A metal hydroxide includes Ni element. An axial lattice constant c ? of the metal hydroxide satisfies: 0.363x+4.2?c?0.363x+4.4, where, based on a total molar mass of a metal element in the metal hydroxide, a molar percentage of the Ni element in the metal hydroxide is x. The lattice constant c of the metal hydroxide falls within a specified value range. The positive electrode material prepared from the metal hydroxide serving as a precursor is of excellent structural stability in a charging and discharging environment, and improves the cycle performance, high-temperature performance, and safety performance of lithium-ion batteries.

A positive electrode active material includes secondary particles. The secondary particles include a plurality of primary particles. The primary particles include a lithium-containing composite metal oxide. Inside the secondary particles, an electron conducting oxide is disposed at at least a part of a grain boundary between the primary particles. The electron conducting oxide has a perovskite structure.

A thermoelectric material, having a formula Tb.sub.xM1.sub.y-xM2.sub.zO.sub.w where M1 is one of Ca, Mg, Sr, Ba and Ra, M2 is at least one of Co, Fe, Ni, and Mn, x ranges from 0.01 to 5; y is 1, 2, 3, or 5; z is 1, 2, 3, or 4; and w is 1, 2, 3, 4, 5, 7, 8, 9, or 14. The thermoelectric material is chemically stable within 5% for one year and is also non-toxic. The thermoelectric material can also be incorporated into a thermoelectric system which can be used to generate electricity from waste heat sources or to cool an adjacent region.

A two-step thermochemical gas reduction process based on poly-cation oxides includes repeatedly cycling a thermal reduction step and a gas reduction step. In the thermal reduction the poly-cation oxide is heated to produce a reduced poly-cation oxide and oxygen. In the gas reduction step, the reduced poly-cation oxide is reacted with a gas to reduce the gas, while reoxidizing the poly-cation oxide. The poly-cation oxide has at least two distinct crystal structures at two distinct temperatures and is capable of undergoing a reversible phase transformation between the two distinct crystal structures. For example, the poly-cation oxide may be an entropy tuned mixed metal oxide, such as an entropy stabilized mixed metal oxide, where the entropy-tuning is achieved via change in crystal structure of one of more of the compounds involved. The gas reduction process may be used for water splitting, CO.sub.2 splitting, NO.sub.x reduction, and other gas reduction processes.

A material for forming an electrode represented by the formula:

Li.sub.1+x-aD1.sub.aNm.sub.1-x-y-z-b1Ni.sub.y-b2D2.sub.bCo .sub.z-b3O.sub.2-

where 0<a0.2, 0<b0.2,b1+b2+b3=b, 0.1x0.5, 0y<1, 0z0.5, and 00.3 and D1 includes sodium (Na) and D2 includes yttrium (Y).

A single-crystalline LnBM.sub.2O.sub.5+ or LnBM.sub.2O.sub.5.5+ compound is provided, which includes an ordered oxygen vacancy structure; wherein Ln is a lanthanide, B is an alkali earth metal, M is a transition metal, O is oxygen, and 01. Methods of making and using the compound, and devices and compositions including same are also provided.

A single-crystalline LnBM.sub.2O.sub.5+ or LnBM.sub.2O.sub.5.5+ compound is provided, which includes an ordered oxygen vacancy structure; wherein Ln is a lanthanide, B is an alkali earth metal, M is a transition metal, O is oxygen, and 01. Methods of making and using the compound, and devices and compositions including same are also provided.