Polar superlattices

The supramolecular structure of block co-polymers allows the design of useful materials properties such as polarity leading to potential applications as second-order nonlinear optical materials, as well as piezo-, pyro-, and ferroelectricity. It is possible to prepare polar superlattices by mixing (blending) a 1 1 ratio of a polystyrene)-6-poly(butadiene)-6-poly-(tert-butyl methacrylate) triblock copolymer (SBT) and a poly (styrene)-Apoly (tert-butyl methacrylate) diblock copolymer (st). The result is a polar, lamellar material with a domain spacing of about 60 nm, Figure 14.10. 

M. E. Van der Boom, A. G. Richter, J. E. Malinsky, P. A. Lee, N. R. Armstrong, P. Dutta, and T. J. Marks, Single reactor route to polar superlattices. Layer-by-layer self-assembly of large-response molecular electrooptic materials by protection-deprotection, Chem. Mater. 13, 15-17 (2001). 

Fig. 10. The leh-hand diagram shows an organic superlattice with a unique polar axis. The two types of molecule involved could be a fatty acid and a fatty amine. The insert is designed to show that these two materials have dipole moments in opposite senses with respect lo the hydrophobic chain. Thus, the V-lype film has a resultant dipole moment...

These nanodomain superlattices were written by moving the hvafm tip along the polar Z+-face with a velocity of around 50 p.m/sec. The width of the tailored strips was greatly affected by the tip velocity and was measured to be between 50 and 1500 nm a larger tip velocity resulted in narrower domains. 

Fig. 21.4 Temperature dependencies of normalized Raman intensities of TO2 (solid triangles) and TO4 (open triangles) phonons for (a) SLs [(BaTi03)2(SrTi03)4] x 40 and [(BaTi03)5(SrTi03)4] x 25 (b) SLs [(BaTi03)g(SrTi03)4] x 40 and [(BaTi03)8(SrTi03)4] x 10. The dash-dotted lines are fits to linear temperature dependence, (c) and (d) - three-dimensional phase-field model calculations of polarization as a function of temperature in the same superlattice...

Raman spectra as a function of temperature are shown in Fig. 21.6b for the C2B4S2 SL. Other superlattices exhibit similar temperature evolution of Raman spectra. These data were used to determine Tc using the same approach as described in the previous section, based on the fact that cubic centrosymmetric perovskite-type crystals have no first-order Raman active modes in the paraelectric phase. The temperature evolution of Raman spectra has indicated that all SLs remain in the tetragonal ferroelectric phase with out-of-plane polarization in the entire temperature range below T. The Tc determination is illustrated in Fig. 21.7 for three of the SLs studied SIBICI, S2B4C2, and S1B3C1. Again, the normalized intensities of the TO2 and TO4 phonon peaks (marked by arrows in Fig. 21.6b) were used. In the three-component SLs studied, a structural asymmetry is introduced by the presence of the three different layers, BaTiOs, SrTiOs, and CaTiOs, in each period. Therefore, the phonon peaks should not disappear from the spectra completely upon transition to the paraelectric phase at T. Raman intensity should rather drop to some small but non-zero value. However, this inversion symmetry breakdown appears to have a small effect in terms of atomic displacement patterns associated with phonons, and this residual above-Tc Raman intensity appears too small to be detected. Therefore, the observed temperature evolution of Raman intensities shows a behavior similar to that of symmetric two-component superlattices. 

Shimuta T, Nakagawara O, Makino T, Arai S, Tabata H, Kawai T (2002) Enhancement of remanent polarization in epitaxial BaTiOa/SrTiOa superlattices with asymmetric structure. J Appl Phys 91 2290... 

Lee HN, Christen HM, Chisholm ME, Rouleau CM, Lowndes DH (2005) Strong polarization enhancement in asymmetric three-component ferroelectric superlattices. Nature 433 395... 

Neaton JB, Rabe KM (2003) Theory of polarization enhancement in epitaxial BaTiOa/ SrTiOs superlattices. Appl Phys Lett 82 1586... 

Nakhmanson SM, Rabe KM, Vanderbilt D (2006) Predicting polarization enhancement in multicomponent ferroelectric superlattices. Phys Rev B 73 060101(R)... 

Dawber M, Lichtensteiger C, Cantoni M, Veithen M, Ghosez P, Johnston K, Rabe KM, Triscone J-M (2005) Unusual behavior of the ferroelectric polarization in PbTi03/SrTi03 superlattices. Phys Rev Lett 95 177601... 

Johnston K, Huang X, Neaton JB, Rabe KM (2005) First-principles study of symmetry lowering and polarization in BaTiQs/SrTiQs superlattices with in-plane expansion. Phys Rev B 71 100103(R)... 

We have already seen that the intensity of a superlattice line from an ordered solid solution is much lower than that of a fundamental line. Will it ever be so low that the line cannot be detected We can make an approximate estimate by ignoring the variation in multiplicity factor and Lorentz-polarization factor from line to line, and assuming that the relative integrated intensities of a superlattice and fundamental line are given by their relative F values. For fully ordered AuCus, for example, we find from Eqs. (13-1) that... 

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