**8. Conclusion**

The perovskite is a mineral series composed of calcium titanate. Many transition metal oxides show that very versatile perovskite structure. The rich variety of physical properties

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such as high-temperature superconductivity and colossal magnetoresistance observed in these compounds makes them very attractive from both fundamental and applied perspectives.

There are different methods of synthesis. Among them, one of the most used is that known as ceramic method, although not the most efficient one. The freeze-drying method offers purer materials by reducing the heating time and working at not so high temperatures.

The general chemical formula for perovskite compounds is *AB*X3, where *A* and *B* are two cations of very different sizes, and X is an anion that bonds to both. The *A* atoms are larger than the *B* atoms. The ideal cubic-symmetry structure has the *B* atoms in 6-fold coordination, surrounded by an octahedron of anions, and the *A* atoms in 12-fold cuboctahedral coordination. The relative ion size requirements for stability of the cubic structure are quite stringent, so slight buckling and distortion can produce several lowersymmetry distorted versions, in which the coordination numbers of *A* cations, *B* cations or both are reduced. The orthorhombic and tetragonal phases are the most common non-cubic variants.

The X-ray diffraction pattern of a pure substance is like a fingerprint of the substance. The powder diffraction method is thus ideally suited for characterization and identification of polycrystalline phases, and therefore of perovskites.

The Rietveld method allows us to characterize the polycrystalline materials by a least squares approach to refine a theoretical line profile until it matches the measured profile shown in the pattern.

It is possible to go further in the study of the structure of the perovskites by means of neutron diffraction, although it is true to say that large facilities are needed to carry out such study.
