A perovskite material represented by Formula 1:

Li.sub.xA.sub.yM.sub.zO.sub.3-Formula 1 wherein in Formula 1, 0<x1, 0<y1, 0<x+y<1, 0<z1.5, 01, A is H, Na, K, Rb, Cs, Ca, Sr, Ba, Y, La, Ce, Pr, Nd, Pm, Sm, Gd, Tb, Dy, Ho, Er, or a combination thereof, and M is Ni, Pd, Pb, Fe, Ir, Co, Rh, Mn, Cr, Ru, Re, Sn, V, Ge, W, Zr, Mo, Hf, U, Nb, Th, Ta, Bi, Li, H, Na, K, Rb, Cs, Ca, Sr, Ba, Y, La, Ce, Pr, Nd, Pm, Sm, Gd, Tb, Dy, Ho, Er, Mg, Al, Si, Sc, Zn, Ga, Ag, Cd, In, Sb, Pt, Au, or a combination thereof.

A mixed conductor represented by Formula 1:

A.sub.xTi.sub.5yG.sub.zO.sub.12Formula 1 wherein, in Formula 1, A is a monovalent cation, G is at least one of a monovalent cation, a divalent cation, a trivalent cation, a tetravalent cation, a pentavalent cation, or a hexavalent cation, with the proviso that G is not Ti or Cr, wherein 0<x<2, 0.3<y<5, 0<z<5, and 0<3.

In a garnet-type or garnet-like LLZ-based lithium ion-conductive oxide material, a high ion conductivity is realized. Specifically, the lithium ion-conductive oxide material contains each element of Li, La, Zr and O and at least an A element, the A element has a d electron, and is in a cation state where regular octahedral coordination preference in stabilization of an anion of oxygen by a ligand field becomes 50 kJ/mol or more, and a mole ratio A/La of the A element to La is 0.01 or more and 0.45 or less.

In general, according to one embodiment, there is provided an active material. The active material contains a composite oxide having an orthorhombic crystal structure. The composite oxide is represented by a general formula of Li.sub.2+wNa.sub.2xM1.sub.yTi.sub.6zM2.sub.zO.sub.14+. In the general formula, the M1 is at least one selected from the group consisting of Cs and K; the M2 is at least one selected from the group consisting of Zr, Sn, V, Nb, Ta, Mo, W, Fe, Co, Mn, and Al; and w is within a range of 0w4, x is within a range of 0<x<2, y is within a range of 0y<2, z is within a range of 0<z6, and is within a range of 0.50.5.

A layered double hydroxide is represented by the following formula (I): Ni.sup.2+.sub.1?(x+y+z)Fe.sup.3+.sub.xV.sup.3+.sub.yCo.sup.3+.sub.z(OH).sub.2A.sup.n?.sub.(x+y+z)/n.Math.mH.sub.2O . . . (I). In one embodiment, in the formula (I), (x+y+z) is from 0.2 to 0.5, x represents more than 0 and 0.3 or less, y represents from 0.04 to 0.49, and z represents more than 0 and 0.2 or less.

An electrode comprising a space group Pna2.sub.1 VOPO.sub.4 lattice, capable of electrochemical insertion and release of alkali metal ions, e.g., sodium ions. The VOPO.sub.4 lattice may be formed by solid phase synthesis of KVOPO.sub.4, milled with carbon particles to increase conductivity. A method of forming an electrode is provided, comprising milling a mixture of ammonium metavanadate, ammonium phosphate monobasic, and potassium carbonate; heating the milled mixture to a reaction temperature, and holding the reaction temperature until a solid phase synthesis of KVOPO.sub.4 occurs; milling the KVOPO.sub.4 together with conductive particles to form a conductive mixture of fine particles; and adding binder material to form a conductive cathode. A sodium ion battery is provided having a conductive NaVOPO.sub.4 cathode derived by replacement of potassium in KVOPO.sub.4, a sodium ion donor anode, and a sodium ion transport electrolyte. The VOPO.sub.4, preferably has a volume greater than 90 .sup.3 per VOPO.sub.4.

A negative thermal expansion material according to an embodiment is represented by a general formula (1): Cu.sub.2-xR.sub.xV.sub.2O.sub.7 (R is at least one element selected from Zn, Ga, and Fe) and includes an oxide sintered compact whose linear expansion coefficient is 10 ppm/K or less.

In general, according to one embodiment, there is provided an active material. The active material contains a composite oxide having an orthorhombic crystal structure. The composite oxide is represented by a general formula of Li.sub.xM1.sub.1yM2.sub.yTi.sub.6zM3.sub.zO.sub.14+. In the general formula, M1 is at least one selected from the group consisting of Sr, Ba, Ca, and Mg; M2 is at least one selected from the group consisting of Cs, K, and Na; M3 is at least one selected from the group consisting of Al, Fe, Zr, Sn, V, Nb, Ta, and Mo; and x is within a range of 2x6, y is within a range of 0<y<1, z is within a range of 0<z6, and is within a range of 0.50.5.

Disclosed is a method of preparing an oxide for hydrogen storage, including a) mixing and calcining vanadium oxide and titanium oxide, b) impregnating the oxide obtained in step a) with a noble metal precursor aqueous solution, and c) subjecting the oxide obtained in step b) to heat treatment in a reducing atmosphere, wherein the oxide obtained in step a) has the composition of Chemical Formula 1 below and is composed of a single-phase TiO.sub.2 crystal phase:

V.sub.1-xTi.sub.xO.sub.2[Chemical Formula 1] (in Chemical Formula 1, 0.05x0.95).

Provided is the positive electrode active material for a potassium ion battery according to the embodiment comprises a compound represented by Formula (1), in which M represents at least one element selected from the group consisting of V, Fe, Co, Ni, and Mn, and x represents a number from 0 to 1; and is a positive electrode for a potassium ion battery comprising the positive electrode active material for a potassium ion battery according to the embodiment, or a potassium ion battery comprising the positive electrode for a potassium ion battery.

KMO.sub.xPO.sub.4F.sub.1-x[Formula (1)]