**2.1. Deformations of hysteresis loop shape of ferroelectrics: pinching and asymmetries**

The study of the hysteresis loops, namely current-electric field (I-E), polarization-electric field (P-E) and strain-electric field (S-E), is one of the most important tools to investigate the behavior and to assess the properties of ferroelectric/ferroelastic materials.[1-3] These curves usually show certain symmetry properties with respect to one or both the two axes, but they are susceptible to substantial modifications of their shapes, frequently observed in certain structures and compositions, which have undergone a certain thermal and electrical history. The most relevant examples of shape modifications of hysteresis loops are represented by *pinched loops* (constricted P-E loops in the region E ≈ 0, remanent polarization approaching to zero), *asymmetric loops* (shift of the P-E loops along the E- and P-axis, suppression of left or right wing of the S-E "butterfly" loop) and *polarization gaps* (relaxation of the remanent polarization at E = 0), which have been found in different ferroelectric/ferroelastic systems in both polycrystalline ceramics and single crystal. It can be generally said that these features can be caused by the development of an *internal bias field Eint*, whose magnitude and distribution depend on the composition/microstructure and on the thermal/electrical history of the system. In most cases, the presence of an internal field in ferroelectric materials can arise during processing (in this case often referred to as *built-in field*) or generated by two thermodynamic processes generally classified as *aging* and *fatigue*. They both share similar features, but they are triggered under different conditions and they can be influenced by different factors, as it will be discussed in the following sections.
