Lithium secondary batteries have been in practical and widespread use as secondary batteries for portable electronic devices Furthermore, in recent years, lithium secondary batteries have drawn attention not only as small-sized secondary batteries for portable electronic devices but also as high-capacity devices for use in vehicles, power storage, etc.  Therefore, there has been a growing demand for higher safety standards, lower costs, longer lives, etc. 
A lithium secondary battery is composed mainly of a cathode, an anode, an electrolyte, a separator, and an armoring material.  Further, the cathode is constituted by a cathode active material, a conductive material, a current collector, and a binder (binding agent). 
In general, the cathode active material is realized by a layered transition metal oxide such as LiCoO2.  However, in a state of full charge, such layered transition metal oxides are prone to cause oxygen desorption at a comparatively low temperature of approximately 150° C., and such oxygen desorption may cause a thermal runaway reaction in the battery.  Therefore, when a battery having such a cathode active material is used for a portable electronic device, there is a risk of an accident such as heating, firing, etc.  of the battery. 
For this reason, in terms of safety, expectations have been placed on lithium manganate (LiMn2O4) having a spinel-type structure, lithium iron phosphate (LiFePO4) having an olivine-type structure, etc.  that are stable in structure and do not emit oxygen in abnormal times. 
Further, in terms of cost, cobalt (Co) is low in degree of existence in the earth's crust and high in price.  For this reason, expectations have been placed on lithium nickel oxide (LiNiO2) or a solid solution thereof (Li(Co1-xNix)O2), lithium manganate (LiMn2O4), lithium iron phosphate (LiFePO4), etc. 
Further, in terms of life, the insertion and desorption of Li into and from a cathode active material along with charging and discharging cause structural destruction in the cathode active material.  For this reason, more expectations have been placed on lithium manganate (LiMn2O4) having a spinel-type structure, lithium iron phosphate (LiFePO4) having an olivine-type structure, etc.  than on layered transition metal oxides because of their structural stability. 
Therefore, for example, such lithium iron phosphate having an olivine-type structure has drawn attention as a cathode active material for a battery in consideration of safety, cost, and life.  However, when lithium iron phosphate having an olivine-type structure is used as a cathode active material for a battery, there are such declines in charge-discharge behavior as insufficient electron conductivity and low average potential. 
In order to improve charge-discharge behavior, there has been proposed an active material represented by general formula AaMb(XY4)cZd (where A is an alkali metal, M is a transition metal, XY4 is PO4 or the like, and Z is OH or the like) (e.g., see Patent Literature 1). 
Further, there have been also proposed an active material, represented by general formula LiMP1-xAxO4 (where M is a transition metal, A is an element having an oxidation number of +4 or less, and 0<X<1), whose P site has been replaced by the element A (e.g., see Patent Literature 2). 
Further proposed as a cathode active material for a nonaqueous electrolyte secondary battery excellent in large-current charge-discharge behavior is a material represented by general formula Li1-xAxFe1-Y-ZMyMezPi1-mXmO4-nZn (where A is Na or K; M is a metal element other than Fe, Li, and Al; X is Si, N, or As; Z is F, Cl, Br, I, S, or N) (e.g., see Patent Literature 3).  Further proposed as an electrode active material that can be economically produced, is satisfactory in charging capacity, and is satisfactory in rechargeability over many cycles is a material represented by general formula Aa+xMbP1-xSixO4 (where A is Ki or Na, or K; and M is a metal) (e.g., see Patent Literature 4). 
There has also been disclosed lithium transition metal phosphorus, such as LiFePO4, which includes at least two coexisting phases including a lithium-rich transition metal phosphate phase and a lithium-poor transition metal phosphate phase, the coexisting phases being different from each other in molar volume by approximately 5.69 (e.g., see Table 2 of Patent Literature 5).