. In their study, Hickey and Jahns [119] demonstrated a correlation between cell expansion and the strain on the cell’s housing. The strain imposed on the cell’s housing by internal expansion mechanisms can be quantified using either strain gauges or optical solutions such as fiber braggs grating (FBG) sensors.

Strain Gauges

Strain gauges convert distortions from stress and strain into electrical resistance, which can be measured. Hickey and Jahns [119] combined measurements with strain gauges and tactile displacement sensors to assess the feasibility of SoC estimation. For this purpose $5.5$ $\mathrm{Ah}$ prismatic cells were cycled. Three strain gauges were placed, with two gauges on the opposing side near the center of the cell and the third gauge near the exhaust vent. The tactile sensor served as a reference placed at the center of the cell. Figure 9 shows strain measurements at the vent position on prismatic cells are comparable with the 1D-displacement measurements during a discharge pulse measurement with a current of $0.5$ C. Moreover, SoC estimation of the battery cells is possible with this apparatus.

Choi et al. [120] performed tests under abuse conditions using carbon nanotube (CNT)-based strain sensors to measure the volume change of a pouch bag caused by excessive temperature fluctuations. For this purpose a cell is heated to approximately 90 °C until gas leakage occurs due to excessive gas production. The complete deformation of the cell with good time resolution is measured, leading to the conclusion that this setup could be used for real-time measurements.

Willenberg et al. [121] investigated the correlation of the overall impact of the cell expansion on the cell ageing. They cycled 51 commercially available 18650 cylindrical cells with an NCA cathode and an anode made of graphite and a small amount of silicon. The nominal capacity of the cell is 3,350 $\mathrm{m}$$\mathrm{Ah}$. The cell had an initial diameter of 18.55 mm and is wound 19 times in the housing. The cell was aged with at $0.5$ C with a average SoC of 50% and a cycle depth of 50%. They found, that there is a discrepancy in the diameter change between the charge and the discharge cycles. The authors explained this behavior as being caused by the different intercalation stages of lithium ions during charge and discharge. For the 51 cycled cells, they found an average diameter change of the cells of 10.7 $\mathsf{\mu }$$\mathrm{m}$ with a standard deviation of 4.4 $\mathsf{\mu }$$\mathrm{m}$. Up until the cell diminished to a state of health (SoH) of 80%, there was a slight increase in the irreversible diameter change. In contrast, a large increase in the irreversible change occurred when the cell approached a SoH of 60%. After 700 cycles, they found a significant increase in the cell diameter, as well as in the temperature of the cell. Postmortem analyses showed the irreversible diameter change in form of a deformation of the inner windings. The authors concluded that there was a correlation between the capacity fade of the battery cell and the change of the battery cell diameter. They also showed that it is possible to measure both the reversible and irreversible volume change in cylindrical battery cells using strain gauges.

Optical Fiber Sensors

Fiber Braggs Grating (FBG) have been established as a standard fiber optic sensor for monitoring battery conditions. Typically employed for measuring in situ strain and temperature, this sensor type is based on an optical fiber with a grating featuring a defined period [122]. The grating is inscribed into the optical fiber core by the interference of two coherent ultaviolet (UV) light beams [123].

Figure 10 (a) shows the unloaded FBG sensor on the left side. A broadband light source is used to send a certain light intensity $I_I$ through the optical fiber. The grating then acts as a filter and reflects a light intensity $I_B$ with a pre-defined wavelength, referred to as the Bragg wavelength. The remaining light intensity $I_T$, composed of the unfiltered wavelengths, is transmitted and monitored using an optical sensor. The Bragg wavelength can be represented as

$${\lambda }_B=2n_{eff}\Lambda$$

(5)

with ${\lambda }_B$ as the Bragg wavelength, $n_{eff}$ as the effective refractive index of the grating and $\mathsf{\Lambda }$ as the period of the grating [124] . The Bragg wavelength can be influenced by external effects such as strain or temperature [125]. In the case of an applied strain on the optical fiber, the period of the grating ${\lambda }_{UV}$ changes. As a result, the reflected Bragg wavelength changes as well. The wavelength increases for tensile forces and decreases for pressure forces applied on the length of the fiber, as shown in Figure 10 (b). The resulting wavelength shift can be described as

$${\displaystyle \frac{\Delta {\lambda }_B}{{\lambda }_B}}=\left(1-p_e\right)·\epsilon$$

(6)

with $p_e$ as the photoelastic coefficient and $\epsilon$ as the strain $\Delta l/l_0$ [126].

A secondary influence on the reflected wavelength is the external temperature, as shown in Figure 10 (c). A change in the temperature results in a change in the effective refractive index $n_{eff}$ [127]. The change due to thermal influences is effectively a superposition of a change of the refractive index and thermal expansion. The shift in refractive index has a dominant effect and accounts for up to $95\%$ of the expansion, with thermal expansion playing a minor role [128].

FBG sensors are immune to electromagnetic interference, chemically inert, mechanically robust and the use of multiple sensors is possible [122,125]. Many of the proposed methods, including optical fiber sensors, were developed to measure the temperature of the battery cell and not the strain induced due to reversible and irreversible expansion [122,129,130,131,132]. Since the main focus of this review is the expansion behavior of lithium-ion battery cells, the strain measurement of optical fiber sensors is of greater relevance.

Yang et al. [133] were the first who had applied FBG sensors onto the surface of battery cells. Their aim was to monitor the external temperature of the battery cell surface. For this purpose, seven Bragg sensors on one string were installed and coupled to the top and the bottom of three cells. The seventh sensor is installed in the climate chamber to measure the ambient temperature. They were able to measure the temperature under different charging conditions. Compared to thermocouples, this sensor was also able to response to dynamic inputs.

Sommer et al. [134] extended the measurements beyond temperature monitoring, to the characterization of intercalation stages of lithium-ion batteries during charging and discharging cycles. For this purpose, they installed two FBG sensors on the top of a 15 $\mathrm{Ah}$ NMC/G pouch cell. They used a temperature compensation method based on a reference FBG sensor proposed by Rao [135]. This method makes use of one FBG sensor bonded directly to the surface of the cell to measure both thermal and strain effects, and a second FBG sensor that is loosely attached to measure only thermal influences. The measurement from the second sensor are subtracted from the first, to isolate for strain. The cell was then clamped between two pressure plates with foam on either side to allow the breathing of the cell. The breathing of the cell refers to the reversible expansion occurring during charge and discharge cycles. Using these measurements, a correlation was established between the derivative of the SoC and the shift of wavelengths with respect to the measured voltage, during cycling under normal conditions. The authors concluded that the shift of wavelengths, which define the strain on the surface of the cell due to cell expansion, can indicate the different intercalation stages for charging and discharging. In a second publication [136], they monitored the relaxation behavior of the same cell with the same sensor configuration but without the pressure plate. They demonstrated that it is possible to measure the ion diffusion of lithium-ions intercalating into the graphite host lattice. For higher temperature values at higher SoCs, the wavelength shift is less than at lower temperatures. In these experiments the wavelength shift began to differ for SoC levels of approximately 65%. They concluded that the ion diffusion in the host lattice is a thermodynamic process and the higher temperature helps to overcome the van der Waals gap between two adjacent graphite layers. After a longer period of rest, the ions are distributed homogeneously in the lattice and consequently the wavelength shift decreases.

Meyer et al. [137] observed the strain behavior, and consequently, the volume change of a battery cell with two FBG sensors. One sensor was directly attached to the surface to measure external strain and thermal effects on the cell surface, while a second sensor, housed in a heat-conductive protection tube, was installed on the cell’s surface to specifically measure external thermal influences. Measurements were made on a 40 $\mathrm{Ah}$ NMC/G battery cell and was cycled under normal and accelerated aging conditions. To accelerate the aging of the cell, tests were performed under increased temperature conditions. The normal condition tests were not heat compensated and showed the superposition of both the external strain and thermal influences. In the accelerated aging tests, the thermal influences were compensated, and a correlation between the relative capacity loss over 400 cycles and increases in the strain difference was present.

Raghavan et al. [138] investigated a solution to embed FBG sensors inside a pouch cell and seal the pouch bag around this sensor. The sensors were placed in the middle of the cell area in the middle of the electrode stack. To measure strain and temperature, one sensor was located in a thermally-conductive housing tube and one was directly attached directly on the separator. The number of cycles to reach the end-of-life for the cell with embedded FBG sensors was approximately 200 cycles less than for an equivalent cell without the embedded sensors. Regardless, the cell reached a cycle life of more than 1,100 cycles. They concluded that estimations of SoC and SoH made with information from the embedded sensors are more accurate than predictions made without.

Bae et al. [139] extended the strain monitoring of battery cells by embedding the FBG sensor directly into the graphite structure of the negative electrode. They compared this solution with a configuration where the sensor was attached between the graphite and separator layer on the negative electrode. Electrochemical performance tests confirmed that there is no significant influence of the implanted sensor on the performance of the electrode. Figure 11 compares the wavelength shift for a charging cycle for both the attached sensor (left) and the implanted sensor (right). The shift occurs with increasing SoC towards longer wavelengths. In the implanted approach the shift is observed, in addition to a split in the observed wavelengths. This is explained as the superposition of two different applied stresses on the sensor. The attached sensor is only influenced by the longitudinal stress in the direction of the fiber. The transversal stress is, in this case, relieved by the flexible separator foil. In contrast, the implanted sensor is influenced by the longitudinal stress as well as by the transverse stress, due to its location in the more rigid structure of the graphite. Since the sensor diameter is on the same order of magnitude as the thickness of the negative electrode, the authors suggest that the results are qualitative.

Nascimento et al. [140] extended the FBG sensor with a fabry-perot (FP) cavity sensor. FP cavity sensors are typically used for strain or pressure measurements. This sensor is robust against temperature shifts. It is designed with two parallel reflecting surfaces and the phase of the reflective wavelength is measured. Any shift in the phase can give insights on the applied longitudinal strain or pressure. If the FBG sensor is located near the FP sensor, it is possible to measure temperature and strain with a single hybrid sensor. To test this sensor, the authors placed three sensors close to the tabs of the cell, in the center of the cell and on opposing side of the tabs. The sensors are located between two separator layers inside the cell. It is then possible to measure internal strain and temperature. Single FBG sensors were placed on the surface of the cell in same location as the hybrid-sensors to compare the temperature results. The hybrid sensors show a slightly higher temperature increase than the a single sensor mounted on the surface. The authors concluded that with this hybrid sensor it is possible to monitor the internal temperature and strain in battery cells.

Most of these solutions focus on extended safety measurements for battery management systems (BMSs) in automotive applications [134,136,137,138,141,142,143,144]. The objective of these measurements is to improve SoC and SoH estimations, increasing safety in dynamic-use applications, like EVs. Future efforts are leveraging machine learning (ML) and artificial intelligence (AI) to gain better insights from FBG sensor measurements in the estimation of critical conditions [145].

4. Comparison of Techniques

5. Conclusions

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