2. Experimental

treatment and produces nanostructured powders which are of primary interest in the current

The perovskite, ABO3 type structure of BT is cubic (above 120�C) with Ba ion (larger A cation) located at the cube corners, Ti ion (smaller B cation) at the body center, and oxygen at the face centre, forming octahedra around each Ti ion. It is considered an FCC-derivative structure in which the larger A cation and oxygen together form an FCC lattice, while the smaller B cation occupies the octahedral interstitial sites in the FCC array. The Ba ion occupies the space formed between eight neighboring octahedra, giving the Ba, Ti and the oxygen ions coordination number of 12, 6 and 6, respectively. BaTiO3 can accept the substitution of foreign cations on two distinct sites, the A-site (Ba) and the B-site (Ti). The stability of the perovskite compounds

BT undergoes a series of structural phase transitions upon cooling from high temperature. In the temperature range of 1430–1620�C, barium titanate assumes a hexagonal structure. In the 130–1430�C range, BT is cubic and nonpolar (space group Pm3m), thus centrosymmetric and nonpiezoelectric. When the temperature is below the Curie temperature (130�C), the cubic structure (paraelectric) is slightly distorted to a tetragonal (P4mm) structure (ferroelectric) which is noncentrosymmetric, with an accompanying movement of Ti atoms inside the O6 octahedra. In turn, oxygen ions all shift in the opposite direction [100]. Not only does this result in distortion of oxygen octahedron, but the opposite displacement of negative and positive charges within the unit cell leads to the formation of an electric dipole moment, and hence to the appearance of spontaneous polarization and ferroelectric properties. In the tetragonal phase, the direction of the vector of spontaneous polarization Ps (i.e., polar direction) lies parallel to the direction of one of the original cubic [100] directions. When the temperature is below 5�C, the tetragonal structure transforms to an orthorhombic ferroelectric phase (C2mm) with the polar axis parallel to a face diagonally, and the direction of spontaneous polarization transfers to a pseudocubic [110]. At as low as �90�C, it further transforms to a rhombohedral structure (R3m) with the polar axis along a body diagonal and is spontaneously polarized

The Goldschmidt tolerance factor for a perovskite structure (ABO3) is given by the formula:

<sup>t</sup> <sup>¼</sup> rA <sup>þ</sup> rO √2ð Þ rB þ rO

where rA rB and rO are the A-site, B-site, and oxygen ionic radii, respectively. There are three possible values of 't': (1) t ≥ 1: show ferroelectricity. (2) t < 1: This antiferroelectric perovskite. (3)

(1)

arises mainly from the electrostatic charge of the ions when perfectly integrated.

trend of miniaturization and integration of electronic components [31, 32].

1.3. Barium titanate (BaTiO3) perovskite structure

150 Recent Advances in Porous Ceramics

1.4. Structural phase transitions in barium titanate

along a [111] direction.

t = 1: perfect cubic structure.

#### 2.1. Sample preparation

All samples used in this study were prepared by the conventional solid state and mechanochemical technique from fine powders of metal oxides or metal carbonates. The nominal purity of the initial powders, as well as their manufacturers are given in Table 1.
