**1. Introduction**

The worldwide growing demand for energy has led to increasing dependence on fossil fuels from few and unstable regions of the globe. Oppositely, clamors for more restrictive environ‐ mental regulation have pointed out the development of cleaner power supplies that meet the increasing demand for electricity.

The use of natural gas or their liquid fuels, the first and second generation of biofuel, and, even, hydrogen has been pointed as "clean" power supplies for the growing demand. Other classic solutions cover hydropower, solar, wind, and nuclear supplies which have enforcement power and limitations described by literature.

Piezoelectricity is a good alternative for clean and environmental power supply. It does not generate waste or pollutants because it does not need fuels or additives. Some revolutionary applications of this type of energy can be enumerated: piezoelectric plates in shoe soles can generate energy for charging portable electronic devices; piezoelectric plates in floors can be an alternative for lighting squares or dance clubs; and, even in a futuristic vision, piezoelectric materials can be used in pavements of highways or streets to generate inexpensive energy. This type of power supply can bring benefits to society and to environment because it can be obtained sustainably and be capable to replace other power supplies.

The piezoelectric effects were discovered in 1880 by brothers Pierre and Jacques Currie in quartz crystals. Ever since, piezoelectricity has been leading numerous researches in devel‐ opment of electronic transducer systems. The effect consists basically in conversion of mechanical energy to electrical energy (from Greek term "piezo" for pressure). In 1881, Lippman, using the thermodynamic analysis, predicted the existence of inverse piezoelectric effect, which consists in appearance of material deformation submitted to an electric field.

Two conditions must be presented simultaneously in a crystal to have piezoelectric property. First, it is the presence of uncentersymmetric characteristic in the crystalline structure of the material. Second, it is the existence of a material polarization when submitted under mechan‐ ical stress.

The piezoelectric effect is a reversible process for materials which present direct (internal generation of electric charge resulting from applied mechanical stress) and reverse (internal generation of mechanical stress resulting from applied electric field) effects. For example, lead zirconate titanate crystals generate measurable piezoelectricity when static structure is deformed by 0.1% from initial dimension. Oppositely, these same crystals change 0.1% of their static dimensions submitted to an external electric field.

Oxides as perovskites have a general formula ABO3, where A is a large cation-like alkaline metals, earth metals, and rare earth metals and B is a small cation-like transition metals. Most common perovskites are those where A is a cation of rare earth metal with oxidation state +3 and B is a transition metal with the same valence state [1].

The perovskite structure is the most important piezoelectric crystalline ceramic. This structure is a network of cornered linked oxygen octahedral holes with a large cation filling the dodec‐ ahedral holes. The piezoelectric properties in perovskite structure result from uncentersym‐ metric characteristic, since this physical property is originated from crystal anisotropy.

**1. Introduction**

64 Piezoelectric Materials

ical stress.

increasing demand for electricity.

and limitations described by literature.

The worldwide growing demand for energy has led to increasing dependence on fossil fuels from few and unstable regions of the globe. Oppositely, clamors for more restrictive environ‐ mental regulation have pointed out the development of cleaner power supplies that meet the

The use of natural gas or their liquid fuels, the first and second generation of biofuel, and, even, hydrogen has been pointed as "clean" power supplies for the growing demand. Other classic solutions cover hydropower, solar, wind, and nuclear supplies which have enforcement power

Piezoelectricity is a good alternative for clean and environmental power supply. It does not generate waste or pollutants because it does not need fuels or additives. Some revolutionary applications of this type of energy can be enumerated: piezoelectric plates in shoe soles can generate energy for charging portable electronic devices; piezoelectric plates in floors can be an alternative for lighting squares or dance clubs; and, even in a futuristic vision, piezoelectric materials can be used in pavements of highways or streets to generate inexpensive energy. This type of power supply can bring benefits to society and to environment because it can be

The piezoelectric effects were discovered in 1880 by brothers Pierre and Jacques Currie in quartz crystals. Ever since, piezoelectricity has been leading numerous researches in devel‐ opment of electronic transducer systems. The effect consists basically in conversion of mechanical energy to electrical energy (from Greek term "piezo" for pressure). In 1881, Lippman, using the thermodynamic analysis, predicted the existence of inverse piezoelectric effect, which consists in appearance of material deformation submitted to an electric field.

Two conditions must be presented simultaneously in a crystal to have piezoelectric property. First, it is the presence of uncentersymmetric characteristic in the crystalline structure of the material. Second, it is the existence of a material polarization when submitted under mechan‐

The piezoelectric effect is a reversible process for materials which present direct (internal generation of electric charge resulting from applied mechanical stress) and reverse (internal generation of mechanical stress resulting from applied electric field) effects. For example, lead zirconate titanate crystals generate measurable piezoelectricity when static structure is deformed by 0.1% from initial dimension. Oppositely, these same crystals change 0.1% of their

Oxides as perovskites have a general formula ABO3, where A is a large cation-like alkaline metals, earth metals, and rare earth metals and B is a small cation-like transition metals. Most common perovskites are those where A is a cation of rare earth metal with oxidation state +3

The perovskite structure is the most important piezoelectric crystalline ceramic. This structure is a network of cornered linked oxygen octahedral holes with a large cation filling the dodec‐

obtained sustainably and be capable to replace other power supplies.

static dimensions submitted to an external electric field.

and B is a transition metal with the same valence state [1].

The first perovskite structure developed was barium titanate (BaTiO3). The polymorphous forms of BaTiO3 have been likened displacing the central Ti+4 ion within its oxygen octahedron toward one, two, and, then, three of the six adjacent oxygen ions as the temperature is lowered. This is a simplification of the actual atomic displacements, but it is a useful first approximation for structure understanding. For a revision about the role of the perovskite structure in ceramic science and technology, see literature [2].

The pragmatic application of theory in science follows two strategies: (i) there is readiness of experimental information of the interested system's properties (the application's results for the theory in study of those properties can be confronted to experimental data which will serve as guide to corroborate the applied concepts or to suggest changes) and (ii) experimental data are not available (the resulting forecasts of the application of theory can be used by experi‐ mentalists as guide to facilitate the rational money application and the time reduction for the system under investigation).

In last decade, we have been reported in literature a series of articles about theoretical studies of perovskites. Basically, our purpose is to investigate the possible existence of piezoelectric properties in those materials, using developed basis sets for the appropriate environment of their crystals. In our approaches, different theoretical methods have been used and the results suggest or not this property.

In this chapter, we show that the strategies have been used to study piezoelectricity in ceramic materials as perovskites using basis sets obtained by our research group. To obtain extended basis sets, we will show computer details using generator coordinate Hartree-Fock (GCHF) method [3] and the procedures used to contract extended basis sets as well as the strategy used to evaluate their quality in molecular environment. In addition, we will show the supplement of polarization and diffuse functions to best represent the studied crystal environment and the theoretical methods used in our articles in literature. We will also discuss conditions how our obtained basis sets and standard basis sets from packages in literature can be used to develop studies of piezoelectricity in perovskites.

Finally, we will present and discuss the obtained results for investigation of piezoelectricity with standard basis sets for barium and lanthanum titanates and last considerations related to this chapter.
