Scaling of decay lengths for surface states in the gaps of one-dimensional semi-infinite superlattices

We look at some one-dimensional semi-infinite superlattices with an underlying Hamiltonian that is of the nearest neighbour, tight binding type. A real space rescaling procedure which is exact in one dimension is applied to obtain the location of the subbands. It has been found that these subbands never overlap in 1D, and we interpret this as a band repulsion effect. Relevance in the case of a disordered system where this band repulsion crosses over to the well-known level repulsion is discussed. Then with a proper matching at the boundary we solve for the sets of denumerably infinite number of decaying solutions (the surface states) in the gaps. These types of states have been proposed quite some time ago. We look at detail theirexact analytical solutions in 1D and find that their decay lengths near the band edges diverge as |E–E _b|^–v, wherev=1/2 andE _b is the nearest band edge. The decay lengths and their divergence exponent match extremely well with those obtained from transfer matrix method. Some recent experiments on quantum well structures seem to have observed such states.     

Pressure dependence of the compressibility of alkali halides

The parameterC ₁=[(1/K _T )/P] _T , which describes the pressure variation of the compressibility, has been examined correlating the thermodynamical and interatomic potential approaches employing fewer approximations than has been usual heretofore. General expressions have been derived forC ₁ by including the thermal correction terms, which have generally been ignored in previous studies concerning thermal properties of ionic crystals. The parameterC ₁ has also been related to the Grüneisen parameter, , using a relation given earlier. The applicability of the derived equations is investigated and discussed for alkali halides employing few realistic potential forms. A good general accord is found with the available experimental data, which exhibits an essential improvement over other theoretical determinations.     

Polarographische Untersuchung der Nickel- und der Zinkkomplexe der Adipinsäure

Zusammenfassung Die Nickel- und Zinkkomplexe der Adipinsäure werden polarographisch untersucht. Es zeigt sich, daß Zink reversibel reduziert wird, wogegen Nickel eine irreversible Stufe ergibt. Die Stabilitätskonstanten des Zink—Adipinsäurekomplexes werden nachDeFord undHume berechnet. Der Einfluß des pH-Wertes auf die Zink- und die Nickelstufe wird untersucht. Zink und Nickel werden in Gegenwart vieler störender Kationen halbquantitativ bestimmt.

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The said complexes have been studied by polarography. Zn is found to be reversibly reduced while Ni gives an irreversible wave. Stability constants of the Zn complex are calculated byDeFord andHume method. Effect of pH on Zn and Ni wave are reported. Estimations of Zn or Ni are carried out separately or in presence of interfering cations.

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Mit 7 Abbildungen     

Gravimetric determination of thorium and zirconium

Summary Thorium and zirconium can be quantitatively precipitated by quinaldinic acid atph 2.7 and 3, respectively. As the precipitates are of nonstoichiometric composition they are to be ignited to oxides. By this reagent thorium can be quantitatively separated from arsenic (As³⁺), mercury (Hg²⁺), rare earths, manganese, magnesium and alkaline earths and zirconium from all the aforesaid ions excepting rare earths which contaminate to a slight extent.     

Synthesis and characterization of square-planar palladium(II) complexes containing anti- and syn-furan-2-aldoxime

Summary Fifteen palladium(II) square-planar complexes containing monodentate and/or bidentate anti- and syn-furan-2-aldoxime (FDH) have been isolated and characterized by elemental analysis, molecular weight determination, conductance studies, magnetic moments and i.r. spectral studies. The monodentate ligand coordinates through the nitrogen atom while the bidentate ligand coordinates through the furan oxygen atom and the nitrogen atom. The C-O-C stretching frequency of the furan ring may be taken as the criterion for the denticity of this ligand and is observed at 1240 and 1270 cm^– in anti- and syn-furan-2-aldoxime respectively. A shift to lower frequency occurs (in the complex) if the ligand is bidentate, however this frequency is unaffected if the ligand is monodentate.     

Quantitative estimations of ferric iron by phosphoric acid in aqueous-alcoholic medium

Summary The only method recommended for the direct estimation of ferric iron in presence of HCl is to reduce the ferric iron to ferrous iron and then to titrate against KMnO₄ solution by adding Reinhardt-Zimmermann reagent (MnSO₄ + H₂SO₄ + H₃PO₄). The solubility of the phosphato complexes of ferric chloride and phosphoric acid is much reduced by adding a nonaqueous solvent, ethyl alcohol or acetone. This property has been availed of to find out a method of estimating ferric iron directly against standard solution of phosphoric acid in aqueous-nonaqueous medium using K₄Fe(CN)₆ or cupferron as external indicators. A slight discrepancy at the end point, however, exists in the direct titration but it can be removed by applying a correction factor determined from the estimated results.     

Reactions of dimethyl acetylenedicarboxylate—X: Reaction with salicylaldehyde,ortho hydroxyacetophenone, 2-hydroxychalcones and 2,2′-dihydroxychalcones

Salicylaldehyde reacts with dimethyl acetylenedicarboxylate in benzene solution to give a mixture of dimethyl o-formylphenoxymaleate, dimethyl o-formylphenoxyfumarate, 2,3-dicarbomethoxychrom - 2 - en - 4 - ol, 2,3 - dicarbomethoxychrom - 3 - en - 2 - ol, dimethyl (2,3 - dicarbomethoxychrom - 2 - en - 4 - yl) - oxalacetate and dimethyl fumarate. 2,3 - Dicarbomethoxychrom - 3 - en - 2 - ol in this reaction is formed from 2,3 - dicarbomethoxychrom - 2 - en - 4 - ol through a benzopyrylium intermediate. The reaction of salicylaldehyde with excess of dimethyl acetylenedicarboxylate, however, gives a mixture of 2,3 - dicarbomethoxychrom - 3 - en - 2 - ol and dimethyl (2,3 - dicarbomethoxychrom - 3 - en) - 2 - oxyfumarate. 2,3 - Dicarbomethoxychrom - 3 - en - 2 - ol itself reacts further with dimethyl acetylenedicarboxylate to give 2,3,12 - tricarbomethoxychrom - 3,4 - eno[2,3 - b] pyrone. Similarly, the reaction of o-hydroxyacetophenone with dimethyl acetylendicarboxylate gives a mixture of dimethyl o-acetylphenoxymaleate, dimethyl o-acetylphenoxyfumarate, 2,3 - dicarbomethoxy - 4 - methylchrom - 2 - en - 4 - ol and 2,3 - dicarbomethoxy - 4 - methylchrom - 3 - en - 2 - ol. Both 2-hydroxychalcone and 2 - hydroxy - 4′ - methoxychalcone give mixtures of chalcone - 2 - oxymaleate and chalcone - 2 - oxyfumarate. The reaction of 2,2t?-dihydroxychalcone, however, gives 2′-hydroxyflavone, in addition to the expected maleate and fumarate. Similar reactions of 5 - chloro - 2,2′ - dihydroxychalcone and of 3,5 - dibromo - 2,2′ - dihydroxychalcone, on the other hand, give 2,3 - dicarbomethoxy - 4 - (o - hydroxyphenacyl) - 6 - chlorochrom - 2 - ene and 2,3 - dicarbomethoxy - 4 - (o - hydroxyphenacyl) 6,8 - dibromochrom - 2 - ene, respectively, together with the corresponding maleates and fumarates.     

Synthesis of (±) lupinifoun, di-o-methyl xanthohumol and isoxanthohumol and related compounds

Nuclear prenylation of naringenin (7) with 2-methylbut-3-en-2-ol in the presence of boron trifluoride etherate gives a mixture of 6-C-prenyl-(11), 8-C-prenyl-(15) and 6,8-di-C-prenyl-(8) derivatives. On formic acid cyclisation, 11 yielded two monodihydropyrans (12 and 13), but 15 afforded only one viz 16; similarly 8 formed the bisdihydropyran 10. Methylation of 8-C-prenyl naringenin (15) with Me₂SO₄ resulted in the formation of di-O-methyl derivatives of xanthohumol (22) and isoxanthohumol (23).

Cyclodehydrogenation of 6,8-di-C-prenyl-naringenin (8) with DDQ gave a mono-C-prenyl-2,2-dimethylpyran (1) corresponding to (±) lupinifolin. The angular isomer (2) was also formed. The structure of natural flemichin-B therefore needs further consideration. Similarly, cyclodehydrogenation of 6-C-(11)- and 8-C-prenyl-(15) naringenins afforded the corresponding linear (24) and angular (25) derivatives which have been characterized by conversion into known chalcones 26 and 27 by O-methylation.