TheL <ω-theory of the class of Archimedian real closed fields

For the classA of uncountable Archimedian real closed fields we show that the statement TheL ^<-theory ofA is complete is independent of ZFC. In particular we have the following results:Assuming the Continuum-Hypothesis (CH) is incomplete. Conversely it is possible to build a model of set theory in which is complete and decidable. The latter can also be deduced from the Proper Forcing Axiom (PFA). In this case turns out to be equivalent to the elementary theory of the real numbers (by a quantifier-elimination procedure).Formally: is incomplete. is complete and decidable.     

Hg2(OH)[BF4], the First Basic Mercurous Tetrafluoroborate

The first basic mercurous tetrafluoroborate, Hg₂(OH)[BF₄], was obtained through a synproportionation reaction of red mercuric oxide, HgO, and elemental mercury in a 35% solution of HBF₄ in water as colourless single crystals. The crystal structure (orthorhombic, Pbca, Z = 8, a = 985.0(1), b = 991.0(1), c = 1141.0(2) pm) contains [(HO)_1/2—Hg—Hg—(OH)_1/2]⁺ zig‐zag chains that are further connected via weak Hg—OH interchain interactions to layers between which the [BF₄]^— are located in an up and down fashion.     

LiTiCl3: Synthesis and thermal behaviour

LiTiCl₃ is obtained as one example within an ample solid solution, Li_24–2nTi_nCl₂₄ (?4?n?10), by synpropotionation of TiCl₃ and Ti in the presence of LiCl (2:1:3 molar ratio) in sealed tantalum tubes at 750°C. It crystallizes with the inverse spinel-type structure according to (Li_0.67)^[4](Li_0.67Ti_1.33)^[4]Cl₄ with, at 25°C, a = 1048.62(4) pm, space group Fd3m. Thermal expansion is linear with α = 4.85 × 10^?5K^?1 up to about 300°C and thereafter, when the migration of Li⁺ from tetrahedral to octahedral interstices becomes increasingly important, it exhibits a relative decrease resulting, finally, in the phase transition to a NaCl-type structure that is observed for the first time at about 575°C.     

Ternäre Lithium-Selten-Erd-Nitrate mit einsamen Nitrationen: Li3[M(NO3)5](NO3) (M = Gd?Lu,Y). Die Kristallstruktur von Li3Er(NO3)6

Ternary Lithium Rare Earth Nitrates with Lonesome Nitrate Ions: Li₃[M(NO₃)₅](NO₃) (M = Gd? Lu, Y). The Crystal Structure of Li₃Er(NO₃)₆ Single crystals of the ternary nitrate Li₃Er(NO₃)₆ are obtained from a solution of “Er(NO₃)₃” in the melt of LiNO₃. In Li₃Er(NO₃)₆ (monoclinic, P2₁/n, Z = 4; a = 776.0(1); b = 748.86(8); c = 2 396(1) pm; β = 90.76(3)°; R1 = 0.0490; wR2 = 0.0792), Er³⁺ is surrounded by five bidentate nitrate ligands yielding the anionic units [Er(NO₃)₅]^2?. These are arranged in the direction of the 2₁ screw axis. Two lonesome NO₃^? ions are in the middle of such a “helix” and are connected by Li⁺ with the anions [Er(NO₃)₅]^2?. The helices are moved against each other by about half of the lattice constant a and are connected by further Li⁺ ions.     

1H-CRAMPS Solid-State NMR and X-Ray Crystal Studies of Inclusion Complexes Formed from 3,3′-bis(9-Hydroxy-9-fluorenyl)-2,2′-binaphthyl Hosts with Acetone

The crystal structures of inclusion compounds of 3,3-bis(9-hydroxy-9-fluorenyl)-2,2-binaphthyl host (1) and its chloro (2) or bromo (3) derivatives substituted in 2,7-positions of the fluorene units with acetone guests (1A–3A) were determined by X-ray studies as well as by ¹H-CRAMPS solid-state NMR. Using this NMR technique allows identification of differently bound guest molecules due to their different chemical shifts caused by the influence of the ring current effects of the host aryl units.     

Helical unwinding in polymer-dispersed ferroelectric liquid crystals

We demonstrate that ferroelectric liquid crystals dispersed in a polymer matrix can form uniaxially aligned elliptical droplets. The alignment is controlled by mechanical shear during the polymerization of a UV-curable adhesive. The possibility of prealignment makes polymer-dispersed ferroelectric liquid crystals suitable for application in flexible electro-optical displays. In contrast to surface stabilized ferroelectric liquid crystal displays, the electro-optical effect in our system is due to the deformed-helix ferroelectric (DHF) effect.     

XRD-Studies of SiC/Si layers on carbon substrates

Structural investigations of thin films of SiC, SiC with free silicon and various titanium suicides (TiSi₂, TiSi and Ti₅Si₃) are described. The crystal phases have been identified using X-ray diffractometry. The growth of reaction products from surface reactions between silicon and deposited titanium can be observed.Dedicated to Professor Dr. rer.nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday