The subject matter described herein includes a method of separating a mixture of trivalent rare-earth elements, based on their reduction potential, and solubility in a divalent state. The method includes adding the mixture of trivalent rare-earth elements to a tetraborate salt with deionized water to form a salt mixture, grinding the salt mixture with boric acid to form a solid mixture, wetting the solid mixture with water to form a paste, heating the paste to form a resultant product, dissolving the resultant product, thereby creating a residual solid in aqueous solution, wherein the residual solid includes a second mixture of trivalent rare-earth elements, and the aqueous solution includes a substantially singular element of a divalent rare-earth element in an aqueous state, and removing the residual solid, thereby separating the divalent rare-earth element from the mixture of trivalent rare-earth elements.

A method of preparing borosulfate materials avoids the need for fuming sulfuric acid, also known as oleum. Instead, B(OH).sub.3 present in solution in concentrated sulfuric acid at 5% to 15% by weight is reacted with a cation source at 100-250° C. under dynamic vacuum while in connection with a receiving vessel comprising a desiccant and separate from the reaction vessel, thereby causing formation of a borosulfate material in the reaction vessel while eliminated water is collected in the receiving vessel.

A method of preparing borosulfate materials avoids the need for fuming sulfuric acid, also known as oleum. Instead, B(OH).sub.3 present in solution in concentrated sulfuric acid at 5% to 15% by weight is reacted with a cation source at 100-250° C. under dynamic vacuum while in connection with a receiving vessel comprising a desiccant and separate from the reaction vessel, thereby causing formation of a borosulfate material in the reaction vessel while eliminated water is collected in the receiving vessel.

A method of forming a dissolvable part of amorphous borate includes: preparing a mixture comprising one or more boron compounds and one or more alkali compounds, at least one of the one or more boron compounds and the one or more alkali compounds being hydrous; heating the mixture to a melting temperature for a predetermined time to melt the mixture and release water from the mixture to form an anhydrous boron compound that is moldable, wherein the amount of alkali compound being selected to achieve an alkali oxide content of between about 10 to 25%; with the anhydrous boron compound at a molding temperature, molding the anhydrous boron compound in a mold; and cooling the anhydrous boron compound to form a solid.

A method of forming a dissolvable part of amorphous borate includes: preparing a mixture comprising one or more boron compounds and one or more alkali compounds, at least one of the one or more boron compounds and the one or more alkali compounds being hydrous; heating the mixture to a melting temperature for a predetermined time to melt the mixture and release water from the mixture to form an anhydrous boron compound that is moldable, wherein the amount of alkali compound being selected to achieve an alkali oxide content of between about 10 to 25%; with the anhydrous boron compound at a molding temperature, molding the anhydrous boron compound in a mold; and cooling the anhydrous boron compound to form a solid.

A positive electrode active material including a nickel-containing lithium transition metal oxide containing nickel in an amount of 60 mol % or more based on a total number of moles of transition metals excluding lithium, and a coating layer which is formed on a surface of the nickel-containing lithium transition metal oxide and includes a lithium-containing inorganic compound, a nickel oxide, and a nickel oxyhydroxide is provided. A method of preparing the positive electrode active material, and a positive electrode for a lithium secondary battery and a lithium secondary battery which include the positive electrode active material are also provided.

A positive electrode active material including a nickel-containing lithium transition metal oxide containing nickel in an amount of 60 mol % or more based on a total number of moles of transition metals excluding lithium, and a coating layer which is formed on a surface of the nickel-containing lithium transition metal oxide and includes a lithium-containing inorganic compound, a nickel oxide, and a nickel oxyhydroxide is provided. A method of preparing the positive electrode active material, and a positive electrode for a lithium secondary battery and a lithium secondary battery which include the positive electrode active material are also provided.

A method of forming a dissolvable part of amorphous borate includes: preparing a mixture comprising one or more boron compounds and one or more alkali compounds, at least one of the one or more boron compounds and the one or more alkali compounds being hydrous; heating the mixture to a melting temperature for a predetermined time to melt the mixture and release water from the mixture to form an anhydrous boron compound that is moldable, wherein the amount of alkali compound being selected to achieve an alkali oxide content of between about 10 to 25%; with the anhydrous boron compound at a molding temperature, molding the anhydrous boron compound in a mold; and cooling the anhydrous boron compound to form a solid.

A method of forming a dissolvable part of amorphous borate includes: preparing a mixture comprising one or more boron compounds and one or more alkali compounds, at least one of the one or more boron compounds and the one or more alkali compounds being hydrous; heating the mixture to a melting temperature for a predetermined time to melt the mixture and release water from the mixture to form an anhydrous boron compound that is moldable, wherein the amount of alkali compound being selected to achieve an alkali oxide content of between about 10 to 25%; with the anhydrous boron compound at a molding temperature, molding the anhydrous boron compound in a mold; and cooling the anhydrous boron compound to form a solid.

An hBN powder containing an aggregate of primary particles of hBN, the hBN powder having a ratio of an average longer diameter (L.sub.1) to an average thickness (d.sub.1) of the primary particles, [L.sub.1/d.sub.1], of 10 to 25, a tap density of 0.80 g/cm.sup.3 or more, and a BET specific surface area of less than 5.0 m.sup.2/g, in which a particle size distribution curve showing a frequency distribution based on volume of the hBN powder is a bimodal distribution curve having a first peak and a second peak in a range of a particle size of 500 μm or less and having a peak height ratio of a second peak height (H.sub.B) to a first peak height (H.sub.A), [(H.sub.B)/(H.sub.A)], of 0.90 or less, a method for producing the same, and a resin composition and a resin sheet each comprising the hBN powder.