Temperature dependence of the crystal structure and g-values of [(HC(Ph2PO)(3))(2)Cu] (ClO4)(2)center dot 2H(2)O: Influence of dynamic Jahn-Teller coupling and lattice strain interactions

The temperature dependence of the X-ray crystal structure and powder EPR spectrum of [(HC(Ph2PO)(3))(2)CU]-(ClO4)(2)center dot 2H(2)O is reported, and the structure at room temperature confirms that reported previously. Below similar to 100 K, the data imply a geometry with near elongated tetragonal symmetry for the [(HC(Ph2PO)(3))(2)Cu](2+) complex, but on warming the two higher Cu-O bond lengths and g-values progressively converge, and by 340 K the bond lengths correspond to a compressed tetragonal geometry. The data may be interpreted satisfactorily assuming an equilibrium among the energy levels of a Cu-O-6 polyhedron subjected to Jahn-Teller vibronic coupling and a lattice strain. However, agreement with the experiment is obtained only if the orthorhombic component of the lattice strain decreases to a negligible value as the temperature approaches 340 K.

Influence of lattice interactions on the jahn-teller distortion of the [Cu(H2O)(6)](2+) ion: Dependence of the crystal structure of K-2[Cu(H2O)(6)](SO4)(2x)(SeO4)(2-2x) upon the sulfate/selenate ratio

The temperature dependence of the structure of the mixed-anion Tutton salt K-2[Cu(H2O)(6)](SO4)(2x)(SeO4)(2-2x) has been determined for crystals with 0, 17, 25, 68, 78, and 100% sulfate over the temperature range of 85-320 K. In every case, the [Cu(H2O)(6)](2+) ion adopts a tetragonally elongated coordination geometry with an orthorhombic distortion. However, for the compounds with 0, 17, and 25% sulfate, the long and intermediate bonds occur on a different pair of water molecules from those with 68, 78, and 100% sulfate. A thermal equilibrium between the two forms is observed for each crystal, with this developing more readily as the proportions of the two counterions become more similar. Attempts to prepare a crystal with approximately equal amounts of sulfate and selenate were unsuccessful. The temperature dependence of the bond lengths has been analyzed using a model in which the Jahn-Teller potential surface of the [Cu(H2O)(6)](2+) ion is perturbed by a lattice-strain interaction. The magnitude and sign of the orthorhombic component of this strain interaction depends on the proportion of sulfate to selenate. Significant deviations from Boltzmann statistics are observed for those crystals exhibiting a large temperature dependence of the average bond lengths, and this may be explained by cooperative interactions between neighboring complexes.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.