a lithium compound is the volume average particle diameter measured by a laser diffraction method the volume average particle diameter was measured with a laser diffraction scattering particle size distribution measurement device using ethanol as dispersion medium in the measurement the refractive index of ethanol was set as 1 360 and the refractive index of a lithium compound was appropriately set corresponding to the species of the compound for example when the lithium compound was lithium carbonate the refractive index was set to 1 500 as the laser diffraction scattering particle size distribution measurement device la 950 made by horiba ltd was used in the present specification the average particle diameter of primary particles of a titanium compound is the average value of particle diameters of 100 primary particles in an image picture of a transmission electron microscope an electron microscope method in the present specification the average secondary particle diameter of secondary particles of a titanium compound is the volume average particle diameter measured by a laser diffraction method the volume average particle diameter was measured with a laser diffraction scattering particle size distribution measurement device using pure water as dispersion medium in the measurement the refractive index of pure water was set as 1 333 and the refractive index of a titanium compound was appropriately set corresponding to the species of the compound for example when the titanium compound was anatase type titanium.