Scanning tunnelling microscopy of charge-density waves in transition metal chalcogenides

We have used scanning tunnelling microscopes (STMs) operating at liquid helium and liquid nitrogen temperatures to image the charge-density waves (CDWs) in transition metal chalcogenides. The layer structure dichalcogenides TaSe₂, TaS₂, NbSe₂, VSe₂, TiSe₂ and TiS₂ have been studied including representative polytype phases such as 1T, 2H and 4Hb. Experimental results are presented for the complete range of CDW amplitudes and structures observed in these materials. In most cases both the CDW and the surface atomic structure have been simultaneously imaged. Results on the trichalcogenide NbSe₃ are also included.

The formation of the CDW along with the associated periodic lattice distortion gaps the Fermi surface (FS) and modifies the local density-of-states (LDOS) detected by the tunnelling process. The tunnelling microscopes have been operated mostly in the constant current mode which maps the LDOS at the position of the tunnelling tip. The relative amplitudes and profiles of the CDW superlattice and the atomic lattice have been measured and confirm on an atomic scale the CDW structures predicted by X-ray, electron and neutron diffraction. The absolute STM deflections are larger than expected for the CDW induced modifications of the LDOS above the surface and possible enhancement mechanisms are reviewed.

In the 2H trigonal prismatic coordination phases the CDWs involve a relatively small charge transfer and the atomic structure dominates the STM images. In the 1T octahedral coordination phases the charge transfer is large and the CDW structure dominates the STM image with an anomalously large enhancement of the STM profile. Systematic comparison of the STM profiles with band structure and FS information is included.

In the case of the 4Hb mixed coordination phases at the lowest temperatures two nearly independent CDWs form in alternate sandwiches. STM studies on 4Hb crystals with both octahedral and trigonal prismatic surface sandwiches have been carried out. The STM scans detect the relative strengths of the two CDWs as well as the interactions between the two types of CDW structure.

The STM scans are also able to detect defects and domain structure in the CDW image. Several examples will be given demonstrating the potential of the STM to detect these local variations in LDOS on an atomic scale. In contrast to the layer structure crystals the linear chain compound NbSe₃ shows a complex surface atomic structure as well as the formation of two CDWs. The surface atomic structure is resolved in the STM scans and profiles have detected the presence of the CDW modulation at 77K and 4.2K. These results demonstrate the feasibility of detecting CDW structure in the presence of complex atomic structure and using materials where dynamical CDW effects can also be studied by STM.

The range of STM results presented here show that the STM scans are extremely sensitive to the detail of the CDW structure and its effect on the LDOS. Although much of this structure has been deduced from diffraction studies, the ability to examine the CDW structure on an atomic scale with the STM is new. The sensitivity of the STM method suggests potential applications to a wide range of electronic structures in materials.     

Hydroformylation of 1, 1, 1-d3-2-butene. Isotope Effect on the Product Composition

In the hydroformylation of 1,1,1-trideuterio-2-butene with Rh₄ (CO)₁₂ the deuterated pentanals formed contain 75% of 5,5,5-trideuterio-pentanal, the rest being substantially 2,2-dideuterio-pentanal. On the contrary, using Co₂ (CO)₈ as the catalyst precursor, position 1 and 4 are formylated to the same extent.     

Nickel-catalyzed Asymmetric Alkylation of Some Chiral and Achiral Allylic Alcohols. Preliminary communication

[(?) (R)-1,2-bis (Diphenylphosphino)-1-phenylethane]nickel (II) chloride was found to catalyze the asymmetric alkylation of some chiral and achiral allylic alcohols with Grignard reagents, leading to the formation of optically active olefins. Enantiomer discrimination of the substrate takes place in the alkylation of chiral allylic alcohols.     

Enantioselective Alternating Olefin-Carbon Monoxide Copolymerization: A new concept for activity and stereoselectivity

Cationic Pd-complexes modified by dicyclohexyl{(R)-1-[(S)-2-(diphenylphosphino)ferrocenyl]ethyl}phosphine ( 1a ) give very active catalytic systems for the regioregular isotactic specific copolymerization of propene with CO. Other alk-1-enes also give stereoregular and regioregular copolymers, even if with lower productivity. The copolymers are isolated as poly(4-alkyl-tetrahydrofuran-2,2,5,5-tetrayl-2-oxy-2-methylenes) B in the solid state and give the isomeric poly(2-alkyl-1-oxopropane-1,3-diyls) A by dissolution in (CF₃)₂CHOH. Solid polymer A (R = Et) is formed back at least partially when the dissolved material is reprecipitated from MeOH. The use of the related (ferrocenyl)diphosphine ligands 1b ? e and 2 as the catalyst modifier shows that the presence of both elements of chirality and of large substituents on the P-atoms of the ligand is necessary to achieve good stereocontrol, and that the large difference in basicity between the two P-atoms is probably the reason for the good catalytic activity.     

A characterization of hyperelliptic Jacobians

In this paper we will prove a criterion for hyperelliptic Jacobians. LetD be a translation invariant vector field on an indecompssable principally polarized abelian variety (i.p.p.a.v.) (X, Θ), letDΘ be the divisor of the sectionDΘ∈H ⁰ (Θ,O(Θ)|Θ). We have that (X, Θ) is the Jacobian of an hyperelliptic curve iff (Theorem 1) all the component ofDΘ are non reduced and the singular locus of Θ has dimension less thang-2. We will prove our theorem by showing that under the above geometrical condition it is possible to construct a Kodomcev-Petviashvili (K.P.) equation which is satisfied by the theta function corresponding to the principal polarization onX.     

PGSE diffusion, 1H-19F HOESY and NMR studies on several [Rh(1,5-COD)(Biphemp)]X complexes: detecting positional anion effects

Three new salts of Rh(I), [Rh(1,5-COD)(Biphemp)]X, Biphemp = (6,6'-dimethylbiphenyl-2,2'-diyl)bis(diphenylphosphine), X = BF4-, 2a, PF6-, 2b, and CF3SO3-, 2c, were prepared and studied using PGSE diffusion, 1H-19F HOESY and inverse 103Rh (amongst other) NMR methods. Although the immediate coordination sphere of the cation does not sense the change in the anion, the PGSE diffusion and 1H-19F HOESY data suggest that, in addition to some ion pairing, each of the anions in 2 demonstrates selectivity in its approach towards the cation.     

Radiocesium contamination in soil due to the Chernobyl accident

Three different cereal cultivated fields (rice, maize/wheat, wheat/barley) were selected and soil samples were collected in order to study the behaviour of the radiocesium deposited over the crops after the Chernobyl accident fall-out (April 1986) together with its distribution at different ground depths. For each field, soil samples were removed during the sowing (Oct–Nov '86), in Spring (Apr '87) and during the harvest time (Jun–Sept '87). The⁴⁰K concentration and stable potassium content in soil was also evaluated by nuclear spectrometry and by atomic absorption spectrometry. Beside soil sample measurements, the cultivated cereals produced in the 1986 harvest (rice, maize, wheat) were analyzed to evaluate the deposited contamination, and in order to evaluate the contamination during the growth and naturation we also analyzed whole plants (roots, stalks, grains) of the cultivated cereals (rice, wheat, barley) in 1987. Results are presented and discussed.     

Enantioselective Alternating Terpolymerization of Styrene and Ethene with Carbon Monoxide. Preliminary communication

In spite of the higher reactivity of styrene with respect to ethene for the alternating copolymerization with carbon monoxide, catalyzed by chiral (dihydrooxazole)(phosphino)palladium complexes, ethene is preferentially (and randomly) enchained in terpolymerization experiments; enantioface selection for styrene is comparably high in both copolymerization and terpolymerization processes.     

Coherence Stability and Effect of Random Natural Frequencies in Populations of Coupled Oscillators

We consider the (noisy) Kuramoto model, that is a population of $N$ oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion. In the limit $N \rightarrow \infty $ this model is accurately described by a (deterministic) Fokker–Planck equation. We study this equation and obtain quantitatively sharp results in the limit of weak disorder. We show that, in general, even when the natural frequencies have zero mean the oscillators synchronize (for sufficiently strong interaction) around a common rotating phase, whose frequency is sharply estimated. We also establish the stability properties of these solutions (in fact, limit cycles). These results are obtained by identifying the stable hyperbolic manifold of stationary solutions of an associated non disordered model and by exploiting the robustness of hyperbolic structures under suitable perturbations. When the disorder distribution is symmetric the speed vanishes and there is a one parameter family of stationary solutions, as pointed out by Sakaguchi (Prog Theor Phys 79:39–46, 1988): in this case we provide more precise stability estimates. The methods we use apply beyond the Kuramoto model and we develop here the case of active rotator models, that is the case in which the dynamics of each rotator in absence of interaction and noise is not simply a rotation.