Method for reusing active material using cathode scrap

Abstract

To provide a method for recovering an active material from cathode scraps and reusing the same.SOLUTION: A cathode active material reuse method of the present invention comprises the steps of: (a-1) dry grinding cathode scraps, which comprise a cathode active material layer of a lithium composite transition metal oxide on a current collector, so as to desorb the active material layer in the form of powder, and thus separate the active material layer from the current collector; (a-2) heat treating, in air, the active material layer having been desorbed in the form of powder, so as to thermally decompose a binder and a conductive material contained in the active material layer, and thus recover an active material; (b) washing the recovered active material with an aqueous solution of a lithium compound, which is basic in an aqueous solution state, and drying the washed active material; and (c) adding a lithium precursor to the washed active material and annealing the mixture to obtain a reusable active material.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a method for recycling resources during the manufacture of lithium secondary batteries.In particular, the present invention relates to a method for recovering and reusing positive electrode scrap generated during the manufacturing process of lithium secondary batteries or positive electrode active materials of lithium secondary batteries that are discarded after use.This application claims priority to Korean Patent Application No. 10-2020-0134325, filed on October 16, 2020, and the contents disclosed in the specification and drawings of that application are incorporated herein in their entirety. [Background technology]

[0002] Lithium secondary batteries, which can be repeatedly charged and discharged, are gaining attention as an alternative to fossil energy. Lithium secondary batteries have been used primarily in traditional handheld devices such as mobile phones, video cameras, and power tools. However, their application areas have recently been expanding to include electrically powered vehicles (EV, HEV, PHEV), large-capacity energy storage systems (ESS), and uninterruptible power supplies (UPS).

[0003] A lithium secondary battery includes an electrode assembly, which is an assembly of unit cells, each of which has a structure in which a positive electrode plate and a negative electrode plate, each of which has an active material coated on a current collector, are arranged with a separator sandwiched therebetween, and an exterior material, i.e., a battery case, which hermetically houses the electrode assembly together with an electrolyte. The positive electrode active material of a lithium secondary battery is typically a lithium-based oxide, and the negative electrode active material is typically a carbon material. The lithium-based oxide contains metals such as cobalt, nickel, or manganese. Cobalt, nickel, and manganese are particularly valuable metals, and cobalt is a strategic metal. Countries around the world are particularly concerned about supply and demand, and cobalt is known to have unstable supply and demand due to the limited number of cobalt-producing countries. If a supply-demand imbalance occurs in the raw materials of strategic metals, the prices of the raw materials are likely to rise.

[0004] So far, research has focused on recovering and recycling these valuable metals from used and discarded lithium secondary batteries (waste batteries). It would be even more desirable if resources could be recovered from waste materials discarded after punching out positive electrodes or from cathodes that have become defective during the manufacturing process, in addition to waste batteries.

[0005] Currently, in the manufacture of lithium secondary batteries, a cathode current collector 10 in the form of a long sheet, such as aluminum (Al) foil, is coated with a cathode slurry, which is a mixture of cathode active material, conductive material, binder, and solvent, to form a cathode active material layer 20, as shown in Figure 1, to produce a cathode sheet 30, which is then punched out to a specific size to produce a cathode plate 40. The remaining portion after punching is discarded as cathode scrap 50. If the cathode active material could be recovered from the cathode scrap 50 and reused, this would be highly desirable from an industrial, economic, and environmental perspective.

[0006] Existing methods for recovering positive electrode active materials involve dissolving the positive electrode in hydrochloric acid, sulfuric acid, nitric acid, or the like, and then extracting active material elements such as cobalt, nickel, and manganese, which are then reused as raw materials for synthesizing positive electrode active materials. However, acid-based extraction of active material elements has drawbacks, such as environmentally unfriendly processes for recovering pure raw materials and increased process costs due to the need for neutralization and wastewater treatment processes. Another drawback is that lithium, one of the main elements in positive electrode active materials, cannot be recovered. To overcome these drawbacks, a method is needed that allows the positive electrode active material to be directly reused without dissolving it and extracting the active material in its elemental form. Summary of the Invention [Problem to be solved by the invention]

[0007] An object of the present invention is to provide a method for recovering and reusing active material from cathode scrap. [Means for solving the problem]

[0008] In order to solve the above problems, the method for reusing a positive electrode active material of the present invention includes the steps of: (a-1) dry-pulverizing positive electrode scrap including a positive electrode active material layer made of a lithium composite transition metal oxide on a current collector to detach the active material layer in powder form and separating it from the current collector; (a-2) heat-treating the detached active material layer in powder form in air to thermally decompose the binder and conductive material in the active material layer, thereby recovering the active material; (b) washing the recovered active material with an aqueous solution of a lithium compound that is basic in an aqueous solution state, and drying it; and (c) adding a lithium precursor to the washed active material and annealing it to obtain a reusable active material.

[0009] The present invention may further include the step (d) of surface coating the annealed active material.

[0010] The dry milling may be carried out using any one of a pin mill, a disc mill, a cutting mill, and a hammer mill.

[0011] The method may further include a step of shredding or cutting the cathode scrap before dry pulverization.

[0012] The heat treatment can be carried out at 300 to 1,000°C.

[0013] The heat treatment may be carried out at a temperature rate of 5°C / min at 550°C for 30 minutes.

[0014] The aqueous lithium compound solution is prepared to contain greater than 0% and less than or equal to 15% of the lithium precursor, preferably LiOH. The cleaning can be performed within an hour.

[0015] The washing can be carried out by immersing the recovered active material in an aqueous solution of a lithium compound and stirring the same.

[0016] The lithium precursor can be any one or more of LiOH, Li2CO3, LiNO3, and Li2O.

[0017] The lithium precursor may be added in an amount that can compensate for the proportion of lithium lost relative to the proportion of lithium and other metals in the raw active material used in the active material layer.

[0018] For example, the lithium precursor may be added in an amount such that the amount of lithium added is 0.001 to 0.4 molar ratio.

[0019] Furthermore, it is desirable to further add the lithium precursor in an amount that gives a molar ratio of lithium of 0.0001 to 0.1, based on a molar ratio of lithium to other metal of 1:1.

[0020] Annealing can be carried out in air at 400-1,000°C.

[0021] The temperature of the annealing step may be above the melting point of the lithium precursor.

[0022] The active material in the active material layer is recovered in powder form, and no carbon components resulting from carbonization of the binder or conductive material remain on the surface.

[0023] The surface coating step may be a step of coating the surface with at least one of metal, organometallic, and carbon components in a solid or liquid phase manner, followed by heat treatment at 100 to 1,200°C.

[0024] The reusable active material may be represented by the following Chemical Formula 1:

[0025] Li a Ni x Mn y Co z M w O 2+δ (chemical formula 1)

[0026] In Chemical Formula 1, M includes one or more selected from the group consisting of B, W, Al, Ti, and Mg; <a≦1.1、0≦x<0.95、0≦y<0.8、0≦z<1.0、0≦w≦0.1、-0.02≦δ≦0.02、x+y+z+w=1である。

[0027] The reusable active material may have a fluorine (F) content of 100 ppm or less. [Effects of the Invention]

[0028] According to the present invention, waste cathode active material, such as cathode scraps generated in the manufacturing process of lithium secondary batteries, can be reused without using acid, which is environmentally friendly. The method according to the present invention does not require a neutralization process or a wastewater treatment process, thereby reducing the burden on the environment and reducing process costs.

[0029] According to the present invention, it is possible to recover a positive electrode active material without unrecoverable metal elements. The current collector can also be recovered because it is not dissolved. This method is economical because it allows the recovered active material in powder form to be directly reused, rather than extracting active material elements and using them as raw materials for further synthesis of a positive electrode active material.

[0030] According to the present invention, toxic and explosive solvents such as NMP, DMC, acetone, and methanol are not used, making the process safe. Furthermore, simple processes such as heat treatment, cleaning, and annealing are used, making the process easy to manage and suitable for mass production.

[0031] According to the present invention, the electrochemical performance of the recovered active material is not deteriorated, and excellent resistance and capacitance characteristics can be realized.

[0032] In particular, according to the present invention, the active material and the current collector are first separated using dry pulverization. This complete separation of the active material from the current collector ensures a recovery rate of over 95% of the positive electrode active material. Dry pulverization has a high processing rate per hour, making it possible to reuse the positive electrode active material with high productivity.

[0033] The following drawings attached to this specification illustrate preferred embodiments of the present invention and, together with the detailed description of the invention, serve to further understand the technical concept of the present invention, so the present invention should not be interpreted as being limited to the matters described in the drawings. [Brief explanation of the drawings]

[0034] [Figure 1] FIG. 10 is a diagram showing positive electrode scraps that are discarded after the positive electrode plates are punched out of the positive electrode sheet. [Figure 2] 1 is a flowchart of a method for reusing active materials according to the present invention. [Figure 3] 6 is a photograph of the results of each step according to an experimental example of the present invention. [Figure 4] 1 is a SEM photograph of an active material layer after dry pulverization in a method for reusing an active material according to the present invention. [Figure 5] 5 is an SEM photograph of the active material layer of FIG. 4 after heat treatment in air. [Figure 6] 1 is a SEM photograph of an active material that has been dried after being washed to remove LiF in a method for reusing an active material according to the present invention. [Figure 7] The graph shows the results of cell evaluation using the active material of the comparative example. [Figure 8] 1 shows the results of cell evaluation using active materials of Examples and Comparative Examples. DETAILED DESCRIPTION OF THE INVENTION

[0035] Hereinafter, a preferred embodiment of the present invention will be described in detail with reference to the accompanying drawings. Prior to this, the terms and words used in this specification and claims should not be construed as being limited to their ordinary or dictionary meanings, but should be construed as meanings and concepts corresponding to the technical ideas of the present invention, in accordance with the principle that the inventor himself can appropriately define the concepts of terms in order to best explain the invention. Therefore, it should be understood that the embodiments described in this specification and the configurations shown in the drawings are merely the most preferred embodiment of the present invention and do not represent the entire technical ideas of the present invention, and therefore, various equivalents and modifications that can be substituted therefor may exist at the time of filing this application.

[0036] In the following description, reference will be made to the accompanying drawings, which form a part of this application. The embodiments described in the detailed description, drawings, and claims are not intended to be limiting. Other embodiments may be utilized, and other changes may be made, without departing from the spirit and scope of the subject matter disclosed herein. It will be understood that aspects of the invention as generally described herein and illustrated by the drawings may be arranged, substituted, combined, separated, and designed in a variety of other configurations, all of which are expressly contemplated herein.

[0037] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs (hereinafter referred to as "the person skilled in the art").

[0038] The present invention is not limited by the specific embodiments described herein. As will be apparent to those skilled in the art, various changes and modifications can be made without departing from the spirit and scope of the present invention. In addition to those enumerated herein, functionally equivalent methods within the scope of the present invention will become apparent to those skilled in the art from the foregoing description. Such changes and modifications are within the scope of the appended claims. The present invention is limited only by the claims, along with the full scope of equivalents to which such claims are entitled. It should be understood that the present invention is not limited to the specific ways in which it can, of course, be varied. The terminology used herein is used solely for the purpose of describing specific embodiments and is not intended to be limiting.

[0039] In the case of conventional active material recycling processes, the main purpose is to extract valuable metals (nickel, cobalt, manganese, etc.) as elements from the active material of lithium secondary batteries whose performance has deteriorated after use and resynthesize the active material. However, the present invention is different in that it recovers active material from cathode scrap generated during the lithium secondary battery manufacturing process.

[0040] In addition, conventional active material recycling processes require additional chemical methods, such as extracting valuable metals using acid / base dissolution or reduction / melting with additives, and then manufacturing them as metals (direct reduction method) or resynthesizing active materials, which increases the complexity and cost of the process. However, the present invention relates to a method for directly reusing positive electrode active materials without dissolving them.

[0041] To directly reuse the positive electrode active material, the current collector must be removed from the positive electrode, which can be done by high-temperature heat treatment to remove the binder, by dissolving the binder using a solvent, by dissolving the current collector itself, or by dry grinding and sieving to separate the active material.

[0042] When using a solvent to dissolve the binder, the stability of the solvent is important. NMP is the most efficient solvent, but it has drawbacks such as toxicity and high cost. Another drawback is the need for a solvent recovery process, such as reprocessing waste solvent. Dissolving the current collector is less expensive than using a solvent. However, it is difficult to remove foreign matter from the surface of the reused active material, and hydrogen gas is generated during the current collector removal process, which poses an explosion risk. It is difficult to completely separate the current collector and active material using dry grinding and sieving. The particle size distribution of the active material changes during the grinding process, making binder removal difficult, which can lead to deterioration of battery performance when reused.

[0043] In the present invention, the active material and current collector are first separated using dry pulverization. This dry pulverization completely separates the active material from the current collector, ensuring a recovery rate of over 95% of the positive electrode active material. The binder and conductive material are then removed by heat treatment. This heat treatment is performed in air, so no special equipment configuration is required. It is a relatively simple process that requires only heating, making it advantageous for mass production and commercialization. Meanwhile, foreign matter must not remain on the surface of the reused active material. The present invention also proposes a step for removing foreign matter from the surface of the reused active material.

[0044] Hereinafter, a method for reusing an active material according to an embodiment of the present invention will be described with reference to Fig. 2. Fig. 2 is a flowchart of the method for reusing an active material according to the present invention.

[0045] Referring to FIG. 2, first, a cathode scrap to be discarded is prepared (step S10).

[0046] As described with reference to FIG. 1, the positive electrode scrap may be the portion remaining after punching out a positive electrode sheet including a positive electrode active material layer on a current collector. Furthermore, the positive electrode scrap may be prepared by collecting positive electrodes that have become defective during the process. Alternatively, the positive electrode scrap may be prepared by separating positive electrodes from used and discarded lithium secondary batteries.

[0047] For example, a slurry prepared by mixing an active material such as lithium cobalt oxide (LiCoO2) or an NCM active material containing nickel, cobalt, and manganese, carbon black (a carbon-based conductive material), and polyvinylidene fluoride (PVdF) (a binder) with N-methyl pyrrolidone (NMP) may be coated on a sheet-shaped current collector made of aluminum foil, and then dried in a vacuum oven at about 120°C to prepare a positive electrode sheet. After that, positive electrode plates of a certain size may be punched out, and the remaining positive electrode scrap may be prepared.

[0048] Lithium composite transition metal oxides are used as the positive electrode active material for lithium secondary batteries, with lithium cobalt oxide (LiCoO2), lithium manganese oxide (LiMnO2 or LiMn2O4, etc.), lithium iron phosphate compounds (LiFePO4, etc.), and lithium nickel oxide (LiNiO2, etc.) being the most commonly used. To improve the low thermal stability of LiNiO2 while maintaining its excellent reversible capacity, nickel-manganese-based lithium composite metal oxides, in which part of the nickel (Ni) is replaced with manganese (Mn), which has excellent thermal stability, and NCM lithium composite transition metal oxides, in which manganese (Mn) and cobalt (Co) are replaced, are used. The present invention is particularly suited to the reuse of LCO and NCM active materials.

[0049] As described above, the cathode scrap has an active material layer on a metal foil current collector such as aluminum foil. The active material layer is formed by coating a slurry containing an active material, a conductive material, a binder, a solvent, etc., and after the solvent evaporates, the binder connects the active material and the conductive material. Therefore, removing the binder can separate the active material from the current collector.

[0050] Next, the cathode scrap is shredded to an appropriate size (step S20). Shredding refers to cutting the cathode scrap into pieces that are easy to handle. After shredding, the cathode scrap has a size of about 10 cm x 10 cm. This can be further cut into smaller pieces. During cutting, the cathode scrap can be cut into pieces that are, for example, 1 cm x 1 cm.

[0051] The crushing, including shredding and cutting, may be performed taking into consideration the handling of the cathode scrap and the desired properties of the equipment used in subsequent processes. For example, if equipment that requires continuous processing for loading and unloading the cathode scrap is used, the cathode scrap should have good fluidity, so excessively large cathode scrap should be crushed.

[0052] Next, the crushed cathode scrap is dry-pulverized to separate the active material layer in powder form and the current collector (step S25). Dry pulverization can be performed using any one of a pin mill, disc mill, cutting mill, and hammer mill. Preferably, a pin mill is used. In this way, the pin mill can ensure a recovery rate of over 95% of the cathode active material in the form of powder of 5 mm or less. The pin mill equipment can process more than 500 kg per hour. Therefore, if the process is performed for 10 hours per day, an electrode separation effect of up to 5 tons can be achieved.

[0053] A pin mill is a device that has a structure in which rotating pins attached to a rotor and pins attached to a stationary platen interlock with each other. When raw materials are fed into the center of the mill, they are dispersed with the air flow generated by the rotation and crushed by the impact between the rotating and stationary plates using the brittleness of the raw materials. Only the crushed materials that can pass through the holes formed in the ring-shaped screen are extracted.

[0054] Using such a pin mill, it is possible to crush the material to the desired degree and particle size by adjusting the pin shape, number, and size range of the screen being used. When crushed cathode scrap is crushed using a pin mill, the current collector pieces are cut into smaller pieces, and the more brittle active material layer is separated from the current collector pieces. The more flexible current collector pieces remain inside the screen as they are rolled into a round shape, leaving only the active material layer in a fine powder form that passes through the screen. Although the active material layer is broken and no longer contiguous enough to be called a layer, the active material, binder, and conductive material remain solidified and remain in a powder form. In this way, the difference in brittleness and softness between the active material layer and the current collector makes it possible to separate them using only dry milling.

[0055] Next, the active material layer separated in powder form is heat-treated in air (step S30).

[0056] In the present invention, heat treatment is performed to thermally decompose the binder and conductive material in the active material layer. Because heat treatment can be performed at 300 to 1,000°C, it is also referred to as high-temperature heat treatment. Temperatures below 300°C can make it difficult to remove the binder. When heat treatment is performed on positive electrode scrap in the presence of a current collector without dry pulverization, the heat treatment must be performed at a temperature below the melting point of the current collector. However, in the present invention, heat treatment is performed on a detached active material layer from which the current collector has already been separated, so the heat treatment temperature is not limited by the current collector.

[0057] The heat treatment time should be maintained long enough to fully decompose the binder. For example, it should be around 30 minutes. Preferably, it should be 30 minutes or longer. The longer the heat treatment time, the longer it takes for the binder to decompose, but once it reaches a certain time, there will be no difference in the decomposition effect. Preferably, the heat treatment time should be between 30 minutes and 5 hours.

[0058] The heat treatment equipment may be a furnace of various types, for example, a box-type furnace, or, in consideration of productivity, a rotary kiln capable of continuous treatment.

[0059] After the heat treatment, the material may be cooled slowly or rapidly in air.

[0060] For example, the heat treatment may be performed at 550°C for 30 minutes with a temperature increase rate of 5°C / min. The temperature increase rate may be such that it can be easily implemented in, for example, a box-type furnace, and that heating can be performed without causing thermal shock to the powdered active material. 550°C facilitates thermal decomposition of the binder. At this temperature, if the heat treatment is performed for less than 10 minutes, the thermal decomposition is insufficient, so the heat treatment must be performed for 10 minutes or more, and preferably for 30 minutes or more.

[0061] The heat treatment in air causes the binder and conductive material in the active material layer to be thermally decomposed and removed as CO2 and H2O. As the binder is removed, the solidified active material to be recovered can be broken down and sorted in powder form.

[0062] It is important that the heat treatment in step S30 be performed in air. If the heat treatment is performed in a reducing gas or inert gas atmosphere, the binder and conductive material will not be thermally decomposed but will be carbonized. Carbonization will leave carbon components on the surface of the active material, reducing the performance of the reused active material. If the heat treatment is performed in air, the carbon materials in the binder and conductive material will react with oxygen and be burned into CO and CO2 gas, resulting in the removal of most of the binder and conductive material without any residue.

[0063] Therefore, according to the present invention, the active material is recovered in powder form, and carbon components generated by carbonization of the binder or conductive material do not remain on the surface.

[0064] Next, the recovered active material is washed and dried (step S40). It is important to wash with an aqueous solution of a lithium compound that is basic in aqueous solution. This lithium compound solution is prepared to contain more than 0% but not more than 15% of a lithium compound, preferably LiOH. The amount of LiOH is preferably 15% or less. If an excessive amount of LiOH is used, it may remain on the surface of the active material even after washing, which may affect the subsequent annealing process. To maximize the cleanliness of the active material surface prior to annealing, adding an excessive amount of LiOH is not good for the process, so it is limited to 15% or less.

[0065] Washing can be performed by immersing the recovered active material in such an aqueous lithium compound solution. After immersion, washing can be performed within one week, preferably one day, and more preferably within one hour. Washing for more than one week may result in a decrease in capacity due to excessive lithium elution. Therefore, washing is preferably performed within one hour. Washing involves immersing the active material in an aqueous lithium compound solution that exhibits basicity in the aqueous solution and stirring the solution while immersed. Simultaneous stirring is recommended. Immersing the active material in the aqueous lithium compound solution without stirring slows the washing process and may result in lithium elution. Simultaneous stirring minimizes process time, so stirring is preferably performed simultaneously with the impregnation with the aqueous lithium compound solution. Drying can be performed in air in a convection oven after filtration.

[0066] Washing with an aqueous solution of a lithium compound that is alkaline in aqueous solution can remove LiF and metal fluorides present on the surface of the recycled active material, thereby modifying the surface. During the heat treatment in step S30, the binder and conductive material in the active material layer are vaporized and removed as CO2 and HO. During this process, CO2 and HO react with lithium on the surface of the active material to form Li2CO3 and LiOH, or F present in the binder, such as PVdF, reacts with lithium and other metals in the positive electrode active material and lithium in the added lithium precursor to form LiF or metal fluorides. If such LiF or metal fluorides remain, battery performance will deteriorate when the active material is reused. In the present invention, a washing step, step S40, is added to remove reactants formed on the surface of the recycled active material during the heat treatment step S30, thereby preventing foreign matter from remaining on the surface of the recycled active material.

[0067] In step S40, it is important to wash with an aqueous solution of a lithium compound that is basic in aqueous solution. Using a sulfuric acid or hydrochloric acid solution instead of an aqueous solution of a lithium compound that is basic in aqueous solution can wash away F from the surface of the active material, but it will dissolve transition metals (Co, Mg) present in the active material, reducing the performance of the reused cathode active material. The aqueous solution of a lithium compound that is basic in aqueous solution used in the present invention is highly desirable because it not only removes even trace amounts of binder that may remain after the thermal decomposition in step S30, but also prevents the dissolution of transition metals present in the active material and compensates for the amount of lithium that would otherwise be dissolved during the washing process.

[0068] Furthermore, if LiF remains, it may act as a resistive layer. According to the present invention, through step S40, the LiF content on the surface of the recovered active material can be adjusted to less than 500 ppm, thereby improving capacity. Preferably, the F content can be 100 ppm or less. More preferably, the F content can be 30 ppm or less.

[0069] Next, a lithium precursor is added to the washed active material, and the material is annealed (step S50).

[0070] During the previous steps S30 and S40, lithium loss may occur in the active material, and in step S50, this lithium loss is replenished.

[0071] Furthermore, in step S50, the crystalline structure of the active material is restored by annealing, thereby restoring or improving the properties of the reused active material to the same level as a fresh active material that has never been used.

[0072] During the previous steps S30 and S40, a deformed structure may appear on the surface of the active material. For example, in step S40, Ni in an NCM-based lithium transition metal composite active material may convert into rock salt [NiCO3·2Ni(OH)2)H20] with water, forming a spinel structure. Manufacturing a battery in this state can result in poor battery performance, such as reduced capacity. In the present invention, the crystalline structure is restored through step S50. For example, the NCM-based lithium transition metal composite active material is further restored to a hexagonal crystalline structure. This allows the initial performance to be restored or improved to a level similar to that of a fresh active material.

[0073] The lithium precursor of step S50 can be any one or more of LiOH, Li2CO3, LiNO3, and Li2O.

[0074] The lithium precursor is added in an amount sufficient to compensate for the loss of lithium relative to the ratio of lithium to other metals in the raw active material (i.e., fresh active material) used in the active material layer. For example, if the ratio of lithium to other metals in the fresh active material is 1, the lithium precursor can be added in an amount that results in a 0.001 to 0.4 molar ratio. Preferably, the lithium precursor is added in an amount that results in a 0.01 to 0.2 molar ratio. Addition of an excess amount of lithium precursor beyond the amount of lithium lost during cleaning or other processes will result in unreacted lithium precursor remaining in the reused active material, which can increase the resistance during reuse of the active material. Therefore, it is important to add an appropriate amount of lithium precursor.

[0075] In addition, it is preferable to add lithium to the lithium precursor in an amount that provides a 0.0001 to 0.1 molar ratio based on a 1:1 molar ratio of lithium to other metals. The reason for adding such an excess amount of lithium is to form a surface protective layer on the active material by surface coating, which will be explained in detail below. When a secondary battery is manufactured from such an active material, side reactions caused by the electrolyte can be suppressed while maintaining the life characteristics.

[0076] Annealing can be performed in air at 400 to 1,000°C. The annealing temperature can be 600 to 900°C. The annealing temperature can vary within a limited range depending on the type of lithium precursor. The annealing time is preferably 1 hour or more, more preferably around 5 hours. A long annealing time allows sufficient recovery of the crystal structure, but even if the annealing time is long, it does not significantly affect performance. The annealing time is, for example, 15 hours or less. The annealing equipment can be the same as or similar to that used in the heat treatment step S30.

[0077] For example, when Li2CO3 is used as the lithium precursor, the annealing temperature is preferably 700 to 900°C, more preferably 710 to 780°C. This is because the melting point of Li2CO3 is 723°C, and more preferably 750°C. When LiOH is used as the lithium precursor, the annealing temperature is preferably 400 to 600°C, more preferably 450 to 480°C. This is because the melting point of LiOH is 462°C.

[0078] The annealing temperature is preferably above the melting point of the lithium precursor, but should not exceed 1,000°C because temperatures above 1,000°C can cause thermal decomposition of the positive electrode active material, resulting in a decrease in performance.

[0079] Through this step S50, a reusable active material is obtained.

[0080] The present invention is characterized in that the active material in powder form is separated from the current collector by dry pulverization of the cathode scrap in step S25. Because this is a physical separation, the chemical properties of the current collector and the active material are not changed.

[0081] Of course, it is also possible to separate the positive electrode active material layer by performing heat treatment with the current collector intact without dry pulverization. However, if the current collector is separated by heat treatment alone without dry pulverization, the current collector and electrode are large in volume, and the mixing process involving oxygen contact is important, resulting in a lower throughput per unit volume than the dry pulverization method proposed in the present invention. As proposed in the present invention, the active material powder separated from the current collector by the dry pulverization method can be processed in large quantities by the heat treatment process. When using pin mill equipment, not only can a positive electrode active material recovery rate of 95% or more be ensured, but the amount of electrode separation processed per hour is at least 500 kg or more, and productivity can be maximized due to the advantage of continuous processing.

[0082] Furthermore, when heat treating cathode scrap with the current collector remaining intact without dry crushing, there is a restriction that the heat treatment must be limited to 550°C or less due to the problem of oxidation of the aluminum current collector. However, according to the present invention, because the current collector is separated prior to the heat treatment, the heat treatment temperature can exceed the melting point of the current collector, 550°C. In other words, pre-separation of the current collector has the advantage that it can be heated at a high temperature without any restrictions on the heat treatment temperature during the heat treatment to remove the binder and conductive material.

[0083] Next, as an optional step, step S60 may be further performed, in which a surface coating is performed on the active material annealed in step S50.

[0084] The surface coating step may involve coating the surface with one or more of a metal, organometallic, or carbon component using a solid or liquid phase method, followed by heat treatment at 100 to 1,200°C. Heat treatment at temperatures above 1,200°C may result in performance degradation due to thermal decomposition of the positive electrode active material. For the surface coating, methods such as mixing, milling, spray drying, and grinding may be used as the solid or liquid phase method.

[0085] In the case of an NCM active material, B, BW, W, etc. may be coated, and in the case of an LCO active material, Al, Mg, Ti, etc. If the heat treatment temperature required for coating must be high, step S60 may be performed before step S50. That is, after the surface coating is performed, a lithium precursor is added and annealed.

[0086] The surface coating forms a surface protective layer made of dissimilar metals. If the molar ratio of lithium to other metals in the positive electrode active material is 1:1, and the lithium in the active material reacts with the surface coating material, reducing the molar ratio of lithium to other metals in the positive electrode active material to less than 1:1, full capacity cannot be achieved. Therefore, in the previous step S30, additional lithium is added through the addition of a lithium precursor to achieve a 1:1 molar ratio of lithium to other metals in the positive electrode active material, and an excess amount of lithium is added to achieve a 0.0001–0.1 molar ratio relative to the other metals in the positive electrode active material. This allows the surface protective layer to be formed even when the molar ratio of lithium to other metals in the positive electrode active material is 1:1 during the surface coating.

[0087] Specifically, when a metal oxide such as B, W, or BW is coated on an active material and then heat-treated, a lithium boron oxide layer is formed on the surface of the active material, which acts as a surface protection layer. Lithium, added in a molar ratio of 0.0001 to 0.1 in step S50, reacts with the metal oxide such as B, W, or BW in step S60, preventing the molar ratio of lithium to other metals in the positive electrode active material from decreasing below 1:1, thereby preventing capacity loss.

[0088] The reusable active material obtained by the method described above may be represented by the following Chemical Formula 1:

[0089] Li a Ni x Mn y Co z M w O 2+δ (chemical formula 1)

[0090] In Chemical Formula 1, M includes one or more selected from the group consisting of B, W, Al, Ti, and Mg; <a≦1.1、0≦x<0.95、0≦y<0.8、0≦z<1.0、0≦w≦0.1、-0.02≦δ≦0.02、x+y+z+w=1である。

[0091] The reusable active material may have an F content of 100 ppm or less. According to the present invention, since the active material with a reduced F content can be recovered, when it is reused as an active material, excellent resistance and capacitance characteristics can be realized.

[0092] According to the present invention, LiF or metal fluorides are removed in the washing step S40. The washing and drying steps using an aqueous lithium compound solution that is basic in aqueous solution are safe and inexpensive, and have the advantages of removing LiF or metal fluorides without losing other elements, preventing the elution of transition metals, and compensating for lithium loss that occurs during the process. The annealing step is also safe and inexpensive, and has the advantage of restoring the crystalline structure, i.e., improving crystallinity, thereby restoring the battery characteristics of the reused active material.

[0093] The reusable active material obtained by the present invention has a particle size distribution similar to that of fresh active material, eliminating the need for additional processing to adjust the particle size distribution. Because carbon components resulting from the carbonization of the binder or conductive material do not remain on the surface, steps to remove such carbon components are unnecessary. Therefore, the active material obtained by the method of FIG. 2 can be reused as is for the manufacture of positive electrodes without additional processing.

[0094] The recycled active material can be used 100% as it is without adjusting the composition, or it can be mixed with fresh active material, and then mixed with a conductive material, a binder, and a solvent to prepare a slurry.

[0095] Experimental examples of the present invention will be described in detail below.

[0096] <Experimental Example 1> FIG. 3 shows photographs of the results at each stage according to an experimental example of the present invention.

[0097] Figure 3(a) is a photograph of shredded cathode scrap. Waste cathode scrap was collected and shredded to a size of approximately 10 cm x 10 cm.

[0098] Figure 3(b) is a photograph of the cut cathode scrap. The shredded cathode scrap was further cut into thin strips measuring 1 cm x 1 cm.

[0099] Figure 3(c) is a photograph of the current collector pieces after the cut cathode scraps were crushed using a pin mill, and Figure 3(d) is a photograph of the powdered active material layer detached from the current collector pieces after crushing using a pin mill. It can be seen that the active material layer is almost completely separated from the current collector by dry crushing using a pin mill.

[0100] FIG. 4 is an SEM photograph of the active material layer shown in FIG. 3(d), and FIG. 5 is an SEM photograph of the active material layer of FIG. 4 after heat treatment in air. The SEM photographs were taken using a standard SEM device used in laboratories. For example, they can be taken using a Hitachi S-4200. However, there are no deviations due to the measurement device or method.

[0101] In Figure 4, before heat treatment, the binder is present in the active material layer and the active material layer has the form of solidified particles, whereas in Figure 5, it can be seen that the binder has been removed by heat treatment and the solidified particles have been broken down. This shows that the binder and conductive material are removed by heat treatment in air alone, as proposed in the present invention, and that almost no binder or conductive material remains on the surface of the active material.

[0102] 6 shows an SEM image of a dried active material after washing to remove LiF, which is one example of a method for reusing an active material according to the present invention. Adding a lithium precursor to this active material and annealing it results in a reused active material with a shape almost identical to that of the fresh active material.

[0103] <Experimental Example 2> Positive electrode scraps were prepared using a cathode active material composed of NCM lithium composite transition metal oxide and an LCO active material. Powdered active material was separated by a dry grinding step according to the method for reusing active material in accordance with the present invention, and then heat-treated in air at 550°C for 30 minutes. Some of the scraps were then immersed in a LiOH aqueous solution for 10 minutes to perform the cleaning step according to the method for reusing active material in accordance with the present invention, while the remaining scraps were not cleaned. The amount of residual F was analyzed to determine the Li / metal molar ratio and the amount of residual LiF in the active material, and the results are shown in Table 1.

[0104] Sample 1 is fresh LCO active material. Sample 2 is LCO positive electrode scrap that was subjected to the heat treatment described above but not washed. Sample 3 is LCO positive electrode scrap that was subjected to the heat treatment described above and then washed.

[0105] Sample 4 is a fresh NCM active material. Sample 5 is NCM positive electrode scrap that was subjected to the heat treatment described above but not washed. Sample 6 is NCM positive electrode scrap that was subjected to the heat treatment described above and then washed.

[0106] [Table 1]

[0107] ND means that the measured value was 30 ppm or less. Samples 1 and 4 were fresh active materials, so almost no F was detected.

[0108] In Samples 2 and 5, which were not washed, the residual F amounts were measured at 1900 mg / kg and 1450 mg / kg, respectively. However, in Samples 3 and 6, which were washed, it was confirmed that LiF was completely dissolved in the washing solution and removed to the point that it was undetectable. This indicates that LiF is generated when LCO and NCM cathode scraps are heat treated, but is completely removed when the washing step is performed as proposed in the present invention.

[0109] Meanwhile, the Li / metal molar ratios of Samples 2 and 5 were found to be reduced by approximately 0.2–0.5 compared to fresh active materials Samples 1 and 4. Samples 3 and 6 also showed a further reduction of approximately 0.2–0.5 compared to Samples 2 and 5. In particular, the NCM active material has a larger specific surface area than LCO, which likely explains the greater reduction in the Li / metal molar ratio due to the transition to a spinel structure. This suggests that lithium is lost during the heat treatment step to remove the binder and conductive material, as well as during the surface modification step by cleaning. Therefore, we propose that the method for reusing an active material according to the present invention also includes a step of replenishing missing lithium by adding a lithium precursor during annealing.

[0110] <Experimental Example 3> As the positive electrode scrap, a positive electrode scrap having a composition of NCM lithium composite transition metal oxide:carbon black as a conductive material:PVdF as a binder=96.25:1.5:2.25 was prepared.

[0111] Comparative Example 1 is a fresh active material.

[0112] In Comparative Examples 2 and 3, the positive electrode scrap was not dry-pulverized, but instead heat-treated in air as positive electrode scrap with a positive electrode active material layer on a current collector. The heat treatment was performed at 550°C for 30 minutes. The current collector was separated by the heat treatment, and the active material was recovered in powder form. In Comparative Example 2, the recovered active material was not washed. In Comparative Example 3, washing was performed.

[0113] In Comparative Example 4 and Example 1, positive electrode scrap was dry-pulverized using a pin mill to separate the current collector and active material layer, and then only the powdery active material layer detached from the current collector was heat-treated in air. The heat treatment was carried out at 550°C for 30 minutes, as in Comparative Examples 2 and 3. In Comparative Example 4, the recovered active material was not washed. In Example 1, washing was carried out in the same manner as in Comparative Example 3.

[0114] The amount of residual F was analyzed to determine the Li / metal molar ratio and the amount of residual LiF in the active material. The results are shown in Table 2.

[0115] [Table 2]

[0116] The experimental results show that there is a slight difference in the amount of F remaining after heat treatment, but there is no significant difference in the amount of F remaining after cleaning. In addition, the measurement results for the Li / metal molar ratio are also similar between Comparative Example 3 and Example 1 (within an error range of ±0.02), which indicates that the analytical values ​​after cleaning are similar even though the initial electrode separation process is different.

[0117] <Experimental Example 4> Cathode active materials were prepared and their electrochemical performance was evaluated using the methods described in the following examples and comparative examples. 96.25 wt% of the cathode active materials recovered or prepared from the examples and comparative examples, 1.5 wt% of carbon black (a conductive material), and 2.25 wt% of PVdF (a binder) were weighed and mixed with NMP to form a slurry to fabricate a cathode. Coin Half Cells (CHCs) were then fabricated and their electrochemical performance was evaluated. The voltage was set to 3-4.3 V, and initial formation charge / discharge was performed at 0.1 C / 0.1 C. The electrolyte used in the cells was a carbonate-based electrolyte with a 3:7 ratio of ethylene carbonate (EC):ethyl methyl carbonate (EMC) containing some additives. Discharge conditions were 0.5 C / 1 C and 0.5 C / 2 C.

[0118] In Comparative Example 5, 0.1 mol of lithium precursor (Li2CO3) was added to Comparative Example 3 of Experimental Example 3, and annealed at 750°C for 5 hours. Then, H3BO3 was added to form a surface protective layer so that the boron content was 500 ppm, and the surface coating was heat-treated at 300°C for 5 hours.

[0119] In Example 2, Example 1 of Experimental Example 3 was subjected to annealing and surface coating in the same manner as in Comparative Example 5.

[0120] Table 3 shows the experimental results.

[0121] [Table 3]

[0122] The electrical performance evaluation results showed that Comparative Example 5 and Example 2 showed similar levels of initial capacity (0.1C / 0.1C) and also showed similar levels at high C-rates. That is, even though the initial current collector separation process was different, the same cell performance results could be obtained by using the same cleaning, lithium precursor addition annealing, and surface coating processes.

[0123] <Experimental Example 5> Positive electrode active materials were prepared according to the methods described in the following Examples and Comparative Examples, and their electrochemical performances were evaluated.

[0124] Example 3 The reused active material was collected using the method for recycling active materials of the present invention as described above. A cathode scrap, which had been punched out to form a cathode plate containing an active material (NCM-based lithium composite transition metal oxide), was prepared, and steps S20 and S25 were performed together to obtain a powdered active material layer. In step S30, heat treatment was performed in air at 550°C for 30 minutes. In step S40, cleaning was performed using LiOH for 10 minutes. In step S50, a lithium precursor (Li2CO3) was added in an amount sufficient to add lithium at a molar ratio of 0.09 based on the molar ratio of lithium to other metals in the raw active material (ICP analysis), and the resulting material was annealed at 750°C for 15 hours. Theoretically, in the case of a flash active material, the molar ratio of lithium to other metals is 1:1, but because the average error of the ICP equipment used to confirm this is ±0.05, preferably ±0.02, the molar ratio of lithium to other metals in the raw active material measured by ICP may be 1±0.05:1. In this experiment, the lithium precursor was added based on the analysis ratio from the ICP analysis.

[0125] Example 4 In addition to Example 3, the recovery process of the surface protective layer of the active material in step S60 was also carried out.

[0126] Comparative Example 6 Instead of recycled active material, fresh NCM-based lithium composite transition metal oxide was used.

[0127] Comparative Example 7 As described above, only the heat treatment in step S30 of the method for reusing an active material of the present invention was performed to remove the binder and conductive material. Since step S25 of the method for reusing an active material of the present invention was not performed, the Al current collector was separated during step S30. Step S30 was performed under the same conditions as in Example 3. In the method for reusing an active material of the present invention, the surface modification in step S40, the crystalline structure recovery in step S50, and the surface coating process in step S60 were not performed.

[0128] Comparative Example 8 In addition to Comparative Example 7, the active material was collected after the surface modification step S40 of the method for reusing an active material of the present invention was further performed. That is, the surface modification step was performed, but the crystal structure recovery step S50 and the surface coating step S60 of the method for reusing an active material of the present invention were not performed. Step S40 was performed under the same conditions as in Example 3.

[0129] Comparative Example 9 In addition to Comparative Example 7, in the method for reusing an active material according to the present invention as described above, the surface modification of step S40 was not performed, and only the crystalline structure recovery of step S50 was performed to collect an active material that was an NCM-based lithium transition metal composite oxide. Unlike Example 3, the annealing for the crystalline structure recovery was performed without adding a lithium precursor.

[0130] Comparative Example 10 Similar to Example 3, only steps S30, S40, and S50 were performed, except for step S25. Annealing for crystal structure recovery was performed without adding a lithium precursor, unlike Example 3.

[0131] ICP analysis was performed on the positive electrode active materials recovered or prepared in the examples and comparative examples to analyze the amount of remaining LiF, the ratio of lithium to other metals in the active material, and the amount of specific elements such as B and W.

[0132] The positive electrode active material recovered or prepared in each of the Examples and Comparative Examples was weighed out at 96.25 wt%, the conductive carbon black at 1.5 wt%, and the binder PVdF at 2.25 wt%, and these were mixed with NMP to prepare a slurry to manufacture a positive electrode. Then, a coin half cell (CHC) was manufactured and its electrochemical performance was evaluated.

[0133] In order to confirm the amount of LiF remaining in the active materials recovered in Comparative Examples 7 and 8, F was detected and analyzed by ICP. The results are shown in Table 4 below.

[0134] [Table 4]

[0135] Referring to Table 4, it can be seen that the F content in the recovered positive electrode active material was significantly lower in Comparative Example 8 than in Comparative Example 7. That is, it can be seen that LiF was completely dissolved in the lithium compound aqueous solution by washing and removed to the extent that it was not detectable by ICP. Therefore, it can be seen that LiF was significantly removed by step S40.

[0136] To determine whether there was a change in the lithium content in the positive electrode active material during steps S30 and S40, the ratio of lithium to other metals in the active material was analyzed by ICP, and the results are shown in Table 5 below.

[0137] [Table 5]

[0138] Referring to Table 5, it can be seen that the ratio of lithium to other metals in Comparative Example 7, which underwent heat treatment S30, was reduced by about 0.2 to 0.5 compared to Comparative Example 6, and that the ratio of lithium to other metals in Comparative Example 8, which underwent washing and drying S40, was reduced by about 0.2 to 0.5 compared to Comparative Example 7. The NCM-based lithium transition metal composite oxide has a relatively large particle specific surface area, and the change to a spinel structure results in a greater reduction in the ratio of lithium compared to other metals. This indicates that it is necessary to supplement the deficient lithium.

[0139] Table 5 shows values ​​measured by ICP analysis, and as mentioned above, ICP analysis has an error of about ±0.02. Therefore, even in Comparative Example 6, which is a flash active material, the ratio of lithium to other metals may be less than 1. Therefore, the amount of lithium precursor added to compensate for the lost lithium is determined based on the ratio (molar ratio by ICP analysis) of lithium to other metals in the raw active material (i.e., flash active material) used in the active material layer.

[0140] Figures 7 and 8 show the results of cell evaluation using the active materials of the examples and comparative examples. The capacity was evaluated according to the number of cycles at different currents, and rate performance was evaluated. The evaluation was performed using a standard laboratory charge / discharge testing device. There was no deviation due to the measurement device or method. In the graphs of Figures 7 and 8, the horizontal axis represents the number of cycles, and the vertical axis represents the capacity.

[0141] The voltage was set to 3 to 4.3 V, and the initial formation charge / discharge was performed at 0.1 C / 0.1 C. The electrolyte used to make up the cell was a carbonate-based electrolyte with an EC:EMC ratio of 3:7, containing some additives.

[0142] 7, comparing Comparative Example 7 before surface modification and Comparative Example 8 after surface modification after a primary heat treatment (550°C / 30 minutes) to remove the binder and conductive material, the electrode capacity of Comparative Example 8, which underwent surface modification, was found to be significantly reduced. This is because, as described above, Ni in the NCM-based lithium transition metal composite oxide was converted into chlorine by moisture, resulting in a reduction in capacity.

[0143] However, when annealing (750°C / 15 hours) without surface modification was performed, which corresponds to Comparative Example 9, there was almost no effect on capacity improvement compared to Comparative Example 7. This is due to the LiF remaining on the surface of the active material when surface modification is not performed. Incidentally, Table 4 explains that LiF can only be removed to a satisfactory extent by performing cleaning.

[0144] When surface modification and annealing are performed together after the first heat treatment, the capacity increases, as can be seen from Comparative Example 10. This is because, although the capacity decreases after the surface modification step, as in Comparative Example 8, after LiF is removed by the surface modification, Ni rock salt is reduced by annealing, and the structure is restored to a hexagonal crystal.

[0145] Next, referring to FIG. 8, the capacity improvement of Example 3 compared to Comparative Example 10 is confirmed. Example 3, compared to Comparative Example 10, adds a lithium precursor during annealing. This shows that adding a lithium precursor compensates for the lithium lost in the previous step, thereby improving the capacity. The loss of lithium during heat treatment and washing was explained with reference to Table 5.

[0146] The lithium compound was added in an amount corresponding to the loss in the lithium content of the existing positive electrode active material based on the results of ICP analysis (Table 5). As a result, it was confirmed through additional experiments that when a 0.09 to 0.1 mole ratio was added, the same level of capacity improvement effect as in Comparative Example 6 was achieved.

[0147] As described above, the present invention enables the recovery of active material from cathode scraps at a level that allows for direct reuse. It is safe because it does not require the use of toxic and explosive solvents such as NMP, DMC, acetone, or methanol, and it is suitable for mass production because it uses simple and safe methods such as heat treatment, washing, drying, and annealing.

[0148] As described above, according to the present invention, cathode scraps can be reused using a simple, environmentally friendly, and economical method. Furthermore, even if the cathode active material made of the thus-prepared NCM-based lithium transition metal composite oxide is reused as it is to manufacture a lithium secondary battery, there is no problem with the performance of the battery.

[0149] Although the present invention has been described above with reference to limited embodiments and drawings, it goes without saying that the present invention is not limited thereto, and various modifications and variations can be made by a person having ordinary skill in the art to which the present invention pertains within the technical spirit of the present invention and the scope of the claims. [Explanation of symbols]

[0150] 10 Positive electrode current collector 20 Cathode active material layer 30 Positive electrode sheet 40 positive electrode plate 50 cathode scrap

Claims

1. (a-1) dry-pulverizing a cathode scrap including a cathode active material layer made of a lithium composite transition metal oxide on a current collector to remove the active material layer in a powder form and separate it from the current collector; (a-2) recovering the active material by thermally treating the active material layer separated in powder form in air to thermally decompose the binder and the conductive material in the active material layer; (b) washing the recovered active material with an aqueous solution of a lithium compound that is basic in an aqueous solution state, and then drying; (c) adding a lithium precursor to the washed active material and annealing it to obtain a reusable active material; The lithium compound aqueous solution is prepared to contain more than 0% and not more than 15% LiOH, and the washing is carried out within 1 hour; The method for reusing a positive electrode active material, wherein the dry grinding is performed using a pin mill.

2. 10. The method of claim 1, further comprising the step of (d) surface-coating the annealed active material.

3. 3. The method of claim 1, further comprising shredding or cutting the cathode scrap before the dry pulverization.

4. The method for reusing a positive electrode active material according to any one of claims 1 to 3, wherein the heat treatment is carried out at a temperature of 300 to 1,000°C.

5. The method for reusing a positive electrode active material according to claim 1 , wherein LiF and metal fluorides present on the surface of the active material are removed by the washing.

6. 6. The method for reusing a positive electrode active material according to claim 1, wherein the washing is performed by immersing the recovered active material in the aqueous lithium compound solution while stirring the solution.

7. The lithium precursor is LiOH, Li ２ CO ３ , LiNO ３ and Li ２ 7. The method for reusing a positive electrode active material according to claim 1, wherein the positive electrode active material is one or more of:

8. 8. The method for reusing a positive electrode active material according to claim 1, wherein the lithium precursor is added in an amount sufficient to compensate for a proportion of lost lithium relative to a proportion of lithium and other metals in a raw active material used for the active material layer.

9. 9. The method of claim 8, wherein the lithium precursor further contains lithium in an amount of 0.0001 to 0.1 molar ratio based on a 1:1 molar ratio of lithium to the other metal.

10. 10. The method for reusing a positive electrode active material according to claim 1, wherein the annealing is carried out in air at 400 to 1,000°C.

11. The method for reusing a positive electrode active material according to claim 1 , wherein the annealing step is performed at a temperature exceeding the melting point of the lithium precursor.

12. 3. The method of claim 2, wherein the surface coating step comprises coating the surface with at least one of a metal, an organic metal, and a carbon component in a solid or liquid phase, followed by heat treatment at 100 to 1,200°C.

13. The reusable active material is represented by the following chemical formula 1: Li ａ Ni ｘ Mn ｙ Co ｚ M ｗ O ２＋δ (Chemical Formula 1) 13. The method of claim 1, wherein, in Chemical Formula 1, M comprises at least one selected from the group consisting of B, W, Al, Ti, and Mg, and 1<a≦1.1, 0≦x<0.95, 0≦y<0.8, 0≦z<1.0, 0≦w≦0.1, −0.02≦δ≦0.02, and x+y+z+w=1.

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