Electronic structure and phonon thermodynamics of iron alloys

Inelastic neutron scattering (INS) and nuclear-resonant inelastic x-ray scattering (NRIXS) were used to measure phonon spectra of FeV as a B2- ordered compound and as a bcc solid solution. Contrary to the behavior of ordering alloys studied to date, the phonons in the B2-ordered phase are softer than in the solid solution. Ordering increases the vibrational entropy, which stabilizes the ordered phase to higher temperatures. Ab initio calculations show that the number of electronic states at the Fermi level increases upon ordering, enhancing the screening between ions, and reducing the interatomic force constants. The effect of screening is larger at the V atomic sites than at the Fe atomic sites.

The phonon spectra of Au-rich alloys of fcc Au-Fe were also measured. The main effect on the vibrational entropy of alloying comes from a stiffening of the Au partial phonon density of states (DOS) with Fe concentration that increases the miscibility gap temperature. The magnitude of the effect is non- linear and it is reduced at higher Fe concentrations. Force constants were calculated for several compositions and show a local stiffening of Au–Au bonds close to Fe atoms, but Au–Au bonds that are farther away do not show this effect. Phonon DOS curves calculated from the force constants reproduced the experimental trends. The Au–Fe bond is soft and favors ordering, but a charge transfer from the Fe to the Au atoms stiffens the Au–Au bonds enough to favor unmixing. The stiffening is attributed to two main effects comparable in magnitude: an increase in electron density in the free-electron-like states, and stronger sd-hybridization.

INS and NRIXS measurements were performed at elevated temperatures on B2-ordered FeTi and NRIXS measurements were performed at high pressures. The high-pressure behavior is quasi- harmonic. The softening of the phonon DOS curves with temperature is strongly nonharmonic. Calculations of the force constants and Born-von Karman fits to the experimental data show that the bonds between second nearest neighbors (2nn) are much stiffer than those between 1nn, but fits to the high temperature data show that the former softens at a faster rate with temperature. The Fe–Fe bond softens more than the Ti–Ti bond. The unusual stiffness of the 2nn bond is explained by the calculated charge distribution, which is highly aspherical and localized preferentially in the t2g orbitals. Ab initio molecular dynamics (AIMD) simulations show a charge transfer from the t2g orbitals to the eg orbitals at elevated temperatures. The asphericity decreases linearly with temperature and is more severe at the Fe sites.

Mechanistic aspects of the Ziegler-Natta polymerization

The isotope effect on propagation rate was determined for four homogeneous ethylene polymerization systems. The catalytic system Cp_2Ti(Et)Cl + EtA1Cl_2 has a k^H_p/k^D_p = 1.035 ± 0.03. This result strongly supports an insertion mechanism which does not involve a hydrogen migration during the rate determining step of propagation (Cossee mechanism). Three metal-alkyl free systems were also studied. The catalyst I_2 (PMe_3)_3Ta(neopentylidene)(H) has a k^H_p/k^D_p = 1.709. It is interpreted as a primary isotope effect involving a non-linear a-hydrogen migration during the rate determining step of propagation (Green mechanism). The lanthanide complexes Cp*_2LuMe•Et_2O and Cp*_2YbMe•Et_2O have a k^H_p/k^D_p = 1.46 and 1.25, respectively. They are interpreted as primary isotope effects due to a partial hydrogen migration during the rate determining step of propagation.

The presence of a precoordination or other intermediate species during the polymerization of ethylene by the mentioned metal-alkyl free catalysts was sought by low temperature NMR spectroscopy. However, no evidence for such species was found. If they exist, their concentrations are very small or their lifetimes are shorter than the NMR time scale.

Two titanocene (alkenyl)chlorides (hexenyl 1 and heptenyl 2 were prepared from titanocene dichloride and a THF solution of the corresponding alkenylmagnesium chloride. They do not cyclize in solution when alone, but cyclization to their respective titanocene(methyl(cycloalkyl) chlorides occurs readily in the presence of a Lewis acid. It is demonstrated that such cyclization occurs with the alkenyl ligand within the coordination sphere of the titanium atom. Cyclization of 1 with EtAlCl_2 at 0°C occurs in less than 95 msec (ethylene insertion time), as shown by the presence of 97% cyclopentyl-capped oligomers when polymerizing ethylene with this system. Some alkyl exchange occurs (3%). Cyclization of 2 is slower under the same reaction conditions and is not complete in 95 msec as shown by the presence of both cyclohexyl-capped oligomers (35%) and odd number α-olefin oligomers (50%). Alkyl exchange is more extensive as evidenced by the even number n-alkanes (15%).

Cyclization of 2-d_1 (titanocene(hept-6-en-1-yl-1-d_1)chloride) with EtA1Cl_2 demonstrated that for this system there is no α-hydrogen participation during said process. The cyclization is believed to occur by a Cossee-type mechanism. There was no evidence for precoordination of the alkenyl double bond during the cyclization process.