The behavior of a Mode-Ⅰ interface crack in piezoelectric materials was investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips was negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. It is found that the stress and the electric displacement singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials. The solution of the present paper can be returned to the exact solution when the upper half plane material is the same as the lower half plane material.
We have performed the first-principles calculation to investigate the origins of ferroelectricities and different po- larization behaviours of superlattices BaTiO3/SrTiO3 and PbTiO3/SrTiO3. The density of state （DOS） and electronic charge profiles show that there are strong hybridizations between atoms Ti and O and between atoms Pb and O which play very important roles in producing the ferroelectricities of superlattices BaTiO3/SrTiO3 and PbTiO3/SrTiO3. Ow- ing to the decline of internal electric field in SrTiO3 （ST） layer, the tetragonality and polarizations of superlattices decrease with increasing the fraction of SrTiO3 in the superlattices. We find that the polarization of PbTiO3/SrTiO3 is largerthan that of BaTiO3/SrTiO3 at the same ratio of components, because the polarization mismatch between PbTiO3 and SrTiO3 is larger than that between BaTiO3 and SrTiO3. The polarization and tetragonality are en- hanced with respect to those of bulk tetragonal BaTiO3 in the superlattices BaTiO3/SrTiO3, while the polarization and tetragonality are reduced with respect to those of bulk tetragonal PbTiO3 in superlattices PbTiO3/SrTiO3.
Visible converted emissions produced at an excitation of 286 nm in Zn Nb2O6 ceramics doped with rare-earth ions(RE= Eu3+, Tm3+, Er3+or a combination of these ions) were investigated with the aim of increasing the photovoltaic efficiency of solar cells. The structure of RE:Zn Nb2O6 ceramics was confirmed by x-ray diffraction patterns. The undoped Zn Nb2O6 could emit a blue emission under 286-nm excitation, which is attributed to the self-trapped excitons’ recombination of the efficient luminescence centers of edge-shared Nb O6 groups. Upon 286-nm excitation, Eu:Zn Nb2O6, Tm:Zn Nb2O6, and Er:Zn Nb2O6 ceramics showed blue, green, and red emissions, which correspond to the transitions of5D0→7FJ(J = 1–4)(Eu3+),1G4→3H6(Tm3+), and2H11/2/4S3/2→4I15/2(Er3+), respectively. The calculated CIE chromaticity coordinates of Eu:Zn Nb2O6, Tm:Zn Nb2O6, and Er:Zn Nb2O6are(0.50, 0.31),(0.14, 0.19), and(0.29, 0.56), respectively. RE ionco-doped Zn Nb2O6 showed a combination of characteristic emissions. The chromaticity coordinates of Eu/Tm:Zn Nb2O6,Eu/Er:Zn Nb2O6, and Tm/Er:ZnNb2O6 were calculated to be(0.29, 0.24),(0.45, 0.37), and(0.17, 0.25).
