Patent Publication Number: US-2021184213-A1

Title: Positive active material for lithium rechargeable battery, manufacturing method thereof, and lithium rechargeable battery including same positive active material

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority to and the benefit of Korean Patent Application No. 10-2017-0177562 filed in the Korean Intellectual Property Office on Dec. 21, 2017, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     (a) Field of the Invention 
     The present disclosure relates to a positive active material for a lithium rechargeable battery, a manufacturing method thereof, and a lithium rechargeable battery including the positive active material. 
     (b) Description of the Related Art 
     A positive active material that is one of elements configuring a lithium rechargeable battery directly serves in realization of energy density of the battery, and also becomes a factor in determining a life-span characteristic. In relation to this, researches on ternary positive active materials bases on nickel, cobalt, and manganese have recently been in active progress, and are mainly used to manufacture a positive electrode precursor using a co-precipitation method. The manufacturing of a ternary positive electrode precursor using a co-precipitation method signifies a method for injecting nickel sulfate, cobalt sulfate, and cobalt manganese in a 1-3M concentration into a reactor, and performing co-precipitation by using an ammonia solution as a complexing agent and caustic soda as a precipitator. The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention, and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art. 
     SUMMARY OF THE INVENTION 
     Providing orientation to a precursor for a ternary positive electrode material used in the lithium rechargeable battery is generally known to mostly produce excellent electrochemical characteristics such as capacity, rate control, or cycle lifespan compared to a positive electrode material with no orientation, as a c-axis direction is perpendicularly arranged with respect to a direction in which lithium is intercalated or de-intercalated. 
     However, the precursor to which orientation is provided is known to be realized only when a concentration gradient is given to the precursor, and the concentration of metal ions in an inflow tank must change in order to realize this, so only batch-based process driving is allowable. 
     Further, to realize the batch process, a plurality of influent tanks for configuring a core and a shell are needed. Therefore, the method for assigning orientation in prior art has a drawback of high processing costs, compared to the general precursor manufacturing process. 
     The present invention realizes the orientation that is realizable in the conventional batch reactor in a flow reactor to thereby implement a skill for manufacturing a positive electrode precursor with orientation when there is no concentration gradient. 
     The discovery that a positive electrode material with orientation is possible through a concentration gradient represents an approach based on realizing experience-based orientation. 
     The present inventor analyzed the effect of the concentration gradient on formation of the precursor to deduce an effect for providing orientation of the precursor when there is no concentration gradient. 
     While the conventional general method for assigning orientation represents a method for forming a precursor by changing a concentration of metal ions that are input when a co-precipitation precursor is manufactured, the present invention relates to a method for assigning orientation not by changing the concentration of metal ions but by changing a process variable. 
     When the orientation is assigned by changing the process variable, a batch-type process used for assigning orientation in conventional art may be changed to a flow process, thereby generating an advantage of substantially reducing production cost of the precursor. In addition, in the case of applying it to the batch process, the manufacturing cost is reduced and no precise composition control is needed by reducing at least two types of inflow tanks for controlling the concentration of metal ions that are an influent to one type, so time control and pump control for manufacturing an oriented precursor may be simplified. 
     The present invention proposes a skill for manufacturing a positive electrode precursor with orientation when there is no concentration gradient by allowing orientation realizable by a conventional batch reactor to be realized by a flow reactor. 
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Exemplary embodiments of the present invention will now be described in detail. However, these are presented as examples, and the present invention is not limited thereto and is only defined by the scope of the claims to be described later. 
     In general, to manufacture an oriented positive electrode precursor, a precursor is generated by using a core solution mainly forming an internal composition and a shell solution mainly forming an external composition. 
     In detail, the concentration of metal ions is changed by partly generating an internal portion of the precursor with the core solution and inputting the shell solution to the core solution, and an external portion of the precursor is generated by inputting a metal ion solution in the changed concentration to a reactor. 
     In this instance, a concentration gradient is formed from the interior of the precursor toward the exterior thereof, showing a characteristic of orientation. Conventional art used a process for realizing a concentration gradient in the precursor so as to impart orientation to the precursor. For this reason, it had a drawback of only applying a batch-type reaction when attempting to realize the positive electrode material with orientation. The present invention proposes a method for manufacturing an oriented positive electrode material by changing not a concentration gradient but a processing condition. 
     Regarding a basic idea on the present invention, a principle of an orientation realizing mechanism includes: simplifying a dissolution phenomenon of ions in a solution based on nickel, manganese, and cobalt and not the concentration gradient with a concept of supersaturation, applying the same to an actual process, and acquiring an oriented positive electrode material. 
     In general, when a co-precipitation area with no complexing agent is calculated in the case of manganese, cobalt, and nickel ions used in the ternary positive electrode material, precipitation occurs at pH 7.5 in the case of manganese ions, at pH 9.2 in the case of cobalt ions, and at equal to or greater than pH 9.6 in the case of nickel ions. 
     However, in the presence of ammonia, which occurs in the actual co-precipitation condition, precipitation happens in a pH range that is much higher than the above-proposed value of pH in the case of nickel or cobalt that may be combined with ammonia. This is because the nickel and cobalt ions that may configure a complex with ammonia have a very high formation constant for indicating stability of the complex. 
     A complex compound combined with ammonia becomes very high, compared to the co-precipitation range when there is no ammonia. 
     In addition, regarding complex formation constants of the cobalt and nickel ions that may configure a complex with ammonia, the complex formation constants of the two materials are substantially different from each other, and in detail, the constant shows the value of 5×10 4  in the case of Co(NH 3 ) 6   2+  that is a complex of the cobalt ions, and the constant shows the value of 2×10 8  in the case of Ni(NH 3 ) 6   2+  that is a complex of the nickel ions, so the complex of the nickel ions exists in a more stable way. 
     For the above-noted reason, Ni(NH 3 ) 6   2+  undergoes precipitation in a higher pH range than Co(NH 3 ) 6   2 +, and the complex of the nickel ions frequently remains in a supernatant after a reaction in the case of co-precipitation driving. 
     Therefore, when the solubility of the metal ammonia complex compound is reversely estimated based on the above-noted precipitation phenomenon, the nickel complex compound ions (Ni(NH 3 ) 6   2+ ) may be considered to have the highest solubility, and the cobalt complex compound ions (Co(NH 3 ) 6   2+ ) may then be determined to have high solubility in a same driving condition of the process for manufacturing a ternary positive electrode precursor. 
     The manganese ions may not form a complex, so the solubility may be relatively very much lower than the nickel and cobalt ions. That is, in the same processing conditions such as concentration and pH by which the ternary positive electrode precursor is manufactured, an agitation speed, and a temperature, the solubility of the metal ions in the reactor may be considered to be increased as the composition of nickel in a precursor inflow solution increases, and the solubility of the metal ions may be considered to be reduced as the composition of manganese increases. 
     The major idea of the present invention is to analyze the conventional art according to understanding on the above-described concept and suggest a method for and realizing new orientation. 
     The conventional orientation realizing method is to realize the concentration gradient of the precursor, and the core solution used in an initial stage has a high nickel concentration, while the solution using a shell solution includes a large amount of manganese ions, so it is found that the solubility of the metal ions is low. That is, regarding the conventional method for realizing a precursor with orientation, the solubility of metal ions is very high in a center of the precursor, and the solubility of metal ions is gradually lowered toward the outside thereof. 
     The conventional art also uses a batch reactor, so the concentration of ions in the initial solution existing in the reactor is gradually lowered as the reaction progresses, and as a result, the conventional orientation realizing method may be deemed to be a driving method for maintaining the concentration of metal ions in the solution at less than a supersaturated state from start to end and preventing steep precipitation or crystal nuclei from being generated in a middle of the reaction. 
     To summarize such points and make a determination, the orientation realizing mechanism according to prior art may be analyzed, by the concept of the present invention, to be a method for manufacturing a precursor using a self-assembly phenomenon to the maximum by growing crystal while suppressing precipitation and nucleation in a maximum way. 
     Therefore, the present invention proposes a method for realizing orientation in a flow reactor based on the above-noted mechanism. 
     The present invention confirms that it is possible to manufacture a positive electrode material with orientation according to a process variable by using the conventional precursor manufacturing mechanism. That is, when co-precipitation driving is progressed in the condition of suppressing nucleation by controlling the process variable, orientation may be imparted in the situation of no concentration gradient in the influent according to a driving time. 
     The process variables in the precursor co-precipitation process include a reactor agitation speed, an inflow amount of ammonia against metal ions, a value of pH in the reactor, a temperature inside the reactor, and a reactor residence time. 
     An increase of the agitation speed is determined to impart orientation. In detail, it is found that, when the agitation speed of the reactor is a linear velocity that is equal to or greater than 3 m/s and equal to or less than 15 m/s, the precursor with orientation is acquired. The agitation speed with the above-noted velocity may be generally realized to be in a range that is equal to or greater than 80 rpm in a 1 cubic meter-level Taylor reactor. 
     It is found that orientation is shown as a use of ammonia that is a complexing agent input to a metal ion material increases. In the present invention, the precursor with orientation is obtained when the input flow of ammonia against metal ions is 1:0.95 to 1:1.5 as a molar ratio. In detail, the precursor with the best orientation may be obtained when it is 1:1.1 to 1:1.2. 
     As the temperature of the reactor lowers, the nucleation is suppressed and orientation is then obtained. The orientation may be obtained at 25 to 55° C., and the precursor with the best orientation is obtainable at 30 to 45° C. 
     It is the most advantageous to minimize a reactor residence time. Regarding the present reactor, the precursor with orientation is obtained when the residence time is 30 min to 4 h, and in detail, the best orientation is obtained when it is 30 min to 1 h. 
     Based upon such the idea, the orientation is realized by changing the agitation speed of the reactor, the ratio of ammonia, the reaction temperature, and the residence time. The above-noted orientation realizing method is applicable to a Taylor reactor and a batch reactor for manufacturing a positive electrode precursor as well as the continuous tank reactor. 
     Desired exemplary embodiments of the present invention, a comparative example compared thereto, and estimated examples thereof will now be described. However, the exemplary embodiments to be described below are examples of the present invention, and the present invention is not limited thereto. 
     EXPERIMENTAL EXAMPLE 
     Manufacturing a Positive Active Material 
     A positive electrode precursor is manufactured by applying a 50 liter Couette-Taylor flow reactor. 
     Regarding the initial condition in the reactor, pH is adjusted to be 10.7 by using a solution that is a mixture of 25 wt % caustic soda and 28 wt % ammonia at a weight percent of 85:15. NaOH is then added according to a reactor driving pH. To inject a reactant, a metal sulfate solution of a 2.5M concentration mixed with a nickel sulfate, a cobalt sulfate, and a manganese sulfate at a molar ratio of 88:9.5:2.5 is continuously added. 
     The temperature inside the reactor is changed according to respective conditions as expressed in the tables below, and driving is performed while maintaining the temperature. The mole flow (mol/min) of ammonia against the mole flow (mol/min) of the metal sulfate solution is also changed according to the reference given in the tables. Co-precipitation is performed by adjusting pH to be in a targeted range by use of NaOH. 
     Tests other than the change of agitation speed have a set condition of driving a Taylor reactor with the linear velocity of 11.0 m/s and a residence time of 1 h. The manufactured co-precipitation precursor is obtained, an ICP analysis is performed, and a calcination process is performed for 15 h at 750° C. with the molar ratio of LiOH with the composition of 1.03 against metal to thus obtain a final positive electrode material. 
     Electrochemical Characteristic Estimating Method 
     An electrochemical estimation is performed by using a CR2032-type coin cell. A slurry for manufacturing an electrode plate has the ratio of positive electrode:conductive material (Denka black):binder (PVDF, KF1100)=96.5:2.0:1.5 wt %, and viscosity of the slurry is adjusted by adding NMP (N-methyl-2-pyrrolidone) so that a solid amount may be about 30%. 
     The manufactured slurry is coated on a foil of Al that is 15 μm thick by using a doctor blade, and is then dry rolled. An electrode loading amount is 14.6 mg/cm 2 , and rolling density is 3.1 g/cm 3 . 
     The electrolyte solution generated by adding 1.5% of VC to a 1M LiPF6 in EC:DMC:EMC=3:4:3 (vol %) is used, a coin cell is manufactured by using a 
     PP separation film and a lithium cathode (200 μm, Honzo metal), an aging process is performed at room temperature for 10 h, and a charging and discharging test is performed. 
     Capacity estimation is performed with 200 mAh/g as a reference capacity, and an applied charging and discharging condition includes a CC/CV of 2.5 to 4.25 V and a cut-off of 1/20 C. 
     Initial capacity performs a 0.2C charging/0.2 C discharging after a 0.1 C charging/0.1 C discharging. 
     An output characteristic is obtained by measuring discharging capacity while increasing a C-rate at 0.1 C/0.2 C/0.5 C/1 C/1.3 C/1.5 C/2 C, and a high-temperature cycle lifespan characteristic is measured thirty times at a high temperature of 45° C. in the 0.3 C charging/0.3 C discharging condition. 
     Orientation Analysis Method 
     To analyze orientation of positive electrode material powder particles, several tens to several hundreds of positive electrode material powder particles are fixed to a polymer resin and a mounting process is performed. After the mounting process is progressed, a polishing process is performed to a dried sample for a first time by using sandpaper, and the sample is transferred to an ion milling device so that a secondary surface process is performed thereto. When a cross-sectional image of the powder is observed to find that a hemispherical positive electrode material (a circular cross-section) is acquired after the ion milling process is finished, an operation for processing the cross-section of the positive electrode material is finished. The sample of which the cross-section is processed is moved to EBSD equipment and its orientation is analyzed. The orientation in directions of [001], [120], and [210] is analyzed with reference to a misorientation angle of +/−30 degrees. A reference structure uses a hexagonal structure, and a pole figure is acquired with respect to an ND axis and an RD axis. 
     Estimation Example 1: Manipulating Variables of [a Total Number of Moles of Metal Ions in a Metal Salt Aqueous Solution: a Number of Moles of Ammonia], and Controlling Other Variables Within a Range of a Comparative Example 
     As expressed in Table 1 to Table 4, one variable is given, and other variables are controlled. The results are given in Table 1 below. 
     As can be known from Table 1 to Table 4, a property of the positive electrode material is excellent in the range of 1:0.95 to 1:1.5. Further preferably, it is excellent in the range of 1:1.1 to 1:1.2. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
               
                   
                 less than 30 degrees of 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 misorientation angle (Δg) 
                 Direction of 
                 Sphericity 
                 Density 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Manipulating 
                 Direction of 
                 Direction of 
                 Direction of 
                 [120] + 
                 l/w 
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 variables 
                 [001] 
                 [210] 
                 [120] 
                 [210] 
                 (Long axis 
                   
                 25° C., 
               
               
                   
                 Molar ratio 
                 with 
                 with 
                 with 
                 with 
                 diameter/short 
                 25° C. 
                 20 kN 
               
               
                   
                 of metal 
                 respect 
                 respect 
                 respect 
                 respect 
                 axis diameter of 
                 Tap 
                 Roll 
               
               
                 No. 
                 ions:ammonia 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 cross-section) 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 A01 
                 1:0.65 
                 15 
                 40 
                 45 
                 85 
                 1.81 
                 1.3 
                 1.8 
               
               
                 A02 
                 1:0.75 
                 18 
                 41 
                 41 
                 82 
                 1.72 
                 1.6 
                 2.2 
               
               
                 A03 
                 1:0.85 
                 19 
                 37 
                 44 
                 81 
                 1.51 
                 1.8 
                 2.5 
               
               
                 A04 
                 1:0.95 
                 22 
                 37 
                 41 
                 78 
                 1.46 
                 2.2 
                 3.0 
               
               
                 A05 
                 1:1.00 
                 24 
                 37 
                 39 
                 76 
                 1.23 
                 2.3 
                 3.1 
               
               
                 A06 
                 1:1.10 
                 29 
                 35 
                 36 
                 71 
                 1.13 
                 2.5 
                 3.4 
               
               
                 A07 
                 1:1.15 
                 32 
                 34 
                 34 
                 68 
                 1.13 
                 2.6 
                 3.5 
               
               
                 A08 
                 1:1.20 
                 34 
                 31 
                 35 
                 66 
                 1.02 
                 2.5 
                 3.4 
               
               
                 A09 
                 1:1.25 
                 34 
                 32 
                 35 
                 67 
                 1.02 
                 2.1 
                 2.9 
               
               
                 A10 
                 1:1.35 
                 34 
                 33 
                 34 
                 67 
                 1.03 
                 2.0 
                 2.7 
               
               
                 A11 
                 1:1.45 
                 33 
                 32 
                 35 
                 67 
                 1.04 
                 1.8 
                 2.5 
               
               
                 A12 
                 1:1.5  
                 34 
                 31 
                 36 
                 67 
                 1.03 
                 1.7 
                 2.3 
               
               
                 A13 
                 1:1.55 
                 33 
                 33 
                 34 
                 67 
                 1.06 
                 1.6 
                 2.3 
               
               
                 A14 
                 1:1.65 
                 32 
                 33 
                 35 
                 68 
                 1.09 
                 1.6 
                 2.3 
               
               
                 A15 
                 1:1.75 
                 30 
                 34 
                 36 
                 70 
                 1.0 
                 1.6 
                 2.2 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
               
                   
                 misorientation angle (Δg) of 
                   
               
            
           
           
               
               
               
               
            
               
                   
                 less than 30 degrees 
                   
                 Density 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Manipulating 
                 Direction of 
                 Direction of 
                 Direction of 
                 Direction of 
                   
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 variables 
                 [001] 
                 [210] 
                 [120] 
                 [120] + 
                   
                   
                 25° C., 
               
               
                   
                 Molar ratio 
                 with 
                 with 
                 with 
                 [210] 
                   
                 25° C. 
                 20 kN 
               
               
                   
                 of metal 
                 respect 
                 respect 
                 respect 
                 with respect 
                 Sphericity 
                 Tap 
                 Roll 
               
               
                 No. 
                 ions:ammonia 
                 to RD axis 
                 to RD axis 
                 to RD axis 
                 to RD axis 
                 l/w 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 A01 
                 1:0.65 
                 63 
                 20 
                 18 
                 38 
                 1.81 
                 1.3 
                 1.8 
               
               
                 A02 
                 1:0.75 
                 49 
                 24 
                 27 
                 51 
                 1.72 
                 1.6 
                 2.2 
               
               
                 A03 
                 1:0.85 
                 38 
                 27 
                 35 
                 62 
                 1.51 
                 1.8 
                 2.5 
               
               
                 A04 
                 1:0.95 
                 29 
                 28 
                 43 
                 71 
                 1.46 
                 2.2 
                 3.0 
               
               
                 A05 
                 1:1.00 
                 25 
                 29 
                 46 
                 75 
                 1.23 
                 2.3 
                 3.1 
               
               
                 A06 
                 1:1.10 
                 18 
                 32 
                 50 
                 82 
                 1.13 
                 2.5 
                 3.4 
               
               
                 A07 
                 1:1.15 
                 15 
                 33 
                 52 
                 85 
                 1.13 
                 2.6 
                 3.5 
               
               
                 A08 
                 1:1.20 
                 13 
                 35 
                 52 
                 87 
                 1.02 
                 2.5 
                 3.4 
               
               
                 A09 
                 1:1.25 
                 14 
                 34 
                 52 
                 86 
                 1.02 
                 2.1 
                 2.9 
               
               
                 A10 
                 1:1.35 
                 15 
                 35 
                 50 
                 85 
                 1.03 
                 2.0 
                 2.7 
               
               
                 A11 
                 1:1.45 
                 14 
                 37 
                 49 
                 86 
                 1.04 
                 1.8 
                 2.5 
               
               
                 A12 
                 1:1.5  
                 14 
                 38 
                 47 
                 86 
                 1.03 
                 1.7 
                 2.3 
               
               
                 A13 
                 1:1.55 
                 14 
                 34 
                 52 
                 86 
                 1.06 
                 1.6 
                 2.3 
               
               
                 A14 
                 1:1.65 
                 13 
                 33 
                 54 
                 87 
                 1.09 
                 1.6 
                 2.3 
               
               
                 A15 
                 1:1.75 
                 15 
                 32 
                 53 
                 85 
                 1.03 
                 1.6 
                 2.2 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                 Manipulating variables 
                   
                   
                   
                   
                   
               
               
                   
                 Molar ratio of metal 
               
               
                 No. 
                 ions:ammonia 
                 D10 
                 D25 
                 D50 
                 D75 
                 D90 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 A01 
                 1:0.65 
                 8.9 
                 10.0 
                 11.7 
                 13.8 
                 16.3 
               
               
                 A02 
                 1:0.75 
                 8.4 
                 9.4 
                 11.0 
                 13.0 
                 15.3 
               
               
                 A03 
                 1:0.85 
                 7.7 
                 8.7 
                 10.2 
                 12.0 
                 14.1 
               
               
                 A04 
                 1:0.95 
                 12.6 
                 14.1 
                 16.5 
                 19.5 
                 23.0 
               
               
                 A05 
                 1:1.00 
                 12.5 
                 14.1 
                 16.4 
                 19.4 
                 22.9 
               
               
                 A06 
                 1:1.10 
                 12.8 
                 14.4 
                 16.8 
                 19.8 
                 23.3 
               
               
                 A07 
                 1:1.15 
                 12.7 
                 14.3 
                 16.7 
                 19.7 
                 23.2 
               
               
                 A08 
                 1:1.20 
                 12.9 
                 14.5 
                 17.0 
                 20.0 
                 23.6 
               
               
                 A09 
                 1:1.25 
                 12.7 
                 14.2 
                 16.6 
                 19.6 
                 23.1 
               
               
                 A10 
                 1:1.35 
                 12.4 
                 13.9 
                 16.3 
                 19.2 
                 22.6 
               
               
                 A11 
                 1:1.45 
                 12.1 
                 13.6 
                 16.1 
                 8.8 
                 22.2 
               
               
                 A12 
                 1:1.5  
                 11.9 
                 13.3 
                 16.0 
                 18.4 
                 21.7 
               
               
                 A13 
                 1:1.55 
                 9.7 
                 10.9 
                 12.7 
                 15.0 
                 17.7 
               
               
                 A14 
                 1:1.65 
                 9.4 
                 10.6 
                 12.4 
                 14.6 
                 17.2 
               
               
                 A15 
                 1:1.75 
                 9.0 
                 10.1 
                 11.9 
                 14.0 
                 16.5 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 4 
               
             
            
               
                   
                   
               
               
                   
                   
                 Characteristics 
               
               
                   
                 Characteristics of 25 OR 30° C. 
                 of 45° C. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                 Capacity 
                   
                 Capacity 
                 Capacity 
               
               
                   
                 Initial 
                   
                   
                 maintaining 
                   
                 maintaining 
                 maintaining 
               
               
                   
                 discharging 
                   
                 30 cycle 
                 rate (%) 
                 100 cycle 
                 rate (%) 
                 rate (%) 
               
               
                   
                 capacity 
                 Initial 
                 discharging 
                 after 30 
                 discharging 
                 after 100 
                 after 100 
               
               
                 No. 
                 @0.2 C 
                 efficiency 
                 capacity 
                 cycles 
                 capacity 
                 cycles 
                 cycles 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 A01 
                 192.3 
                 84.0 
                 175.4 
                 85 
                 149.1 
                 78 
                 37 
               
               
                 A02 
                 198.8 
                 86.8 
                 188.2 
                 89 
                 167.4 
                 85 
                 45 
               
               
                 A03 
                 201.0 
                 87.8 
                 189.6 
                 91 
                 172.5 
                 92 
                 80 
               
               
                 A04 
                 205.4 
                 89.7 
                 196.5 
                 97 
                 190.6 
                 95 
                 85 
               
               
                 A05 
                 206.7 
                 90.3 
                 196.7 
                 97 
                 190.8 
                 95 
                 86 
               
               
                 A06 
                 207.6 
                 90.7 
                 196.5 
                 98 
                 192.5 
                 95 
                 86 
               
               
                 A07 
                 208.2 
                 90.8 
                 197.1 
                 98 
                 193.1 
                 96 
                 86 
               
               
                 A08 
                 208.7 
                 91.2 
                 197.7 
                 98 
                 193.7 
                 96 
                 85 
               
               
                 A09 
                 209.3 
                 91.0 
                 196.5 
                 98 
                 192.6 
                 96 
                 86 
               
               
                 A10 
                 210.2 
                 91.1 
                 196.7 
                 98 
                 192.8 
                 96 
                 86 
               
               
                 A11 
                 211.3 
                 91.8 
                 196.4 
                 97 
                 190.5 
                 95 
                 85 
               
               
                 A12 
                 211.2 
                 91.4 
                 195.8 
                 97 
                 190.0 
                 95 
                 85 
               
               
                 A13 
                 211.4 
                 90.6 
                 193.1 
                 95 
                 167.9 
                 87 
                 76 
               
               
                 A14 
                 210.7 
                 89.7 
                 189.7 
                 90 
                 153.6 
                 81 
                 65 
               
               
                 A15 
                 210.8 
                 88.0 
                 180.1 
                 88 
                 117.1 
                 65 
                 37 
               
               
                   
               
            
           
         
       
     
     Estimation Example 2: Manipulating Reaction pH Variable, and Controlling Other Variables Within a ange of Comparative Example 
     As expressed in Table 5 to Table 8, one variable is given, and other variables are controlled. The results are expressed in Table 5 to Table 8. 
     As can be known from Table 5 to Table 8, the pH range of 10.5 to 12 is found to be excellent. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 5 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 misorientation angle (Δg) of 
                   
                   
                   
               
               
                   
                 less than 30 degrees 
                 Direction of 
                 Sphericity 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Direction of 
                 Direction of 
                 Direction of 
                 [120] + 
                 l/w 
                 Density 
               
               
                   
                 [001] 
                 [210] 
                 [120] 
                 [210] 
                 (Long axis 
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Manipulating 
                 with 
                 with 
                 with 
                 with 
                 diameter/short 
                 25° C. 
                   
               
               
                   
                 variables 
                 respect 
                 respect 
                 respect 
                 respect 
                 axis diameter of 
                 Tap 
                 
                   
                 
               
               
                 No. 
                 Processing pH 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 cross-section) 
                 density 
                 
                   
                 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 B01 
                 9.0 
                 32 
                 33 
                 35 
                 68 
                 1.12 
                 1.66 
                 
                   
                 
               
               
                 B02 
                 9.5 
                 33 
                 33 
                 34 
                 67 
                 1.13 
                 1.76 
                 
                   
                 
               
               
                 B03 
                 10.0 
                 34 
                 31 
                 36 
                 67 
                 1.12 
                 1.87 
                 
                   
                 
               
               
                 B04 
                 10.5 
                 33 
                 32 
                 35 
                 67 
                 1.09 
                 2.0 
                 
                   
                 
               
               
                 B05 
                 11.0 
                 34 
                 31 
                 35 
                 66 
                 1.08 
                 2.5 
                 
                   
                 
               
               
                 B06 
                 11.5 
                 29 
                 35 
                 36 
                 71 
                 1.17 
                 2.5 
                 
                   
                 
               
               
                 B07 
                 12.0 
                 22 
                 37 
                 41 
                 74 
                 1.36 
                 2.3 
                 
                   
                 
               
               
                 B08 
                 12.5 
                 18 
                 41 
                 41 
                 82 
                 1.73 
                 1.6 
                 
                   
                 
               
               
                   
               
               
                     indicates data missing or illegible when filed 
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 6 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
               
                   
                 misorientation angle (Δg) of 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 less than 30 degrees 
                 Direction of 
                   
                 Density 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Direction of 
                 Direction of 
                 Direction of 
                 [120] + 
                   
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                 [001] 
                 [210] 
                 [120] 
                 [210] 
                   
                   
                 25° C., 
               
               
                   
                 Manipulating 
                 with 
                 with 
                 with 
                 with 
                   
                 25° C. 
                 20 kN 
               
               
                   
                 variables 
                 respect 
                 respect 
                 respect 
                 respect 
                 Sphericity 
                 Tap 
                 Roll 
               
               
                 No. 
                 Processing pH 
                 to RD axis 
                 to RD axis 
                 to RD axis 
                 to RD axis 
                 l/w 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 B01 
                 9.0 
                 15 
                 32 
                 53 
                 85 
                 1.12 
                 1.66 
                 2.3 
               
               
                 B02 
                 9.5 
                 15 
                 38 
                 47 
                 85 
                 1.13 
                 1.76 
                 2.3 
               
               
                 B03 
                 10.0 
                 14 
                 34 
                 52 
                 87 
                 1.12 
                 1.87 
                 2.4 
               
               
                 B04 
                 10.5 
                 14 
                 34 
                 52 
                 86 
                 1.09 
                 2.0 
                 3.0 
               
               
                 B05 
                 11.0 
                 13 
                 35 
                 52 
                 87 
                 1.08 
                 2.5 
                 3.4 
               
               
                 B06 
                 11.5 
                 18 
                 32 
                 50 
                 82 
                 1.17 
                 2.5 
                 3.4 
               
               
                 B07 
                 12.0 
                 22 
                 31 
                 47 
                 78 
                 1.36 
                 2.3 
                 3.1 
               
               
                 B08 
                 12.5 
                 49 
                 24 
                 27 
                 51 
                 1.73 
                 1.6 
                 2.2 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 7 
               
               
                   
               
               
                   
                 Manipulating variables 
                   
                   
                   
                   
                   
               
               
                 No. 
                 Processing pH 
                 D10 
                 D25 
                 D50 
                 D75 
                 D90 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 B01 
                 9.0 
                 9.1 
                 10.2 
                 11.9 
                 14.1 
                 16.6 
               
               
                 B02 
                 9.5 
                 12.0 
                 13.4 
                 15.7 
                 18.5 
                 21.8 
               
               
                 B03 
                 10.0 
                 12.5 
                 14.0 
                 16.4 
                 19.3 
                 22.7 
               
               
                 B04 
                 10.5 
                 12.8 
                 14.3 
                 16.7 
                 19.7 
                 23.2 
               
               
                 B05 
                 11.0 
                 13.0 
                 14.6 
                 17.1 
                 20.1 
                 23.7 
               
               
                 B06 
                 11.5 
                 12.6 
                 14.2 
                 16.5 
                 19.5 
                 23.0 
               
               
                 B07 
                 12.0 
                 12.7 
                 14.2 
                 16.6 
                 19.6 
                 23.1 
               
               
                 B08 
                 12.5 
                 8.5 
                 9.5 
                 11.1 
                 13.1 
                 15.4 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 8 
               
             
            
               
                   
                   
               
               
                   
                   
                 Characteristics 
               
               
                   
                 Characteristics of 25 OR 30° C. 
                 of 45° C. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                 Capacity 
                   
                 Capacity 
                 Capacity 
               
               
                   
                 Initial 
                   
                   
                 maintaining 
                   
                 maintaining 
                 maintaining 
               
               
                   
                 discharging 
                   
                 30 cycle 
                 rate (%) 
                 100 cycle 
                 rate (%) 
                 rate (%) 
               
               
                   
                 capacity 
                 Initial 
                 discharging 
                 after 30 
                 discharging 
                 after 100 
                 after 100 
               
               
                 No. 
                 @0.2 C 
                 efficiency 
                 capacity 
                 cycles 
                 capacity 
                 cycles 
                 cycles 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 B01 
                 192.3 
                 84.0 
                 175.4 
                 85 
                 149.2 
                 78 
                 44 
               
               
                 B02 
                 198.8 
                 86.8 
                 188.2 
                 89 
                 167.5 
                 85 
                 65 
               
               
                 B03 
                 201.0 
                 87.8 
                 189.6 
                 91 
                 172.6 
                 92 
                 76 
               
               
                 B04 
                 205.4 
                 89.7 
                 196.5 
                 97 
                 190.6 
                 95 
                 83 
               
               
                 B05 
                 206.7 
                 90.3 
                 196.7 
                 97 
                 190.8 
                 95 
                 84 
               
               
                 B06 
                 208.7 
                 90.8 
                 196.5 
                 97 
                 192.6 
                 96 
                 85 
               
               
                 B07 
                 208.2 
                 91.2 
                 197.1 
                 98 
                 193.2 
                 96 
                 85 
               
               
                 B08 
                 209.3 
                 92.1 
                 181.0 
                 88 
                 117.0 
                 65 
                 37 
               
               
                   
               
            
           
         
       
     
     Estimation Example 3: Manipulating Residence Time Variable of Metal Salt Solution, and Controlling Other Variables Within the Range of Comparative Example 
     As expressed in Table 9 to Table 12, one variable is given, and other variables are controlled. The results are expressed in Table 9 to Table 12. 
     As can be found from Table 9 to Table 12, the residence time in the range of 30 minutes to 4 hours is found to be excellent. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 9 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
               
                   
                 misorientation angle (Δg) of 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 less than 30 degrees 
                 Direction of 
                 Sphericity 
                 Density 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Direction of 
                 Direction of 
                 Direction of 
                 [120] + 
                 l/w 
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Manipulating 
                 [001] 
                 [210] 
                 [120] 
                 [210] 
                 (Long axis 
                   
                 25° C. 
               
               
                   
                 variables 
                 with 
                 with 
                 with 
                 with 
                 diameter/short 
                 25° C. 
                 20 kN 
               
               
                   
                 Residence 
                 respect 
                 respect 
                 respect 
                 respect 
                 axisdiameter of 
                 Tap 
                 Roll 
               
               
                 No. 
                 time 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 cross-section) 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 C01 
                 15 
                 min 
                 32 
                 34 
                 35 
                 68 
                 1.31 
                 1.3 
                 2.3 
               
               
                 C02 
                 30 
                 min 
                 33 
                 33 
                 34 
                 67 
                 1.02 
                 1.7 
                 2.3 
               
               
                 C03 
                 1 
                 h 
                 34 
                 31 
                 36 
                 67 
                 1.01 
                 1.8 
                 2.5 
               
               
                 C04 
                 2 
                 h 
                 34 
                 31 
                 35 
                 66 
                 1.01 
                 2.4 
                 3.5 
               
               
                 C05 
                 3 
                 h 
                 29 
                 35 
                 36 
                 71 
                 1.09 
                 2.2 
                 3.4 
               
               
                 C06 
                 4 
                 h 
                 19 
                 37 
                 44 
                 71 
                 1.21 
                 2.4 
                 3.4 
               
               
                 C07 
                 6 
                 h 
                 18 
                 41 
                 41 
                 82 
                 1.22 
                 2.5 
                 3.4 
               
               
                 C08 
                 8 
                 h 
                 19 
                 40 
                 41 
                 81 
                 1.27 
                 2.5 
                 3.5 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 10 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 misorientation angle (Δg) of 
                   
                   
                 Density 
               
               
                   
                 less than 30 degrees 
                 RD axis 
                   
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Manipulating 
                 RD axis 
                 RD axis 
                 RD axis 
                 respect 
                   
                   
                 25° C., 
               
               
                   
                 variables 
                 respect 
                 respect 
                 respect 
                 [120] + 
                   
                 25° C. 
                 20 kN 
               
               
                   
                 Residence 
                 [001] 
                 [210] 
                 [120] 
                 [210] 
                 Sphericity 
                 Tap 
                 Roll 
               
               
                 No. 
                 time 
                 direction 
                 direction 
                 direction 
                 direction 
                 l/w 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 C01 
                 15 
                 min 
                 15 
                 32 
                 53 
                 85 
                 1.31 
                 1.3 
                 2.3 
               
               
                 C02 
                 30 
                 min 
                 14 
                 34 
                 52 
                 86 
                 1.02 
                 1.7 
                 2.3 
               
               
                 C03 
                 1 
                 h 
                 15 
                 38 
                 47 
                 85 
                 1.01 
                 1.8 
                 2.5 
               
               
                 C04 
                 2 
                 h 
                 14 
                 34 
                 52 
                 86 
                 1.01 
                 2.4 
                 3.5 
               
               
                 C05 
                 3 
                 h 
                 25 
                 29 
                 46 
                 75 
                 1.09 
                 2.2 
                 3.4 
               
               
                 C06 
                 4 
                 h 
                 38 
                 27 
                 35 
                 62 
                 1.21 
                 2.4 
                 3.4 
               
               
                 C07 
                 6 
                 h 
                 49 
                 24 
                 27 
                 51 
                 1.22 
                 2.5 
                 3.4 
               
               
                 C08 
                 8 
                 h 
                 50 
                 20 
                 30 
                 50 
                 1.27 
                 2.5 
                 3.5 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 11 
               
               
                   
               
               
                   
                 Manipulating variables 
                   
                   
                   
                   
                   
               
               
                 No. 
                 Residence time 
                 D10 
                 D25 
                 D50 
                 D75 
                 D90 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 C01 
                 15 
                 min 
                 9.1 
                 10.0 
                 11.8 
                 13.9 
                 16.4 
               
               
                 C02 
                 30 
                 min 
                 9.7 
                 10.8 
                 12.6 
                 14.9 
                 17.6 
               
               
                 C03 
                 1 
                 h 
                 12.1 
                 13.5 
                 15.8 
                 18.7 
                 22.1 
               
               
                 C04 
                 2 
                 h 
                 12.8 
                 14.4 
                 16.9 
                 19.9 
                 23.5 
               
               
                 C05 
                 3 
                 h 
                 15.4 
                 17.3 
                 20.3 
                 23.9 
                 28.2 
               
               
                 C06 
                 4 
                 h 
                 14.8 
                 16.6 
                 19.4 
                 22.9 
                 27.0 
               
               
                 C07 
                 6 
                 h 
                 14.1 
                 15.9 
                 18.6 
                 21.9 
                 25.8 
               
               
                 C08 
                 8 
                 h 
                 13.5 
                 15.1 
                 17.7 
                 20.9 
                 24.7 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 12 
               
             
            
               
                   
                   
               
               
                   
                   
                 Characteristics 
               
               
                   
                 Characteristics of 25 OR 30° C. 
                 of 45° C. 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Capacity 
                   
                 Capacity 
                 Capacity 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                 maintaining 
                   
                 maintaining 
                 maintaining 
               
               
                   
                 30 cycle 
                 rate (%) 
                 100 cycle 
                 rate (%) 
                 rate (%) 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Residence 
                 Initial 
                 discharging 
                 after 30 
                 discharging 
                 after 100 
                 after 100 
               
               
                 No. 
                 time 
                 efficiency 
                 capacity 
                 cycles 
                 capacity 
                 cycles 
                 cycles 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 C01 
                 15 
                 min 
                 91.4 
                 189.7 
                 88 
                 117.0 
                 65 
                 37 
               
               
                 C02 
                 30 
                 min 
                 91.8 
                 196.4 
                 97 
                 188.4 
                 95 
                 86 
               
               
                 C03 
                 1 
                 h 
                 91.0 
                 196.5 
                 98 
                 188.5 
                 96 
                 86 
               
               
                 C04 
                 2 
                 h 
                 91.2 
                 197.7 
                 98 
                 193.6 
                 96 
                 85 
               
               
                 C05 
                 3 
                 h 
                 89.7 
                 196.7 
                 97 
                 190.8 
                 95 
                 83 
               
               
                 C06 
                 4 
                 h 
                 87.8 
                 189.6 
                 91 
                 172.4 
                 92 
                 76 
               
               
                 C07 
                 6 
                 h 
                 86.8 
                 188.2 
                 89 
                 167.3 
                 85 
                 65 
               
               
                 C08 
                 8 
                 h 
                 84.0 
                 175.4 
                 85 
                 149.0 
                 78 
                 44 
               
               
                   
               
            
           
         
       
     
     Estimation Example 4: Manipulating Agitation Speed Variable, and Controlling Other Variables Within the Range of Comparative Example 
     As expressed in Table 13 to Table 16, one variable is given, and other variables are controlled. The results are expressed in Table 13 to Table 16. 
     As can be known from Table 13 to Table 16, the agitation speed in the range of 80 to 200 rpm is found to be excellent. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 13 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
               
                   
                 misorientation angle (Δg) of 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 less than 30 degrees 
                 Direction of 
                 Sphericity 
                 Density 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Direction of 
                 Direction of 
                 Direction of 
                 [120] + 
                 l/w 
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Manipulating 
                 [001] 
                 [210] 
                 [120] 
                 [210] 
                 (Long axis 
                   
                 25° C., 
               
               
                   
                 variables 
                 with 
                 with 
                 with 
                 with 
                 diameter/short 
                 25° C. 
                 20 kN 
               
               
                   
                 Agitation 
                 respect 
                 respect 
                 respect 
                 respect 
                 axis diameter of 
                 Tap 
                 Roll 
               
               
                 No. 
                 speed 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 cross-section) 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 D01 
                 30 
                 15 
                 40 
                 45 
                 85 
                 1.83 
                 1.6 
                 2.1 
               
               
                 D02 
                 50 
                 18 
                 41 
                 41 
                 82 
                 1.52 
                 1.8 
                 2.4 
               
               
                 D03 
                 80 
                 29 
                 35 
                 36 
                 71 
                 1.12 
                 2.5 
                 3.4 
               
               
                 D04 
                 100 
                 34 
                 31 
                 35 
                 66 
                 1.07 
                 2.5 
                 3.4 
               
               
                 D05 
                 200 
                 34 
                 32 
                 35 
                 67 
                 1.07 
                 2.6 
                 3.4 
               
               
                 D06 
                 300 
                 18 
                 41 
                 41 
                 82 
                 1.09 
                 2.3 
                 3.3 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 14 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
               
                   
                 misorientation angle (Δg) of 
                   
               
            
           
           
               
               
               
               
            
               
                   
                 less than 30 degrees 
                   
                 Density 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Direction of 
                 Direction of 
                 Direction of 
                 Direction of 
                   
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Manipulating 
                 [001] 
                 [210] 
                 [120] 
                 [120] + 
                   
                   
                 25° C., 
               
               
                   
                 variables 
                 with 
                 with 
                 with 
                 [210] 
                   
                 25° C. 
                 20 kN 
               
               
                   
                 Agitation 
                 respect 
                 respect 
                 respect 
                 with respect 
                 Sphericity 
                 Tap 
                 Roll 
               
               
                 No. 
                 speed 
                 to RD axis 
                 to RD axis 
                 to RD axis 
                 to RD axis 
                 l/w 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 D01 
                 30 
                 63 
                 20 
                 18 
                 38 
                 1.83 
                 1.6 
                 2.1 
               
               
                 D02 
                 50 
                 49 
                 24 
                 27 
                 51 
                 1.52 
                 1.8 
                 2.4 
               
               
                 D03 
                 80 
                 23 
                 31 
                 46 
                 77 
                 1.12 
                 2.5 
                 3.4 
               
               
                 D04 
                 100 
                 18 
                 32 
                 50 
                 82 
                 1.07 
                 2.5 
                 3.4 
               
               
                 D05 
                 200 
                 15 
                 38 
                 47 
                 85 
                 1.07 
                 2.6 
                 3.4 
               
               
                 D06 
                 300 
                 38 
                 27 
                 35 
                 62 
                 1.09 
                 2.3 
                 3.3 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 15 
               
               
                   
               
               
                   
                 Manipulating variables 
                   
                   
                   
                   
                   
               
               
                 No. 
                 Processing pH 
                 D10 
                 D25 
                 D50 
                 D75 
                 D90 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 D01 
                 30 
                 8.6 
                 10.2 
                 11.9 
                 14.0 
                 16.5 
               
               
                 D02 
                 50 
                 7.8 
                 8.9 
                 10.4 
                 12.2 
                 14.3 
               
               
                 D03 
                 80 
                 13.0 
                 14.6 
                 17.0 
                 20.0 
                 23.5 
               
               
                 D04 
                 100 
                 12.9 
                 14.5 
                 16.9 
                 19.9 
                 23.5 
               
               
                 D05 
                 200 
                 13.1 
                 14.7 
                 17.2 
                 20.2 
                 23.8 
               
               
                 D06 
                 300 
                 9.2 
                 10.3 
                 12.1 
                 14.2 
                 16.7 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 16 
               
             
            
               
                   
                   
               
               
                   
                   
                 Characteristics 
               
               
                   
                 Characteristics of 25 OR 30° C. 
                 of 45° C. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                 Capacity 
                   
                 Capacity 
                 Capacity 
               
               
                   
                 Initial 
                   
                   
                 maintaining 
                   
                 maintaining 
                 maintaining 
               
               
                   
                 discharging 
                   
                 30 cycle 
                 rate (%) 
                 100 cycle 
                 rate (%) 
                 rate (%) 
               
               
                   
                 capacity 
                 Initial 
                 discharging 
                 after 30 
                 discharging 
                 after 100 
                 after 100 
               
               
                 No. 
                 @0.2 C 
                 efficiency 
                 capacity 
                 cycles 
                 capacity 
                 cycles 
                 cycles 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 D01 
                 198.8 
                 86.8 
                 188.2 
                 89 
                 167.4 
                 85 
                 65 
               
               
                 D02 
                 201.0 
                 87.8 
                 189.6 
                 91 
                 172.5 
                 92 
                 76 
               
               
                 D03 
                 207.6 
                 90.7 
                 196.5 
                 98 
                 192.5 
                 95 
                 85 
               
               
                 D04 
                 208.2 
                 90.8 
                 197.1 
                 98 
                 193.1 
                 95 
                 85 
               
               
                 D05 
                 208.7 
                 91.2 
                 197.7 
                 98 
                 193.7 
                 96 
                 85 
               
               
                 D06 
                 209.3 
                 88.0 
                 196.7 
                 88 
                 117.1 
                 65 
                 37 
               
               
                   
               
            
           
         
       
     
     Estimation Example 5: Manipulating Reaction Temperature Variable, and Controlling Other Variables Within the Range of Comparative Example 
     As expressed in Table 17 to Table 20, one variable is given, and other variables are controlled. The results are expressed in Table 17 to Table 20. 
     As can be known from Table 17 to Table 20, the reaction temperature in the range of 30 to 50° C. (in detail, 30 to 45° C.) is found to be excellent. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 17 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
               
                   
                 misorientation angle (Δg) of 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 less than 30 degrees 
                 Direction of 
                 Sphericity 
                 Density 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Direction of 
                 Direction of 
                 Direction of 
                 [120] + 
                 l/w 
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Manipulating 
                 [001] 
                 [210] 
                 [120] 
                 [210] 
                 (Long axis 
                   
                 25° C., 
               
               
                   
                 variable 
                 with 
                 with 
                 with 
                 with 
                 diameter/short 
                 25° C. 
                 20 kN 
               
               
                   
                 Reaction 
                 respect 
                 respect 
                 respect 
                 respect 
                 axis diameter of 
                 Tap 
                 Roll 
               
               
                 No. 
                 temperature 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 cross-section) 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 E01 
                 25 
                 32 
                 33 
                 35 
                 68 
                 1.23 
                 1.8 
                 2.6 
               
               
                 E02 
                 30 
                 34 
                 31 
                 36 
                 67 
                 1.17 
                 2.3 
                 3.4 
               
               
                 E03 
                 35 
                 34 
                 32 
                 35 
                 67 
                 1.09 
                 2.4 
                 3.4 
               
               
                 E04 
                 40 
                 29 
                 35 
                 36 
                 71 
                 1.06 
                 2.6 
                 3.5 
               
               
                 E05 
                 45 
                 24 
                 37 
                 39 
                 76 
                 1.03 
                 2.6 
                 3.5 
               
               
                 E06 
                 50 
                 19 
                 37 
                 44 
                 81 
                 1.11 
                 2.6 
                 3.4 
               
               
                 E07 
                 60 
                 15 
                 40 
                 45 
                 85 
                 1.67 
                 2.5 
                 3.2 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 18 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
               
                   
                 misorientation angle (Δg) of 
                   
               
            
           
           
               
               
               
               
            
               
                   
                 less than 30 degrees 
                   
                 Density 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Direction of 
                 Direction of 
                 Direction of 
                 Direction of 
                   
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Manipulating 
                 [001] 
                 [210] 
                 [120] 
                 [120] + 
                   
                   
                 25° C., 
               
               
                   
                 variables 
                 with 
                 with 
                 with 
                 [210] 
                   
                 25° C. 
                 20 kN 
               
               
                   
                 Reaction 
                 respect 
                 respect 
                 respect 
                 with respect 
                 Sphericity 
                 Tap 
                 Roll 
               
               
                 No. 
                 temperature 
                 to RD axis 
                 to RD axis 
                 to RD axis 
                 to RD axis 
                 l/w 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 E01 
                 25 
                 15 
                 32 
                 53 
                 85 
                 1.23 
                 1.8 
                 2.6 
               
               
                 E02 
                 30 
                 14 
                 34 
                 52 
                 86 
                 1.17 
                 2.3 
                 3.4 
               
               
                 E03 
                 35 
                 14 
                 35 
                 50 
                 85 
                 1.09 
                 2.4 
                 3.4 
               
               
                 E04 
                 40 
                 15 
                 33 
                 52 
                 85 
                 1.06 
                 2.6 
                 3.5 
               
               
                 E05 
                 45 
                 18 
                 32 
                 50 
                 82 
                 1.03 
                 2.6 
                 3.5 
               
               
                 E06 
                 50 
                 29 
                 28 
                 43 
                 71 
                 1.11 
                 2.6 
                 3.4 
               
               
                 E07 
                 60 
                 38 
                 27 
                 35 
                 62 
                 1.67 
                 2.5 
                 3.2 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 19 
               
               
                   
               
               
                   
                 Manipulating variables 
                   
                   
                   
                   
                   
               
               
                 No. 
                 Reaction temperature 
                 D10 
                 D25 
                 D50 
                 D75 
                 D90 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 E01 
                 25 
                 3.7 
                 4.2 
                 5.1 
                 6.0 
                 7.0 
               
               
                 E02 
                 30 
                 5.0 
                 5.7 
                 6.8 
                 8.1 
                 9.5 
               
               
                 E03 
                 35 
                 7.6 
                 8.6 
                 10.2 
                 11.9 
                 14.1 
               
               
                 E04 
                 40 
                 12.5 
                 14.0 
                 16.4 
                 19.4 
                 23.0 
               
               
                 E05 
                 45 
                 12.7 
                 14.3 
                 16.7 
                 19.7 
                 23.2 
               
               
                 E06 
                 50 
                 12.6 
                 14.2 
                 16.6 
                 19.6 
                 23.3 
               
               
                 E07 
                 60 
                 6.3 
                 7.1 
                 8.5 
                 10.0 
                 11.8 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 20 
               
             
            
               
                   
                   
               
               
                   
                   
                 Characteristics 
               
               
                   
                 Characteristics of 25 OR 30° C. 
                 of 45° C. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                 Capacity 
                   
                 Capacity 
                 Capacity 
               
               
                   
                 Initial 
                   
                   
                 maintaining 
                   
                 maintaining 
                 maintaining 
               
               
                   
                 discharging 
                   
                 30 cycle 
                 rate (%) 
                 100 cycle 
                 rate (%) 
                 rate (%) 
               
               
                   
                 capacity 
                 Initial 
                 discharging 
                 after 30 
                 discharging 
                 after 100 
                 after 100 
               
               
                 No. 
                 @0.2 C 
                 efficiency 
                 capacity 
                 cycles 
                 capacity 
                 cycles 
                 cycles 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 E01 
                 211.3 
                 91.8 
                 196.4 
                 97 
                 149.1 
                 78 
                 77 
               
               
                 E02 
                 211.2 
                 91.2 
                 195.8 
                 97 
                 186.0 
                 95 
                 85 
               
               
                 E03 
                 209.3 
                 91.0 
                 196.5 
                 98 
                 188.6 
                 96 
                 86 
               
               
                 E04 
                 210.2 
                 89.7 
                 196.5 
                 97 
                 190.6 
                 95 
                 84 
               
               
                 E05 
                 209.7 
                 91.0 
                 196.6 
                 98 
                 188.7 
                 96 
                 86 
               
               
                 E06 
                 206.7 
                 87.3 
                 189.6 
                 91 
                 179.6 
                 89 
                 81 
               
               
                 E07 
                 195.4 
                 85.7 
                 181.7 
                 86 
                 167.5 
                 81 
                 69 
               
               
                   
               
            
           
         
       
     
     Estimation Example 6: Final Poduct Manufacturing Tests (Comparative Example and exemplary embodiment) 
     An exemplary embodiment (EE) applies a process variable that is in an optimized area and a comparative example (CE) performs a test on a case that is outside the optimized area and showing no orientation. 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 21 
               
               
                   
               
               
                   
                 Molar ratio 
                   
                 Residence 
                 Agitation 
                 Reaction 
               
               
                   
                 metal 
                 Reaction 
                 time 
                 speed 
                 temperature 
               
               
                 No. 
                 ions:ammonia 
                 pH 
                 (h) 
                 (rpm) 
                 (° C.) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 EE1 
                  1:1.10 
                 11.0 
                 1.0 
                 100 
                 45 
               
               
                 EE2 
                 1:1.2 
                 11.0 
                 1.0 
                 100 
                 45 
               
               
                 EE3 
                 1:1.1 
                 10.5 
                 1.0 
                 100 
                 45 
               
               
                 EE4 
                 1:1.1 
                 11.0 
                 0.5 
                 100 
                 45 
               
               
                 EE6 
                 1:1.1 
                 11.0 
                 1.0 
                 200 
                 45 
               
               
                 EE7 
                 1:1.1 
                 11.0 
                 1.0 
                 100 
                 35 
               
               
                 CE1 
                  1:0.85 
                 12.5 
                 4.0 
                 50 
                 60 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 22 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
               
                   
                 misorientation angle (Δg) of 
               
               
                   
                 less than 30 degrees 
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                 Direction of 
                 Sphericity 
                 Density 
               
               
                   
                 Direction of 
                 Direction of 
                 Direction of 
                 [120] + 
                 l/w 
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                 [001] 
                 [210] 
                 [120] 
                 [210] 
                 (Long axis 
                   
                 25° C., 
               
               
                   
                   
                 with 
                 with 
                 with 
                 with 
                 diameter/short 
                 25° C. 
                 20 kN 
               
               
                   
                 Manipulating 
                 respect 
                 respect 
                 respect 
                 respect 
                 axis diameter of 
                 Tap 
                 roll 
               
               
                 No. 
                 variables 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 to ND axis 
                 cross-section) 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 EE1 
                 Orientation 
                 29 
                 35 
                 36 
                 71 
                 1.13 
                 2.5 
                 3.4 
               
               
                   
                 improving 
               
               
                   
                 condition 
               
               
                 EE2 
                 Ammonia 
                 34 
                 32 
                 35 
                 67 
                 1.03 
                 2.4 
                 3.2 
               
               
                   
                 increase 
               
               
                 EE3 
                 pH reduction 
                 32 
                 34 
                 34 
                 68 
                 1.06 
                 2.3 
                 3.2 
               
               
                 EE4 
                 Residence 
                 33 
                 33 
                 34 
                 67 
                 1.02 
                 2.1 
                 3.2 
               
               
                   
                 time 
               
               
                   
                 reduction 
               
               
                 EE6 
                 Agitation 
                 34 
                 31 
                 35 
                 66 
                 1.07 
                 2.4 
                 3.5 
               
               
                   
                 speed 
               
               
                   
                 increase 
               
               
                 EE7 
                 Reaction 
                 34 
                 32 
                 35 
                 67 
                 1.17 
                 2.1 
                 3.1 
               
               
                   
                 temperature 
               
               
                   
                 reduction 
               
               
                 CE1 
                 Orientation 
                 15 
                 40 
                 45 
                 85 
                 1.67 
                 1.3 
                 2.3 
               
               
                   
                 suppressing 
               
               
                   
                 condition 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 23 
               
             
            
               
                   
                   
               
               
                   
                 EBSD analysis result with 
                   
               
               
                   
                 misorientation angle (Δg) of 
                   
               
            
           
           
               
               
               
               
            
               
                   
                 less than 30 degrees 
                   
                 Density 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Direction of 
                 Direction of 
                 Direction of 
                 Direction of 
                   
                 (g/cc) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                 [001] 
                 [210] 
                 [120] 
                 [120] + 
                   
                   
                 25° C., 
               
               
                   
                   
                 with 
                 with 
                 with 
                 [210] 
                   
                 25° C. 
                 20 kN 
               
               
                   
                 Manipulating 
                 respect 
                 respect 
                 respect 
                 with respect 
                 Sphericity 
                 Tap 
                 Roll 
               
               
                 No. 
                 variables 
                 to RD axis 
                 to RD axis 
                 to RD axis 
                 to RD axis 
                 l/w 
                 density 
                 density 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 EE1 
                 Orientation 
                 18 
                 32 
                 50 
                 82 
                 1.13 
                 2.5 
                 3.4 
               
               
                   
                 improving 
               
               
                   
                 condition 
               
               
                 EE2 
                 Ammonia 
                 14 
                 34 
                 52 
                 86 
                 1.03 
                 2.4 
                 3.2 
               
               
                   
                 increase 
               
               
                 EE3 
                 pH reduction 
                 15 
                 33 
                 52 
                 85 
                 1.06 
                 2.3 
                 3.2 
               
               
                 EE4 
                 Residence 
                 14 
                 37 
                 49 
                 86 
                 1.02 
                 2.1 
                 3.2 
               
               
                   
                 time 
               
               
                   
                 reduction 
               
               
                 EE6 
                 Agitation 
                 13 
                 35 
                 52 
                 87 
                 1.07 
                 2.4 
                 3.5 
               
               
                   
                 speed 
               
               
                   
                 increase 
               
               
                 EE7 
                 Reaction 
                 14 
                 37 
                 49 
                 86 
                 1.17 
                 2.1 
                 3.1 
               
               
                   
                 temperature 
               
               
                   
                 reduction 
               
               
                 CE1 
                 Orientation 
                 63 
                 20 
                 18 
                 38 
                 1.67 
                 1.3 
                 2.3 
               
               
                   
                 suppressing 
               
               
                   
                 condition 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 24 
               
             
            
               
                   
                   
               
               
                   
                   
                 Characteristics 
               
               
                   
                 Characteristics of 25 OR 30° C. 
                 of 45° C. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                 Capacity 
                   
                 Capacity 
                 Capacity 
               
               
                   
                 Initial 
                   
                   
                 maintaining 
                   
                 maintaining 
                 maintaining 
               
               
                   
                 discharging 
                   
                 30 cycle 
                 rate (%) 
                 100 cycle 
                 rate (%) 
                 rate (%) 
               
               
                   
                 capacity 
                 Initial 
                 discharging 
                 after 30 
                 discharging 
                 after 100 
                 after 100 
               
               
                 No. 
                 @0.2 C 
                 efficiency 
                 capacity 
                 cycles 
                 capacity 
                 cycles 
                 cycles 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 EE1 
                 208.7 
                 91.2 
                 197.7 
                 98 
                 193.7 
                 96 
                 85 
               
               
                 EE2 
                 209.3 
                 91.0 
                 196.5 
                 98 
                 192.6 
                 96 
                 86 
               
               
                 EE3 
                 210.2 
                 91.1 
                 196.7 
                 98 
                 192.8 
                 96 
                 86 
               
               
                 EE4 
                 211.4 
                 90.6 
                 193.1 
                 95 
                 179.8 
                 93 
                 84 
               
               
                 EE6 
                 207.6 
                 90.7 
                 196.5 
                 98 
                 192.5 
                 95 
                 86 
               
               
                 EE7 
                 213.6 
                 92.8 
                 198.3 
                 98 
                 194.5 
                 97 
                 89 
               
               
                 CE1 
                 210.8 
                 88.0 
                 180.1 
                 88 
                 117.1 
                 65 
                 37 
               
               
                   
               
            
           
         
       
     
     The present invention is not limited to the exemplary embodiments and may be produced in various forms, and it will be understood by those skilled in the art to which the present invention pertains that exemplary embodiments of the present invention may be implemented in other specific forms without modifying the technical spirit or essential features of the present invention. Therefore, it should be understood that the aforementioned exemplary embodiments are illustrative in terms of all aspects and are not limited.