SYNTHESIS AND CRYSTAL-STRUCTURE OF A NEW LANTHANIDE CYCLOOCTATETRAENE COMPLEX (ETA-8-C8H8)ER(MU-ETA-8-C8H8)K(MU-ETA-8-C8H8)ER(MU-ETA-8-C8H8)K(THF)4

The tetranuclear nearly-linear complex (eta-8-C8H8)Er(mu-eta-8-C8H8)K(mu-eta-8-C8H8)Er(mu-eta-8-C8H8)K(THF)4 (THF = tetrahydrofuran) is first synthesised by the reaction of benzylcyclopentadienyl erbium dichloride (PhCH2C5H4)ErCl2.3THF with cyclooctatetraenyl potassium K2C8H8 in 1:1 molar ratio in THF; a single crystal X-ray study has shown that the complex has the tetralayer-sandwich structure and that the adjacent Er3+ and K+ ions are bridged by eta-8-cyclooctatetraenyl group.

SYNTHESIS AND STRUCTURE OF (ETA-5-C5H5)2YB.DME

(eta-5-C5H5)2YbCl.THF reacts with an equivalent molecular quantity of K(2,4-C7H11) (2,4-dimethyl pentadienyl potassium), and treatment of the product with DME yields (eta-5-C5H5)2Yb.DME. The crystal of (eta-5-C5H5)2Yb.DME belongs to the orthorhombic space group Fdd2 with a = 13.678(4) angstrom, b = 23.255(6) angstrom, c = 9.192(2) angstrom and Z = 8. The crystal parameters are found to differ from previously reported data.

THE SYNTHESES OF THE COMPLEXES (ETA-5-C5H5)LN(ETA-8-C8H8).NTHF AND (ETA-5-C9H7)LN(ETA-8-C8H8).2THF AND THE CRYSTAL-STRUCTURE DETERMINATION OF (ETA-5-C5H5)PR(ETA-8-C8H8).2THF AND (ETA-5-C9H7)PR(ETA-8-C8H8).2THF

LnCL3 reacts with NaC5H5 and K2C8H8 to yield the complexes (eta-5-C5H5)Ln(eta-8-C8H8).nTHF (Ln = Pr, Nd, n = 2; Ln = Gd, n = 1) and LnCl3 reacts with KC9H7 and K2C8H8 to yield the complexes (eta-5-C9H7)Ln(eta-8-C8H8).2THF (Ln = Pr, Nd; eta-5-C9H7 = indenyl); crystallography reveals (eta-5-C5H5)Pr(eta-8-C8H8).2THF and (eta-5-C9H7)Pr(eta-8-C8H8).2THF not to possess the parallel ring sandwich structure.

SYNTHESES AND CRYSTAL-STRUCTURES OF TRIINDENYLLANTHANIDE COMPLEXES (ETA-5-C9H7)3LN.OC4H8 (LN=ND,GD,ER)

The complexes named in the title (eta-5-C9H7)3Ln.OC4H8 (Ln = Nd, Gd, Er) were synthesized by the reaction of anhydrous lanthanide trichlorides with indenyl potassium and cyclooctadienyl potassium (1:2:1 molar ratio) in THF. The complexes were characterized by elemental analysis, infrared and H-1-NMR spectroscopy, and mass spectrometry. In addition, the crystal structures of (eta-5-C9H7)3Nd.OC4H8 (1) and (eta-5-C9H7)3Gd.OC4H8 (2) were determined by an X-ray diffraction study. Complexes 1 and 2 belong to hexagonal space group P6(3) with unit cell parameters a = b = 11.843(3), c = 10.304(4) angstrom, V = 1251.7(9) angstrom-3, D(c) = 1.49 g.cm-3, Z = 2 for 1, and a = b = 11.805(2), c = 10.236(2) angstrom, V = 1235.4(6) angstrom-3 D(c) = 1.54 g.cm-3, Z = 2 for 2. The structures were solved by Patterson and Fourier techniques and refined by least-squares to final discrepancy indices of R = 0.049, R(w) = 0.053 using 925 independent reflections with I greater-than-or-equal-to 3-sigma(I) for 1, and R = 0.023, R(w) = 0.025 using 1327 independent reflections with I greater-than-or-equal-to 3-sigma(I) for 2. Coordination numbers for Nd3+ and Gd3+ are 10; the average bond lengths Nd-O and Gd-O are 2.557(21) and 2.459(13) angstrom, respectively. The structural studies showed the complexes to have 3-fold symmetry, but the THF molecule has no such symmetry; consequently the arrangement of carbon atoms in the THF molecule are disordered.

SYNTHESIS OF [LI.3DME] [(ETA-5-C5H5)3NDC6H5]

The phenyl derivatives of lanthanides Sc(C_6H_5)_3, Y(C_6H_5)_3, LiLa (C_6H_5)_4 and LiPr(C_6H_5)_4 were prepared by Hart et al. in 1970, and dis(cyclopentadienyl) phenyl complexes of lanthanides have been isolated recently. We reported here the synthesis and crystallography parameters of a new type of phenyl derivative of neodymium:

Influence of inertial and thermal effects on the dynamic growth of voids in porous ductile materials

The influence of inertial, thermal and rate - sensitive effects on the void growth at high strain rate in a thermal - viscoplastic solid is investigated by means of a theoretical model presented in the present paper. Numerical analysis of the model suggests that inertial, thermal and rate - sensitive effects are three major factors which greatly influence the behavior of void growth in the high strain rate case. Comparison of the mathematical model proposed in the present work and Johnson's model shows that if the temperature - dependence is considered, material viscosity eta can take the experimentally measured values.

Note on the instability of capillary jet with thermocapillarity

In this paper, we examine a new basic state of long axisymmetric liquid zone, subjected to axial temperature gradients which induce steady viscous flow driven by thermocapillarity. Axial velocity 1/4S-1/2R(B) of liquid zone connects pulling velocity of single crystal. The stability of liquid zone with pulling velocity 1/4S-1/2R(B) to small axisymmetric disturbance is examined The eigenvalue problems on the stability are derived. A special case (eta = 0) is discussed.

Growth of zero-mean-shear turbulent-mixed layer with suspended particles in a 2-layer fluid system

The growth behaviour of zero-mean-shear turbulent-mixed layer containing suspended solid particles has been studied experimentally and analysed theoretically in a two-layer fluid system. The potential model for estimating the turbulent entrainment rate of the mixed layer has also been suggested, including the results of the turbulent entrainment for pure two-layer fluid. The experimental results show that the entrainment behaviour of a mixed layer with the suspended particles is well described by the model. The relationship between the entrainment distance and the time, and the variation of the dimensionless entrainment rate E with the local Richardson number Ri1 for the suspended particles differ from that for the pure two-layer fluid by the factors-eta-1/5 and eta-1, respectively, where eta = 1 + sigma-0-DELTA-rho/DELTA-rho-0.

Nonequilibrium statistical mechanics of two-dimensional turbulence

The vorticity dynamics of two-dimensional turbulence are investigated analytically, applying the method of Qian (1983). The vorticity equation and its Fourier transform are presented; a set of modal parameters and a modal dynamic equation are derived; and the corresponding Liouville equation for the probability distribution in phase space is solved using a Langevin/Fokker-Planck approach to obtain integral equations for the enstrophy and for the dynamic damping coefficient eta. The equilibrium spectrum for inviscid flow is found to be a stationary solution of the enstrophy equation, and the inertial-range spectrum is determined by introducing a localization factor in the two integral equations and evaluating the localized versions numerically.

Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).