Patent Publication Number: US-2022223831-A1

Title: Secondary battery and manufacturing method of positive electrode active material

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     One embodiment of the present invention relates to a positive electrode active material, a secondary battery, and manufacturing methods of the positive electrode active material and the secondary battery. Furthermore, one embodiment of the present invention relates to a portable information terminal and a vehicle each including a secondary battery. 
     One embodiment of the present invention relates to an object or a manufacturing method. The present invention relates to a process, a machine, manufacture, or a composition of matter. One embodiment of the present invention relates to a semiconductor device, a display device, a light-emitting device, a power storage device, a lighting device, an electronic device, or a manufacturing method thereof. 
     Note that in this specification, a semiconductor device generally means a device that can function by utilizing semiconductor characteristics. An electrooptic device, a semiconductor circuit, and an electronic device are all semiconductor devices. 
     Note that a power storage device in this specification refers to every element and device having a function of storing electric power. For example, a power storage device (also referred to as secondary battery) such as a lithium-ion secondary battery, a lithium-ion capacitor, and an electric double layer capacitor are included in the category of the power storage device. 
     2. Description of the Related Art 
     In recent years, a variety of power storage devices, such as lithium-ion secondary batteries, lithium-ion capacitors, and air batteries, have been actively developed. In particular, demand for lithium-ion secondary batteries with high output and high energy density has rapidly grown with the development of the semiconductor industry, for portable information terminals such as mobile phones, smartphones, and laptop computers; portable music players; digital cameras; medical equipment; next-generation clean energy vehicles such as hybrid vehicles (HVs), electric vehicles (EVs), and plug-in hybrid vehicles (PHVs); and the like. The lithium-ion secondary batteries are essential for today&#39;s information society as rechargeable energy supply sources. 
     Patent Document 1 discloses a positive electrode active material for a lithium-ion secondary battery with high capacity and excellent charge and discharge cycle performance. 
     REFERENCE 
     Patent Document 
     
         
         [Patent Document 1] PCT International Publication No. WO2020/099978 
       
    
     SUMMARY OF THE INVENTION 
     An object of one embodiment of the present invention is to provide a positive electrode active material with high charge and discharge capacity. Another object is to provide a positive electrode active material with high charge and discharge voltage. Another object is to provide a positive electrode active material that is less likely to deteriorate. Another object is to provide a novel positive electrode active material. Another object is to provide a secondary battery with high charge and discharge capacity. Another object is to provide a secondary battery with high charge and discharge voltage. Another object is to provide a secondary battery with high safety or high reliability. Another object is to provide a secondary battery that is less likely to deteriorate. Another object is to provide a secondary battery with a long lifetime. Another object is to provide a novel secondary battery. 
     Another object of one embodiment of the present invention is to provide a novel substance, active material, or power storage device or a manufacturing method thereof. 
     Note that the description of these objects does not preclude the existence of other objects. One embodiment of the present invention does not have to achieve all these objects. Other objects can be derived from the description of the specification, the drawings, and the claims. 
     In the invention disclosed in this specification, a positive electrode active material is formed in such a manner that a cobalt compound (also referred to as a precursor) is obtained by a coprecipitation method, a mixture obtained by mixing the cobalt compound and a lithium compound is heated at first heating temperature, the heated mixture is ground or crushed, and further heated at second heating temperature that is higher than the first heating temperature. 
     Moisture is released by the heating at the first heating temperature, and then heating is performed at the second heating temperature that is higher than the first heating temperature. Performing the heat treatment twice can improve the mixing state of the mixture, and when a secondary battery is fabricated with the mixture, voids of a secondary particle in the secondary battery can be reduced. Furthermore, the twice heat treatment can improve the crystallinity. 
     The first heating temperature is higher than or equal to 400° C. and lower than or equal to 700° C. 
     The second heating temperature is higher than 700° C. and lower than or equal to 1050° C. 
     In the case where an additive element typified by aluminum is added to the mixture, a lithium compound and an aluminum compound are added before the heat treatment at the first heating temperature. 
     One embodiment of the invention disclosed in this specification is a method of forming a positive electrode active material, including: supplying an aqueous solution containing a water-soluble nickel salt, a water-soluble cobalt salt, and a water-soluble manganese salt and an alkaline solution to a reaction tank; performing mixing in the reaction tank to precipitate a cobalt compound; heating a mixture obtained by mixing the cobalt compound, a lithium compound, and an aluminum compound at first heating temperature; performing grinding or crushing on the mixture; and heating the ground or crushed mixture at second heating temperature that is higher than the first heating temperature. 
     By the coprecipitation method of precipitating the cobalt compound, an aqueous solution containing a water-soluble nickel salt, a water-soluble cobalt salt, and a water-soluble manganese salt and an alkaline solution are supplied to a reaction tank, mixing is performed in the reaction tank to precipitate a cobalt compound (hydroxide containing cobalt, manganese, and nickel), and the cobalt compound and a lithium compound are mixed to form a mixture. The reaction is referred to as a neutralization reaction, an acid-base reaction, or a coprecipitation reaction in some cases. The compound containing at least nickel, cobalt, and manganese is referred to as a cobalt compound or a precursor of lithium cobaltate in some cases regardless of the contained amount of cobalt. 
     As the aqueous solution containing a water-soluble nickel salt, a nickel sulfate aqueous solution or a nickel nitrate aqueous solution can be used. 
     As the aqueous solution containing a water-soluble cobalt salt, a cobalt sulfate aqueous solution or a cobalt nitrate aqueous solution can be used. 
     As the aqueous solution containing a water-soluble manganese salt, a manganese sulfate aqueous solution or a manganese nitrate aqueous solution can be used. 
     In the case where aluminum is added as an additive element to the mixture, an aqueous solution containing aluminum is further supplied to the reaction tank. In the case where magnesium is added as an additive element to the mixture, an aqueous solution containing magnesium is further supplied to the reaction tank. In the case where calcium is added as an additive element to the mixture, an aqueous solution containing calcium is further supplied to the reaction tank. 
     The pH inside the reaction tank is preferably greater than or equal to 9.0 and less than or equal to 11.0, more preferably greater than or equal to 10.0 and less than or equal to 10.5. 
     When an aqueous solution and an alkaline solution are mixed to precipitate a cobalt compound, a chelating agent is added. Examples of the chelating agent include glycine, oxine, 1-nitroso-2-naphthol, 2-mercaptobenzothiazole, and ethylenediaminetetraacetic acid (EDTA). Note that two or more kinds selected from glycine, oxine, 1-nitroso-2-naphthol, and 2-mercaptobenzothiazole may be used. The chelating agent is dissolved in pure water, which is used as a chelate aqueous solution. The chelating agent is a complexing agent that forms a chelate compound, and preferred to a general complexing agent. A complexing agent may be used instead of the chelating agent, and an example of the complexing agent is an ammonia water. 
     The use of the chelate aqueous solution is preferable because it is easy to control the pH in the reaction tank for obtaining a cobalt compound. Furthermore, the use of the chelate aqueous solution is preferable also because the chelate aqueous solution prevents generation of unnecessary crystal nuclei and promotes crystal growth. When unnecessary nuclei are prevented from occurring, impalpable particles are also prevented from occurring; accordingly, a composite hydroxide with favorable particle size distribution can be obtained. The use of the chelate aqueous solution can retard an acid-base reaction, and the reaction that gradually progresses can result in almost-spherical secondary particles. Glycine has a function of keeping the pH greater than or equal to 9.0 and less than or equal to 10.0 or the vicinity of the range. Using a glycine aqueous solution as the chelate aqueous solution is preferable because it is easy to control the pH of the reaction tank for obtaining the cobalt compound. Furthermore, the concentration of glycine in the glycine aqueous solution is preferably greater than or equal to 0.05 mol/L and less than or equal to 0.09 mol/L. 
     The positive electrode active material obtained in the above manner includes crystal having a hexagonal crystal layered structure. The crystal is not limited to a single crystal (also referred to as a crystallite). In the case where the crystal is polycrystalline, some crystallites gather to form a primary particle. The primary particle indicates a particle recognized as a grain having a single smooth plane when observed with a scanning electron microscope (SEM). The secondary particle indicates a group of aggregated primary particles. In the SEM observation, boundaries or color differences are observed between primary particles which are different in crystallinity, crystal orientation, or composition. Thus, the different primary particles can be visually recognized as different regions in many cases. For the aggregation of the primary particles, there is no particular limitation on the bonding force between the plurality of primary particles. The bonding force may be one of covalent bonding, ionic bonding, a hydrophobic interaction, the Van der Waals force, and other molecular interactions, or a plurality of bonding forces may work together. 
     When the coprecipitation method is employed, the secondary particle is formed in some cases. 
     The crystal having a hexagonal crystal layered structure includes one or more selected from a first transition metal, a second transition metal, and a third transition metal. Specifically, NiCoMn-based material (also referred to as NCM) represented by LiNi x Co y Mn z O 2  (x&gt;0, y&gt;0, z&gt;0, 0.8&lt;x+y+z&lt;1.2) where the first transition metal is nickel, the second transition metal is cobalt, and the third transition metal is manganese, can be used. Specifically, it is preferable that the relations 0.1x&lt;y&lt;8x and 0.1x&lt;z&lt;8x be satisfied, for example. For example, x, y, and z preferably satisfy the ratio x:y:z=1:1:1 or the neighborhood thereof. Alternatively, for example, x, y, and z preferably satisfy the ratio x:y:z=5:2:3 or the neighborhood thereof, x:y:z=8:1:1 or the neighborhood thereof, x:y:z=9:0.5:0.5 or the neighborhood thereof, x:y:z=6:2:2 or the neighborhood thereof, or x:y:z=1:4:1 or the neighborhood thereof. 
     The positive electrode active material obtained in the above manner may contain one or more selected from a group formed of Al, Mg, Ca, Zr, V, Cr, Fe, Cu, Zn, Ga, Ge, Sr, Y, Nb, Mo, Sn, Ba, and La as necessary, in addition to the first transition metal, the second transition metal, and the third transition metal. In order that a secondary battery including the positive electrode active material has higher capacity retention rate after charge and discharge cycles, the positive electrode active material preferably contains Al, Mg, Ca, or Zr. 
     The secondary battery including the positive electrode active material is also a structure disclosed in this specification. The secondary battery includes a positive electrode including the positive electrode active material and a negative electrode including a negative electrode active material. A separator is positioned between the positive electrode and the negative electrode. The separator is used for preventing short circuit, providing a secondary battery with high safety or high reliability. 
     In the case where aluminum is added to the positive electrode active material, when the above method is regarded as the first method, there are other methods. The second method is a method in which after the heat treatment is performed at the second heating temperature, aluminum is added. The third method is a method using an aqueous solution containing aluminum as one of aqueous solutions used for the coprecipitation method. 
     As described above, there are three methods of adding aluminum to the positive electrode active material. In the case where aluminum is added to the positive electrode active material, one or more of the above three methods can be employed. For example, in the case where a large amount of aluminum is added, the following procedure is possible: aluminum is added with use of an aluminum-containing aqueous solution at the time of the coprecipitation method, lithium and aluminum are added and mixed, heating is performed at the first heating temperature to release moisture, heating is performed at the second heating temperature that is higher than the first heating temperature, aluminum is added after the second heating, and then third heating is performed. 
     Performing heat treatment twice in one embodiment of the present invention improves the mixing state of the mixture, which can reduce voids of the secondary particle when a secondary battery is fabricated. In addition, heat treatment performed twice in total can improve the crystallinity. Thus, a positive electrode active material with high capacity can be provided. A positive electrode active material which is relatively stable even when charge and discharge are repeated can be provided. A highly safe or highly reliable secondary battery can be provided. 
     Note that the description of these effects does not preclude the existence of other effects. One embodiment of the present invention does not necessarily have all the effects listed above. Other effects will be apparent from and can be derived from the description of the specification, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an example of a formation flow of a positive electrode active material of one embodiment of the present invention. 
         FIG. 2  shows an example of a formation flow of a positive electrode active material of one embodiment of the present invention. 
         FIG. 3  shows an example of a formation flow of a positive electrode active material of one embodiment of the present invention. 
         FIG. 4  shows an example of a formation flow of a positive electrode active material of one embodiment of the present invention. 
         FIG. 5  is a cross-sectional view showing a reaction tank used in one embodiment of the present invention. 
         FIG. 6A  is a perspective exploded view of a coin-type secondary battery,  FIG. 6B  is a perspective view of a coin-type secondary battery, and  FIG. 6C  is a cross-sectional perspective view thereof. 
         FIG. 7A  shows an example of a cylindrical secondary battery.  FIG. 7B  shows an example of a cylindrical secondary battery.  FIG. 7C  shows an example of a plurality of cylindrical secondary batteries.  FIG. 7D  shows an example of a power storage system including a plurality of cylindrical secondary batteries. 
         FIGS. 8A and 8B  show examples of a secondary battery, and  FIG. 8C  illustrates the internal state of a secondary battery. 
         FIGS. 9A to 9C  show an example of a secondary battery. 
         FIGS. 10A and 10B  each show the appearance of a secondary battery. 
         FIGS. 11A to 11C  show a method of manufacturing a secondary battery. 
         FIGS. 12A to 12C  show structure examples of a battery pack. 
         FIGS. 13A and 13B  show an example of a secondary battery. 
         FIGS. 14A to 14C  show an example of a secondary battery. 
         FIGS. 15A and 15B  show an example of a secondary battery. 
         FIG. 16A  is a perspective view of a battery pack of one embodiment of the present invention,  FIG. 16B  is a block diagram of a battery pack, and  FIG. 16C  is a block diagram of a vehicle having a motor. 
         FIGS. 17A to 17D  show examples of transport vehicles. 
         FIGS. 18A and 18B  show power storage devices of embodiments of the present invention. 
         FIG. 19A  shows an electric bicycle,  FIG. 19B  shows a secondary battery of the electric bicycle, and  FIG. 19C  shows an electric motorcycle. 
         FIGS. 20A to 20D  show examples of electronic devices. 
         FIG. 21  shows the results of crushing strength. 
         FIG. 22  shows a cross-sectional observation photograph of a positive electrode. 
         FIGS. 23A and 23B  show charge and discharge cycle performance of secondary batteries at 25° C. 
         FIGS. 24A and 24B  show charge and discharge cycle performance of secondary batteries at 45° C. 
         FIG. 25  is a SEM image of particles in this example. 
         FIG. 26  is a SEM image of particles in a comparative example. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Note that the present invention is not limited to the description below, and it is easily understood by those skilled in the art that modes and details of the present invention can be modified in various ways. In addition, the present invention should not be construed as being limited to the description in the following embodiments. 
     Embodiment 1 
     In this embodiment, an example of a method of forming a positive electrode active material  200 A in which an additive element is added to a cobalt compound obtained by a coprecipitation method will be described with reference to  FIG. 1 . Note that the flow diagram in  FIG. 1  shows the order of components (the order of steps) connected with lines.  FIG. 1  does not show timings of components which are not directly connected with lines. For example, although a mixed solution  901  and a mixed solution  902  are shown at the same level in  FIG. 1 , steps or treatments of the mixed solutions  901  and  902  are not necessarily performed at the same time. 
     In this embodiment, a coprecipitation precursor where Co, Ni, and Mn exist in one particle is formed by a coprecipitation method, a lithium salt and aluminum are mixed to the coprecipitation precursor, and then heating is performed. 
     As shown in  FIG. 1 , a cobalt aqueous solution is prepared as an aqueous solution  890 , and an alkaline solution is prepared as an aqueous solution  892 . The aqueous solution  890  and an aqueous solution  893  are mixed to form the mixed solution  901 . The aqueous solution  892  and an aqueous solution  894  are mixed to form the mixed solution  902 . These mixed solutions  901  and  902  are made to react to form a cobalt compound. This reaction is referred to as a neutralization reaction, an acid-base reaction, or a coprecipitation reaction, and this cobalt compound is referred to as a precursor of lithium cobaltate (or a coprecipitation precursor) in some cases. Note that a reaction caused by performing steps surrounded by the chain line in  FIG. 1  can be referred to as a coprecipitation reaction. 
     &lt;Cobalt Aqueous Solution&gt; 
     An example of the cobalt aqueous solution is an aqueous solution containing cobalt sulfate (e.g., CoSO 4 ), cobalt chloride (e.g., CoCl 2 ), cobalt nitrate (e.g., Co(NO 3 ) 2 ), cobalt acetate (e.g., C 4 H 6 CoO 4 ), cobalt alkoxide, an organocobalt complex, or hydrate of any of these. Alternatively, instead of the cobalt aqueous solution, an organic acid of cobalt, such as cobalt acetate, or hydrate of the organic acid of cobalt may be used. Note that in this specification, the organic acid includes citric acid, oxalic acid, formic acid, and butyric acid, in addition to acetic acid. 
     For example, an aqueous solution obtained by dissolving these in pure water can be used. The cobalt aqueous solution shows acidity, and thus can be referred to as an acid aqueous solution. The cobalt aqueous solution can be referred to as a cobalt source in a process of forming a positive electrode active material. 
     &lt;Nickel Aqueous Solution&gt; 
     As a nickel aqueous solution, an aqueous solution of nickel sulfate, nickel chloride, nickel nitrate, or hydrate of any of these can be used. Alternatively, an aqueous solution of an organic acid salt of nickel, such as nickel acetate, or hydrate of the organic acid salt of nickel can be used. Alternatively, an aqueous solution of nickel alkoxide or an organonickel complex can be used. The nickel aqueous solution can be referred to as a nickel source in a process of forming a positive electrode active material. 
     &lt;Manganese Aqueous Solution&gt; 
     As a manganese aqueous solution, an aqueous solution of manganese salt, such as manganese sulfate, manganese chloride, or manganese nitrate, or hydrate of any of these can be used. Alternatively, an aqueous solution of an organic acid salt of manganese, such as manganese acetate, or hydrate of the organic acid salt of manganese can be used. Alternatively, an aqueous solution of manganese alkoxide or an organomanganese complex can be used. The manganese aqueous solution can be referred to as a manganese source in a process of forming a positive electrode active material. 
     The above-described cobalt aqueous solution, nickel aqueous solution, and manganese aqueous solution are prepared and mixed, whereby the aqueous solution  890  is formed. 
     &lt;Alkaline Solution&gt; 
     An example of the alkaline solution is an aqueous solution containing sodium hydroxide, potassium hydroxide, lithium hydroxide, or ammonia. For example, an aqueous solution obtained by dissolving any of these in pure water can be used. An aqueous solution obtained by dissolving two or more kinds selected from sodium hydroxide, potassium hydroxide, and lithium hydroxide in pure water may be used. 
     &lt;Reaction Conditions&gt; 
     In the case where the aqueous solution  890  and the aqueous solution  892  are made to react by the coprecipitation method, the pH of the reaction system is set to greater than or equal to 9.0 and less than or equal to 11.0, and preferably greater than or equal to 9.8 and less than or equal to 10.3. For example, in the case where the aqueous solution  892  is put into a reaction tank and the aqueous solution  890  is dropped into the reaction tank, the pH of the aqueous solution in the reaction tank is preferably kept in the above range. The same applies to the case where the aqueous solution  890  is put into the reaction tank and the aqueous solution  892  is dropped. The dropping rate of the aqueous solution  890  or the aqueous solution  892  is preferably greater than or equal to 0.1 mL/min. and less than or equal to 0.8 mL/min., in which case the pH condition can be controlled easily. The reaction tank includes at least a reaction container. 
     An aqueous solution in the reaction tank is preferably stirred with a stirring means. The stirring means includes a stirrer or an agitator blade. Two to six agitator blades can be provided; for example, in the case where four agitator blades are provided, they may be placed in a cross shape seen from above. The number of rotations of the stirring means is preferably greater than or equal to 800 rpm and less than or equal to 1200 rpm. 
     The temperature in the reaction tank is adjusted to be higher than or equal to 50° C. and lower than or equal to 90° C. The dropping of the aqueous solution  892  or the aqueous solution  890  is preferably started after the temperature becomes the above temperature. 
     The inside of the reaction tank is preferably an inert atmosphere. For example, in the case of a nitrogen atmosphere, a nitrogen gas is preferably introduced at a flow rate of 0.5 L/min. or more and 2 L/min. or less. 
     In the reaction tank, a reflux condenser is preferably provided. With the reflux condenser, the nitrogen gas can be released from the reaction tank and water can be returned to the reaction tank. 
     Through the above reaction, a cobalt compound is precipitated in the reaction tank. Filtration is performed to collect the cobalt compound. After a reaction product precipitated in the reaction tank is washed with pure water, an organic solvent (e.g., acetone) having a low boiling point is preferably added before the filtration is performed. 
     The cobalt compound after the filtration is preferably dried. For example, drying is performed in a vacuum at 60° C. or higher and 90° C. or lower for 0.5 hours or longer and 3 hours or shorter. In this manner, the cobalt compound can be obtained. 
     The cobalt compound obtained through the above reaction includes cobalt hydroxide (e.g., Co(OH) 2 ). The cobalt hydroxide after the filtration is obtained as the secondary particle which is aggregation of the primary particles. In this specification, the secondary particle refers to the primary particles which agglutinate to share part of grain boundaries (an outer periphery of the primary particles) and do not easily separate from one another (independent particles). That is, the secondary particle may have a grain boundary. 
     Next, a lithium compound and a compound  910  as an oxide containing an additive element are prepared. 
     &lt;Lithium Compound&gt; 
     Examples of the lithium compound include lithium hydroxide (e.g., LiOH), lithium carbonate (e.g., Li 2 CO 3 ), and lithium nitrate (e.g., LiNO 3 ). In particular, a material having a low melting point among lithium compounds, such as lithium hydroxide (melting point: 462° C.), is preferably used. Since a positive electrode active material having a high nickel proportion is likely to cause cation mixing as compared to lithium cobaltate, first heating needs to be performed at low temperature. Therefore, it is preferable to use a material having a low melting point. The lithium compound is weighed out such that the number of lithium atoms is larger than 0.89 and smaller than 1.07 when the total number of nickel atoms, cobalt atoms, manganese atoms, and oxygen atoms is 1. 
     &lt;Compound  910 &gt; 
     As an additive element source, one or more selected from an aluminum salt, a magnesium salt, and a calcium salt are used. As the compound  910 , one or more selected from aluminum oxide, aluminum hydroxide, magnesium oxide, magnesium hydroxide, basic magnesium carbonate ((MgCO 3 ) 3 Mg(OH) 2 .3H 2 O), calcium oxide, calcium carbonate, and calcium hydroxide are used. In this embodiment, an aluminum salt is used as the additive element source and aluminum hydroxide (Al(OH) 3 ) is used as the compound  910 . The compound  910  used as the additive element source is weighed out to be contained with a desired amount by a practitioner in consideration of the composition of the cobalt compound. For example, when the sum of nickel, cobalt, manganese, and oxygen contained in the cobalt compound is regarded as 1, aluminum, magnesium, or calcium is preferably added in the range greater than or equal to 0.5 atomic % and less than or equal to 3 atomic % of the sum. 
     In this embodiment, the cobalt compound, the lithium compound, and the aluminum hydroxide were weighed out to have desired amounts and mixed to form a mixture  903 . For the mixing, a mortar or a stirring mixer is used. 
     Next, the first heating is performed. As a firing device used for the first heating, an electric furnace such as rotary kiln can be used. 
     Then, grinding or crushing is performed with a mortar to loosen the secondary particles fixed one another, and the ground or crushed mixture is collected. Furthermore, classification may be performed using a sieve. In this embodiment, a crucible made of aluminum oxide (also referred to as alumina) with a purity of 99.9% is used. It is preferable that the material subjected to heating be collected after the material is transferred from the crucible to the mortar because impurities are prevented from mixing into the material. The mortar is preferably made of a material that is less likely to release impurities. Specifically, it is preferable to use a mortar made of alumina with a purity of 90% or higher, preferably 99% or higher. 
     Next, the second heating is performed. As a firing device used for the second heating, an electric furnace such as rotary kiln can be used. 
     The second heating temperature is at least higher than the first heating temperature, and preferably higher than 700° C. and lower than or equal to 1050° C. The time of the second heating is preferably longer than or equal to one hour and shorter than or equal to 20 hours. The second heating is preferably performed in an oxygen atmosphere, and in particular, preferably performed while oxygen is supplied. For example, the flow rate is 10 L/min. per inner capacity 1 L of the furnace. Specifically, the heating is preferably performed while a container containing the mixture  903  is covered with a lid. 
     Then, grinding or crushing is performed with a mortar to loosen the secondary particles fixed one another, and the ground or crushed mixture is collected. Furthermore, classification may be performed using a sieve. 
     Through the above steps, the positive electrode active material  200 A can be formed. The positive electrode active material  200 A obtained through the above steps is NCM to which Al is added, and thus called NCMA in some cases. 
     Embodiment 2 
     Embodiment 1 shows an example in which a lithium compound and a compound that is an oxide containing an additive element are mixed into a cobalt compound obtained by a coprecipitation method, and this embodiment shows, using  FIG. 2 , an example in which a lithium compound is mixed into a cobalt compound obtained by a coprecipitation method, the mixture is subjected to heat treatment to form a mixture  905 , and the mixture  905  and the compound  910  are mixed. 
     Note that the procedure up to the step of obtaining the cobalt compound by a coprecipitation method is the same as that described in Embodiment 1; thus, detailed description thereof is omitted here. 
     In this embodiment, the cobalt compound and the lithium compound are weighed out to have desired amounts and mixed to form a mixture  904 . 
     Next, the first heating is performed. As a firing device used for the first heating, an electric furnace such as rotary kiln can be used. 
     Next, second heating is performed to obtain the mixture  905 . As a firing device used for the second heating, an electric furnace such as rotary kiln can be used. 
     The second heating temperature is at least higher than the first heating temperature, and preferably higher than 700° C. and lower than or equal to 1050° C. The time of the second heating is preferably longer than or equal to one hour and shorter than or equal to 20 hours. The second heating is preferably performed in an oxygen atmosphere, and in particular, preferably performed while oxygen is supplied. For example, the flow rate is 10 L/min. per inner capacity 1 L of the furnace. Specifically, the heating is preferably performed while a container containing the mixture  904  is covered with a lid. 
     Then, grinding or crushing is performed with a mortar to loosen the secondary particles fixed one another, and the ground or crushed mixture secondary is collected. Furthermore, classification may be performed using a sieve. 
     Then, the obtained mixture  905  and the compound  910  are mixed. As the compound  910 , one or more selected from aluminum oxide, aluminum hydroxide, magnesium oxide, magnesium hydroxide, basic magnesium carbonate ((MgCO 3 ) 3 Mg(OH) 2 .3H 2 O), calcium oxide, calcium carbonate, and calcium hydroxide are used. An aluminum salt is used as the additive element source and aluminum hydroxide (Al(OH) 3 ) is used as the compound  910 . The compound  910  used as the additive element source is weighed out to be contained with a desired amount by a practitioner in consideration of the compositions of the lithium compound and the cobalt compound. 
     Then, the third heating is performed. The third heating temperature is at least higher than the first heating temperature, and preferably higher than 700° C. and lower than or equal to 1050° C. The time of the third heating is shorter than that of the second heating, and preferably longer than or equal to one hour and shorter than or equal to 20 hours. The third heating is preferably performed in an oxygen atmosphere, and in particular, preferably performed while oxygen is supplied. For example, the flow rate is 10 L/min. per inner capacity 1 L of the furnace. Specifically, the heating is preferably performed while a container containing the mixture  905  is covered with a lid. 
     Then, grinding or crushing is performed with a mortar to loosen the secondary particles fixed one another, and the ground or crushed mixture is collected. Furthermore, classification may be performed using a sieve. 
     Through the above steps, the positive electrode active material  200 A can be formed. Although the same reference numeral  200 A is used for the positive electrode active materials in this embodiment and Embodiment 1, the processes therefor are partly different; therefore, the composition of the positive electrode active material  200 A may be different between this embodiment and Embodiment 1. 
     Embodiment 3 
     In this embodiment, nickel sulfate, cobalt sulfate, and manganese sulfate are weighed out to have desired amounts and mixed. The mixed solution  901  obtained by mixing the aqueous solution  890  containing these to the aqueous solution  893 , the mixed solution  902  obtained by mixing the aqueous solution  892 , which is an alkaline solution, and the aqueous solution  894 , and a mixed solution  906  obtained by mixing an aqueous solution  896  containing an additive element and an aqueous solution  895  are prepared. The aqueous solutions  893 ,  894 ,  895  are, but not particularly limited to, aqueous solutions serving as a chelating agent, and may be pure water. 
     In  FIG. 3 , the aqueous solution  896  containing an additive element is further used as a material for forming a cobalt compound by a coprecipitation method. In the case where aluminum is added as an additive element, an aluminum aqueous solution is further supplied to the reaction tank. In the case where aluminum is added as an additive element, an aqueous solution containing aluminum is further supplied to the reaction tank. In the case where magnesium is added as an additive element to the mixture, an aqueous solution containing magnesium is further supplied to the reaction tank. In the case where calcium is added as an additive element to the mixture, an aqueous solution containing calcium is further supplied to the reaction tank. 
     The pH inside the reaction tank is preferably greater than or equal to 9.0 and less than or equal to 11.0, more preferably greater than or equal to 10.0 and less than or equal to 10.5. 
     Note that the process after the step of forming the cobalt compound by a coprecipitation method is the same as that in Embodiment 1; thus, detailed description thereof is omitted here. 
     As shown in  FIG. 3 , the cobalt compound obtained by a coprecipitation method and the lithium compound are mixed to form a mixture  907 . 
     After the mixture  907  is obtained, the first heating is performed. As a firing device used for the first heating, an electric furnace such as rotary kiln can be used. 
     Next, the second heating is performed. As a firing device used for the second heating, an electric furnace such as rotary kiln can be used. 
     The second heating temperature is at least higher than the first heating temperature, and preferably higher than 700° C. and lower than or equal to 1050° C. The time of the second heating is preferably longer than or equal to one hour and shorter than or equal to 20 hours. The second heating is preferably performed in an oxygen atmosphere, and in particular, preferably performed while oxygen is supplied. For example, the flow rate is 10 L/min. per inner capacity 1 L of the furnace. Specifically, the heating is preferably performed while a container containing the mixture  907  is covered with a lid. 
     Then, grinding or crushing is performed with a mortar to loosen the secondary particles fixed one another, and the ground or crushed mixture is collected. Furthermore, classification may be performed using a sieve. 
     Through the above steps, the positive electrode active material  200 A can be formed. Although the same reference numeral  200 A is used for the positive electrode active materials in this embodiment and Embodiment 1, the processes therefor are partly different; therefore, the composition of the positive electrode active material  200 A may be different between this embodiment and Embodiment 1. 
     The process flow in this embodiment is not limited to that shown in  FIG. 3 . 
       FIG. 4  shows a process flow that is a modification example of  FIG. 3 . 
     The process until the cobalt compound is obtained by a coprecipitation method in  FIG. 4  is the same as that shown in  FIG. 3 . After that, second mixing of an additive element, two times heating, and third mixing of an additive element are performed in the example of  FIG. 4 . 
     In  FIG. 4 , after the cobalt compound is obtained as in the case of  FIG. 3 , the cobalt compound, a lithium compound, and the compound  910  are mixed to form a mixture  908 . 
     After the mixture  908  is obtained, the first heating is performed. As a firing device used for the first heating, an electric furnace such as rotary kiln can be used. 
     Next, the second heating is performed. As a firing device used for the second heating, an electric furnace such as rotary kiln can be used. 
     The second heating temperature is at least higher than the first heating temperature, and preferably higher than 700° C. and lower than or equal to 1050° C. The time of the second heating is preferably longer than or equal to one hour and shorter than or equal to 20 hours. The second heating is preferably performed in an oxygen atmosphere, and in particular, preferably performed while oxygen is supplied. For example, the flow rate is 10 L/min. per inner capacity 1 L of the furnace. Specifically, the heating is preferably performed while a container containing the mixture  908  is covered with a lid. 
     Then, grinding or crushing is performed with a mortar to loosen the secondary particles fixed one another, and the ground or crushed mixture is collected. Furthermore, classification may be performed using a sieve. 
     Then, the obtained mixture  909  and the compound  910  are mixed. 
     Then, the third heating is performed. The third heating temperature is at least higher than the first heating temperature, and preferably higher than 700° C. and lower than or equal to 1050° C. The time of the third heating is preferably longer than or equal to one hour and shorter than or equal to 20 hours. The third heating is preferably performed in an oxygen atmosphere, and in particular, preferably performed while oxygen is supplied. For example, the flow rate is 10 L/min. per inner capacity 1 L of the furnace. Specifically, the heating is preferably performed while a container containing the mixture  909  is covered with a lid. 
     Then, grinding or crushing is performed with a mortar to loosen the secondary particles fixed one another, and the ground or crushed mixture is collected. Furthermore, classification may be performed using a sieve. 
     Through the above steps, the positive electrode active material  200 A can be formed. Although the same reference numeral  200 A is used for the positive electrode active materials in  FIG. 3  and  FIG. 4 , the processes therefor are partly different; therefore, the composition of the positive electrode active material  200 A may be different between the formation flows in  FIG. 3  and  FIG. 4 . 
       FIG. 4  shows an example in which mixing of an additive element is performed three times, but one embodiment of the present invention is not particularly limited to this. The number of times of mixing an additive element may be one or plural. Alternatively, different kinds of additive elements may be used in combination. When the formation flow in  FIG. 4  is used, three kinds of additive elements can be added to the positive electrode active material  200 A. 
     This embodiment can be freely combined with any of the other embodiments. 
     Embodiment 4 
     In this embodiment, a coprecipitation apparatus that performs a coprecipitation method in the formation method described in Embodiments 1 to 3 is described. 
     A synthesis apparatus  170  shown in  FIG. 5  includes a reaction tank  171 , and the reaction tank  171  includes a reaction container. A separable flask may be used in a lower portion of the reaction container and a separable cover may be used in an upper portion. The separable flask may be a cylindrical type or a round type. A cylindrical separable flask has a flat bottom. The atmosphere in the reaction tank  171  can be controlled through at least one inlet of the separable cover. For example, the atmosphere preferably contains nitrogen. In that case, it is preferable to make nitrogen flow in the reaction tank  171 . Nitrogen is preferably subjected to bubbling in an aqueous solution  192  in the reaction tank  171 . The synthesis apparatus  170  may include a reflux condenser connected to at least one inlet of the separable cover. This reflux condenser allows an atmosphere gas in the reaction tank  171 , e.g., nitrogen, to be ejected and water to return to the reaction tank  171 . An amount of airflow necessary for ejecting a gas generated by a thermal decomposition reaction caused by heat treatment may flow as an atmosphere in the reaction tank  171 . 
     The steps of a coprecipitation method surrounded by the chain line in  FIG. 1  are described with reference to  FIG. 1  and  FIG. 5 . 
     First, the aqueous solution  894  (a chelating agent) is put in the reaction tank  171 , and then the mixed solution  901  and the aqueous solution  892  (an alkaline solution) are dropped into the reaction tank  171 . The aqueous solution  192  in  FIG. 5  is in the state where dropping has started. Note that the aqueous solution  894  is sometimes referred to as a filling liquid. In some cases, the filling liquid is referred to as an adjusting liquid, and referred to as an aqueous solution before reaction, that is, an aqueous solution in an initial state. 
     Other components of the synthesis apparatus  170  shown in  FIG. 5  are described. The synthesis apparatus  170  includes a stirrer  172 , a stirrer motor  173 , a thermometer  174 , a tank  175 , a tube  176 , a pump  177 , a tank  180 , a tube  181 , a pump  182 , a tank  186 , a tube  187 , a pump  188 , and a control device  190 . 
     The stirrer  172  can stir the aqueous solution  192  in the reaction tank  171 , and the stirrer motor  173  is included as a power source that makes the stirrer  172  rotate. The stirrer  172  includes a paddle-type agitator blade (denoted as a paddle blade), and the paddle blade includes two to six blades. The blade may have an inclination of greater than or equal to 40° and less than or equal to 70°. 
     The thermometer  174  can measure the temperature of the aqueous solution  192 . The temperature of the reaction tank  171  can be controlled using a thermoelectric element such that the temperature of the aqueous solution  192  is constant. An example of the thermoelectric element is a Peltier element. Although not shown, a pH meter is also provided in the reaction tank  171 , and the pH of the aqueous solution  192  can be measured. 
     The tanks can store different raw material aqueous solutions. For example, the tanks can be filled with the mixed solution  901  and the aqueous solution  892 . A tank filled with the aqueous solution  894  serving as a filling liquid may be prepared. A pump is provided for each tank, and with the use of the pump, the raw material aqueous solution can be dropped into the reaction tank  171  through a tube. The amount of the raw material aqueous solution to be dropped, i.e., the solution sending amount can be controlled by the pump. In addition to the pump, a valve may be provided for the tube  176 , and the amount of the raw material aqueous solution to be dropped, i.e., the solution sending amount may be controlled with the valve. 
     The control device  190  is electrically connected to the stirrer motor  173 , the thermometer  174 , the pump  177 , the pump  182 , and the pump  188 , and can control the number of rotations of the stirrer  172 , the temperature of the aqueous solution  192 , and the amount of each raw material aqueous solution to be dropped. 
     The number of rotations of the stirrer  172 , specifically, the number of rotations of the paddle blade is preferably, for example, greater than or equal to 800 rpm and less than or equal to 1200 rpm. The stirring is preferably performed while the aqueous solution  192  is heated at a temperature higher than or equal to 50° C. and lower than or equal to 90° C. In that case, the mixed solution  901  is preferably dropped into the reaction tank  171  at a constant rate. The number of rotations of the paddle blade is not limited to a constant number and can be adjusted as appropriate. For example, the number of rotations can be changed in accordance with the amount of liquid in the reaction tank  171 . Moreover, the dropping rate of the mixed solution  901  can be adjusted. The dropping rate is preferably adjusted in order to keep the pH in the reaction tank  171  constant. The dropping rates may be controlled so that the aqueous solution  892  is dropped when the pH in the reaction tank  171  is changed from a desired pH value during dropping of the mixed solution  901 . The pH value is greater than or equal to 9.0 and less than or equal to 11.0, preferably greater than or equal to 9.8 and less than or equal to 10.3. 
     Through the above process, a reaction product precipitates in the reaction tank  171 . The reaction product includes a cobalt compound. This reaction can be called coprecipitation, and the process is called a coprecipitation process in some cases. 
     This embodiment can be freely combined with any of the other embodiments. 
     Embodiment 5 
     An example of a coin-type secondary battery is described.  FIG. 6A ,  FIG. 6B , and  FIG. 6C  are an exploded perspective view, an external view, and a cross-sectional view of a coin-type (single-layer flat) secondary battery. Coin-type secondary batteries are mainly used in small electronic devices. In this specification, coin-type batteries include button-type batteries. 
     For easy understanding,  FIG. 6A  is a schematic view showing overlap (a vertical relation and a positional relation) between components. Thus,  FIG. 6A  and  FIG. 6B  do not completely correspond with each other. 
     In  FIG. 6A , a positive electrode  304 , a separator  310 , a negative electrode  307 , a spacer  322 , and a washer  312  are overlaid. They are sealed with a negative electrode can  302  and a positive electrode can  301 . Note that a gasket for sealing is not illustrated in  FIG. 6A . The spacer  322  and the washer  312  are used to protect the inside or fix the position of the components inside the cans at the time when the positive electrode can  301  and the negative electrode can  302  are bonded with pressure. For the spacer  322  and the washer  312 , stainless steel or an insulating material is used. 
     The positive electrode  304  is a stack in which a positive electrode active material layer  306  is formed over a positive electrode current collector  305 . 
     To prevent a short circuit between the positive electrode and the negative electrode, the separator  310  and a ring-shaped insulator  313  are provided to cover the side surface and top surface of the positive electrode  304 . The separator  310  has a larger flat surface area than the positive electrode  304 . 
       FIG. 6B  is a perspective view of a completed coin-type secondary battery. 
     In a coin-type secondary battery  300 , the positive electrode can  301  doubling as a positive electrode terminal and the negative electrode can  302  doubling as a negative electrode terminal are insulated from each other and sealed by a gasket  303  made of polypropylene. The positive electrode  304  includes the positive electrode current collector  305  and the positive electrode active material layer  306  provided in contact with the positive electrode current collector  305 . The negative electrode  307  includes a negative electrode current collector  308  and a negative electrode active material layer  309  provided in contact with the negative electrode current collector  308 . The negative electrode  307  is not limited to having a stacked-layer structure, and lithium metal foil or lithium-aluminum alloy foil may be used. 
     Note that only one surface of each of the positive electrode  304  and the negative electrode  307  used for the coin-type secondary battery  300  is provided with an active material layer. 
     For the positive electrode can  301  and the negative electrode can  302 , a metal having corrosion resistance to an electrolyte solution, such as nickel, aluminum, or titanium, an alloy of such a metal, or an alloy of such a metal and another metal (e.g., stainless steel) can be used. The positive electrode can  301  and the negative electrode can  302  are preferably covered with nickel and aluminum in order to prevent corrosion due to the electrolyte solution, for example. The positive electrode can  301  and the negative electrode can  302  are electrically connected to the positive electrode  304  and the negative electrode  307 , respectively. 
     The negative electrode  307 , the positive electrode  304 , and the separator  310  are immersed in the electrolyte solution. Then, as illustrated in  FIG. 6C , the positive electrode  304 , the separator  310 , the negative electrode  307 , and the negative electrode can  302  are stacked in this order with the positive electrode can  301  positioned at the bottom, and the positive electrode can  301  and the negative electrode can  302  are bonded with pressure with the gasket  303  therebetween. In this manner, the coin-type secondary battery  300  is manufactured. 
     The coin-type secondary battery  300  can have high capacity, high charge and discharge capacity, and excellent cycle performance. Note that in the case where the coin-type secondary battery  300  is an all-solid-state battery, the separator  310  between the negative electrode  307  and the positive electrode  304  can be omitted. 
     [Cylindrical Secondary Battery] 
     An example of a cylindrical secondary battery is described with reference to  FIG. 7A . As illustrated in  FIG. 7A , a cylindrical secondary battery  616  includes a positive electrode cap (battery cap)  601  on the top surface and a battery can (outer can)  602  on the side surface and bottom surface. The positive electrode cap  601  and the battery can (outer can)  602  are insulated from each other by a gasket (insulating gasket)  610 . 
       FIG. 7B  schematically illustrates a cross section of a cylindrical secondary battery. The cylindrical secondary battery illustrated in  FIG. 7B  includes the positive electrode cap (battery cap)  601  on the top surface and the battery can (outer can)  602  on the side and bottom surfaces. The positive electrode cap  601  and the battery can (outer can)  602  are insulated from each other by the gasket (insulating gasket)  610 . 
     Inside the battery can  602  having a hollow cylindrical shape, a battery element in which a strip-like positive electrode  604  and a strip-like negative electrode  606  are wound with a strip-like separator  605  located therebetween is provided. Although not illustrated, the battery element is wound around the central axis. One end of the battery can  602  is close and the other end thereof is open. For the battery can  602 , a metal having corrosion resistance to an electrolyte solution typified by nickel, aluminum, or titanium, an alloy of such a metal, or an alloy of such a metal and another metal (e.g., stainless steel) can be used. The battery can  602  is preferably covered with nickel and aluminum in order to prevent corrosion due to the electrolyte solution. Inside the battery can  602 , the battery element in which the positive electrode, the negative electrode, and the separator are wound is provided between a pair of insulating plates  608  and  609  that face each other. The inside of the battery can  602  provided with the battery element is filled with a nonaqueous electrolyte solution (not illustrated). As the nonaqueous electrolyte solution, an electrolyte solution similar to that for the coin-type secondary battery can be used. 
     Since the positive electrode and the negative electrode of the cylindrical storage battery are wound, active materials are preferably formed on both sides of the current collectors. Although  FIGS. 7A to 7D  each illustrate the secondary battery  616  in which the height of the cylinder is larger than the diameter of the cylinder, one embodiment of the present invention is not limited thereto. In a secondary battery, the diameter of the cylinder may be larger than the height of the cylinder. Such a structure can reduce the size of a secondary battery, for example. 
     The positive electrode active material  200 A shown in Embodiment 1 is used in the positive electrode  604 , whereby the cylindrical secondary battery  616  can have high capacity, high charge and discharge capacity, and excellent cycle performance. 
     A positive electrode terminal (positive electrode current collecting lead)  603  is connected to the positive electrode  604 , and a negative electrode terminal (negative electrode current collecting lead)  607  is connected to the negative electrode  606 . Both the positive electrode terminal  603  and the negative electrode terminal  607  can be formed using a metal material of aluminum. The positive electrode terminal  603  and the negative electrode terminal  607  are resistance-welded to a safety valve mechanism  613  and the bottom of the battery can  602 , respectively. The safety valve mechanism  613  is electrically connected to the positive electrode cap  601  through a positive temperature coefficient (PTC) element  611 . The safety valve mechanism  613  cuts off electrical connection between the positive electrode cap  601  and the positive electrode  604  when the internal pressure of the battery exceeds a predetermined threshold. The PTC element  611 , which is a thermally sensitive resistor whose resistance increases as temperature rises, limits the amount of current by increasing the resistance, in order to prevent abnormal heat generation. Barium titanate (BaTiO 3 )-based semiconductor ceramic can be used for the PTC element. 
       FIG. 7C  illustrates an example of a power storage system  615 . The power storage system  615  includes a plurality of secondary batteries  616 . The positive electrodes of the secondary batteries are in contact with and electrically connected to conductors  624  isolated by an insulator  625 . The conductor  624  is electrically connected to a control circuit  620  through a wiring  623 . The negative electrodes of the secondary batteries are electrically connected to the control circuit  620  through a wiring  626 . As the control circuit  620 , a protection circuit for preventing overcharge or overdischarge can be used. 
       FIG. 7D  illustrates an example of the power storage system  615 . The power storage system  615  includes a plurality of secondary batteries  616 , and the plurality of secondary batteries  616  are sandwiched between a conductive plate  628  and a conductive plate  614 . The plurality of secondary batteries  616  are electrically connected to the conductive plate  628  and the conductive plate  614  through a wiring  627 . The plurality of secondary batteries  616  may be connected in parallel or connected in series. Alternatively, the plurality of secondary batteries  616  may be connected in parallel and then connected in series. With the power storage system  615  including the plurality of secondary batteries  616 , large electric power can be extracted. 
     The plurality of secondary batteries  616  may be connected in series after being connected in parallel. 
     A temperature control device may be provided between the plurality of secondary batteries  616 . The secondary batteries  616  can be cooled with the temperature control device when overheated, whereas the secondary batteries  616  can be heated with the temperature control device when cooled too much. Thus, the performance of the power storage system  615  is less likely to be influenced by the outside temperature. 
     In  FIG. 7D , the power storage system  615  is electrically connected to the control circuit  620  through a wiring  621  and a wiring  622 . The wiring  621  is electrically connected to the positive electrodes of the plurality of secondary batteries  616  through the conductive plate  628 . The wiring  622  is electrically connected to the negative electrodes of the plurality of secondary batteries  616  through the conductive plate  614 . 
     Other Structure Examples of Secondary Battery 
     Structure examples of secondary batteries are described with reference to  FIGS. 8A to 8C  and  FIGS. 9A to 9C . 
     A secondary battery  913  illustrated in  FIG. 8A  includes a wound body  950  provided with a terminal  951  and a terminal  952  inside a housing  930 . The wound body  950  is immersed in an electrolyte solution inside the housing  930 . The terminal  952  is in contact with the housing  930 . The use of an insulator inhibits contact between the terminal  951  and the housing  930 . Note that in  FIG. 8A , the housing  930  divided into two pieces is illustrated for convenience; however, in the actual structure, the wound body  950  is covered with the housing  930 , and the terminal  951  and the terminal  952  extend to the outside of the housing  930 . For the housing  930 , a metal material (e.g., aluminum) or a resin material can be used. 
     Note that as illustrated in  FIG. 8B , the housing  930  in  FIG. 8A  may be formed using a plurality of materials. For example, in the secondary battery  913  in  FIG. 8B , a housing  930   a  and a housing  930   b  are attached to each other, and the wound body  950  is provided in a region surrounded by the housing  930   a  and the housing  930   b.    
     For the housing  930   a , an insulating material typified by an organic resin can be used. In particular, when an insulating material typified by an organic resin is used for the side on which an antenna is formed, blocking of an electric field by the secondary battery  913  can be inhibited. When an electric field is not significantly blocked by the housing  930   a , an antenna may be provided inside the housing  930   a . For the housing  930   b , a metal material can be used, for example. 
       FIG. 8C  illustrates the structure of the wound body  950 . The wound body  950  includes a negative electrode  931 , a positive electrode  932 , and separators  933 . The wound body  950  is obtained by winding a sheet of a stack in which the negative electrode  931  and the positive electrode  932  overlap with the separator  933  therebetween. Note that a plurality of stacks each including the negative electrode  931 , the positive electrode  932 , and the separators  933  may be overlaid. 
     As illustrated in  FIGS. 9A to 9C , the secondary battery  913  may include a wound body  950   a . The wound body  950   a  illustrated in  FIG. 9A  includes the negative electrode  931 , the positive electrode  932 , and the separators  933 . The negative electrode  931  includes a negative electrode active material layer  931   a . The positive electrode  932  includes a positive electrode active material layer  932   a.    
     The positive electrode active material  200 A shown in Embodiment 1 is used in the positive electrode  932 , whereby the secondary battery  913  can have high capacity, high charge and discharge capacity, and excellent cycle performance. 
     The separator  933  has a larger width than the negative electrode active material layer  931   a  and the positive electrode active material layer  932   a , and is wound to overlap the negative electrode active material layer  931   a  and the positive electrode active material layer  932   a . In terms of safety, the width of the negative electrode active material layer  931   a  is preferably larger than that of the positive electrode active material layer  932   a . The wound body  950   a  having such a shape is preferable because of its high degree of safety and high productivity. 
     As illustrated in  FIG. 9B , the negative electrode  931  is electrically connected to the terminal  951 . The terminal  951  is electrically connected to a terminal  911   a . The positive electrode  932  is electrically connected to the terminal  952 . The terminal  952  is electrically connected to a terminal  911   b.    
     As illustrated in  FIG. 9C , the wound body  950   a  and an electrolyte solution are covered with the housing  930 , whereby the secondary battery  913  is completed. The housing  930  is preferably provided with a safety valve and an overcurrent protection element. A safety valve is a valve to be released by a predetermined internal pressure of the housing  930  in order to prevent the battery from exploding. 
     As illustrated in  FIG. 9B , the secondary battery  913  may include a plurality of wound bodies  950   a . The use of the plurality of wound bodies  950   a  enables the secondary battery  913  to have higher charge and discharge capacity. The description of the secondary battery  913  in  FIGS. 8A to 8C  can be referred to for the other components of the secondary battery  913  in  FIGS. 9A and 9B . 
     &lt;Laminated Secondary Battery&gt; 
     Next, examples of the appearance of a laminated secondary battery are shown in  FIGS. 10A and 10B .  FIGS. 10A and 10B  each illustrate a positive electrode  503 , a negative electrode  506 , a separator  507 , an exterior body  509 , a positive electrode lead electrode  510 , and a negative electrode lead electrode  511 . 
       FIG. 11A  illustrates the appearance of the positive electrode  503  and the negative electrode  506 . The positive electrode  503  includes a positive electrode current collector  501 , and a positive electrode active material layer  502  is formed on a surface of the positive electrode current collector  501 . The positive electrode  503  also includes a region where the positive electrode current collector  501  is partly exposed (hereinafter referred to as a tab region). The negative electrode  506  includes a negative electrode current collector  504 , and a negative electrode active material layer  505  is formed on a surface of the negative electrode current collector  504 . The negative electrode  506  also includes a region where the negative electrode current collector  504  is partly exposed, that is, a tab region. The areas and the shapes of the tab regions included in the positive electrode and the negative electrode are not limited to those illustrated in  FIG. 11A . 
     &lt;Method for Manufacturing Laminated Secondary Battery&gt; 
     Here, an example of a method for manufacturing the laminated secondary battery having the appearance illustrated in  FIG. 10A  will be described with reference to  FIGS. 11B and 11C . 
     First, the negative electrode  506 , the separator  507 , and the positive electrode  503  are stacked.  FIG. 11B  illustrates the negative electrodes  506 , the separators  507 , and the positive electrodes  503  that are stacked. The secondary battery described here as an example includes five negative electrodes and four positive electrodes. The component at this stage can also be referred to as a stack including the negative electrodes, the separators, and the positive electrodes. Next, the tab regions of the positive electrodes  503  are bonded to each other, and the positive electrode lead electrode  510  is bonded to the tab region of the positive electrode on the outermost surface. The bonding can be performed by ultrasonic welding. In a similar manner, the tab regions of the negative electrodes  506  are bonded to each other, and the negative electrode lead electrode  511  is bonded to the tab region of the negative electrode on the outermost surface. 
     Then, the negative electrodes  506 , the separators  507 , and the positive electrodes  503  are placed over the exterior body  509 . 
     Subsequently, the exterior body  509  is folded along a dashed line as illustrated in  FIG. 11C . Then, the outer edges of the exterior body  509  are bonded to each other. The bonding can be performed by thermocompression. At this time, a part (or one side) of the exterior body  509  is left unbonded (to provide an inlet) so that an electrolyte solution can be introduced later. 
     Next, the electrolyte solution (not illustrated) is introduced into the exterior body  509  from the inlet of the exterior body  509 . The electrolyte solution is preferably introduced in a reduced pressure atmosphere or in an inert atmosphere. Lastly, the inlet is sealed by bonding. In this manner, the laminated secondary battery  500  can be manufactured. 
     The positive electrode active material  200 A shown in Embodiment 1 is used in the positive electrodes  503 , whereby the secondary battery  500  can have high capacity, high charge and discharge capacity, and excellent cycle performance. 
     Examples of Battery Pack 
     Examples of a secondary battery pack of one embodiment of the present invention that is capable of wireless charging using an antenna will be described with reference to  FIGS. 12A to 12C . 
       FIG. 12A  illustrates the appearance of a secondary battery pack  531  that has a rectangular solid shape with a small thickness (also referred to as a flat plate shape with a certain thickness).  FIG. 12B  illustrates the structure of the secondary battery pack  531 . The secondary battery pack  531  includes a circuit board  540  and a secondary battery  513 . A label  529  is attached to the secondary battery  513 . The circuit board  540  is fixed by a sealant  515 . The secondary battery pack  531  also includes an antenna  517 . 
     As for the internal structure of the secondary battery  513 , the secondary battery  513  may include a wound body or a stack. 
     In the secondary battery pack  531 , a control circuit  590  is provided over the circuit board  540  as illustrated in  FIG. 12B , for example. The circuit board  540  is electrically connected to a terminal  514 . Moreover, the circuit board  540  is electrically connected to the antenna  517  and a positive electrode lead and a negative electrode lead  551  and  552  of the secondary battery  513 . 
     Alternatively, as illustrated in  FIG. 12C , a circuit system  590   a  provided over the circuit board  540  and a circuit system  590   b  electrically connected to the circuit board  540  through the terminal  514  may be included. 
     Note that the shape of the antenna  517  is not limited to a coil shape and may be a linear shape or a plate shape, for example. Furthermore, an antenna typified by a planar antenna, an aperture antenna, a traveling-wave antenna, an EH antenna, a magnetic-field antenna, or a dielectric antenna may be used. Alternatively, the antenna  517  may be a flat-plate conductor. The flat-plate conductor can serve as one of conductors for electric field coupling. That is, the antenna  517  can function as one of two conductors of a capacitor. Thus, electric power can be transmitted and received not only by an electromagnetic field or a magnetic field but also by an electric field. 
     The secondary battery pack  531  includes a layer  519  between the antenna  517  and the secondary battery  513 . The layer  519  has a function of blocking an electromagnetic field from the secondary battery  513 , for example. As the layer  519 , a magnetic material can be used, for example. 
     The contents in this embodiment can be freely combined with the contents in any of the other embodiments. 
     Embodiment 6 
     This embodiment will describe an example where an all-solid-state battery is manufactured using the positive electrode active material  200 A shown in Embodiment 1. 
     As illustrated in  FIG. 13A , a secondary battery  400  of one embodiment of the present invention includes a positive electrode  410 , a solid electrolyte layer  420 , and a negative electrode  430 . 
     The positive electrode  410  includes a positive electrode current collector  413  and a positive electrode active material layer  414 . The positive electrode active material layer  414  includes a positive electrode active material  411  and a solid electrolyte  421 . The positive electrode active material  200 A shown in Embodiment 1 is used as the positive electrode active material  411 . The positive electrode active material layer  414  may also include a conductive additive and a binder. 
     The solid electrolyte layer  420  includes the solid electrolyte  421 . The solid electrolyte layer  420  is positioned between the positive electrode  410  and the negative electrode  430  and is a region that includes neither the positive electrode active material  411  nor a negative electrode active material  431 . 
     The negative electrode  430  includes a negative electrode current collector  433  and a negative electrode active material layer  434 . The negative electrode active material layer  434  includes the negative electrode active material  431  and the solid electrolyte  421 . The negative electrode active material layer  434  may also include a conductive additive and a binder. Note that when metallic lithium is used as the negative electrode active material  431 , metallic lithium does not need to be processed into particles; thus, the negative electrode  430  that does not include the solid electrolyte  421  can be formed, as illustrated in  FIG. 13B .  FIG. 13B  shows an example in which the negative electrode active material  431  is deposited by a sputtering method. The use of metallic lithium for the negative electrode  430  is preferable, in which case the energy density of the secondary battery  400  can be increased. 
     As the solid electrolyte  421  included in the solid electrolyte layer  420 , a sulfide-based solid electrolyte, an oxide-based solid electrolyte, or a halide-based solid electrolyte can be used, for example. 
     Examples of the sulfide-based solid electrolyte include a thio-LISICON-based material (e.g., Li 10 GeP 2 S 12  and Li 3.25 Ge 0.25 P 0.75 S 4 ), sulfide glass (e.g., 70Li 2 S.30P 2 S 5 , 30Li 2 S.26B 2 S 3 .44LiI, 63Li 2 S.36SiS 2 .1Li 3 PO 4 , 57Li 2 S.38SiS 2 .5Li 4 SiO 4 , and 50Li 2 S.50GeS 2 ), and sulfide-based crystallized glass (e.g., Li 7 P 3 S 11  and Li 3.25 P 0.95 S 4 ). The sulfide-based solid electrolyte has advantages such as high conductivity of some materials, low-temperature synthesis, and ease of maintaining a path for electrical conduction after charging and discharging because of its relative softness. 
     Examples of the oxide-based solid electrolyte include a material with a perovskite crystal structure (e.g., La 2/3−x Li 3 xTiO 3 ), a material with a NASICON crystal structure (e.g., Li 1-y Al y Ti 2-y (PO 4 ) 3 ), a material with a garnet crystal structure (e.g., La 7 La 3 Zr 2 O 12 ), a material with a LISICON crystal structure (e.g., Li 14 ZnGe 4 O 16 ), LLZO (Li 7 La 3 Zr 2 O 12 ), oxide glass (e.g., Li 3 PO 4 —Li 4 SiO 4  and 50Li 4 SiO 4 .50Li 3 BO 3 ), and oxide-based crystallized glass (e.g., Li 1.07 Al 0.69 Ti 1.46 (PO 4 ) 3  and Li 1.5 Al 0.5 Ge 1.5 (PO 4 ) 3 ). The oxide-based solid electrolyte has an advantage of stability in the air. 
     Examples of the halide-based solid electrolyte include LiAlCl 4 , Li 3 InBr 6 , LiF, LiCl, LiBr, and LiI. Moreover, a composite material in which pores of porous aluminum oxide or porous silica are filled with such a halide-based solid electrolyte can be used as the solid electrolyte. 
     Alternatively, different solid electrolytes may be mixed and used. 
     In particular, Li 1+x Al x Ti 2−x (PO 4 ) 3  (0≤x≤1) having a NASICON crystal structure (hereinafter LATP) is preferable because LATP contains aluminum and titanium, each of which is the element the positive electrode active material used in the secondary battery  400  of one embodiment of the present invention is allowed to contain, and thus a synergistic effect of improving the cycle performance is expected. Moreover, higher productivity due to the reduction in the number of steps is expected. Note that in this specification, a material having a NASICON crystal structure refers to a compound that is represented by M 2 (XO 4 ) 3  (M: transition metal; X: S, P, As, Mo, or W) and has a structure in which MO 6  octahedra and XO 4  tetrahedra that share common corners are arranged three-dimensionally. 
     [Exterior Body and Shape of Secondary Battery] 
     An exterior body of the secondary battery  400  of one embodiment of the present invention can employ a variety of materials and have a variety of shapes, and preferably has a function of applying pressure to the positive electrode, the solid electrolyte layer, and the negative electrode. 
       FIGS. 14A to 14C  show an example of a cell for evaluating materials of an all-solid-state battery. 
       FIG. 14A  is a schematic cross-sectional view of the evaluation cell. The evaluation cell includes a lower component  761 , an upper component  762 , and a fixation screw/butterfly nut  764  for fixing these components. By rotating a pressure screw  763 , an electrode plate  753  is pressed to fix an evaluation material. An insulator  766  is provided between the lower component  761  and the upper component  762  that are made of a stainless steel material. An  0  ring  765  for hermetic sealing is provided between the upper component  762  and the pressure screw  763 . 
     The evaluation material is placed on an electrode plate  751 , surrounded by an insulating tube  752 , and pressed from above by the electrode plate  753 .  FIG. 14B  is an enlarged perspective view of the evaluation material and its vicinity. 
     A stack of a positive electrode  750   a , a solid electrolyte layer  750   b , and a negative electrode  750   c  is shown here as an example of the evaluation material, and its cross section is shown in  FIG. 14C . Note that the same portions in  FIGS. 14A to 14C  are denoted by the same reference numerals. 
     The electrode plate  751  and the lower component  761  that are electrically connected to the positive electrode  750   a  correspond to a positive electrode terminal. The electrode plate  753  and the upper component  762  that are electrically connected to the negative electrode  750   c  correspond to a negative electrode terminal. The electric resistance can be measured while pressure is applied to the evaluation material through the electrode plate  751  and the electrode plate  753 . 
     The exterior body of the secondary battery of one embodiment of the present invention is preferably a package having excellent airtightness. For example, a ceramic package or a resin package can be used. The exterior body is sealed preferably in a closed atmosphere where the outside air is blocked, for example, in a glove box. 
       FIG. 15A  is a perspective view of a secondary battery of one embodiment of the present invention that has an exterior body and a shape different from those in  FIGS. 14A to 14C . The secondary battery in  FIG. 15A  includes external electrodes  771  and  772  and is sealed with an exterior body including a plurality of package components. 
       FIG. 15B  illustrates an example of a cross section along the dashed-dotted line in  FIG. 15A . A stack including the positive electrode  750   a , the solid electrolyte layer  750   b , and the negative electrode  750   c  is surrounded and sealed by a package component  770   a  including an electrode layer  773   a  on a flat plate, a frame-like package component  770   b , and a package component  770   c  including an electrode layer  773   b  on a flat plate. For the package components  770   a ,  770   b , and  770   c , an insulating material such as a resin material or ceramic can be used. 
     The external electrode  771  is electrically connected to the positive electrode  750   a  through the electrode layer  773   a  and functions as a positive electrode terminal. The external electrode  772  is electrically connected to the negative electrode  750   c  through the electrode layer  773   b  and functions as a negative electrode terminal. 
     The use of the positive electrode active material  200 A shown in Embodiment 1 achieves an all-solid-state secondary battery having a high energy density and favorable output characteristics. 
     The contents in this embodiment can be combined with the contents in any of the other embodiments as appropriate. 
     Embodiment 7 
     An example which is different from the cylindrical secondary battery in  FIG. 7D  is described in this embodiment. An example in which the present invention is applied to an electric vehicle (EV) is described with reference to  FIG. 16C . 
     The electric vehicle is provided with first batteries  1301   a  and  1301   b  as main secondary batteries for driving and a second battery  1311  that supplies electric power to an inverter  1312  for starting a motor  1304 . The second battery  1311  is also referred to as a cranking battery and a starter battery. The second battery  1311  specifically needs high output and does not necessarily have high capacity, and the capacity of the second battery  1311  is lower than that of the first batteries  1301   a  and  1301   b.    
     The internal structure of the first battery  1301   a  may be the wound structure illustrated in  FIG. 8A  or  FIG. 9C  or the stacked structure illustrated in  FIG. 10A  or  FIG. 10B . Alternatively, the first battery  1301   a  may be the all-solid-state battery in Embodiment 5. Using the all-solid-state battery in Embodiment 5 as the first battery  1301   a  achieves high capacity, a high degree of safety, and reduction in size and weight. 
     Although this embodiment shows an example where the two first batteries  1301   a  and  1301   b  are connected in parallel, three or more batteries may be connected in parallel. In the case where the first battery  1301   a  can store sufficient electric power, the first battery  1301   b  may be omitted. By constituting a battery pack including a plurality of secondary batteries, large electric power can be extracted. The plurality of secondary batteries may be connected in parallel, connected in series, or connected in series after being connected in parallel. A plurality of secondary batteries can be collectively referred to as an assembled battery. 
     An in-vehicle secondary battery includes a service plug or a circuit breaker that can cut off high voltage without the use of equipment in order to cut off electric power from a plurality of secondary batteries. The first battery  1301   a  is provided with such a service plug or a circuit breaker. 
     Electric power from the first batteries  1301   a  and  1301   b  is mainly used to rotate the motor  1304  and is also supplied to in-vehicle parts for 42 V (such as an electric power steering  1307 , a heater  1308 , and a defogger  1309 ) through a DC-DC circuit  1306 . In the case where there is a rear motor  1317  for the rear wheels, the first battery  1301   a  is used to rotate the rear motor  1317 . 
     The second battery  1311  supplies electric power to in-vehicle parts for 14V (such as an audio  1313 , a power window  1314 , and a lamp  1315 ) through a DC-DC circuit  1310 . 
     The first battery  1301   a  is described with reference to  FIG. 16A . 
       FIG. 16A  illustrates an example in which nine rectangular secondary batteries  1300  form one battery pack  1415 . The nine rectangular secondary batteries  1300  are connected in series; one electrode of each battery is fixed by a fixing portion  1413  made of an insulator, and the other electrode of each battery is fixed by a fixing portion  1414  made of an insulator. Although this embodiment shows an example in which the secondary batteries are fixed by the fixing portions  1413  and  1414 , they may be stored in a battery container box (also referred to as a housing). Since a vibration or a jolt is assumed to be given to the vehicle from the outside (a road surface), the plurality of secondary batteries are preferably fixed by the fixing portions  1413  and  1414  and a battery container box. Furthermore, the one electrode of each battery is electrically connected to a control circuit portion  1320  through a wiring  1421 . The other electrode of each battery is electrically connected to the control circuit portion  1320  through a wiring  1422 . 
       FIG. 16B  shows an example of a block diagram of the battery pack  1415  illustrated in  FIG. 16A . 
     The control circuit portion  1320  includes a switch portion  1324  that includes at least a switch for preventing overcharge and a switch for preventing overdischarge, a control circuit  1322  for controlling the switch portion  1324 , and a portion for measuring the voltage of the first battery  1301   a . The control circuit portion  1320  is set to have the upper limit voltage and the lower limit voltage of the secondary battery used, and imposes the upper limit of current from the outside, and the upper limit of output current to the outside. The range from the lower limit voltage to the upper limit voltage of the secondary battery falls within the recommended voltage range. When a voltage falls outside the range, the switch portion  1324  operates and functions as a protection circuit. 
     The control circuit portion  1320  can also be referred to as a protection circuit because it controls the switch portion  1324  to prevent overdischarge and overcharge. For example, when the control circuit  1322  detects a voltage that is likely to cause overcharge, current is interrupted by turning off the switch in the switch portion  1324 . Furthermore, a function of interrupting current in accordance with a temperature rise may be set by providing a PTC element in the charge and discharge path. The control circuit portion  1320  includes an external terminal  1325  (+IN) and an external terminal  1326  (−IN). 
     The switch portion  1324  can be formed by a combination of an n-channel transistor and a p-channel transistor. The switch portion  1324  is not limited to including a switch having a Si transistor using single crystal silicon; the switch portion  1324  may be formed using a power transistor containing germanium (Ge), silicon germanium (SiGe), gallium arsenide (GaAs), gallium aluminum arsenide (GaAlAs), indium phosphide (InP), silicon carbide (SiC), zinc selenide (ZnSe), gallium nitride (GaN), or gallium oxide (GaO x , where x is a real number greater than 0). 
     The first batteries  1301   a  and  1301   b  mainly supply electric power to in-vehicle parts for 42 V (for a high-voltage system), and the second battery  1311  supplies electric power to in-vehicle parts for 14 V (for a low-voltage system). A lead battery is usually used for the second battery  1311  due to cost advantage. 
     In this embodiment, an example in which a lithium-ion secondary battery is used as both the first battery  1301   a  and the second battery  1311  is described. As the second battery  1311 , a lead storage battery, an all-solid-state battery, or an electric double layer capacitor may alternatively be used. For example, the all-solid-state battery in Embodiment 3 may be used. Using the all-solid-state battery in Embodiment 3 as the second battery  1311  achieves high capacity, a high degree of safety, and reduction in size and weight. 
     Regenerative energy generated by rolling of tires  1316  is transmitted to the motor  1304  through a gear  1305 , and is stored in the second battery  1311  through a motor controller  1303 , a battery controller  1302 , and the control circuit portion  1321 . Alternatively, the regenerative energy is stored in the first battery  1301   a  through the battery controller  1302  and the control circuit portion  1320 . Alternatively, the regenerative energy is stored in the first battery  1301   b  through the battery controller  1302  and the control circuit portion  1320 . For efficient charging with regenerative energy, the first batteries  1301   a  and  1301   b  are preferably capable of fast charging. 
     The battery controller  1302  can set the charging voltage and charge current of the first batteries  1301   a  and  1301   b . The battery controller  1302  can set charge conditions in accordance with charging characteristics of a secondary battery used, so that fast charging can be performed. 
     Although not illustrated, when the electric vehicle is connected to an external charger, a plug of the charger or a connection cable of the charger is electrically connected to the battery controller  1302 . Electric power supplied from the external charger is stored in the first batteries  1301   a  and  1301   b  through the battery controller  1302 . Some chargers are provided with a control circuit, in which case the function of the battery controller  1302  is not used; to prevent overcharge, the first batteries  1301   a  and  1301   b  are preferably charged through the control circuit portion  1320 . In addition, a plug of the charger or a connection cable of the charger is sometimes provided with a control circuit. The control circuit portion  1320  is also referred to as an electronic control unit (ECU). The ECU is connected to a controller area network (CAN) provided in the electric vehicle. The CAN is a type of a serial communication standard used as an in-vehicle LAN. The ECU includes a microcomputer. Moreover, the ECU uses a CPU or a GPU. 
     External chargers installed at charging stations have a 100 V outlet, a 200 V outlet, or a three-phase 200V outlet with 50 kW. Furthermore, charging can be performed by electric power supplied from external charging equipment with a contactless power feeding method. 
     For fast charging, secondary batteries that can withstand charging at high voltage have been desired to perform charging in a short time. 
     The above-described secondary battery in this embodiment uses the positive electrode active material  200 A shown in Embodiment 1. Moreover, it is possible to achieve a secondary battery in which graphene is used as a conductive additive, the electrode layer is formed thick to suppress a reduction in capacity while increasing the loading amount, and the electrical characteristics are significantly improved in synergy with maintenance of high capacity. This secondary battery is particularly effectively used in a vehicle and can achieve a vehicle that has a long range, specifically a driving range per charge of 500 km or greater, without increasing the proportion of the weight of the secondary battery to the weight of the entire vehicle. 
     Specifically, in the secondary battery in this embodiment, the use of the positive electrode active material  200 A shown in Embodiment 1 can increase the operating voltage, and the increase in charging voltage can increase the available capacity. Moreover, using the positive electrode active material  200 A shown in Embodiment 1 in the positive electrode can provide an automotive secondary battery having excellent cycle performance. 
     Next, examples in which the secondary battery of one embodiment of the present invention is mounted on a vehicle, typically a transport vehicle, will be described. 
     Mounting the secondary battery illustrated in any of  FIG. 7D ,  FIG. 9C , and  FIG. 16A  on vehicles can achieve next-generation clean energy vehicles such as hybrid vehicles (HVs), electric vehicles (EVs), and plug-in hybrid vehicles (PHVs). The secondary battery can also be mounted on transport vehicles such as agricultural machines, motorized bicycles including motor-assisted bicycles, motorcycles, electric wheelchairs, electric carts, boats and ships, submarines, aircraft such as fixed-wing aircraft and rotary-wing aircraft, rockets, artificial satellites, space probes, planetary probes, and spacecraft. The secondary battery of one embodiment of the present invention can have high capacity. Thus, the secondary battery of one embodiment of the present invention is suitable for reduction in size and weight and is preferably used in transport vehicles. 
       FIGS. 17A to 17D  illustrate examples of transport vehicles using one embodiment of the present invention. An automobile  2001  illustrated in  FIG. 17A  is an electric vehicle that runs on the power of an electric motor. Alternatively, the automobile  2001  is a hybrid electric vehicle capable of driving using either an electric motor or an engine as appropriate. In the case where the secondary battery is mounted on the vehicle, the secondary battery exemplified in Embodiment 4 is provided at one position or several positions. The automobile  2001  illustrated in  FIG. 17A  includes a battery pack  2200 , and the battery pack includes a secondary battery module in which a plurality of secondary batteries are connected to each other. Moreover, the battery pack preferably includes a charge control device that is electrically connected to the secondary battery module. 
     The automobile  2001  can be charged when the secondary battery included in the automobile  2001  is supplied with electric power through external charging equipment by a plug-in system or a contactless power feeding system. In charging, a given method such as CHAdeMO (registered trademark) or Combined Charging System can be employed as a charging method, the standard of a connector, and the like as appropriate. A charging device may be a charging station provided in a commerce facility or a power source in a house. For example, with the use of the plug-in technique, the power storage device mounted on the automobile  2001  can be charged by being supplied with electric power from outside. The charging can be performed by converting AC electric power into DC electric power through a converter typified by an AC-DC converter. 
     Although not illustrated, the vehicle may include a power receiving device so that it can be charged by being supplied with electric power from an above-ground power transmitting device in a contactless manner. In the case of the contactless power feeding system, by fitting a power transmitting device in a road or an exterior wall, charging can be performed not only when the vehicle is stopped but also when driven. In addition, the contactless power feeding system may be utilized to perform transmission and reception of electric power between two vehicles. Furthermore, a solar cell may be provided in the exterior of the vehicle to charge the secondary battery when the vehicle stops and moves. To supply electric power in such a contactless manner, an electromagnetic induction method or a magnetic resonance method can be used. 
       FIG. 17B  illustrates a large transporter  2002  having a motor controlled by electricity as an example of a transport vehicle. A secondary battery module of the transporter  2002  includes a cell unit of four secondary batteries with a nominal voltage of 3.0 V or higher and 5.0 V or lower, for example, and 48 cells are connected in series to have a maximum voltage of 170 V. A battery pack  2201  has the same function as that in  FIG. 17A  except, for example, the number of secondary batteries configuring the secondary battery module; thus, the description is omitted. 
       FIG. 17C  illustrates a large transportation vehicle  2003  having a motor controlled by electricity as an example. A secondary battery module of the transportation vehicle  2003  has more than 100 secondary batteries with a nominal voltage of 3.0 V or higher and 5.0 V or lower connected in series, and the maximum voltage is 600 V. With the use of the positive electrode using the positive electrode active material  200 A shown in Embodiment 1, a secondary battery having favorable rate characteristics and charge and discharge cycle performance can be fabricated, which can contribute to higher performance and a longer life of the transport vehicle  2003 . A battery pack  2202  has the same function as that in  FIG. 17A  except the number of secondary batteries configuring the secondary battery module; thus, the description is omitted. 
       FIG. 17D  illustrates an aircraft  2004  having a combustion engine as an example. The aircraft  2004  illustrated in  FIG. 17D  is regarded as a transport vehicle because it has wheels for takeoff and landing, and includes a battery pack  2203  that includes a charge control device and a secondary battery module configured by connecting a plurality of secondary batteries. 
     The secondary battery module of the aircraft  2004  has eight 4 V secondary batteries connected in series and has a maximum voltage of 32 V, for example. The battery pack  2203  has the same function as that in  FIG. 17A  except, for example, the number of secondary batteries configuring the secondary battery module; thus, the description is omitted. 
     The contents in this embodiment can be combined with the contents in any of the other embodiments as appropriate. 
     Embodiment 8 
     In this embodiment, examples in which the secondary battery of one embodiment of the present invention is mounted on a building will be described with reference to  FIGS. 18A and 18B . 
     A house illustrated in  FIG. 18A  includes a power storage device  2612  including the secondary battery of one embodiment of the present invention and a solar panel  2610 . The power storage device  2612  is electrically connected to the solar panel  2610  through a wiring  2611 . The power storage device  2612  may be electrically connected to a ground-based charging device  2604 . The power storage device  2612  can be charged with electric power generated by the solar panel  2610 . A secondary battery included in a vehicle  2603  can be charged with the electric power stored in the power storage device  2612  through the charging device  2604 . The power storage device  2612  is preferably provided in the underfloor space, in which case the space on the floor can be effectively used. Alternatively, the power storage device  2612  may be provided on the floor. 
     The electric power stored in the power storage device  2612  can also be supplied to other electronic devices in the house. Thus, the electronic devices can be operated with the use of the power storage device  2612  of one embodiment of the present invention as an uninterruptible power source even when electric power cannot be supplied from the commercial power supply due to power failure. 
       FIG. 18B  illustrates an example of a power storage device of one embodiment of the present invention. As illustrated in  FIG. 18B , a power storage device  791  of one embodiment of the present invention is provided in an underfloor space  796  of a building  799 . The power storage device  791  may be provided with the control circuit portion described in Embodiment 7, and the use of a secondary battery including a positive electrode using the positive electrode active material  200 A shown in Embodiment 1 enables the power storage device  791  to have a long lifetime. 
     The power storage device  791  is provided with a control device  790 , and the control device  790  is electrically connected to a distribution board  703 , a power storage controller (also referred to as control device)  705 , an indicator  706 , and a router  709  through wirings. 
     Electric power is transmitted from a commercial power source  701  to the distribution board  703  through a service wire mounting portion  710 . Moreover, electric power is transmitted to the distribution board  703  from the power storage device  791  and the commercial power source  701 , and the distribution board  703  supplies the transmitted electric power to a general load  707  and a power storage load  708  through outlets (not illustrated). 
     The general load  707  is, for example, an electrical device typified by a TV or a personal computer. The power storage load  708  is, for example, an electrical device typified by a microwave, a refrigerator, or an air conditioner. 
     The power storage controller  705  includes a measuring portion  711 , a predicting portion  712 , and a planning portion  713 . The measuring portion  711  has a function of measuring the amount of electric power consumed by the general load  707  and the power storage load  708  during a day (e.g., from midnight to midnight). The measuring portion  711  may also have a function of measuring the amount of electric power of the power storage device  791  and the amount of electric power supplied from the commercial power source  701 . The predicting portion  712  has a function of predicting, on the basis of the amount of electric power consumed by the general load  707  and the power storage load  708  during a given day, the demand for electric power consumed by the general load  707  and the power storage load  708  during the next day. The planning portion  713  has a function of making a charge and discharge plan of the power storage device  791  on the basis of the demand for electric power predicted by the predicting portion  712 . 
     The indicator  706  can show the amount of electric power consumed by the general load  707  and the power storage load  708  that is measured by the measuring portion  711 . An electrical device typified by a TV or a personal computer can also show it through the router  709 . Furthermore, a portable electronic terminal typified by a smartphone or a tablet can also show it through the router  709 . The indicator  706 , the electrical device, and the portable electronic terminal can also show the demand for electric power depending on a time period (or per hour) that is predicted by the predicting portion  712 . 
     The contents in this embodiment can be combined with the contents in any of the other embodiments as appropriate. 
     Embodiment 9 
     This embodiment will describe examples in which the power storage device of one embodiment of the present invention is mounted on a motorcycle and a bicycle. 
       FIG. 19A  illustrates an example of an electric bicycle using the power storage device of one embodiment of the present invention. The power storage device of one embodiment of the present invention can be used for an electric bicycle  8700  in  FIG. 19A . The power storage device of one embodiment of the present invention includes a plurality of storage batteries and a protection circuit, for example. 
     The electric bicycle  8700  is provided with a power storage device  8702 . The power storage device  8702  can supply electric power to a motor that assists a rider. The power storage device  8702  is portable, and  FIG. 19B  shows the state where the power storage device  8702  is removed from the electric bicycle. The power storage device  8702  incorporates a plurality of storage batteries  8701  included in the power storage device of one embodiment of the present invention, and can display the remaining battery level on a display portion  8703 . The power storage device  8702  includes a control circuit portion  8704  capable of charge control or anomaly detection for the secondary battery, which is exemplified in Embodiment 7. The control circuit portion  8704  is electrically connected to a positive electrode and a negative electrode of the storage battery  8701 . The control circuit portion  8704  may include the small solid-state secondary battery illustrated in  FIGS. 15A and 15B . When the small solid-state secondary battery illustrated in  FIGS. 15A and 15B  is provided in the control circuit portion  8704 , electric power can be supplied to store data in a memory circuit included in the control circuit portion  8704  for a long time. When the control circuit portion  8704  is used in combination with a secondary battery having a positive electrode using the positive electrode active material  200 A shown in Embodiment 1, the synergy on safety can be obtained. 
       FIG. 19C  illustrates an example of a motorcycle using the power storage device of one embodiment of the present invention. A motor scooter  8600  illustrated in  FIG. 19C  includes a power storage device  8602 , side mirrors  8601 , and indicators  8603 . The power storage device  8602  can supply electric power to the indicators  8603 . The power storage device  8602  including a plurality of secondary batteries having a positive electrode using the positive electrode active material  200 A shown in Embodiment 1 can have high capacity and contribute to a reduction in size. 
     In the motor scooter  8600  illustrated in  FIG. 19C , the power storage device  8602  can be held in an under-seat storage unit  8604 . The power storage device  8602  can be held in the under-seat storage unit  8604  even with a small size. 
     The contents in this embodiment can be combined with the contents in any of the other embodiments as appropriate. 
     Embodiment 10 
     In this embodiment, examples of electronic devices each including the secondary battery of one embodiment of the present invention will be described. Examples of the electronic device including the secondary battery include a television device (also referred to as a television or a television receiver), a monitor of a computer and the like, a digital camera, a digital video camera, a digital photo frame, a mobile phone (also referred to as a cellular phone or a mobile phone device), a portable game console, a portable information terminal, an audio reproducing device, and a large-sized game machine such as a pachinko machine. Examples of the portable information terminal include a laptop personal computer, a tablet terminal, an e-book reader, and a mobile phone. 
       FIG. 20A  illustrates an example of a mobile phone. A mobile phone  2100  includes a housing  2101  in which a display portion  2102  is incorporated, an operation button  2103 , an external connection port  2104 , a speaker  2105 , and a microphone  2106 . The mobile phone  2100  includes a secondary battery  2107 . The use of the secondary battery  2107  having a positive electrode using the positive electrode active material  200 A shown in Embodiment 1 achieves high capacity and a structure that accommodates space saving due to a reduction in size of the housing. 
     The mobile phone  2100  is capable of executing a variety of applications such as mobile phone calls, e-mailing, viewing and editing texts, music reproduction, Internet communication, and a computer game. 
     With the operation button  2103 , a variety of functions such as time setting, power on/off, on/off of wireless communication, setting and cancellation of a silent mode, and setting and cancellation of a power saving mode can be performed. For example, the functions of the operation button  2103  can be set freely by the operating system incorporated in the mobile phone  2100 . 
     The mobile phone  2100  can employ near field communication based on an existing communication standard. For example, mutual communication between the mobile phone  2100  and a headset capable of wireless communication can be performed, and thus hands-free calling is possible. 
     Moreover, the mobile phone  2100  includes the external connection port  2104 , and data can be directly transmitted to and received from another information terminal via a connector. In addition, charging can be performed via the external connection port  2104 . Note that the charging operation may be performed by wireless power feeding without using the external connection port  2104 . 
     The mobile phone  2100  preferably includes a sensor. As the sensor, a human body sensor such as a fingerprint sensor, a pulse sensor, or a temperature sensor, a touch sensor, a pressure sensitive sensor, or an acceleration sensor is preferably mounted. 
       FIG. 20B  illustrates an unmanned aircraft  2300  including a plurality of rotors  2302 . The unmanned aircraft  2300  is also referred to as a drone. The unmanned aircraft  2300  includes a secondary battery  2301  of one embodiment of the present invention, a camera  2303 , and an antenna (not illustrated). The unmanned aircraft  2300  can be remotely controlled through the antenna. A secondary battery including a positive electrode using the positive electrode active material  200 A shown in Embodiment 1 has a high energy density and a high degree of safety, and thus can be used safely for a long time over a long period of time and is preferable as the secondary battery included in the unmanned aircraft  2300 . 
       FIG. 20C  illustrates an example of a robot. A robot  6400  illustrated in  FIG. 20C  includes a secondary battery  6409 , an illuminance sensor  6401 , a microphone  6402 , an upper camera  6403 , a speaker  6404 , a display portion  6405 , a lower camera  6406 , an obstacle sensor  6407 , a moving mechanism  6408 , and an arithmetic device. 
     The microphone  6402  has a function of detecting a speaking voice of a user and an environmental sound. The speaker  6404  has a function of outputting sound. The robot  6400  can communicate with the user using the microphone  6402  and the speaker  6404 . 
     The display portion  6405  has a function of displaying various kinds of information. The robot  6400  can display information desired by the user on the display portion  6405 . The display portion  6405  may be provided with a touch panel. Moreover, the display portion  6405  may be a detachable information terminal, in which case charging and data communication can be performed when the display portion  6405  is set at the home position of the robot  6400 . 
     The upper camera  6403  and the lower camera  6406  each have a function of taking an image of the surroundings of the robot  6400 . The obstacle sensor  6407  can detect an obstacle in the direction where the robot  6400  advances with the moving mechanism  6408 . The robot  6400  can move safely by recognizing the surroundings with the upper camera  6403 , the lower camera  6406 , and the obstacle sensor  6407 . 
     The robot  6400  further includes, in its inner region, the secondary battery  6409  of one embodiment of the present invention and a semiconductor device or an electronic component. A secondary battery including a positive electrode using the positive electrode active material  200 A shown in Embodiment 1 has a high energy density and a high degree of safety, and thus can be used safely for a long time over a long period of time and is preferable as the secondary battery  6409  included in the robot  6400 . 
       FIG. 20D  illustrates an example of a cleaning robot. A cleaning robot  6300  includes a display portion  6302  placed on the top surface of a housing  6301 , a plurality of cameras  6303  placed on the side surface of the housing  6301 , a brush  6304 , operation buttons  6305 , a secondary battery  6306 , and a variety of sensors. Although not illustrated, the cleaning robot  6300  is provided with a tire, and an inlet. The cleaning robot  6300  is self-propelled, detects dust  6310 , and sucks up the dust through the inlet provided on the bottom surface. 
     For example, the cleaning robot  6300  can determine whether there is an obstacle such as a wall, furniture, or a step by analyzing images taken by the cameras  6303 . In the case where the cleaning robot  6300  detects an object that is likely to be caught in the brush  6304  (e.g., a wire) by image analysis, the rotation of the brush  6304  can be stopped. The cleaning robot  6300  further includes, in its inner region, the secondary battery  6306  of one embodiment of the present invention and a semiconductor device or an electronic component. A secondary battery including a positive electrode using the positive electrode active material  200 A shown in Embodiment 1 has a high energy density and a high degree of safety, and thus can be used safely for a long time over a long period of time and is preferable as the secondary battery  6306  included in the cleaning robot  6300 . 
     The contents in this embodiment can be combined with the contents in any of the other embodiments as appropriate. 
     Example 
     In this example, the average crushing strength of the positive electrode active material obtained in accordance with Embodiment 1 was measured. The positive electrode active material obtained in accordance with Embodiment 1 is composed of a primary particle and a secondary particle formed by aggregation of the primary particles. 
     The average crushing strength is calculated in such a manner that test pressure (load) is applied to a particle arbitrarily selected and the displacement volume of the particle is measured with use of a microparticle compressive strength analyzer (nanoindenter). In this example, 10 particles were selected, measurement was performed, and then the obtained crushing strengths are subjected to arithmetic mean to obtain the average crushing strength. In this example, NS-A300 produced by Nano Seeds Corporation was used as the microparticle compressive strength analyzer. 
     A cobalt compound including nickel, cobalt, and manganese with an element ratio Ni:Co:Mn=8:1:1 was obtained by a coprecipitation method in accordance with Embodiment 1, and then lithium and aluminum were added. After lithium and aluminum were added and mixed, first heat treatment was performed at 500° C. for 10 hours, the temperature was returned to room temperature and crushing was performed, and then second heat treatment was performed at 800° C. for 10 hours. Note that NCMA was obtained by adding Al at 1 atomic % with respect to the total of nickel, manganese, cobalt, and oxygen. 
       FIG. 21  shows measurement results of the microparticle compressive strength in this example.  FIG. 21  shows 10 measurement values, and a circle shows the average value of the 10 measurement values. 
       FIG. 21  shows measurement results of a comparative example, NCM, which was obtained in the following manner: a cobalt compound including nickel, cobalt, and manganese with an element ratio Ni:Co:Mn=8:1:1 (also referred to as a nickel compound because the proportion of nickel is high) was obtained by the coprecipitation method in accordance with Embodiment 1; lithium is added and mixed; and heat treatment was performed at 800° C. for 10 hours. That is, heat treatment was performed only once for the comparative example. The average particle diameter of the comparative example (NCM) was 11 μm. The crushing strength of the comparative example (NCM) was in the range from 83.23 MPa to 263.29 MPa, and the average crushing strength was 174.32 MPa. Note that the average particle diameter (D50, also referred to as a median diameter) can be measured with a particle diameter distribution analyzer using a laser diffraction and scattering method or by observation with a SEM or a TEM. In this example, a laser diffraction particle size analyzer SALD-2200 produced by Shimadzu Corporation was used. 
       FIG. 26  shows the comparative example on which heat treatment (at 800° C. for 10 hours) was performed once. Arrows in  FIG. 26  indicate portions which cannot be mixed well. 
       FIG. 25  is a SEM image of NCM obtained in the following manner: the cobalt compound including nickel, cobalt, and manganese with an element ratio Ni:Co:Mn=8:1:1 was obtained by a coprecipitation method in accordance with Embodiment 1; the compound was subjected to heat treatment twice (first heat treatment was performed at 500° C. for 10 hours, the temperature was returned to room temperature and crushing was performed, and then second heat treatment was performed at 800° C. for 10 hours). The secondary particle of NCM in  FIG. 25  shows an example of a secondary particle which does not contain aluminum. It was confirmed that the mixing state in  FIG. 25  was improved as compared with that of the comparative example in  FIG. 26 . This is probably because the heat treatment at 500° C. for 10 hours that was performed before the heat treatment at 800° C. for 10 hours can release moisture and the like contained in a precursor, which enabled uniform mixing. 
     The average particle diameter of this example (NCMA) was 9.3 μm. The crushing strength of this example was in the range from 166.5 MPa to 333.83 MPa and the average crushing strength thereof was 270.32 MPa. It was found that NCMA of this example has a higher average crushing strength than NCM of the comparative example. 
     It can be said that a positive electrode active material with high crushing strength has high particle strength. In the case where pressing is performed in a process of forming a positive electrode, particles are less likely to break. Furthermore, use of NCMA of this example as a positive electrode material of a secondary battery can prevent the secondary particle from being partially broken by expansion and contraction during charging and discharging. Accordingly, a positive electrode active material with high crushing strength can increase the capacity retention rate in a charging cycle. 
     In order to confirm the effect of increasing the capacity retention rate in the charging cycle, in this example, the positive electrode active material (NCMA) of one embodiment of the present invention was formed under the above-described conditions, a plurality of coin-type battery cells were fabricated, and the cycle characteristics of the cells were evaluated. 
     The positive electrode active material obtained by the method described in Embodiment 1 was used as positive electrode active materials of samples. Acetylene black was used as a conductive additive, the positive electrode active material and the conductive additive were mixed to form a slurry, and the slurry was applied to a current collector of aluminum. 
     After the current collector was coated with the slurry, the solvent was volatilized. Then, pressure was applied at 210 kN/m and then at 1467 kN/m. Through the above steps, the positive electrode was obtained. In the positive electrode, the carried amount was approximately 7 mg/cm 2 .  FIG. 22  shows an observation photograph of a cross section of part of the positive electrode. 
     CR2032 coin-type battery cells (diameter: 20 mm, height: 3.2 mm) were fabricated with the use of the formed positive electrodes. 
     A lithium metal was used for a counter electrode. 
     As an electrolyte in the sample, 1 mol/L lithium hexafluorophosphate (LiPF 6 ) was used. As the electrolytic solution, a solution in which ethylene carbonate (EC) and diethyl carbonate (DEC) were mixed at a volume ratio of 3:7 was used. The amount of vinylene carbonate (VC) added as an additive was set to 2 wt % with respect to the whole solvent. 
     As a separator, 25-μm-thick polypropylene was used. 
     A positive electrode can and a negative electrode can that were formed of stainless steel (SUS) were used. 
     In the evaluation of cycle characteristics, the charging voltage was 4.5 V. The measurement temperatures were 25° C. and 45° C. CC/CV charging (0.5 C, 0.05 C cut) and CC discharging (0.5 C, 2.7 V cut) were performed, and a 10-minute break was taken before the next charging. Note that 1 C was set to 200 mA/g in this example. 
       FIGS. 23A and 23B  show cycle characteristics at a measurement temperature of 25° C. The vertical axis in  FIG. 23A  represents discharge capacity and the vertical axis in  FIG. 23B  represents the discharge capacity retention rate. 
       FIGS. 24A and 24B  show cycle characteristics at a measurement temperature of 45° C. The vertical axis in  FIG. 24A  represents discharge capacity and the vertical axis in  FIG. 24B  represents the discharge capacity retention rate. 
     Note that the comparative example in  FIGS. 24A and 24B  is NCM with an element ratio Ni:Co:Mn=8:1:1. 
     From the results of  FIG. 23B , it was confirmed that NCMA, the positive electrode active material with higher crushing strength than that of NCM of the comparative example, has a high capacity retention rate in a charging cycle. 
     A battery cell was fabricated in the following manner: a cobalt compound including nickel, cobalt, and manganese with an element ratio Ni:Co:Mn=8:1:1 (also referred to as a nickel compound because the proportion of nickel is high) was obtained by the coprecipitation method in accordance with Embodiment 1; heat treatment was performed twice (first heat treatment was performed at 500° C. for 10 hours, the temperature was returned to room temperature, crushing was performed, and then second heat treatment was performed at 800° C. for 10 hours). The discharge capacity of a half cell of the comparative example (heat treatment was performed once) was 213 mAh/g (measurement temperature: 45° C.), whereas the discharge capacity of a half cell of NCM (heat treatment was performed twice) was 227 mAh/g (measurement temperature: 45° C.), which is larger than the comparative example. These results show effectiveness of twice-heat treatment process even when aluminum is not added. 
     This application is based on Japanese Patent Application Serial No. 2021-001989 filed with Japan Patent Office on Jan. 8, 2021 and Japanese Patent Application Serial No. 2021-020833 filed with Japan Patent Office on Feb. 12, 2021, the entire contents of which are hereby incorporated by reference.