Patent Publication Number: US-2018040890-A1

Title: Lithium complex oxide for lithium secondary battery positive active material and method of preparing the same

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     A claim for priority under 35 U.S.C. §119 is made to Korean Patent Application No. 10-2016-0098645 filed Aug. 2, 2016, No. 10-2016-0130563 filed Oct. 10, 2016, in the Korean Intellectual Property Office, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND 
     Embodiments of the inventive concept described herein relate to a lithium complex oxide for a secondary battery and a method of preparing the same, and more particularly, relate to a lithium complex oxide for a secondary battery, and a method of preparing the same, improving the characteristics of capacity, resistance, and battery lifetime with different interplanar distances of crystalline structure between a primary particle locating on the surface of a secondary particle and a primary particle locating in the secondary particle by coating different elements on the surface, in consideration of inclination to functional degradation but reduction of residual lithium after a washing for removing the residual lithium in a preparation process, for a positive active material where lithium ion pathways in a-axis and c-axis of a crystalline structure. 
     With an increase of technology and demand for mobile devices, secondary batteries as energy sources are increasing in demand. Among secondary batteries, lithium (Li) secondary batteries are being now commercialized and widely used on the merits of high energy density and operating potential, long cycle lifetime, and low discharge rate. 
     A positive active material for a lithium secondary battery usually employs a lithium-contained cobalt oxide (LiCoO 2 ). It is also considered therefor even to use a lithium-contained manganese oxide such as layered crystalline structure of LiMnO 2  or spinel crystalline structure of LiMn 2 O 4 , or a lithium-contained nickel oxide such as LiNiO 2 . 
     Among those positive active materials, LiCoO 2  is most frequently used because of good characteristics of battery lifetime and charge/discharge efficiency, but there is a limit to competitiveness of cost in mass use as power sources for middle/large-scale batteries of electric vehicles because cobalt (Co) is rare and expensive as a resource, and small in capacity. Although the lithium manganese oxide such as LiMnO 2  or LiMn 2 O 4 , as the positive active material, is low in price, eco-friendly, and highly stable in heat, it is deteriorative in high temperature and cycle characteristics. 
     A method of preparing a lithium complex oxide generally includes the steps of manufacturing transition metal precursors, mixing a lithium compound and the transition metal precursors, and then baking the mixture. During this, LiOH and/or Li 2 CO 3  are/is used for the lithium compound. It is generally preferred to use Li 2 CO 3  in the case that Ni content of the positive active material is equal to or lower than 65% and preferred to use LiOH in the case that Ni content of the positive active material is equal to or higher than 65%. 
     However, a nickel (Ni) rich system containing nickel equal to or higher than 65%, reactive at a low temperature, has a problem of having much residual lithium which remains in a form of LiOH and Li 2 CO 3  on the surface of a positive active material. The residual lithium, that is, unreacted LiOH and Li 2 CO 3  generate gas and a swelling effect by reacting with an electrolyte in the battery, and then cause high temperature stability to be seriously worse. Additionally, the unreacted LiOH also causes gelation because its viscosity is high when mixing slurry before manufacturing electrode plates. 
     To remove such unreacted Li, a washing process is executed generally after preparing a positive active material, thereby much reducing residual lithium. However, during the washing process, the surface of the positive active material was damaged and degraded in characteristics of capacity and efficiency. Additionally, there was another problem to increase resistance in high temperature storage. Therefore, it is necessary to improve the characteristics of capacity, efficiency, and battery lifetime as well as to reduce residual lithium. 
     SUMMARY 
     Embodiments of the inventive concept provide a lithium complex oxide of a new structure improving the characteristics of capacity, resistance, and battery lifetime as well as reducing residual lithium. 
     According to an aspect of the inventive concept, a lithium complex oxide secondary particle is formed by coagulation of a plurality of primary particles, wherein a primary particle locating on a surface part of the secondary particle includes a Co-coated layer at a part that is in contact with a surface of the secondary particle, and Co ions have a grade of concentration toward a center of the primary particle from the Co-coated layer in the primary particle locating on the surface part of the secondary particle. 
     A lithium complex oxide secondary particle according to the inventive concept is a secondary particle formed by coagulation of primary particles and characterized in that the surface of a primary particle, among the primary particles, locating on the surface part of the secondary particle includes a Co-coated layer. That is, a lithium complex oxide secondary particle according to the inventive concept does not include a Co-coated layer over the overall area of primary particles forming the secondary particle, but include a Co-coated later on the surface of a primary particle locating on the surface part of the secondary particle. 
     For a lithium complex oxide secondary particle according to the inventive concept, in defining a primary particle locating on the surface part of the secondary particle, a thickness of the surface part of the secondary particle is characterized to be 0.3 to 1 μm from the outer shell of the secondary particle. 
     In the lithium complex oxide secondary particle according to the inventive concept, a thickness of a Co-coated layer formed on the surface of a primary particle locating on the surface part of the secondary particle may be in 50 to 150 nm from the outer shell of the secondary particle. The Co-coated layer formed on the surface of the primary particle may be formed over the overall area of the primary particle locating on the surface part of the secondary particle, or may be partly formed at a part which is in contact with the surface of the primary particle locating on the surface part of the secondary particle. 
     In the lithium complex oxide secondary particle according to the inventive concept, the primary particle locating on the surface part of the secondary particle may have the grade of Co concentration in 0.05 to 0.07 mol % per one nm toward the center of the particle. 
     In the lithium complex oxide secondary particle according to the inventive concept, the primary particle locating on the surface part of the secondary particle may have Co concentration of a boundary of the primary particle that is higher than Co concentration of the inside of the primary particle. 
     In the lithium complex oxide secondary particle according to the inventive concept, the primary particle locating on the surface part of the secondary particle may satisfy that dc/dh is 2 to 10, where the dc is a length toward the center and the dh is a length vertical to the center. 
     The lithium complex oxide secondary particle according to the inventive concept may satisfy the following Relation 1, 
         d 1&gt; d 2,  [Relation 1]
 
     where the d1 is an interplanar distance of a crystalline structure in a primary particle locating in the internal part of the secondary particle and the d2 is an interplanar distance of a crystalline structure in a primary particle locating on the surface part of the secondary particle. 
     In the lithium complex oxide secondary particle according to the inventive concept, interplanar distances may be different between a primary particle locating in the internal part of the secondary particle and a primary particle locating on the surface part of the secondary particle. An interplanar distance of a primary particle locating in the internal part of the secondary particle may be formed larger than an interplanar distance of a primary particle locating on the surface part of the secondary particle. 
     In the lithium complex oxide secondary particle according to the inventive concept may satisfy the following Relation 2 
         d 1&gt; d 3&gt; d 2, with the  d 1, the  d 2, and  d 3,  [Relation 2]
 
     where the d3 is an interplanar distance of a crystalline structure at a boundary of the Co-coated layer in the primary particle locating on the surface part of the secondary particle. 
     In the lithium complex oxide secondary particle according to the inventive concept, an interplanar distance of a crystalline structure may be variable as the surface of the primary particle locating on the surface part of the secondary particle includes a Co-coated layer. 
     In the lithium complex oxide secondary particle according to the inventive concept, the d1, which is the interplanar distance of the crystalline structure in the primary particle locating in the internal part of the secondary particle, may be equal to or larger than 4.8 nm. 
     In the lithium complex oxide secondary particle according to the inventive concept, the d2, which is the interplanar distance of the crystalline structure in the primary particle locating on the surface part of the secondary particle, may be equal to or smaller than 4.7 nm. 
     In the lithium complex oxide secondary particle according to the inventive concept, the interplanar distances d1 and d2 may mean averages of 10 adjacent interplanar distances based on an interplanar distance of a part which is measured by a crystalline structure spectrometry such as TEM analysis for a positive active material. 
     The lithium complex oxide secondary particle according to the inventive concept may have at least one peak at positions (104), (110), (113), (101), (102), and (003) during XRD analysis. 
     The lithium complex oxide secondary particle according to the inventive concept may have a bound energy (P1) of spin-orbit-spit 2p3/2 peak and a bound energy (P2) of 2p1/2 peak in a Co 2p core-level spectrometry obtained through XPS measurement, and the P1 and the P2 are ranged respectively in 779 eV≦P1≦780 eV and 794 eV≦P2≦795 eV. 
     The lithium complex oxide secondary particle according to the inventive concept may have a ratio of peak intensity (I 531 ) around 531 eV and peak intensity (I 528 ) around 528.5 eV during an O 1s core-level spectrometry that is obtained through XPS measurement, and wherein the ratio is I 531 /I 528 ≦2. 
     The lithium complex oxide secondary particle according to the inventive concept may have a ratio between peak intensity (I 289 ) around 289 eV and peak intensity (I 284 ) around 284.5 eV during a C is core-level spectrometry that is obtained through XPS measurement, and wherein the ratio is I 289 /I 284 ≦0.9. 
     The lithium complex oxide secondary particle according to the inventive concept may be given by the following Formula 1, 
       Li X1 Ni 1−(x1+y1+z1) Co x1 M1 y1 M2 z1 M3 r1 O a ,  [Formula 1]
 
     wherein, in the Formula 1, M1 is Mn or Al, and M2 and M3 are metals selected from a group of Al, Ba, B, Co, Ce, Cr, F, Li, Mg, Mn, Mo, P, Sr, Ti, and Zr, and wherein 0.95≦X1≦1.05, 1.50≦a≦2.1, 0.02≦x1≦0.25, 0.01≦y1≦0.20, 0≦z≦0.20, and 0≦r1≦0.20. 
     According to another aspect of the inventive concept, a method of preparing a lithium complex oxide secondary particle includes manufacturing precursors of lithium secondary battery positive active material given by the flowing Formula 2, 
       Ni 1−(x2+y2+z2) Co x2 M1 y2 M2 z2 (OH) 2 ,  [Formula 2]
 
     wherein, in Formula 2, M1 is Mn or Al, and M2 is a metal selected from a group of Al, Ba, B, Co, Ce, Cr, F, Li, Mg, Mn, Mo, P, Sr, Ti, and Zr, and wherein 0≦x2≦0.25, 0≦y2≦0.20, and 0≦z2≦0.20, reacting precursors of lithium secondary battery positive active material with a lithium compound and manufacturing a positive active material by first thermal treating the reactant, washing the positive active material with distilled water or an alkaline solution, reactively coating the washed positive active material with a solution containing M2 that is a metal selected from the group of Al, Ba, B, Co, Ce, Cr, F, Li, Mg, Mn, Mo, P, Sr, Ti, and Zr; drying particles of the positive active material; and mixing the dried positive active material with M3 that is a metal selected from the group of Al, Ba, B, Co, Ce, Cr, F, Li, Mg, Mn, Mo, P, Sr, Ti, and Zr and doping the metal M3 into the particles by second thermal treating the mixture. 
     In the method of preparing a lithium complex oxide secondary particle, the reactively coating may include reactively coating the washed positive active material with a solution containing Co ion. 
     In the method of preparing a lithium complex oxide secondary particle, the solution including Co in the reactively coating has concentration of 1 to 10 mol %. 
     Another aspect of the inventive concept provides a lithium complex oxide secondary particle prepared by a method according to embodiments of the inventive concept. 
     Another aspect of the inventive concept provides a lithium secondary battery including a lithium complex oxide secondary particle according to embodiments of the inventive concept. 
     The lithium secondary battery according to the inventive concept may have residual lithium equal to or smaller than 6,000 ppm. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The above and other objects and features will become apparent from the following description with reference to the following figures, wherein like reference numerals refer to like parts throughout the various figures unless otherwise specified, and wherein: 
         FIG. 1  shows a result of measuring diffraction patterns and interplanar distances of an LiCoO 2  positive active material of Comparison 1 according to the inventive concept; 
         FIG. 2  shows a result of measuring TEM and EDX photographs of a positive active material prepared according to an embodiment of the inventive concept; 
         FIG. 3  shows a result of measuring diffraction patterns and interplanar distances of a positive active material prepared according to an embodiment of the inventive concept; 
         FIG. 4  shows a result of measuring TEM and EDX photographs of a positive active material prepared according to an embodiment of the inventive concept; 
         FIG. 5  shows a result of measuring diffraction patterns and interplanar distances of a positive active material prepared according to an embodiment of the inventive concept; 
         FIG. 6  shows a result of measuring respective variations of concentration for Ni, Co, and Al toward the center from the surface of a positive active material prepared according to an embodiment of the inventive concept; 
         FIG. 7  shows a result of measuring an EDX photograph of a positive active material prepared according to an embodiment of the inventive concept; 
         FIG. 8  shows a result of measuring diffraction patterns and interplanar distances of a positive active material prepared according to an embodiment of the inventive concept; 
         FIG. 9  shows a result of measuring TEM and EDX photographs of a positive active material prepared according to an embodiment of the inventive concept; 
         FIG. 10  shows a result of measuring respective variations of concentration for Ni, Co, and Al toward the center from the surface of a positive active material prepared according to an embodiment of the inventive concept; 
         FIG. 11  shows a result of measuring respective variations of concentration for Ni, Co, and Al toward the center from a third spot of a positive active material prepared according to an embodiment of the inventive concept; 
         FIGS. 12 to 14  show results of measuring diffraction patterns and interplanar distances of positive active materials manufactured by comparison examples and embodiments of the inventive concept; 
         FIGS. 15 and 16  show results of measuring EDX photographs of positive active materials manufactured by comparison examples of the inventive concept; 
         FIGS. 17 to 19  show results of measuring diffraction patterns and interplanar distances of positive active materials manufactured by comparison examples and embodiments of the inventive concept; 
         FIGS. 20 and 21  show results of measuring respective variations of concentration for Ni, Co, and Al toward the center from the surface of a positive active material prepared according to an embodiment of the inventive concept; 
         FIGS. 22 to 25  show results of measuring XRD of positive active materials manufactured by comparison examples and embodiments of the inventive concept; 
         FIG. 26  shows a result of measuring XPS of positive active materials manufactured by a comparison example and an embodiment of the inventive concept; and 
         FIGS. 27A to 31E  show results of measuring the characteristics of batteries including positive active materials manufactured by comparison examples and embodiments of the inventive concept. 
     
    
    
     DETAILED DESCRIPTION 
     Hereafter, embodiments of the inventive concept will be described in detail with reference to the accompanying figures. The inventive concept may not be however restrictive to the embodiments proposed below. 
     &lt;Comparison 1&gt; 
     A LiCoO 2  positive active material, which is commercially sold, was used for Comparison 1. 
     &lt;Experimental Example&gt; Measuring Distance Between Crystalline Structures 
       FIG. 1  shows respective diffraction patterns and interplanar distances for a primary particle which locates in the internal part of the secondary particle, and a primary particle locating on the surface part of the secondary particle of the LiCoO 2  positive active material of Comparison 1. 
     After mounting the LiCoO 2  positive active material on a carbon grid, coating the LiCoO 2  positive active material with carbon and PT, and then magnifying the coated LiCoO 2  positive active material in 20 million or 25 million times through a TEM pre-treatment that slices the coated LiCoO 2  positive active material, ten interplanar distances were measured left and light around an interplanar distance to be known. 
     As shown in  FIG. 1 , diffraction patterns of the primary particles locating in the secondary particle of the LiCoO 2  positive active material and locating on the surface part of the secondary particle were all in hexagonal structure, and interplanar distances of the primary particles locating in the internal part of the secondary particle and locating on the surface part of the secondary particle were all measured as 4.70 nm. 
     &lt;Embodiment 1&gt; Manufacturing Positive Active Material 
     First, NiCo(OH) 2  precursors were manufactured through a co-precipitation. Then, a lithium secondary battery positive active material was manufactured by adding Li 2 CO 3  and LiOH as lithium compounds to the manufactured precursors, adding Al and Mg as M1 thereto, and processing the mixture in first thermal treatment. 
     After preparing distilled water, the manufactured lithium secondary battery positive active material was washed by injecting the distilled water in uniform temperature. 
     Afterward, the surface of the positive active material was washed and coated with Co as M2 by agitating the positive active material while injecting a cobalt sulfate solution of 0.03 mol into the positive active material washing liquid for one hour in a specific ratio, and then dried at 120° C. under a vacuum. 
     Then, the lithium secondary battery positive active material was manufactured by adding Ti as M3 to the coated positive active material and processing the Ti-added positive active material in second thermal treatment at 450° C. 
     &lt;Experimental Example&gt; Measuring TEM and EDX 
     TEM and EDX photographs were taken from the positive active material manufactured through Embodiment 1 and shown in  FIG. 2 . 
     As shown in  FIG. 2 , the positive active material manufactured through Embodiment 1 of the inventive concept has Co concentration that is higher on the surface of the secondary particle and lower toward the inside from the surface of the secondary particle. Co concentration is ununiform in the secondary particle with a grade. 
     &lt;Experimental Example&gt; Measuring Interplanar Distances Between Crystalline Structures 
       FIG. 3  shows respective diffraction patterns and interplanar distances for primary particles locating in the internal part of the secondary particle manufactured through Embodiment 1 and locating on the surface part on which Co and Ti are coated. 
     As shown in  FIG. 3 , the thickness of a Co-coated layer is about 80 nm, and the diffraction pattern of the primary particle locating in the internal part of the secondary particle is in hexagonal structure. For the primary particle locating in the internal part of the secondary particle, 10 adjacent interplanar distances were measured as 4.88 nm on average in a TEM photograph. Comparatively, the primary particle locating on the surface part having the Co-coated layer was measured as exhibiting a diffraction pattern of hexagonal structure with an interplanar distance of 4.73 nm. 
     From this result, it can be seen that the interplanar distance of the primary particle locating on the surface part was relatively reduced in comparison with the primary particle locating in the internal part of the secondary particle which was not coated with cobalt, and the interplanar distance of the primary particle locating on the surface part was changed similar to an interplanar distance of LiCoO 2  of a comparison example. 
     &lt;Embodiment 2&gt; Manufacturing Positive Active Material 
     A positive active material of Embodiment 2 was manufactured in the same as Embodiment 1, except that concentration of a cobalt solution added to the positive active material washing liquid is 4 mol %. 
     &lt;Experimental Example&gt; Measuring TEM and EDX 
       FIG. 4  shows a result of measuring TEM and EDX photographs of the positive active material manufactures through Embodiment 2. 
     As shown in  FIG. 4 , it can be seen that the positive active material manufactured through Embodiment 2 of the inventive concept has Co concentration that is higher on the surface of the secondary particle and lower toward the inside of the secondary particle. That is, Co concentration of the positive active material is ununiform and distributed in a grade. 
     &lt;Experimental Example&gt; Measuring Distances Between Crystalline Structures 
       FIG. 5  shows a result of measuring respective diffraction patterns and interplanar distances of primary particles locating in the internal part of the positive active material manufactured through Embodiment 1 and locating on the surface where Co and Ti are coated. 
     As shown in  FIG. 5 , it was measured that a thickness of the Co-coated layer was about 90 nm, a diffraction pattern of the primary particle locating in a secondary particle was in a hexagonal structure, and an average of 10 adjacent interplanar distances of the primary particle locating in the internal part of the secondary particle was measured as 4.85 nm in a TEM photograph, while the primary particle locating on the surface part of the Co-coated layer had a diffraction pattern of hexagonal structure but an interplanar distance thereof was measured as 4.73 nm. 
     It can be seen that, comparative to the primary particle locating in the Co-uncoated secondary particle, the interplanar distance of the primary particle locating on the surface part was reduced and changed similar to the interplanar distance of LiCoO 2  of a comparison example. 
     &lt;Embodiment 3&gt; Manufacturing NCM-Based Positive Active Material 
     In the same manner with Embodiment 1, a positive active material of Embodiment 3 was manufactured by executing a coating process with 5 mol % concentration of a cobalt solution added to the positive active material washing liquid. 
     &lt;Experimental Example&gt; Concentration Scanning 
       FIG. 6  shows a result of measuring respective concentration variations of No, Co, and Al from the surface of the secondary particle of the positive active material, which is manufactured through Embodiment 3, toward the center of the particle. 
     From  FIG. 6 , it can be seen that the positive active material manufactured through Embodiment 3 of the inventive concept has Co concentration that becomes higher toward the center from the surface in the Co-coated layer where Co is coated, but after the Co-coated layer, the Co concentration turns to be reduced as close as the center and a thickness of the Co-coated layer is 0.1 μm. 
     &lt;Experimental Example&gt; TEM and EDX 
       FIG. 7  shows a result of measuring respective EDX photographs for Ni, Co, and Al from the surface of the secondary particle of the positive active material, which is manufactured through Embodiment 3, toward the center of the particle. 
     From  FIG. 7 , it can be seen that the positive active material manufactured through Embodiment 3 of the inventive concept has Co concentration that becomes higher toward the center from the surface in the Co-coated layer where Co is coated, but after the Co-coated layer, the Co concentration turns to be reduced as close as the center and concentration of the Co-coated layer is higher along the boundaries of the primary particles. 
     &lt;Experimental Example&gt; Measuring Distances Between Crystalline Structures 
       FIG. 8  shows a result of measuring respective diffraction patterns and interplanar distances of primary particles locating in the positive active material manufactured through Embodiment 3 and locating on the surface on which Co and Ti are coated. 
     As shown in  FIG. 8 , it was measured that a thickness of the Co-coated layer was about 100 nm, a diffraction pattern of the primary particle locating in a secondary particle was in a hexagonal structure, and an average of 10 adjacent interplanar distances of the primary particle locating in the secondary particle was measured as 4.84 nm in a TEM photograph, while the primary particle locating on the Co-coated layer had a diffraction pattern of hexagonal structure but an interplanar distance thereof was measured as 4.67 nm. 
     It can be seen that, comparative to the primary particle locating in the Co-uncoated secondary particle, the interplanar distance of the primary particle locating on the Co-coated surface was reduced and changed similar to interplanar distances of LiCoO 2  of a comparison example. 
     &lt;Embodiment 4&gt; Manufacturing NCM-Based Positive Active Material 
     In the same manner with Embodiment 1, a positive active material of Embodiment 4 was manufactured by executing a washing and coating process with 10 mol % concentration of a cobalt solution added to the positive active material washing liquid. 
     &lt;Experimental Example&gt; Measuring TEM and EDX 
       FIG. 9  shows a result of measuring TEM and EDX photographs on the surface of the secondary particle of the positive active material manufactured through Embodiment 4. 
     As shown in  FIG. 9 , it can be seen that the positive active material manufactured through Embodiment 4 of the inventive concept has Co concentration that becomes higher on the surface of the secondary particle but turns to be lower as close as the center of the secondary particle. Thus, the Co concentration is ununiform in a grade. 
     Additionally, the EDX measurement shows a Co distribution of bar-shaped primary particle, from which it can be seen that Co concentration is measured as being higher at the periphery of the bar-shaped primary particle. 
     &lt;Experimental Example&gt; Concentration Scanning 
       FIG. 10  shows a result of measuring respective concentration variations of No, Co, and Al from the surface of a secondary particle of the positive active material, which is manufactured through Embodiment 4, toward the center of the particle. 
     From  FIG. 10 , it can be seen that the positive active material manufactured through Embodiment 4 of the inventive concept has Co concentration that becomes higher toward the center from the surface in the Co-coated layer where Co is coated, but after the Co-coated layer, the Co concentration turns to be reduced as close as the center and a thickness of the Co-coated layer is 0.14 nm. 
     &lt;Experimental Example&gt; Concentration Scanning 
       FIG. 11  shows a result of measuring respective concentration variations of No, Co, and Al from three spots on the surface of a secondary particle of the positive active material, which is manufactured through Embodiment 4, toward the center of the secondary particle. 
     From  FIG. 11 , it can be seen that three independent spots on the surface of the secondary particle of the positive active material manufactured through Embodiment 4 have thicknesses of 0.14 μm that forms a uniform grade therein. 
     &lt;Experimental Example&gt; Measuring Distances Between Crystalline Structures 
       FIG. 12  shows a result of measuring respective diffraction patterns and interplanar distances of primary particle locating in a secondary particle of the positive active material manufactured through Embodiment 4 and locating on the surface part where Co and Ti are coated. 
     As shown in  FIG. 12 , it was measured that a thickness of the Co-coated layer was about 140 nm, a diffraction pattern of the primary particle locating in a secondary particle was in a hexagonal structure, and interplanar distance of the primary particle locating in the internal part of the secondary particle was measured as 4.85 nm, while the primary particle locating on the surface part, which was coated with Co and Ti, had a diffraction pattern of hexagonal structure but its interplanar distance thereof was measured as 4.69 nm. 
     It can be seen that, comparative to the primary particle locating in the Co-uncoated secondary particle, the interplanar distance of the primary particle locating on the Co-coated surface was reduced and changed similar to the interplanar distance of LiCoO 2  of a comparison example. 
     &lt;Experimental Example&gt; Measuring Interplanar Distances Between Crystalline Structures at Coated Layer Boundary 
       FIG. 13  shows a result of measuring a diffraction pattern and interplanar distances from a boundary between the inside of a primary particle, which locates on the surface part of a secondary particle of the positive active material manufactured through Embodiment 4, and a coated layer in the primary particle locating on the surface part of the secondary particle. 
     As shown in  FIG. 13 , from the boundary between the inside of the primary particle, which locates on the surface of the secondary particle of the positive active material manufactured through Embodiment 4, and the coated layer, which is coated with Co and Ti, in the primary particle locating on the surface part of the secondary particle, the diffraction pattern was in a hexagonal structure and the interplanar distances were measured as 4.71 nm on average. 
     It can be seen that, comparative to the primary particle locating in the internal part of secondary particle has an interplanar distance of 4.85 nm and the primary particle locating on the surface part of the secondary particle, which is coated with Co and Ti, has an interplanar distance of 4.69 nm, the interplanar distance of the coated layer boundary in the primary particle locating on the surface part of the secondary particle coated with Co and Ti, that is, 4.71 nm, was measured as an intermediate value between the interplanar distance of the primary particle locating in the internal part of the secondary particle and the interplanar distance of the primary particle locating on the surface part of the secondary particle which is coated with Co and Ti. 
     Additionally, it can be seen that the interplanar distance of the primary particle at the coated layer boundary was changed similar to the interplanar distance of LiCoO 2  of a comparison example. 
     &lt;Experimental Example&gt; Measuring Interplanar Distances Between Crystalline Structures at Boundary of Primary Particle 
       FIG. 14  shows diffraction patterns and interplanar distances at boundaries of a primary particle locating on the surface part of a secondary particle, which is coated with Co and Ti, of the positive active material manufactured through Embodiment 4. 
     As shown in  FIG. 14 , from the boundaries of the primary particle locating on the surface part of the secondary particle of the positive active material, the diffraction patterns are in a hexagonal structure and the interplanar distances are measured as 4.69 nm and 4.71 nm as an intermediate value of interplanar distances between a core part and a coated layer part. 
     Additionally, it can be seen that the interplanar distance of the primary particle at the coated layer boundary was changed similar to the interplanar distance of LiCoO 2  of a comparison example. 
     &lt;Embodiment 5&gt; Manufacturing Positive Active Material 
     In the same manner with Embodiment 1, a positive active material of Embodiment 5 was manufactured by manufacturing a lithium secondary battery positive active material, which had been processed through the first thermal treatment, in the composition of Li 1.02 Ni 0.816 Co 0.15 Al 0.034 O 2  without addition of Ti. 
     &lt;Embodiment 6&gt; Manufacturing Positive Active Material 
     In the same manner with Embodiment 1, a positive active material of Embodiment 6 was manufactured by manufacturing a lithium secondary battery positive active material, which had been processed through the first thermal treatment, in the composition of Li 1.02 Ni 0.903 Co 0.08 Al 0.014 Mg 0.003 O 2 . 
     &lt;Embodiment 7&gt; Manufacturing Positive Active Material 
     In the same manner with Embodiment 1, a positive active material of Embodiment 7 was manufactured by manufacturing a lithium secondary battery positive active material, which had been processed through the first thermal treatment, in the composition of Li 1.00 Ni 0.965 Co 0.02 Al 0.014 Mg 0.001 O 2 . 
     &lt;Embodiment 8&gt; Manufacturing Positive Active Material 
     In the same manner with Embodiment 7, a positive active material of Embodiment 8 was manufactured by executing a coating process with 4 mol % concentration of a cobalt solution which was added to the positive active material washing liquid. 
     &lt;Embodiment 9&gt; Manufacturing Positive Active Material 
     In the same manner with Embodiment 7, a positive active material of Embodiment 9 was manufactured by executing a coating process with 5 mol % concentration of a cobalt solution which was added to the positive active material washing liquid. 
     &lt;Embodiment 10&gt; Manufacturing Positive Active Material 
     In the same manner with Embodiment 7, a positive active material of Embodiment 10 was manufactured by manufacturing a lithium secondary battery positive active material, which had been processed through the first thermal treatment, in the composition of Li 1.00 Ni 0.985 Al 0.014 Mg 0.001 O 2 . 
     The final formulas of compositions used in Embodiments 1 to 10 are summarized in Table 1 as follows. 
     
       
         
           
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Final Composition Formula 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 Li X1 Ni 1−(x1+y1+z1) Co x1 M1 y1 M2 z1 M3 r1 O a   
               
               
                   
                 Embodiment 1 
                 Li 1.01 Ni 0.903 Co 0.08 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Embodiment 2 
                 Li 1.01 Ni 0.893 Co 0.09 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Embodiment 3 
                 Li 1.02 Ni 0.883 Co 0.10 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Embodiment 4 
                 Li 1.02 Ni 0.833 Co 0.10 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Embodiment 5 
                 Li 1.02 Ni 0.786 Co 0.18 Al 0.034 O 2   
               
               
                   
                 Embodiment 6 
                 Li 1.02 Ni 0.873 Co 0.11 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Embodiment 7 
                 Li 1.00 Ni 0.933 Co 0.05 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Embodiment 8 
                 Li 1.00 Ni 0.923 Co 0.06 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Embodiment 9 
                 Li 1.00 Ni 0.913 Co 0.07 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Embodiment 10 
                 Li 1.00 Ni 0.953 Co 0.03 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                   
               
            
           
         
       
     
     &lt;Comparison 2&gt; 
     In the same manner with Embodiment 4, a positive active material of Comparison 2 was manufactured by injecting active material particles into a 0.1 mol cobalt solution, coating the active material with cobalt while agitating the mixture, and drying the coated material. 
     &lt;Comparison 3&gt; 
     In the same manner with Embodiment 4, a positive active material of Comparison 3 was manufactured, without including Co during a washing process, by excluding a Ti adding process and a second thermal treatment. 
     &lt;Experimental Example&gt; Measuring TEM and TDX 
       FIG. 15  shows a result of measuring TEM and EDX photographs from the surface of a secondary particle of the positive active material manufactured through Comparison 2. 
     As shown in  FIG. 15 , it can be seen that the positive active material resulted in an uneven surface, without being doped into the inside, because there was no subsequent thermal treatment even though the Co distribution was concentrated on the surface due to the agitation with the active material particles which were injected into the cobalt solution. 
     &lt;Comparison 4&gt; 
     In the same manner with Comparison 3, a positive active material of Comparison 4 was manufactured by adding Ti with concentration of 0.001 mol and then executing a second thermal treatment. 
     &lt;Comparison 5&gt; 
     In the same manner with Comparison 3, a positive active material of Comparison 5 was prepared, without a washing process, after manufacturing a lithium secondary battery positive active material which had been processed through a first thermal treatment. 
     &lt;Comparison 6&gt; 
     In the same manner with Comparison 3, a positive active material of Comparison 6 was prepared by manufacturing a lithium secondary battery positive active material, which had been processed through a first thermal treatment, in the composition of Li 1.00 Ni 0.815 Co 0.15 Al 0.014 O 2 . 
     &lt;Comparison 7&gt; 
     In the same manner with Comparison 4, a positive active material of Comparison 7 was prepared by manufacturing a lithium secondary battery positive active material, which had been processed through a first thermal treatment, in the composition of Li 1.02 Ni 0.903 Co 0.08 Al 0.014 Mg 0.003 O 2 . 
     &lt;Comparison 8&gt; 
     In the same manner with Comparison 4, a positive active material of Comparison 8 was prepared by manufacturing a lithium secondary battery positive active material, which had been processed through a first thermal treatment, in the composition of Li 1.00 Ni 0.965 Co 0.02 Al 0.014  Mg 0.001 O 2 . 
     &lt;Comparison 9&gt; 
     In the same manner with Comparison 4, a positive active material of Comparison 9 was prepared by manufacturing a lithium secondary battery positive active material, which had been processed through a first thermal treatment, in the composition of Li 1.00 Ni 0.965 Al 0.014 Mg 0.001 O 2 . 
     The final formulas of compositions used in Comparisons 1 to 9 are summarized in Table 2 as follows. 
     The final formulas of compositions used in the first baking processes of Comparisons 1 to 9 are summarized in Table 2 as follows. 
     
       
         
           
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Final Composition Formula 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 Li X1 Ni 1−(x1+y1+z1) Co x1 M1 y1 M2 z1 M3 r1 O a   
               
               
                   
                 Comparison 1 
                 LiCoO 2   
               
               
                   
                 Comparison 2 
                 Washed and dried product of Embodiment 4 
               
               
                   
                 Comparison 3 
                 Washed and dried product of Comparison 4 
               
               
                   
                 Comparison 4 
                 Li 1.00 Ni 0.933 Co 0.05 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Comparison 5 
                 Li 1.05 Ni 0.934 Co 0.05 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                   
                 (Unwashed product) 
               
               
                   
                 Comparison 6 
                 Li 1.00 Ni 0.815 Co 0.15 Al 0.035 O 2   
               
               
                   
                 Comparison 7 
                 Li 1.02 Ni 0.903 Co 0.08 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Comparison 8 
                 Li 1.00 Ni 0.963 Co 0.02 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                 Comparison 9 
                 Li 1.00 Ni 0.983 Co 0.05 Al 0.015 Mg 0.001 Ti 0.001 O 2   
               
               
                   
                   
               
            
           
         
       
     
     &lt;Experimental Example&gt; Measuring TEM and TDX 
       FIG. 16  shows a result of measuring TEM and EDX photographs from the surface of a secondary particle of the positive active material manufactured through Comparison 4. 
     As shown in  FIG. 16 , it can be seen that the positive active material manufactured through Comparison 4 has Co concentration uniformly distributed in the particle, because a Co coating process is not preformed after manufacturing an active material, and a Co concentration grade toward the inside of the particle is not found on the surface. 
     &lt;Experimental Example&gt; Measuring Distances Between Crystalline Structures 
       FIG. 17  shows a result of measuring respective a diffraction pattern and interplanar distances from the surface of a secondary particle of the positive active material manufactured through Embodiment 4. 
     As shown in  FIG. 17 , a diffraction pattern of the surface was in a hexagonal structure and the interplanar distances were measured as 4.85 nm on average. 
       FIG. 18  shows a result of measuring a diffraction pattern and interplanar distances of a primary particle locating in a secondary particle of the positive active material manufactured through Comparison 4. 
     As shown in  FIG. 18 , it can be seen that the primary particle locating in the secondary particle of the positive active material has a diffraction pattern of hexagonal structure and interplanar distances of 4.83 nm on average. It can be also seen that, even with a second thermal treatment in the case without a Co coating process, the interplanar distance of the primary particle locating in the secondary particle of the positive active material is almost similar to that of a primary particle locating on the surface part of the secondary particle. 
     &lt;Experimental Example&gt; Measuring Interplanar Distances Between Crystalline Structures at Primary Particle Boundary 
       FIG. 19  shows a result of measuring diffraction patterns and interplanar distances from a boundary of a primary particle locating on the surface part of a secondary particle of the positive active material manufactured through Embodiment 4. 
     As shown in  FIG. 19 , the primary particle locating on the surface part of the secondary particle of the positive active material was measured as having a diffraction pattern of hexagonal structure and interplanar distances of 4.81 nm on average. 
     Additionally, it can be seen from  FIGS. 18 and 19  that, in the case without a Co coating process, diffraction patterns and interplanar distances are similar between the inside and the boundary of the primary particle. 
     &lt;Experimental Example&gt; Concentration Scanning 
       FIG. 20  shows a result of measuring respective concentration of Ni, Co, and Al toward the core from the surface of a secondary particle of the positive active material manufactured through Comparison 4. 
     From  FIG. 20 , it can be seen that the positive active material manufactured through Comparison 4 has uniform concentration of Ni, Co, and Al in the particle. 
     &lt;Experimental Example&gt; Concentration Scanning 
       FIG. 21  shows a result of measuring respective concentration of Ni, Co, and Al in a direction horizontal to the surface direction of a primary particle locating on the surface part of a secondary particle of the positive active material manufactured through Comparison 4. 
     From  FIG. 21 , it can be seen that the positive active material manufactured through Comparison 4 has uniform concentration of Ni, Co, and Al in the particle, without a Co concentration grade due to absence of a CO coating process, and interplanar distances thereof are also similar between the surface and the inside. 
     &lt;Experimental Example&gt; Measuring XRD 
     Results of measuring XRD for LiCoO 2  positive active materials of Embodiment 4 and Comparison 1 are shown in  FIGS. 22 and 23 . 
     As show n  FIGS. 22 and 23 , it can be seen that a Co and Ti coated positive active material, which is manufactured through Embodiment 4 of the inventive concept, is detected with peaks of (104), (110), (113), (101), (102), and (003) as like the case of LiCoO 2  of Comparison 1. 
     &lt;Experimental Example&gt; Measuring XRD 
     A result of measuring XRD for a positive active material of Comparison 2 is shown in  FIG. 24 . 
     As shown in  FIG. 24 , it can be seen that the positive active material manufactured through Comparison 2 of the inventive concept is detected only with a peak by Co(OH) 2  but there are no detection with peaks of (104), (110), (113), (101), (102), and (003). 
     &lt;Experimental Example&gt; Measuring XRD 
       FIG. 25  shows a result of measuring XRD for positive active materials manufactured through Comparison 4, which does not execute a Co coating process, and through Embodiment 4 executing a thermal treatment after a Co coating process. 
     As shown in  FIG. 25 , it can be seen that the positive active material manufactured through Comparison 4, which does not execute the Co coating process of the inventive concept, is not detected with peaks of (104), (110), (113), (101), (102), and (003) that are distinctly detected from LiCoO 2 . 
     &lt;Experimental Example&gt; Measuring XPS 
       FIG. 26  shows results of measuring XPS for positive active materials manufactured through Comparison 4, which does not execute a Co coating process, and through Embodiment 3 executing a coating process with a cobalt solution which has concentration of 5 mol %. 
     As shown in  FIG. 26 , it can be seen that, in the case of coating cobalt during a washing process according to the inventive concept, the Co 2p peak intensity is larger, almost due to Co+3, than that of Comparison 4. Additionally, it can be also seen that the peak intensity by Li 2 CO 3  is more reduced than that of Comparison 4. 
     &lt;Experimental Example&gt; Measuring Residual Lithium 
     A result of measuring amounts of residual lithium from composite oxides manufactured through Embodiments 1 to 10 and Comparisons 4 to 9 is summarized in Table 3 as follows. 
     To measure residual lithium, an active material of 1 g was precipitated in distilled water of 5 g and agitated for 5 minutes. Next, filtrate was taken after the agitation and titration was executed with HCL of 0.1M. Then, the residual lithium was analyzed by measuring a volume of the HCL until pH of the filtrate reaches 5. 
     From Table 3, it can be seen that active materials manufactured through embodiments of the inventive concept have residual lithium which is greatly reduced relative to the case as like as Comparison 5 that does not execute a baking process. 
     
       
         
           
               
               
             
               
                   
                 TABLE 3 
               
             
            
               
                   
                   
               
               
                   
                 Residual Lithium (ppm) 
               
            
           
           
               
               
               
               
            
               
                   
                 LiOH 
                 Li 2 CO 3   
                 Total 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Comparison 4 
                 1043 
                 1787 
                 2830 
               
               
                   
                 Comparison 5 
                 7516 
                 9733 
                 17249 
               
               
                   
                 Comparison 6 
                 2628 
                 987 
                 3615 
               
               
                   
                 Comparison 7 
                 1017 
                 1686 
                 3396 
               
               
                   
                 Comparison 8 
                 1744 
                 1622 
                 3366 
               
               
                   
                 Comparison 9 
                 1856 
                 2212 
                 4068 
               
               
                   
                 Embodiment 1 
                 1506 
                 1996 
                 3502 
               
               
                   
                 Embodiment 2 
                 1432 
                 1971 
                 3403 
               
               
                   
                 Embodiment 3 
                 1562 
                 1549 
                 3111 
               
               
                   
                 Embodiment 4 
                 2142 
                 2450 
                 4592 
               
               
                   
                 Embodiment 5 
                 2556 
                 862 
                 3418 
               
               
                   
                 Embodiment 6 
                 1730 
                 1830 
                 3560 
               
               
                   
                 Embodiment 7 
                 1630 
                 2166 
                 3796 
               
               
                   
                 Embodiment 8 
                 2035 
                 2433 
                 4468 
               
               
                   
                 Embodiment 9 
                 1569 
                 2067 
                 3636 
               
               
                   
                 Embodiment 10 
                 2519 
                 1881 
                 4400 
               
               
                   
                   
               
            
           
         
       
     
     &lt;Manufacturing Example&gt; Manufacturing Battery 
     Slurry was manufactured by mixing the positive active materials, which were manufactured through Embodiments 1 to 10 and Comparisons 4, and 6 to 9, super-P as a conducting agent, and polyvinylidenefluoride (PVdF) as a binding agent in weight ratio of 92:5:3. Then an anode for a lithium secondary battery was manufactured by uniformly coating the slurry on an aluminum foil which has a thickness of 15 μm, and then by drying the slurry-coated aluminum foil at 135° C. under vacuum. 
     A coin battery was manufactured by using the anode and a lithium foil as the other electrode, using a porous polyethylene film (Celgard 2300 made by Celgard LLC; thickness of 25 μm) as a separator, and using a liquid electrolyte in which LiPF6 with concentration of 1.15M was dissolved in a solvent in which ethylene carbonate and ethylmethyl carbonate are mixed in a volume ratio of 3:7. 
     &lt;Experimental Example&gt; Measuring Battery Characteristics—Initial Capacity 
     Results of measuring initial capacities of batteries manufactured with active materials manufactured through Embodiments 1 to 10 and Comparisons 4, and 6 to 9 are respectively shown in  FIG. 27A  (Embodiments 1 to 4, Comparison 4),  FIG. 27B  (Embodiment 5, Comparison 6).  FIG. 27C  (Embodiment 6, Comparison 7),  FIG. 27D  (Embodiments 7 to 9, Comparison 8), and  FIG. 27E  (Embodiment 10, Comparison 9). 
     Referring to  FIGS. 27A to 27E , the coating process executed according to the embodiments of the inventive concept contributed to the characteristics of capacity and efficiency that was measured as being more improved than that of a comparison examples. 
     Results of measuring initial capacities of batteries manufactured with active materials manufactured through Embodiments 1 to 10 and Comparisons 4, and 6 to 9 are summarized in Table 4 as follows. 
     
       
         
           
               
               
             
               
                   
                 TABLE 4 
               
             
            
               
                   
                   
               
               
                   
                 0.1 C Charge/Discharge 
               
            
           
           
               
               
               
               
            
               
                   
                 Charge (mAh/g) 
                 Discharge (mAh/g) 
                 1st Eff. (%) 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                 Embodiment 1 
                 242.2 
                 215.9 
                 89.1 
               
               
                 Embodiment 2 
                 239.9 
                 214.4 
                 89.4 
               
               
                 Embodiment 3 
                 239.0 
                 215.0 
                 90.0 
               
               
                 Embodiment 4 
                 231.7 
                 215.2 
                 92.9 
               
               
                 Embodiment 5 
                 213.9 
                 194.1 
                 90.8 
               
               
                 Embodiment 6 
                 232.5 
                 213.7 
                 91.9 
               
               
                 Embodiment 7 
                 248.9 
                 222.3 
                 89.3 
               
               
                 Embodiment 8 
                 247.2 
                 222.5 
                 90.0 
               
               
                 Embodiment 9 
                 245.1 
                 220.9 
                 90.1 
               
               
                 Embodiment 10 
                 251.8 
                 221.6 
                 88.0 
               
               
                 Comparison 4 
                 244.5 
                 209.7 
                 85.8 
               
               
                 Comparison 6 
                 217.1 
                 190.2 
                 87.6 
               
               
                 Comparison 7 
                 239.3 
                 211.3 
                 88.3 
               
               
                 Comparison 8 
                 255.1 
                 219.0 
                 85.9 
               
               
                 Comparison 9 
                 258.2 
                 221.6 
                 85.8 
               
               
                   
               
            
           
         
       
     
     &lt;Experimental Example&gt; Measuring Battery Characteristics—Efficiency 
     Results of measuring efficiency characteristics of batteries manufactured with active materials manufactured through Embodiments 1 to 10 and Comparisons 4, and 6 to 9 are respectively shown in  FIG. 28A  (Embodiments 1 to 4, Comparison 4),  FIG. 28B  (Embodiment 5, Comparison 6),  FIG. 28C  (Embodiment 6, Comparison 7),  FIG. 28D  (Embodiments 7 to 9, Comparison 8), and  FIG. 28E  (Embodiment 10, Comparison 9). 
     Referring to  FIGS. 28A to 28E , the coating process executed by the embodiments of the inventive concept contributed to making the characteristics of capacity and efficiency measured as being more improved than the comparison examples. 
     Results of measuring the efficiency characteristics of batteries manufactured with active materials manufactured through Embodiments 1 to 10 and Comparisons 4, and 6 to 9 are summarized in Table 5 as follows. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                 ITEM 
                 0.1 C 
                 0.2 C 
                 0.5 C 
                 1.0 C 
                 1.5 C 
                 2.0 C 
               
               
                   
               
             
            
               
                 Embodiment 1 
                 100.0% 
                 97.6% 
                 94.2% 
                 91.8% 
                 90.2% 
                 89.2% 
               
               
                 Embodiment 2 
                 100.0% 
                 97.8% 
                 94.5% 
                 92.3% 
                 90.9% 
                 89.8% 
               
               
                 Embodiment 3 
                 100.0% 
                 97.7% 
                 94.6% 
                 92.3% 
                 90.7% 
                 89.6% 
               
               
                 Embodiment 4 
                 100.0% 
                 97.9% 
                 94.5% 
                 91.9% 
                 90.2% 
                 88.9% 
               
               
                 Embodiment 5 
                 100.0% 
                 98.9% 
                 95.2% 
                 92.2% 
                 90.4% 
                 89.0% 
               
               
                 Embodiment 6 
                 100.0% 
                 97.2% 
                 93.0% 
                 89.9% 
                 88.4% 
                 87.3% 
               
               
                 Embodiment 7 
                 100.0% 
                 96.9% 
                 93.1% 
                 90.2% 
                 88.4% 
                 86.8% 
               
               
                 Embodiment 8 
                 100.0% 
                 96.7% 
                 92.5% 
                 89.5% 
                 87.4% 
                 85.6% 
               
               
                 Embodiment 9 
                 100.0% 
                 97.0% 
                 93.2% 
                 90.5% 
                 88.8% 
                 87.4% 
               
               
                 Embodiment 10 
                 100.0% 
                 96.5% 
                 92.7% 
                 89.7% 
                 87.1% 
                 84.4% 
               
               
                 Comparison 4 
                 100.0% 
                 97.3% 
                 94.2% 
                 92.0% 
                 90.6% 
                 89.6% 
               
               
                 Comparison 6 
                 100.0% 
                 98.3% 
                 94.1% 
                 91.1% 
                 89.4% 
                 88.2% 
               
               
                 Comparison 7 
                 100.0% 
                 96.3% 
                 92.6% 
                 89.4% 
                 86.1% 
                 82.5% 
               
               
                 Comparison 8 
                 100.0% 
                 96.3% 
                 92.6% 
                 89.4% 
                 86.1% 
                 82.5% 
               
               
                 Comparison 9 
                 100.0% 
                 96.3% 
                 92.6% 
                 89.3% 
                 85.9% 
                 82.3% 
               
               
                   
               
            
           
         
       
     
     &lt;Experimental Example&gt; Measuring Battery Characteristics—Lifetime 
     Results of measuring lifetime characteristics of batteries manufactured with active materials manufactured through Embodiments 1 to 10 and Comparisons 4, and 6 to 9 are respectively shown in  FIG. 29A  (Embodiments 1 to 4, Comparison 4),  FIG. 29C  (Embodiment 5, Comparison 6),  FIG. 29C  (Embodiment 6, Comparison 7),  FIG. 29D  (Embodiments 7 to 9, Comparison 8), and  FIG. 29E  (Embodiment 10, Comparison 9). 
     Referring to  FIGS. 29A to 29E , the coating process executed according to the embodiments of the inventive concept contributed to making the characteristics of lifetime measured as being more improved than the comparison examples. 
     Results of measuring the lifetime characteristics of batteries manufactured with active materials manufactured through Embodiments 1 to 10 and Comparisons 4, and 6 to 9 are summarized in Table 6 as follows. 
     
       
         
           
               
               
             
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                 Room Temperature Lifetime 
               
               
                   
                 50th/1st (%) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Embodiment 1 
                 77.4 
               
               
                   
                 Embodiment 2 
                 80.4 
               
               
                   
                 Embodiment 3 
                 78.9 
               
               
                   
                 Embodiment 4 
                 74.9 
               
               
                   
                 Embodiment 5 
                 89.5 
               
               
                   
                 Embodiment 6 
                 55.0 
               
               
                   
                 Embodiment 7 
                 54.6 
               
               
                   
                 Embodiment 8 
                 61.4 
               
               
                   
                 Embodiment 9 
                 63.3 
               
               
                   
                 Embodiment 10 
                 68.5 
               
               
                   
                 Comparison 4 
                 77.5 
               
               
                   
                 Comparison 6 
                 88.7 
               
               
                   
                 Comparison 7 
                 55.0 
               
               
                   
                 Comparison 8 
                 53.1 
               
               
                   
                 Comparison 9 
                 63.0 
               
               
                   
                   
               
            
           
         
       
     
     &lt;Experimental Example&gt; Measuring Battery Characteristics—High Temerature Storage 
     As results of measuring high temperature storage characteristics of batteries manufactured with active materials manufactured through Embodiments 1 to 3 and 5 to 10, and Comparisons 4 and 6 to 9, the results before storage are respectively shown in  FIG. 30A  (Embodiments 1 to 3, Comparison 4),  FIG. 30B  (Embodiment 5, Comparison 6),  FIG. 30C  (Embodiment 6, Comparison 7),  FIG. 30D  (Embodiments 7 to 9, Comparison 8), and  FIG. 30E  (Embodiment 10, Comparison 9), and the results after storage are respectively shown in  FIG. 31A  (Embodiments 1 to 3, Comparison 4),  FIG. 31B  (Embodiment 5, Comparison 6),  FIG. 31C  (Embodiment 6, Comparison 7),  FIG. 31D  (Embodiments 7 to 9, Comparison 8), and  FIG. 31E  (Embodiment 10, Comparison 9). 
     Referring to  FIGS. 30A to 30E and 31A to 31E , the coating process executed by the embodiments of the inventive concept contributed to greatly improving the high temperature storage characteristics because impedances after high temperature storage increased less than those of the comparison examples. 
     Results of measuring the high temperature storage characteristics of batteries manufactured with active materials manufactured through Embodiments 1 to 3, and 5 to 10 and Comparisons 4, and 6 to 9 are summarized in Table 7 as follows. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 7 
               
             
            
               
                   
                   
               
               
                   
                 High Temperature 
                   
               
               
                   
                 Storage (Ohm) 
               
            
           
           
               
               
               
            
               
                   
                 Before Storage 
                 After Storage 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Embodiment 1 
                 4.5 
                 16.1 
               
               
                   
                 Embodiment 2 
                 4.3 
                 16.6 
               
               
                   
                 Embodiment 3 
                 4.3 
                 13.1 
               
               
                   
                 Embodiment 5 
                 4.4 
                 28.5 
               
               
                   
                 Embodiment 6 
                 6.2 
                 6.7 
               
               
                   
                 Embodiment 7 
                 5.0 
                 10.0 
               
               
                   
                 Embodiment 8 
                 4.5 
                 8.6 
               
               
                   
                 Embodiment 9 
                 4.5 
                 8.7 
               
               
                   
                 Embodiment 10 
                 7.2 
                 28.4 
               
               
                   
                 Comparison 4 
                 20.8 
                 40.3 
               
               
                   
                 Comparison 6 
                 10.0 
                 96.2 
               
               
                   
                 Comparison 7 
                 21.9 
                 60.6 
               
               
                   
                 Comparison 8 
                 348.9 
                 656.0 
               
               
                   
                 Comparison 9 
                 434.5 
                 498.0 
               
               
                   
                   
               
            
           
         
       
     
     According to embodiments of the inventive concept, it may be allowable to improve a secondary battery in the characteristics of capacity, resistance, and lifetime with different interplanar distances of crystalline structures between a primary particle locating on the surface part of a secondary particle and a primary particle locating in the internal part of the secondary particle by coating different elements and washing in the processes of forming precursors and/or an active material. 
     While the inventive concept has been described with reference to exemplary embodiments, it will be apparent to those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the inventive concept. Therefore, it should be understood that the above embodiments are not limiting, but illustrative.