Lithium ion secondary battery positive electrode, lithium ion secondary battery and calculation method
By defining a dispersion criterion (Rv<0.320 μm) for lithium-ion secondary battery electrodes using SEM images, the uniform distribution of materials is ensured, enhancing cycle life characteristics and conductive paths, thus improving battery durability.
Patent Information
- Application Number
- JP2024037802
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2024-03-12
- Publication Date
- 2025-09-26
AI Technical Summary
Existing lithium-ion secondary batteries lack a quantitative method to assess the dispersion of positive electrode materials, which affects the number of conductive paths and cycle life characteristics.
A lithium-ion secondary battery positive electrode with a specific dispersion criterion (Rv<0.320 μm) is defined using SEM backscattered electron images, ensuring uniform distribution of active materials, conductive agents, and binders, along with optimized mass proportions and density.
The solution enhances the cycle life characteristics of lithium-ion secondary batteries by maintaining a high number of conductive paths, leading to improved durability and performance.
Smart Images

Figure 2025139067000001_ABST
Abstract
Description
[Technical Field]
[0001] The present invention relates to a lithium ion secondary battery positive electrode, a lithium ion secondary battery, and a calculation method. [Background technology]
[0002] Lithium-ion secondary batteries are used as power sources for conventional electronic devices in a wide range of applications, such as storage batteries for portable devices, electric vehicles, homes, drones, robots, and business facilities (see, for example, Patent Document 1). In particular, lithium-ion secondary batteries for drones are required to have high cycle life characteristics due to their use.
[0003] To improve the cycle life characteristics of lithium-ion batteries, it is necessary to use a positive electrode in which the positive electrode materials (positive electrode active material, conductive agent, binder, etc.) are appropriately dispersed. An electrode in which the positive electrode materials are uniformly dispersed has many conductive paths connecting the active materials within the positive electrode. Even if some of the conductive paths are lost due to repeated charging and discharging, many conductive paths remain, which extends the cycle life.
[0004] Generally, the more homogeneously dispersed the positive electrode material, the more conductive paths there are, resulting in improved cycle life characteristics. On the other hand, if the dispersion is insufficient, the number of conductive paths decreases, resulting in a decrease in cycle life characteristics. [Prior art documents] [Patent documents]
[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2000-11992 Summary of the Invention [Problem to be solved by the invention]
[0006] However, quantifying the state of dispersion and the existence of conductive paths has not been sufficiently performed to date.
[0007] The present invention has been made in view of the above, and has an object to provide a positive electrode for a lithium ion secondary battery, a lithium ion secondary battery, and a calculation method that are excellent in cycle life characteristics. [Means for solving the problem]
[0008] In order to solve the above-mentioned problems and achieve the object, a positive electrode for a lithium ion secondary battery according to the present invention is, in a first aspect, a lithium ion secondary battery positive electrode in which a positive electrode composite layer containing a positive electrode active material capable of absorbing and releasing lithium ions, a conductive agent, and a binder is provided on a current collector and rolled, and is characterized in that in an SEM backscattered electron image of the surface of the positive electrode obtained with a scanning electron microscope (SEM) at a magnification of 5000x, an acceleration voltage of 15 kV, and an irradiation current of PC30, a circle is imagined outside the active material region, the circle does not enter the active material region, and is tangent to the outline of the active material region, and when the standard deviation of the radius of the circle is Rv, Rv<0.320 is satisfied in μm terms.
[0009] Although SEM backscattered electron images can be substituted with secondary electron images, when emphasis is placed on differences in composition, SEM backscattered electron images, which are relatively more closely related to composition, are preferable.
[0010] The Rv indicates the variation in the area and shape of each inter-active material region. A small Rv means that the variation is small and the material is uniformly dispersed. Conversely, a large Rv means that the regions vary greatly and the material is aggregated or unevenly distributed. In this way, Rv can be used to quantify the degree of dispersion of electrode materials.
[0011] In addition to the first aspect, the positive electrode for a lithium ion secondary battery according to the present invention is characterized in that, as a second aspect, the Rv satisfies Rv<0.280.
[0012] Furthermore, as a third aspect, in addition to the first or second aspect, the lithium ion secondary battery positive electrode according to the present invention is characterized in that, relative to the total mass of the positive electrode mixture layer, the mass proportion of the positive electrode active material is 94.0 mass% or more and 98.0 mass% or less, the mass proportion of the conductive agent is 1.0 mass% or more and 5.0 mass% or less, and the mass proportion of the binder is 1.0 mass% or more and 5.0 mass% or less.
[0013] Furthermore, as a fourth aspect, the lithium ion secondary battery positive electrode according to the present invention is characterized in that, in addition to any one of the first to third aspects, the density of the positive electrode mixture layer is 3.3 g / cc or more and 3.7 g / cc or less.
[0014] Furthermore, as a fifth aspect, in addition to any one of the first to fourth aspects, the positive electrode of a lithium ion secondary battery according to the present invention is characterized in that the SEM backscattered electron image is obtained by scanning an area of 17.28 μm × 25.4 μm on the surface of the positive electrode.
[0015] Furthermore, as a sixth aspect, in addition to any one of the first to fifth aspects, the lithium ion secondary battery according to the present invention is characterized in that the SEM backscattered electron image is acquired at a magnification of 5000 times, and the centers of the circles are spaced apart in a grid pattern with an upper limit of 1 μm.
[0016] In addition, as a seventh aspect, a lithium ion secondary battery according to the present invention is characterized by comprising: a positive electrode for lithium ion secondary batteries according to any one of the first to sixth aspects; a negative electrode capable of absorbing and desorbing lithium ions; and a nonaqueous electrolyte solution.
[0017] Furthermore, as an eighth aspect, the calculation method according to the present invention is a calculation method for calculating parameters of a lithium-ion secondary battery positive electrode in which a positive electrode composite layer containing a positive electrode active material capable of absorbing and releasing lithium ions, a conductive agent, and a binder is provided on a current collector and rolled, the calculation method comprising the steps of: acquiring an image that is an SEM backscattered electron image or a secondary electron image of the surface of the positive electrode using a scanning electron microscope (SEM); binarizing the acquired image based on a brightness signal and a threshold value that is set based on the brightness signal of the image; extracting a contour from the binarized image; determining whether each pixel of the image is inside or outside a positive electrode active material region determined with reference to the contour; calculating a circle tangent to the contour for a pixel outside the positive electrode active material region; and calculating the radius of the circle.
[0018] In addition, in a ninth aspect, the calculation method according to the present invention is characterized in that, in addition to the eighth aspect, it further includes a step of calculating a standard deviation of the radii of the circles.
[0019] Furthermore, in a tenth aspect, in addition to the eighth or ninth aspect, the calculation method according to the present invention is characterized in that the threshold value is a median value of brightness signals of the SEM backscattered electron image.
[0020] Furthermore, as an eleventh aspect, in addition to any one of the eighth to tenth aspects, the calculation method according to the present invention is characterized in that the number of pixels of a scale of the SEM backscattered electron image is measured, and the SEM backscattered electron image is smoothed with an upper limit of the number of pixels corresponding to 0.1 μm.
[0021] Furthermore, as a twelfth aspect, in addition to any one of the eighth to eleventh aspects, the calculation method according to the present invention is characterized in that, when the area of the portion surrounded by the contour is smaller than a predetermined area, the portion surrounded by the contour is excluded from the contour for which the circle is calculated. [Effects of the Invention]
[0022] According to the present invention, a positive electrode for a lithium ion secondary battery having excellent cycle life characteristics can be obtained. [Brief explanation of the drawings]
[0023] [Figure 1] FIG. 1 is a perspective view illustrating the configuration of a lithium ion secondary battery according to an embodiment of the present invention. [Figure 2] FIG. 2 is a cross-sectional view taken along line AA shown in FIG. [Figure 3] FIG. 3 is a flowchart showing the flow of a method for calculating a standard deviation according to an embodiment of the present invention. [Figure 4] FIG. 4 is a diagram for explaining calculation of a circle for an SEM image of the positive electrode composite material layer according to Example 1. As shown in FIG. [Figure 5] FIG. 5 is a diagram for explaining calculation of a circle for an SEM image of a positive electrode composite material layer according to Comparative Example 1. In FIG. DETAILED DESCRIPTION OF THE INVENTION
[0024] Hereinafter, embodiments of the present invention will be described, but the present invention is not limited to the following description. Furthermore, various modifications and improvements can be made to the present embodiments, and such modifications and improvements can also be included in the present invention. 1 and 2 show an example of the configuration of a laminated lithium ion secondary battery as an embodiment, but the shape of the lithium ion secondary battery of the present invention is not particularly limited and may be flat, cylindrical, prismatic, coin-shaped, etc. The exterior body of the lithium ion secondary battery is also not particularly limited and known materials such as laminate film, aluminum, aluminum alloy, and stainless steel can be used.
[0025] (Embodiment) Fig. 1 is a perspective view illustrating the configuration of a lithium ion secondary battery according to an embodiment of the present invention, and Fig. 2 is a cross-sectional view taken along line AA shown in Fig. 1.
[0026] The lithium ion secondary battery 1 is a laminated lithium ion battery having an exterior body 2 formed into a bag shape by stacking two laminate films with their heat-sealable resin layers facing each other and heat-sealing the outer periphery.
[0027] The exterior body 2 is formed into a bag shape by stacking two laminate films with their heat-sealable resin layers facing each other and heat-sealing the outer periphery. An electrode group 3 and a nonaqueous electrolyte are contained within the exterior body 2. The electrode group 3 is inserted through an opening in the exterior body 2, and the opening of the exterior body 2 is sealed by heat-sealing, thereby hermetically storing the electrode group 3 within the exterior body 2.
[0028] As the laminate film, a composite film in which a heat-sealable resin layer for heat sealing is provided on a metal layer is preferably used. The metal layer is not particularly limited as long as it prevents moisture from entering from the outside and improves the strength of the entire sheet. For example, aluminum foil, stainless steel foil, etc. can be used as the metal layer. The heat-sealable resin layer is not particularly limited, but polyethylene or polypropylene is preferably used from the viewpoint of the temperature range in which heat sealing is possible and the blocking property against the non-aqueous electrolyte. Here, to protect the metal layer, a protective layer may be provided on the surface opposite to the heat-sealable resin layer. The protective layer is not particularly limited, but nylon, PET, etc. are preferably used. Furthermore, to improve adhesion between the metal layer and the heat-sealable resin layer, an adhesive layer may be provided between them.
[0029] As shown in FIG. 2, the electrode group 3 has a structure in which a positive electrode 4, a negative electrode 5, and a separator 6 interposed between the positive electrode 4 and the negative electrode 5 are stacked as a set with the negative electrode 5 positioned as the outermost layer, and multiple such sets are stacked.
[0030] (positive electrode) The positive electrode 4 is composed of a positive electrode current collector 42 and a positive electrode layer 41 formed on one or both sides of the positive electrode current collector 42. The positive electrode 4 is in the form of a plate.
[0031] The positive electrode layer 41 contains a positive electrode active material, a conductive agent, and a binder.
[0032] <Cathode active material> The positive electrode active material is not particularly limited as long as it is a lithium-containing compound capable of absorbing and releasing lithium. The lithium-containing compound is, for example, a lithium-containing metal oxide or a lithium metal phosphate. Examples of the lithium-containing metal oxide include lithium cobalt composite oxides (e.g., LiCoO2), lithium nickel composite oxides (e.g., LiNiO2), lithium manganese composite oxides (e.g., LiMnO2, Li2MnO3, or LiMn2O4), and lithium nickel manganese composite oxides (e.g., Li(Co 1 / 3 Ni 1 / 3 Mn 1 / 3 )O2, lithium cobalt nickel aluminum composite oxide (e.g., Li(Co 0.15 Ni 0.8 Al 0.05 )O2, lithium nickel manganese composite oxide (e.g., LiNi 0.5 Mn 1.5 Examples of lithium metal phosphate include lithium iron phosphorus composite oxides (e.g., LiFePO4). From the viewpoint of the discharge capacity and average voltage of the positive electrode active material, it is preferable to contain lithium cobalt oxide.
[0033] The average primary particle diameter of the positive electrode active material is preferably 6 μm or more and 9 μm or less. If it is less than 6 μm, the specific surface area of the active material increases, resulting in a lack of conductive paths relative to the specific surface area, which may increase reaction resistance. If it is greater than 9 μm, the diffusibility of lithium ions within the active material particles may decrease, and the specific surface area of the active material may decrease, reducing the reaction area and increasing reaction resistance. The average particle diameter is the median diameter measured using the laser diffraction and scattering method described in JIS standard Z8825:2013. Measurements can be performed using a laser diffraction particle size distribution analyzer, SALD-2300 (Shimadzu Corporation).
[0034] <Conductive agent> The conductive agent is not particularly limited, and known or commercially available ones can be used. Examples of the conductive agent include carbon black such as acetylene black and ketjen black, carbon nanotubes, carbon fiber, activated carbon, graphite, and other conductive carbons. The conductive agent can be used alone or as a mixture of two or more of these.
[0035] <Binder> The binder is not particularly limited, and known or commercially available binders can be used. Examples include fluorine-based resins such as polyvinylidene fluoride (PVDF) and polytetrafluoroethylene (PTFE), polyvinylpyrrolidone (PVP), polyvinyl chloride (PVC), polyethylene (PE), polypropylene (PP), ethylene-propylene copolymer, styrene-butadiene rubber (SBR), acrylic resin, polyvinyl alcohol (PVA), and carboxymethyl cellulose (CMC). The binder can be used as a single substance, or as a mixture or copolymer of two or more substances.
[0036] <Dispersant> A dispersant is not necessarily required, but may be added if it is desired to disperse the conductive agent more effectively. A typical dispersant is polyvinylpyrrolidone (PVP).
[0037] [Electrode composition] In the electrode composition, the higher the positive electrode active material ratio, the higher the energy density; the higher the conductive agent ratio, the better the electronic conductivity; and the higher the binder ratio, the higher the peel strength of the electrode coating surface. Considering these balances, the electrode composition preferably has a positive electrode active material mass ratio of 94.0% to 98.0% by mass, a conductive agent mass ratio of 1.0% to 5.0% by mass, and a binder mass ratio of 1.0% to 5.0% by mass, relative to the total mass of the positive electrode plate composite layer. In this case, if the positive electrode active material mass ratio is less than 94.0% by mass, the energy density cannot be increased. On the other hand, if the positive electrode active material mass ratio is greater than 98.0% by mass, the energy density increases, but the proportion of conductive agent or binder relative to the positive electrode active material decreases, resulting in a decrease in electronic conductivity or peel strength. If the mass ratio of the conductive agent is less than 1.0 mass%, the electronic conductivity decreases, whereas if the mass ratio of the conductive agent is more than 5.0 mass%, the electronic conductivity improves, but the ratio of the binder to the conductive agent becomes insufficient, resulting in a decrease in peel strength. If the mass ratio of the binder is 1.0 mass % or less, the peel strength decreases, whereas if the mass ratio of the binder is more than 5.0 mass %, the binder becomes a resistive component, resulting in a decrease in electronic conductivity.
[0038] <Positive electrode current collector> The positive electrode current collector 42 is not particularly limited, and known or commercially available ones can be used. Examples of the positive electrode current collector 42 include rolled foils made of aluminum, aluminum alloys, copper, nickel, or stainless steel, and porous metals such as porous aluminum. Among these positive electrode current collectors, aluminum or aluminum alloys are preferred because they have high electrical conductivity, excellent corrosion resistance in the electrolyte, and are lightweight metals.
[0039] [Electrode manufacturing method] The positive electrode can be produced, for example, by the following method. First, the positive electrode active material, conductive agent, binder, and dispersant described above are dispersed in a solvent to prepare a positive electrode slurry. A thickener may be further added to the positive electrode slurry. Next, the positive electrode slurry is applied to one or both surfaces of a positive electrode current collector, and then dried to form a positive electrode layer. The positive electrode can be produced by rolling the positive electrode slurry into a plate-shaped positive electrode.
[0040] Rolling is preferably performed so that the electrode density is 3.3 g / cc or more and 3.7 g / cc or less. If the density is less than 3.3 g / cc, the volumetric energy density may decrease and it may be difficult to form a conductive path. If the density is more than 3.7 g / cc, large shear stress is applied to the positive electrode composite layer and the composite layer-current collector foil interface during rolling, which may destroy the bonding between the materials in the positive electrode composite layer and the bonding between the composite layer and the current collector foil interface, reducing the electrode peel strength.
[0041] <Solvent> The solvent used in preparing the positive electrode slurry is not particularly limited, and known or commercially available solvents can be used. Examples of the solvent include N-methyl-2-pyrrolidone (NMP), N,N-dimethylformamide (DMF), N,N-dimethylacetamide (DMA), and water. When polyvinylidene fluoride (PVDF) is used as the binder, N-methyl-2-pyrrolidone (NMP) is preferably used as the solvent. When styrene butadiene rubber (SBR), polytetrafluoroethylene (PTFE), polyvinyl alcohol (PVA), or carboxymethyl cellulose (CMC) is used as the binder, water is preferably used as the solvent. When polyvinylpyrrolidone (PVP) is used as the dispersant, polyvinylpyrrolidone (PVP) is preferably used.
[0042] The positive electrode 4 also has a positive electrode lead 43, which is a positive electrode current collector 42 extending from the positive electrode layer 41. The positive electrode lead 43 extends, for example, from the right side surface in FIG. 2. The positive electrode leads 43 are bundled at their tip ends within the exterior body 2 and joined to each other by ultrasonic welding, resistance welding, or the like. One end of the positive electrode terminal 7 is joined to the joint of the positive electrode lead 43, and the other end extends to the outside through the sealing portion of the exterior body 2.
[0043] In this embodiment, the surface of the positive electrode prepared by the above method was photographed with a scanning electron microscope (SEM), and the obtained SEM backscattered electron image was analyzed to obtain a circle of a group Ri of radii of circles in the region between each active material particle. After obtaining Ri, the standard deviation Rv of Ri was calculated. Details of the image analysis method are as follows.
[0044] FIG. 3 is a flowchart showing the flow of a method for calculating standard deviation according to one embodiment of the present invention. This calculation method is executed using a computer. This computer is configured using one or more pieces of hardware, such as a central processing unit (CPU), a graphics processing unit (GPU), a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or a complex programmable logic device (CPLD), as well as memory in which various programs are pre-installed. There are no particular restrictions on the language used to perform the processing, and any language, such as Python, Java, or VBA, can be selected. The calculation process will be described below as being executed by a control unit included in the computer.
[0045] First, the control unit acquires a backscattered electron image (step S101). This backscattered electron image is an SEM backscattered electron image captured by an SEM. As an example, this SEM backscattered electron image is a 5000x magnification SEM backscattered electron image obtained by scanning a 17.28 μm × 25.4 μm area on the positive electrode surface with an SEM. The scanning range is not limited to 17.28 μm × 25.4 μm. In this case, an auto-contrast / brightness adjustment function (ACB) is used, if available. Regarding the luminance signal, as will be described later, if the maximum value of the image luminance signal is 240 or less, or the median value of the image luminance signal is 120 or more, there is a possibility of a condition such as "whiteout" or "blackout." This may result in an inaccurate standard deviation, as will be described later. Therefore, a new image should be captured and used. In order to avoid the above-mentioned "bloated highlights" and "crushed shadows," in the case of the SEM used in the present invention, scanning under the conditions of an acceleration voltage of 15 kV, a working distance (WD) of 10 mm, and a probe current (PC) of 30 is effective, if not completely avoidable.
[0046] Thereafter, the control unit checks the number of pixels of the scale in the backscattered electron image (step S102). The control unit acquires the magnification of the SEM backscattered electron image and determines how many pixels the scale indicating the length standard is made up of.
[0047] The control unit then smooths the image (step S103). Based on the number of pixels of the scale, the control unit performs smoothing with an upper limit of the number of pixels equivalent to 0.1 μm if the magnification is 5000 times. This smoothing evens out roughness in the image. The upper limit of the number of pixels in the smoothing can be changed depending on the imaging conditions such as the magnification.
[0048] After the smoothing process, the control unit binarizes the image (step S104). The control unit first calculates the luminance signal for each pixel by summing three values: a value obtained by weighting the red luminance by 0.299, a value obtained by weighting the green luminance by 0.587, and a value obtained by weighting the blue luminance by 0.114. If the luminance signal has a decimal point, it may be rounded to 0 or an integer. Any rounding method, such as rounding up, rounding down, or rounding, may be selected. The control unit then calculates the median of the luminance signal of the image and sets the color of each pixel position to either white or black using this median as a threshold. If the luminance signal has a decimal point, it may be rounded to 0 or an integer. Any rounding method, such as rounding up, rounding down, or rounding, may be selected. The control unit converts the image into a two-color image of black and white only by changing the color to the set color.
[0049] Then, the control unit extracts contours from the binarized image (step S105). The control unit extracts the boundary between white and black and depicts it as a contour.
[0050] The reason for using the median value of the image luminance signal as the threshold is that the luminance signal of an image may vary from image to image or depending on the SEM imaging environment. If the threshold is set as the absolute value of the luminance signal, if the luminance signal of the entire image varies even within the same field of view, the contour may change depending on the luminance signal of the image, making it difficult to accurately grasp the boundary of the active material. Furthermore, if a value other than the median is set as the threshold, even if the dispersion state of the electrode surface differs between fields of view, there may be no difference in Rv, and the dispersion state may not be accurately quantified. Therefore, when binarizing, it is preferable to use the median value as the threshold to distinguish between colors.
[0051] After the contour extraction, the control unit assigns a number N to the portion (area) surrounded by the contour (step S106). MAX Numbers up to are assigned to each.
[0052] Then, the control unit calculates the area of each part (step S107). Furthermore, the control unit sets the number N to N=1 (step S108). Note that step S107 and step S108 may be performed first, or may be performed simultaneously.
[0053] The control unit determines that the area of the portion numbered N is 0.5 squared ((0.5) 2 )μm 2 The control unit determines whether the area is equal to or greater than (0.5) (step S109). 2 μm 2 If it is determined that the area is less than (0.5) (step S109: No), the process proceeds to step S112. 2 μm 2 If it is determined that the number is equal to or greater than the number (step S109: Yes), the process proceeds to step S110.
[0054] In step S110, the control unit determines whether the portion with number N is a white region or a black region. For example, if white dots occupy 20% or more of the dots in the region, it is determined to be a white region. In this embodiment, the white region is a region corresponding to the active material, and the black region is a region corresponding to the conductive agent, binder, or voids between the active material particles. If the control unit determines that it is a white region (step S110: Yes), it proceeds to step S112. On the other hand, if the control unit determines that it is a black region (step S110: No), it proceeds to step S111. Note that this step is not limited to this, and in embodiments other than this embodiment, processing in which the white region and the black region are reversed may also be possible.
[0055] In step S111, the control unit incorporates the number N into the group M. As a result, the number N (outline) that is not in the group M is excluded from the processing targets in step S114 and thereafter. The reason for excluding the outline in this way is to distinguish between the outlines of the active material and the outlines of the non-active material. After the capture process, the control unit proceeds to step S112.
[0056] After that, the control unit increments N by 1 (step S112).
[0057] The control unit increases the number N by 1. MAX The control unit determines whether the number N is greater than or equal to N (step S113). MAX If it is determined that the number is equal to or less than N (step S113: No), the process proceeds to step S109, and the above-described process is repeated for the portion of the increased number N. MAX If it is determined that it is greater than the specified value (step S113: Yes), the process proceeds to step S114.
[0058] In step S114, the control unit determines for each pixel whether it is inside or outside the active material region. First, the control unit determines whether each pixel is white or black, and if it is white, then determines whether it is inside or outside the outline region of group M. At this time, the pixels used for the determination may be spaced apart in a grid pattern, with the distance between the determined pixels being an upper limit of 1 μm at a magnification of 5000 times. From the viewpoint of processing speed, it is desirable that the distance between pixels be approximately 1 μm.
[0059] Then, based on the determination result in step S114, the control unit calculates a circle for each pixel determined to be outside the contour region in collection M (step S115). The control unit finds the point on the contour that is closest to the pixel in collection M, and obtains a circle with a radius that is the pixel and the point on the contour. The radius of each circle, converted into μm, is then incorporated into collection Ri. By calculating the radius using the closest point on the contour, each circle can be assumed not to fall within the active material region.
[0060] The control unit calculates the standard deviation Rv of the group Ri of each circle (step S116). In this way, the standard deviation Rv is calculated from the acquired SEM backscattered electron image. In this embodiment, a positive electrode having excellent cycle life characteristics can be obtained by making the standard deviation Rv satisfy Rv<0.320, and more preferably Rv<0.280 from the viewpoint of cycle characteristics.
[0061] [Method for controlling standard deviation Rv] The standard deviation Rv can be controlled by the slurry dispersion method, electrode drying conditions, etc. When controlling the standard deviation Rv using a dispersion method, for example, if a thin-film vortex mixer is used, the shear force applied to the positive electrode material is reduced, reducing dispersibility, and therefore the standard deviation Rv is likely to increase. When a thin-film vortex mixer is used, it is necessary to take into account the kneading time for dispersion and other factors to prevent the standard deviation Rv from becoming too large. When kneading is performed using a planetary mixer and then a solvent is added to reduce the solid content ratio of the slurry (the ratio of the total weight of various positive electrode materials to the total weight of the slurry) and disperse the slurry, the shear force applied to the positive electrode material increases, improving dispersibility, and therefore the standard deviation Rv is likely to decrease. When a planetary mixer is used, it is necessary to take into account the drying conditions described below and other factors to prevent the standard deviation Rv from becoming too small. Note that, in the present invention, kneading refers to kneading at a solid content ratio of 80% or more. The standard deviation Rv can also be controlled by adjusting the drying conditions. For example, a high drying temperature results in a uniform distribution of the conductive agent, resulting in a small standard deviation Rv. However, a low drying temperature results in a uneven distribution of the conductive agent, resulting in a large standard deviation Rv. To achieve a standard deviation Rv of Rv<0.320, for example, the slurry is kneaded in a planetary mixer for one hour, a solvent is added to disperse the slurry until the viscosity reaches 5000 cp, the slurry is applied by die coating, and the electrode is dried at a maximum temperature of 120°C for 7 minutes. Furthermore, if the Rv is too small, excessive dispersion occurs, which is undesirable from the perspective of overall battery performance. Therefore, the lower limit of Rv is set to 0.06, which is approximately 1% of 6 μm, the lower limit of the desirable average particle size of the positive electrode active material.
[0062] (Negative electrode) The negative electrode 5 is composed of a negative electrode current collector 52 and a negative electrode layer 51 formed on one or both sides of the negative electrode current collector 52. Here, the negative electrode layer 51 of the negative electrode 5 located in the outermost layer is formed on the surface of the negative electrode current collector 52 facing the separator 6. In contrast, the negative electrode layers 51 of the negative electrodes 5 located between the positive electrodes 4, excluding the negative electrode 5 located in the outermost layer, are formed on both sides of the negative electrode current collector 52.
[0063] The negative electrode layer 51 contains a negative electrode active material, a conductive agent, and a binder. The negative electrode active material is not particularly limited as long as it is a material capable of absorbing and releasing lithium. Examples of the negative electrode active material include cokes such as pyrolytic carbons, pitch coke, needle coke, and petroleum coke; natural graphite; artificial graphite; mesocarbon microbeads (MCMB); hard carbon; soft carbon; glassy carbon; sintered organic polymer compounds (e.g., phenolic resin, furan resin, etc., sintered and carbonized); carbon fibers; carbon black; activated carbon; metal materials such as Al, Si, and Sn; and alloy materials. Preferred negative electrode active materials are cokes and carbons that have stable charge / discharge characteristics and easily form a solid electrolyte interphase (SEI) coating on their surfaces. Graphite such as natural graphite or artificial graphite is more preferred.
[0064] <Conductive agent> The conductive agent is not particularly limited, and known or commercially available conductive agents can be used. For example, the conductive agent can be the same as that used in the positive electrode described above. Note that a configuration without a conductive agent is also possible.
[0065] <Binder> The binder is not particularly limited, and known or commercially available binders can be used. Examples include fluororesins such as polyvinylidene fluoride (PVDF) and polytetrafluoroethylene (PTFE), fluororubbers, styrene butadiene rubber (SBR), carboxymethyl cellulose (CMC), core-shell binders, polyvinyl alcohol, and polyimide resins such as polyimide and polyamideimide. The binder can be used as a single substance, or as a mixture or copolymer of two or more substances.
[0066] <Negative electrode current collector> The negative electrode current collector 52 is not particularly limited, and a known or commercially available one can be used. For example, rolled foil made of copper, a copper alloy, aluminum, or stainless steel, or a porous metal such as porous aluminum can be used as the negative electrode current collector 52. The negative electrode current collector is preferably made of copper or a copper alloy.
[0067] The negative electrode 5 also has a negative electrode lead 53, for example, in which the negative electrode current collector 52 extends from the negative electrode layer 51. The negative electrode lead 53 extends, for example, from the left side surface in FIG. 2. The negative electrode leads 53 are bundled at their tip ends within the exterior body 2 and joined to each other. One end of the negative electrode terminal 8 is joined to the joint of the negative electrode lead 53, and the other end extends to the outside through the sealing portion of the exterior body 2.
[0068] (Non-aqueous electrolyte) The non-aqueous electrolyte contains a non-aqueous solvent in which a lithium salt is dissolved. Examples of lithium salts include one or a mixture of two or more selected from the group consisting of LiBF, LiPF, Li(FSO)N, Li(CFSO)N, and LiPOF. The nonaqueous solvent is not particularly limited, but examples include one or a mixture of two or more selected from the group consisting of dimethyl carbonate (DMC), diethyl carbonate (DEC), dipropyl carbonate (DPC), ethyl methyl carbonate (EMC), ethylene carbonate (EC), propylene carbonate (PC), methyl propionate, ethyl propionate, propyl propionate, methyl acetate, methyl formate, methyl butyrate, dioxolane, 2-methyltetrahydrofuran, tetrahydrofuran, dimethoxyethane, γ-butyrolactone, acetonitrile, and benzonitrile. DMC, DEC, DPC, EMC, EC, and PC are particularly preferred. Among these, it is preferable to include EC, which is capable of forming a good coating on the negative electrode active material.
[0069] (separator) The separator 6 is not particularly limited, and known or commercially available separators can be used. The separator 6 can be, for example, a microporous membrane or nonwoven fabric made of a polyolefin resin such as a polyethylene resin or a polypropylene resin, a polyimide resin, or a polytetrafluoroethylene (PTFE) resin. The microporous membrane or nonwoven fabric may have a single-layer or multilayer structure. The separator 6 may be a microporous membrane as is, or an inorganic ceramic layer may be formed on one or both sides of the microporous membrane to improve heat resistance and nonaqueous electrolyte replenishment.
[0070] Such lithium-ion secondary batteries are preferably subjected to pretreatments such as initial charging and gas evacuation before use. For example, initial charging involves injecting a nonaqueous electrolyte solution and then performing constant current charging at a minute current value down to 10% of the rated capacity. After such initial charging, gas generated within the exterior body during initial charging is vented. Gas evacuation is performed, for example, by placing the exterior body in a decompression chamber with a portion of the sealed portion open. Gas evacuation can be accelerated, for example, by applying pressure to the exterior body from the outside during gas evacuation.
[0071] When the initial charge is performed at such a small current value, the SEI film is likely to form at 1.2 to 0.8 V vs. Li / Li. + Since the negative electrode potential is maintained at this state for a long period of time, a denser and stronger SEI film can be formed on the surface of the negative electrode active material. Furthermore, during initial charging, there is a high possibility that the nonaqueous electrolyte may not be sufficiently impregnated into the constituent materials of the lithium-ion secondary battery, increasing the risk of lithium deposition due to overvoltage. Therefore, by performing the initial charging at such a small current value, it is possible to suppress the occurrence of overvoltage and thereby suppress lithium deposition. Furthermore, by performing the initial charging at a small current value, it is possible to promote gas generation during the initial charging, and the gas can be efficiently discharged through a portion of the sealing portion of the exterior body that is opened. By sufficiently discharging the gas, it is possible to suppress expansion of the exterior body due to gas generation when the lithium-ion secondary battery is used.
[0072] In the present embodiment described above, the positive electrode is configured so that the standard deviation Rv of the radius Ri of each circle generated outside the active material region satisfies Rv<0.320, thereby making it possible to obtain a lithium ion secondary battery positive electrode with excellent cycle life characteristics.
[0073] In the above-described embodiment, an example has been described in which a contour is extracted from a binarized image, a circle is generated, and the standard deviation of the radius is calculated. However, other parameters besides the standard deviation can also be calculated based on a binarized image or a circle.
[0074] Furthermore, in the above-described embodiment, an example was described in which smoothing, selection of a portion surrounded by a contour, and selection of pixels are performed in calculating the standard deviation. However, for example, smoothing does not need to be performed if it does not affect the calculation of the standard deviation, and if there is no constraint on the time required to calculate the standard deviation, circles may be generated using all contours without selecting portions, or circles may be generated for all pixels.
[0075] Furthermore, in the above-described embodiment, an example in which a backscattered electron image is acquired at 5000 magnifications has been described, but a backscattered electron image captured at other magnifications can also be used. [Example]
[0076] The present invention will be described in more detail below by way of examples, but the present invention is not limited to the following examples in any way.
[0077] Example 1 <Preparation of positive electrode> The positive electrode slurry was prepared by dispersing 96 wt% lithium iron cobaltate (LiCoO2) as the positive electrode active material, 2.6 wt% carbon black as the conductive agent, 1.2 wt% polyvinylidene fluoride (PVDF) as the binder, and 0.2 wt% polyvinylpyrrolidone (PVP) as the dispersant in N-methyl-2-pyrrolidone (NMP) as the solvent. The dispersion method involved kneading the mixture in a planetary mixer for 1 hour, and then adding solvent to achieve a viscosity of 5000 cp. Next, the positive electrode slurry was applied to both sides of aluminum foil (12 μm thick) as the positive electrode current collector, with a coating weight of 15.4 mg / cm. 2 The mixture was then dried for 7 minutes at a maximum temperature of 120° C. Thereafter, the mixture was pressed until the electrode density reached 3.5 g / cc to prepare a positive electrode.
[0078] [Standard deviation calculation] The surface of the obtained positive electrode was photographed using an SEM. The SEM backscattered electron image was obtained by scanning an area of 17.28 μm × 25.4 μm on the positive electrode surface at a magnification of 5000x, an acceleration voltage of 15 kV, and an irradiation current of PC30. Using this SEM backscattered electron image (SEM image), the standard deviation was calculated according to the flowchart shown in Figure 3.
[0079] <Preparation of negative electrode> The negative electrode slurry was prepared by dispersing 98% by weight of graphite as the negative electrode active material and 1.0% by weight each of styrene butadiene rubber (SBR) and carboxymethyl cellulose (CMC) as binders in ion-exchanged water as the solvent. Next, the negative electrode slurry was applied to both sides of a copper foil (6 μm thick) as the negative electrode current collector in a coating amount of 8.3 mg / cm. 2 The mixture was coated using a coater so that the thickness became 1.6 g / cc, and then dried at 80 to 110° C. Thereafter, the mixture was pressed until the electrode density became 1.6 g / cc to prepare a negative electrode.
[0080] <separator> The separator used was a 12 μm thick microporous membrane made of polyethylene (PE) resin, with a 2 μm thick coating layer made of AlOOH (boehmite) on one side thereof.
[0081] <Exterior body> The exterior body consisted of a rectangular first laminate film with a thickness of 151 μm, a recess, and a flat edge around the recess, and a flat, rectangular second laminate film with a thickness of 151 μm. Each of these laminate films had a laminated structure consisting of a heat-sealable resin layer (inner layer), a metal layer, and a protective layer (outer layer). The heat-sealable resin layer was an 80 μm thick polyolefin resin film. The metal layer was an aluminum foil with a thickness of 40 μm. The protective layer was a 25 μm thick polyamide film.
[0082] <Nonaqueous electrolyte> The nonaqueous electrolyte was a 3 / 1 / 4 / 2 volume mixture of ethylene carbonate (EC), diethyl carbonate (DEC), ethyl propionate (EP), and propyl propionate (PP), dissolved in 1.3 mol / L lithium hexafluorophosphate (LiPF6). The additives included 2.25 wt% vinylene carbonate (VC), 1.25 wt% adiponitrile (ADN), 1.25 wt% succinonitrile, and 0.15 wt% lithium tetrafluoroborate (LiBF4) based on the total weight of the electrolyte (EC + DEC + EP + PP + LiPF6).
[0083] <Prototype battery assembly> Using the non-aqueous electrolyte, a prototype battery according to Example 1 was assembled as follows: The prototype battery had the same structure as the lithium-ion secondary battery shown in Figures 1 and 2, except that the manufacturing process for the positive electrode was changed. The positive electrodes, negative electrodes, and separators were each cut to a specified area. Next, as shown in Figure 2, eight positive electrodes and nine negative electrodes were alternately stacked with separators in between to obtain an electrode group. The positive electrode leads and negative electrode leads were bundled at their tips and joined together by ultrasonic welding. An aluminum tab was ultrasonically welded to the joint of the positive electrode lead as a positive electrode terminal. A copper tab was ultrasonically welded to the joint of the negative electrode lead as a negative electrode terminal.
[0084] An electrode group with welded positive and negative terminals was placed in the recess of a first laminate film, and a flat second laminate film was placed over the flat edges around the recess of the first laminate film so that the positive and negative terminals partially extended outward. Three of the four overlapping sides of the first and second laminate films were heat-sealed to each other, and the electrode group was housed in an exterior housing made of the first and second laminate films. Next, 7 g of nonaqueous electrolyte was injected into the remaining side of the exterior housing. This side was then heat-sealed under a reduced pressure of 1 hPa to 100 hPa to obtain a prototype battery after the injection of the nonaqueous electrolyte. The theoretical capacity of the prototype battery was 2.55 Ah.
[0085] After the non-aqueous electrolyte was poured into the prototype battery, the battery was left standing for 12 hours to allow the non-aqueous electrolyte to permeate the constituent materials of the electrode group.
[0086] Next, the positive and negative terminals of the prototype battery were connected to a power source, and the prototype battery was initially charged at a current value of 0.25 C to 10% of its rated capacity. The prototype battery was then placed in a decompression chamber with a portion of the sealed portion of the exterior body open, allowing gas generated within the battery to be vented. The sealed portion of the exterior body was then resealed, and the prototype battery was then charged a second time at a current value of 0.5 C to 10-100% of its rated capacity. The prototype battery was then left standing in a high-temperature environment for 3 hours, after which it was subjected to constant-current charging at a current value of 0.5 C to 4.4 V, and constant-voltage charging to 0.02 C. The rated capacity was then measured at a current value of 0.2 C, and the battery was charged to a state of charge (SOC) of 10% of its rated capacity, yielding a prototype battery according to Example 1.
[0087] Example 2 A prototype battery was obtained in the same manner as in Example 1, except that the dispersion method for producing the positive electrode was to disperse the material for 1 hour using a thin film rotary mixer (the amount of solvent was adjusted so that the slurry viscosity became 5000 cp).
[0088] Example 3 A prototype battery was obtained in the same manner as in Example 1, except that the dispersion method for producing the positive electrode was to disperse the mixture in a thin film vortex mixer for 10 hours (the amount of solvent was adjusted so that the slurry viscosity was 5000 cp), the coating method was die coating, and the drying method was to dry the mixture at a maximum temperature of 95°C for 3 minutes, and then further dry it at a maximum temperature of 130°C for 1 minute.
[0089] Example 4 The positive electrode slurry is composed of 97% by weight of lithium iron cobaltate (LiCoO2), 1.63% by weight of carbon black as a conductive agent, 1.25% by weight of polyvinylidene fluoride (PVDF) as a binder, and 0.12% by weight of polyvinylpyrrolidone (PVP) as a dispersant. The slurry was dispersed by kneading it in a planetary mixer for 1 hour, adding a solvent to make the viscosity 5000cp, and dispersing it. The slurry coating amount was 15.3 mg / cm. 2 A prototype battery was obtained in the same manner as in Example 1, except that the coating method was comma coating, the maximum drying temperature was 120°C, and the drying time was 7 minutes.
[0090] (Comparative Example 1) A prototype battery was obtained in the same manner as in Example 1, except that the dispersion method for producing the positive electrode was to disperse the material using a thin film swirling mixer for 1 hour (the amount of solvent was adjusted so that the slurry viscosity became 5000 cp), the coating method was die coating, and the drying method was to dry the material at a maximum temperature of 95°C for 3 minutes, and then further dry it at a maximum temperature of 130°C for 1 minute.
[0091] (Comparative Example 2) A prototype battery was obtained in the same manner as in Example 1, except that the dispersion method for producing the positive electrode was to disperse the material using a thin film swirling mixer for 1.5 hours (the amount of solvent was adjusted so that the slurry viscosity was 5000 cp), the coating method was die coating, and the drying method was to dry the material at a maximum temperature of 95°C for 3 minutes, and then further dry it at a maximum temperature of 130°C for 1 minute.
[0092] (Comparative Example 3) A prototype battery was obtained in the same manner as in Example 1, except that the dispersion method for producing the positive electrode was to disperse the material using a thin film swirling mixer for 5 hours (the amount of solvent was adjusted so that the slurry viscosity became 5000 cp), the coating method was die coating, and the drying method was to dry the material at a maximum temperature of 95°C for 3 minutes, and then further dry the material at a maximum temperature of 130°C for 1 minute.
[0093] Comparative Example 4 The positive electrode slurry was composed of 95.0 wt% lithium iron cobaltate (LiCoO2), 3.6 wt% carbon black as a conductive agent, 2.2 wt% polyvinylidene fluoride (PVDF) as a binder, and 0.2 wt% polyvinylpyrrolidone (PVP) as a dispersant. The slurry was dispersed using a thin film gyratory mixer for 10 hours, and the slurry coating amount was 15.6 mg / cm. 2 A prototype battery was obtained in the same manner as in Example 1, except that the coating method was comma coating, the drying method was a maximum temperature of 130°C, and the drying time was 7 minutes.
[0094] <Evaluation 1: 45℃, 1C charge / 3C discharge cycle charge / discharge test> A charge-discharge cycle test was conducted in a 45°C environment for each of the prototype batteries of Examples 1 to 3 and Comparative Examples 1 to 3. First, each prototype battery was left to stand in a thermostatic chamber at 45°C for 1 to 3 hours, and then 350 charge-discharge cycles were performed, with one cycle consisting of charge and discharge according to the following charge-discharge condition 1. The discharge capacity retention rate was calculated from the discharge capacity at the first cycle and the discharge capacity at the 350th cycle. The calculation was performed according to the following formula (I). The results are shown in Table 1 below. 350 cycle discharge capacity retention rate / % = (discharge capacity at 350th cycle / discharge capacity at 1st cycle) × 100 (I)
[0095] (Charge / discharge condition 1 (1C charge / 3C discharge cycle charge / discharge test)) Environmental temperature: 45℃ Charge: 1.0C up to 4.4V (Continue charging until the charging current drops to 0.1C) Discharge: 3.0C to 2.5V
[0096] The characteristics of the prototype batteries according to Examples 1 to 4 and Comparative Examples 1 to 4 are shown in Table 1 below. [Table 1]
[0097] Here, the standard deviation Rv in Table 1 is the average value of values for five fields of view for each level of electrode. The discharge capacity retention rate is the average value of values for three cells for each level of cell. When calculating the standard deviation Rv for each level of this example, etc., the image acquired at a magnification of 5000 times is smoothed with an upper limit of the number of pixels equivalent to 0.1 μm, and the area is calculated by 0.5 squared ((0.5) 2 )μm 2 Contours smaller than this were excluded, and areas where white dots accounted for 20% or more of the points within the area were determined to be white areas. The distance between pixels used to determine whether group M was inside or outside the contour area was set to 1 μm.
[0098] The calculation of the standard deviation in Example 1 and Comparative Example 1 will be described with reference to FIGS. 4 and 5. FIG. 4 is a diagram for explaining the calculation of a circle for an SEM image of a positive electrode composite layer according to Example 1. FIG. 5 is a diagram for explaining the calculation of a circle for an SEM image of a positive electrode composite layer according to Comparative Example 1. As shown in FIGS. 4 and 5, a contour is extracted from a binarized image of the SEM image, and a circle inscribed in the contour is generated for a portion having an area equal to or greater than a predetermined area. Then, the standard deviation Rv was calculated for the radius of each circle.
[0099] A cycle life characteristic of 70.0% or more at 45°C and 350 cycles is suitable for use as a lithium-ion battery for drones. The results shown in Table 1 indicate that the prototype batteries according to Examples 1 to 4, which satisfy Rv<0.320, can maintain a cycle life characteristic of 70.0% or more at 45°C and 350 cycles, compared to Comparative Examples 1 to 4, which do not satisfy Rv<0.320. In contrast, Comparative Examples 1 to 4 had cycle life characteristics of 70.0% or less at 45°C and 350 cycles. Therefore, Examples 1 to 4 are suitable for use as a lithium-ion battery for drones. The high cycle life characteristic of Examples 1 to 4 is believed to be due to the large number of conductive paths between the positive electrode active material particles, and even if some of the conductive paths are lost due to repeated charging and discharging, many conductive paths remain. In contrast, in Comparative Examples 1 to 4, there were few conductive paths, and when the conductive paths were lost to a certain extent, the number of remaining conductive paths decreased, which is thought to have reduced the battery reaction within the active material and resulted in a decrease in the cycle discharge capacity retention rate.
[0100] As described above, according to this embodiment, a positive electrode plate for a lithium ion secondary battery having long cycle life characteristics can be provided.
[0101] Although the embodiments of the present invention have been specifically described, the present invention is not limited to these embodiments and examples, and various modifications based on the technical concept of the present invention are possible. [Explanation of symbols]
[0102] 1. Lithium-ion secondary battery 2. Exterior body 3 electrode groups 4 Positive electrode 5 negative electrode 6 Separator 7 Positive terminal 8 Negative terminal 41 Positive electrode layer 42 Positive electrode current collector 51 negative electrode layer 52 Negative electrode current collector
Claims
1. A positive electrode for a lithium ion secondary battery, comprising: a positive electrode mixture layer including a positive electrode active material capable of absorbing and releasing lithium ions, a conductive agent, and a binder, provided on a current collector; and a rolling treatment performed on the positive electrode mixture layer; In an SEM backscattered electron image of the surface of the positive electrode obtained by a scanning electron microscope (SEM) at an acceleration voltage of 15 kV and a working distance (WD) of 10 mm, a circle is assumed to be outside the active material region, the circle does not lie within the active material region, and is in contact with the outline of the active material region, and when the standard deviation of the radius of the circle is Rv, Rv < 0.320 is satisfied in terms of μm. A positive electrode for a lithium ion secondary battery.
2. The Rv satisfies Rv<0.280, 2. The positive electrode for a lithium ion secondary battery according to claim 1 .
3. With respect to the total mass of the positive electrode mixture layer, the mass ratio of the positive electrode active material is 94.0 mass% or more and 98.0 mass% or less, the mass ratio of the conductive agent is 1.0 mass% or more and 5.0 mass% or less, and the mass ratio of the binder is 1.0 mass% or more and 5.0 mass% or less.
2. The positive electrode for a lithium ion secondary battery according to claim 1 .
4. The density of the positive electrode mixture layer is 3.3 g / cc or more and 3.7 g / cc or less.
2. The positive electrode for a lithium ion secondary battery according to claim 1 .
5. The SEM backscattered electron image was obtained by scanning an area of 17.28 μm × 25.4 μm on the surface of the positive electrode.
2. The positive electrode for a lithium ion secondary battery according to claim 1 .
6. The SEM backscattered electron image is acquired at a magnification of 5000 times, and the center of the circle is separated by an upper limit of 1 μm to calculate the distance.
2. The positive electrode for a lithium ion secondary battery according to claim 1 .
7. The positive electrode for a lithium ion secondary battery according to claim 1 or 2, a negative electrode capable of absorbing and releasing lithium ions; a nonaqueous electrolyte; A lithium ion secondary battery comprising:
8. A method for calculating parameters of a lithium ion secondary battery positive electrode in which a positive electrode mixture layer including a positive electrode active material capable of absorbing and releasing lithium ions, a conductive agent, and a binder is provided on a current collector and the positive electrode mixture layer is subjected to a rolling treatment, the method comprising: Obtaining an image, which is an SEM backscattered electron image or a secondary electron image, of the surface of the positive electrode using a scanning electron microscope (SEM); binarizing the acquired image based on a luminance signal and a threshold value set based on the luminance signal of the image; Extracting a contour from the binarized image; determining whether each pixel of the image is inside or outside the positive electrode active material region determined with reference to the contour; calculating a circle tangent to the contour at a pixel outside the positive electrode active material region; Calculating the radius of the circle; A calculation method characterized by:
9. The method of claim 8, further comprising the step of calculating a standard deviation of the radii of the circles.
10. the threshold is the median value of the luminance signal of the image; 9. The calculation method according to claim 8.
11. Set the number of pixels of the scale of the image; smoothing the image up to a maximum number of pixels equivalent to 0.1 μm; 9. The calculation method according to claim 8.
12. If the area of the portion surrounded by the contour is smaller than a predetermined area, the portion surrounded by the contour is excluded from the contour for which the circle is calculated.
8. The calculation method according to claim 7, wherein:
Citation Information
Patent Citations
Nonaqueous electrolyte battery
JP2000011992A