Electric-field-induced local structural phenomena in relaxor ferroelectric PbSc(0.5)Nb(0.5)O3 near the intermediate temperature T* studied by Raman spectroscopy.

Raman spectroscopy at different temperatures and under an external electric field E was applied to PbSc0.5Nb0.5O3 single crystals in order to gain further insights into the mesoscopic-scale coupling processes in perovskite-type (ABO3) relaxor ferroelectrics. Parallel and cross-polarized Raman spectra were collected between 800-80 K with E applied along the cubic [1 0 0], [1 1 0] or [1 1 1] crystallographic directions. The analysis was focused on the field-induced changes in the temperature evolution of three low-energy phonon modes: the Pb-localized mode near 50 cm(-1), the Pb-BO3 translation mode near 150 cm(-1), and the B-cation-localized mode near 250 cm(-1). The results show that competitive ferroelectric (FE) and antiferroelectric (AFE) coupling exists within the system of off-centred Pb(2+) cations, within the system of off-centred B-site cations as well as between off-centred Pb(2+) and B-site cations. The strong AFE-type coupling between Pb(2+) cations along the cubic body diagonal significantly influences the coupling between the B-site cations via the Pb-BO3 mode and results in AFE-type behaviour of the 'microscopic' T* determined from the B-cation-localized mode near 250 cm(-1), which explains the previously reported non-trivial field dependence of the 'macroscopic' characteristic temperatures: the temperature of the dielectric-permittivity maximum Tm, T*, and the Burns temperature TB. The comparative analysis between PbSc0.5Nb0.5O3 and PbSc0.5Ta0.5O3 indicates that two major displacive order parameters couple to form a relaxor state in B-site complex perovskites: the FE order associated with polar shifts of B-site cations and the AFE order associated with polar shifts of A-site cations. The latter penetrates through both polar and non-polar regions, but it is highly frustrated due to the high density of translation-symmetry faults in the chemical NaCl-type B-site order. The frustrated AFE order of off-centred A-site cations might be the key factor for the existence of a relaxor state.

Biological control of crystallographic architecture: hierarchy and co-alignment parameters.

Mytilus edulis prismatic calcite and nacre layers exhibit a crystallographic structural hierarchy which differs substantially from the morphological hierarchy. This makes these biomaterials fundamentally different from classical crystalline materials. Morphological building units are defined by their surrounding organic matrix membranes, e.g. calcite fibers or nacre tablets. The crystallographic building units are defined by crystallographic co-orientation. Electron backscatter diffraction quantitatively shows how crystallographic co-orientation propagates across matrix membranes to form highly co-oriented low-mosaic composite-crystal grains, i.e. calcite fiber bundles with an internal mosaic spread of 0.5° full width at half maximum (FWHM) or nacre towergrains with an internal mosaic spread of 2° FWHM. These low-mosaic composite crystals form much larger composite-crystal supergrains, which exhibit a high mosaicity due to misorientations of their constituting calcite fiber bundles or nacre towergrains. For the aragonite layer these supergrains nucleate in one of three aragonite {110} twin orientations; as a consequence the nacre layer exhibits a twin-domain structure, i.e. the boundaries of adjacent supergrains exhibit a high probability for misorientations around the aragonite c-axis with an angle near 63.8°. Within the supergrains, the constituting towergrains exhibit a high probability for misorientations around the aragonite a-axis with a geometric mean misorientation angle of 10.6°. The calcite layer is composed of a single composite-crystal supergrain on at least the submillimeter length scale. Mutual misorientations of adjacent fiber bundles within the calcite supergrain are mainly around the calcite c-axis with a geometric mean misorientation angle of 9.4°. The c-axis is not parallel to the long axis of the fibers but rather to the (107) plane normal. The frequency distribution for the occurrence of misorientation angles within supergrains reflects the ability of the organism to maintain homoepitaxial crystallization over a certain length scale. This probability density is distributed log-normally which can be described by a geometric mean and a multiplicative standard deviation. Hence, those parameters are suggested to be a numerical measure for the biological control over crystallographic texture.

Chemically induced renormalization phenomena in Pb-based relaxor ferroelectrics under high pressure.

The pressure-induced phase transition sequence in PbSc(0.5)Ta(0.5)O(3) (PST) and PbSc(0.5)Nb(0.5)O(3) (PSN) heavily doped with homo- and heterovalent cations on the A- or B-site of the perovskite-type structure (ABO(3)) was analysed by in situ synchrotron x-ray diffraction and Raman spectroscopy up to pressures of 25 GPa. We focused on the structural phenomena occurring above the first pressure-induced phase transition at p(c1) from a relaxor state to a non-polar rhombohedral phase with antiphase tilting of the BO(6) octahedra. The samples studied were PST doped with Nb(5+) and Sn(4+) on the B-site, PST doped with Ba(2+) and La(3+) on the A-site and PSN doped with Sr(2+) and La(3+) on the A-site. All of them exhibit a second pressure-induced phase transition at p(c2), similar to pure PST and PSN. The second transition involves the development of either order of antiparallel Pb(2+) displacements and complementary a(+)b(-)b(-) octahedral tilts, or a(-)b(-)b(-) (0 ≤ a < b) tilting alone. As in pure PST and PSN, the second phase transition is preceded by the occurrence of unequal octahedral tilts on the local scale. The substitution of Nb(5+) for Ta(5+) as well as the coupled substitution of Sn(4+) for Sc(3+) + Ta(5+) on the octahedral B sites increases the second critical pressure. The doping by Nb(5+) also reduces the length of coherence of antipolar Pb(2+) order developed at p(c2). The isovalent substitution of the larger Ba(2+) for Pb(2+) on the A-site suppresses the antipolar Pb(2+) order due to the induced local elastic stresses and thus significantly increases p(c2). The substitution of smaller cations for Pb(2+) on the A-site generally favours the development of long-range order of antiparallel Pb(2+) displacements because of the chemically enhanced a(-)a(-)a(-) octahedral tilts. However, this ordering is less when the dopant is aliovalent, due to the charge imbalance on the A-site. For all of the relaxors studied here, the dynamic compressibility estimated from the pressure derivative of the wavenumber of the soft mode associated with the first phase transition is larger in the pressure interval between p(c1) and p(c2) than above p(c2). The dynamic compressibility of the phase above p(c2) decreases if the antipolar Pb(2+) order is disturbed.

High-pressure powder neutron diffraction study on lead scandium niobate.

The structural evolution of PbSc(0.5)Nb(0.5)O(3) (PSN) under pressure has been studied by in situ powder neutron diffraction. Rietveld refinements to the data show that the continuous phase transition detected by x-ray diffraction at p(c) = 4.1 GPa (Maier et al 2010 Phys. Rev. B 81 174116) is associated with long-range ordering of antiphase octahedral tilts and local ordering of ferroic Pb displacements. Similar to PbSc(0.5)Ta(0.5)O(3) (PST) (Maier et al 2010 Acta Crystallogr. 66 280-91), antiphase octahedral tilting even exists below the critical pressure in a regime in which the structure retains a cubic metric. In contrast to PST, in which the Pb atomic displacement parameters (DPs) form ellipsoids elongated along the cubic {111} directions, the atomic DPs of Pb in PSN form flattened discs parallel to the cubic {111}-planes. This indicates that in PST the Pb displacements are along the cubic {111} directions, whereas in PSN the local Pb displacements are randomly distributed along the cubic {110} directions. The latter can be explained by the abundance of underbonded oxygen atoms associated with the chemical B-site disorder.