ne tetragonal axis). Experimentally it is found, however, that the material breaks up into smaller regions in which the preferred direction and thus the polarization is uniform. Note that cubic materials have no preferred direction. In tetragonal crystals the polarization points along the c-axis(the longer axis) whereas in rhomb- hedral lattices the polarization is along the body diagonal. The volume in which the preferred axis is pointing in the same direction is called a domain and the border between the regions is called a domain wall. The energy of the multidomain state is slightly lower than the single-domain state and is thus the preferred configuration The direction of the polarization changes by either 90 or 180 as we pass from one uniform region to another. Thus the domains are called 90 and 180 domains. Whether an individual crystallite or grain consists of a single domain depends on the size of the crystallite and external parameters such as strain gradients, impurities, etc. It is also possible that the domain extend beyond the grain boundary and asses two or more grains of the crystal Real materials consist of large numbers of unit cells, and the manifestation of the individual charged groups is n internal and an external electric field when the material is stressed. Internal and external refer to inside and outside of the material. The interaction of an external electric field with a charged group causes a displacement of certain atoms in the group. The macroscopic manifestation of this is a displacement of the surfaces of the material This motion is called the piezoelectric effect, the conversion of an applied field into a corresponding displacement 49.3 Ferroelectric materials PZT (PbZr Tin-sO3 )is an example of a ceramic material which is ferroelectric. We will use PZT as a prototype ystem for many of the ferroelectric attributes to be discussed. The concepts, of course, have general validity The structure of this material is abo where a is lead and b is one or the other atoms ti or Zr. This material consists of many randomly oriented crystallites which vary in size between approximately 10 nm and several microns. The crystalline symmetry of the material is determined by the magnitude of the parameter x. The material changes from rhombohedral to tetragonal symmetry when x>0.48. This transition is almost inde pendent of temperature. The line which divides the two phases is hange of symmetry as a function of composition only). Commercial materials are made with x=0.48, where the d and g sensitivity of the material is maximum. It is clear from Table 49.2 that there are other parameters which can be influenced as well. Doping the material with donors or acceptors often changes the properties dramatically. Thus niobium is important to obtain higher sensitivity and resistivity and to lower the Curie mperature. PZT typically is a p-type conductor and niobium will significantly decrease the conductivity because of the electron which nb+ contributes to the lattice. the nb ion substitutes for the b-site ion ti+ or Zr*. The resistance to depolarization(the hardness of the material)is affected by iron doping Hardness is a definition giving the relative resistance to depolarization. It should not be confused with mechanical hardness. Many other dopants and admixtures have been used, often in very exotic combinations to affect aging, sensi- The designations used in Table 49.2 reflect very few of the many combinations which have been developed. The PzT designation types were originally designed by the U.S. Navy to reflect certain property combinations. These can be obtained with different combinations of compositions and dopants. The examples given in the table are representative of typical PZT materials, but today essentially all applications have their own custom formulation. The name PZT has become generic for the lead zirconate titanates and does not reflect Navy or When PZT ceramic material is prepared, the crystallites and domains are randomly oriented, and therefore the material does not exhibit any piezoelectric behavior[Fig. 49. 2(a)]. The random nature of the displacements for the individual crystallites causes the net displacement to average to zero when an external field is applied The tetragonal axis has three equivalent directions 90 apart and the material can be poled by reorienting the polarization of the domains into a direction nearest the applied field. When a sufficiently high field is applied, ome but not all of the domains will be rotated toward the electric field through the allowed angle 90 or 180o If the field is raised further, eventually all domains will be oriented as close as possible to the direction of the field. Note however, that the polarization will not point exactly in the direction of the field Fig 49.2(b).At nis point, no further domain motion is possible and the material is saturated. As the field is reduced, the majority of domains retain the orientation they had with the field on leaving the material in an oriented state which now has a net polarization. Poling is accomplished for commercial PZT by raising the temperature to c 2000 by CRC Press LLC© 2000 by CRC Press LLC the tetragonal axis). Experimentally it is found, however, that the material breaks up into smaller regions in which the preferred direction and thus the polarization is uniform. Note that cubic materials have no preferred direction. In tetragonal crystals the polarization points along the c-axis (the longer axis) whereas in rhombo￾hedral lattices the polarization is along the body diagonal. The volume in which the preferred axis is pointing in the same direction is called a domain and the border between the regions is called a domain wall. The energy of the multidomain state is slightly lower than the single-domain state and is thus the preferred configuration. The direction of the polarization changes by either 90° or 180° as we pass from one uniform region to another. Thus the domains are called 90° and 180° domains. Whether an individual crystallite or grain consists of a single domain depends on the size of the crystallite and external parameters such as strain gradients, impurities, etc. It is also possible that the domain extend beyond the grain boundary and encompasses two or more grains of the crystal. Real materials consist of large numbers of unit cells, and the manifestation of the individual charged groups is an internal and an external electric field when the material is stressed. Internal and external refer to inside and outside of the material. The interaction of an external electric field with a charged group causes a displacement of certain atoms in the group. The macroscopic manifestation of this is a displacement of the surfaces of the material. This motion is called the piezoelectric effect, the conversion of an applied field into a corresponding displacement. 49.3 Ferroelectric Materials PZT (PbZrxTi(1–x)O3) is an example of a ceramic material which is ferroelectric. We will use PZT as a prototype system for many of the ferroelectric attributes to be discussed. The concepts, of course, have general validity. The structure of this material is ABO3 where A is lead and B is one or the other atoms, Ti or Zr. This material consists of many randomly oriented crystallites which vary in size between approximately 10 nm and several microns. The crystalline symmetry of the material is determined by the magnitude of the parameter x. The material changes from rhombohedral to tetragonal symmetry when x > 0.48. This transition is almost inde￾pendent of temperature. The line which divides the two phases is called a morphotropic phase boundary (change of symmetry as a function of composition only). Commercial materials are made with x ª 0.48, where the d and g sensitivity of the material is maximum. It is clear from Table 49.2 that there are other parameters which can be influenced as well. Doping the material with donors or acceptors often changes the properties dramatically. Thus niobium is important to obtain higher sensitivity and resistivity and to lower the Curie temperature. PZT typically is a p-type conductor and niobium will significantly decrease the conductivity because of the electron which Nb5+ contributes to the lattice. The Nb ion substitutes for the B-site ion Ti 4+ or Zr4+. The resistance to depolarization (the hardness of the material) is affected by iron doping. Hardness is a definition giving the relative resistance to depolarization. It should not be confused with mechanical hardness. Many other dopants and admixtures have been used, often in very exotic combinations to affect aging, sensi￾tivity, etc. The designations used in Table 49.2 reflect very few of the many combinations which have been developed. The PZT designation types were originally designed by the U.S. Navy to reflect certain property combinations. These can be obtained with different combinations of compositions and dopants. The examples given in the table are representative of typical PZT materials, but today essentially all applications have their own custom formulation. The name PZT has become generic for the lead zirconate titanates and does not reflect Navy or proprietary designations. When PZT ceramic material is prepared, the crystallites and domains are randomly oriented, and therefore the material does not exhibit any piezoelectric behavior [Fig. 49.2(a)]. The random nature of the displacements for the individual crystallites causes the net displacement to average to zero when an external field is applied. The tetragonal axis has three equivalent directions 90° apart and the material can be poled by reorienting the polarization of the domains into a direction nearest the applied field. When a sufficiently high field is applied, some but not all of the domains will be rotated toward the electric field through the allowed angle 90° or 180°. If the field is raised further, eventually all domains will be oriented as close as possible to the direction of the field. Note however, that the polarization will not point exactly in the direction of the field [Fig. 49.2(b)]. At this point, no further domain motion is possible and the material is saturated. As the field is reduced, the majority of domains retain the orientation they had with the field on leaving the material in an oriented state which now has a net polarization. Poling is accomplished for commercial PZT by raising the temperature to