The interpretation of these scattering spot arrays is somewhat complicated because some of the scattering spots generated by the reflected X-ray beam overlap those generated by the transmitted X-ray beam.įigure 14. These observations show that the c-axis of the hexagonal structure is oriented along a direction normal to the film plane, whereas the other two axes are randomly aligned in the film plane. These observations indicate that a well-ordered in-plane hexagonal structure of microdomains is present in the film and that a certain lattice plane of the structure is aligned but randomly oriented in the film plane. 35,107 In particular, the out-of-plane scattering spot arrays appear at relative 2 θ f positions from the specular reflection position of 1, 3 1/2, 4 1/2, and 7 1/2. 35,106 As can be seen in Figure 14( a), the scattering patterns contain a number of sharp scattering spots over a wide range of scattering angles. Recently, thin films of a PS- b-PI(37/63) diblock copolymer with HPL structures with ABC or AB stacking sequences were quantitatively analyzed with GIXS formula.
113–115 ABC stacking has rhombohedral symmetry ( R3m) while AB stacking has hexagonal symmetry. The stacking sequences have been proposed as ABC 109,111 or AB 112 arrangements or as a combination of ABC and AB. For example, the stacking sequence of the perforations in HPL morphologies is a subject of particular interest. 109,110 Nevertheless, the HPL structure has received much attention because of its intriguing structural characteristics. 109,110 HPL structure in polymers is known to be metastable and appears in limited temperature ranges between the stable lamellar and gyroid phases. The HPL structure is known to be metastable and appears in limited temperature ranges between the stable lamellar and gyroid phases. Hexagonally perforated layer (HPL) structure is one of the most complicated structures in polymers, particularly block copolymers. Kim, in Polymer Science: A Comprehensive Reference, 2012 2.16.3.2.3 Hexagonally perforated layer structure in block copolymers As a result, an increase in Ti concentration from 47% to 52% results not only in the continuous rotation of the spontaneous polarization from to, but also in the change of the oxygen octahedra rotation axis from to. This phase involves the coexistence of ferroelectricity and rotation of oxygen octahedra, but is associated with the tetragonal symmetry (unlike R3c and Cc). Interestingly, for the largest Ti concentrations, a new tetragonal phase with the I4cm space was suggested and confirmed experimentally. Recently ( Kornev et al., 2006) the Cc phase existence was confirmed as one of the ground states of PZT but the oxygen octahedra in this Cc phase rotate neither about the direction nor about the direction, but rather about an axis that is between these two directions. (2005) suggests a Cc phase and underlines the ability of such phase to bridge the R3c and Cm phases. Moreover recent models involving mixing with Cc phase were also considered ( Cox et al., 2005 Ranjan et al., 2005). Later, the same group reported that the correct space group for this phase is in fact Cc ( Hatch et al., 2002). Persistence of superlattice reflections inside the concentration range of the monoclinic phase raises the question of the exact space group for these concentration: if long ranged, a Pc, instead of Cm, space group should be considered from Rietveld analysis ( Ranjan et al., 2002). However a distinction must be made regarding the low-temperature rhombohedral phase in which a rotation of oxygen octahedra occurs along the direction in addition to the ferroelectric shifts of the R3m phase, inducing an R3c phase.
A unique monoclinic phase of the M A type was evidenced in addition to the adjacent tetragonal and rhombohedral phases.
The situation in PZT ( Fig. 14.16) has been discussed by several authors, in particular by Noheda (2002).