Shape derivatives in Kondratiev spaces for conical diffraction

This paper studies conical diffraction problems with non‐smooth grating structures. We prove the existence, uniqueness and regularity results for solutions in weighted Sobolev spaces of Kondratiev type. An a priori estimate that follows from these results is then used to prove shape differentiability of solutions. Finally, a characterization of the shape derivative as a solution of a modified transmission problem is given. Copyright © 2012 John Wiley & Sons, Ltd.     

Photorefractive properties of Cr-doped Sr0.61Ba0.39Nb2O6 related to crystal purity and doping concentration

The purity and the concentrations of the constituents Sr, Ba, Nb and Cr were determined in single crystals of chromium-doped Sr_0.61Ba_0.39Nb₂O₆ (SBN) by instrumental neutron activation analysis (INAA) and X-ray fluorescence analysis (XRF). Experiments with different Cr concentrations C_Cr reveal constant Sr and Ba concentrations as well as a decreasing Nb concentration with an increasing C_Cr. Therefore, Cr is incorporated at Nb lattice sites. The distribution coefficient of Cr is 1.2 between 100 and about 7000 ppm Cr and 1 above. From measurements of the holographic two-beam coupling gain Γ for different C_Cr, we deduced response times for the buildup of holographic gratings. The saturation value of Γ depends in a nonlinear manner on C_Cr and reaches its maximum at about 6000 ppm Cr. The inverse photorefractive response time of the grating erasure depends linearly on the erasure intensity for all doping concentrations. Thus a one-center model can be assumed for the charge transport in SBN:Cr. Received: 8 December 2000 / Revised version: 23 January 2001 / Published online: 21 March 2001     

Critical concentrations in Ba-doped incipient ferroelectric SrTiO3

Temperature-induced variations of light refraction and dielectric permittivity in single-crystal Sr_1−x Ba_xTiO₃ (x=0.02, 0.05, 0.07, and 0.14), Sr_1−x Ca_xTiO₃ (x=0.014), and in nominally pure strontium titanate have been studied within the 17–300 K temperature range. The spontaneous polar contribution to the refractive index has been isolated. It was used to calculate the temperature and concentration dependences of the polarization autocorrelation function 〈P _s ^2〉 in the Sr_1−x Ba_xTiO₃ system. For x⩽0.07, the polarization P _s=〈P _s ² 〉^1/2 varies proportional to (x−x _g)^1/2, where x _g=0.0027 is the new critical concentration in Sr_1−x Ba_xTiO₃, below which short-range polar order vanishes. Fiz. Tverd. Tela (St. Petersburg) 39, 704–710 (April 1997)     

Reaktionen von Phosphorigsäure-bis(dimethylamid) und Phosphorsaäure-tris(methylamid) mit PCI3

Reactions of Phosphorous Bis(dimethylamide) and Phosphoric Tris(methylamide) with PCI₃ From the products of the reaction between phosphorous bis(dimethylamide) and PCl₃ in the presence of pyridine the pentakis(dimethylamide) of acid can be isolated. The reaction between phosphoric tris(methylamide) and PCl₃ in the presence of pyridine yields crystalline O = P[NCH³? PCl₂]₃ which can be converted into O = P[NCH³? PF₂]₃ with SbF₃ or AsF₃. The nmr data of the new compounds and some by-products of the reaction are given and discussed.     

Neutron scattering study of transverse magnetism in the metamagnet FeBr2

In order to clarify the nature of the additional phase transition at H ₁ ( T ) < H _c ( T ) of the layered antiferromagnetic (AF) insulator FeBr ₂ as found by Aruga Katori et al. (1996) we measured the intensity of different Bragg-peaks in different scattering geometries. Transverse AF ordering is observed in both AF phases, AF I and AF II. Its order parameter exhibits a peak at T ₁ = T ( H ₁ ) in temperature scans and does not vanish in zero field. Possible origins of the step-like increase of the transverse ferromagnetic ordering induced by a weak in-plane field component when entering AF I below T₁ are discussed. Received 27 September 1999 and Received in final form 6 December 1999     

Phase transitions in Sr 0.61 Ba 0.39 Nb 2 O 6 :Ce 3+ : II. Linear birefringence studies of spontaneous and precursor polarization

The linear birefringence (LB) of Sr _0.61-x Ba _0.39 Nb ₂ O ₆ :Ce ³⁺ x (SBN61:Ce) has been measured as a function of temperature within the range of . Large tails have been observed above the ferroelectric phase transition temperatures T _c = 350, 328, 320 and 291 K for the concentrations x = 0, 0.0066, 0.0113 and 0.0207, respectively. Within an Ornstein-Zernike analysis the critical exponents , and are determined. It suggests that pure SBN61 belongs to the 3D Ising universality class. Doping with Ce ³⁺ ions, which seem to act as random fields, enhances the relaxor properties. The critical exponents and of SBN61:Ce shift against those of the three-dimensional random-field Ising model. Received 1 October 1999