Lehigh University

About: Lehigh University is a education organization based out in Bethlehem, Pennsylvania, United States. It is known for research contribution in the topics: Catalysis & Fracture mechanics. The organization has 12684 authors who have published 26550 publications receiving 770061 citations.

Mixed boundary value problems in mechanics

Abstract: Definitions in the case of multiple series equations and multiple integral equations are examined. In considering the solution of a given mixed boundary value problem perhaps the simplest technique is the direct application of the method of complex potentials provided the problem admits such potentials and the domain and the boundary conditions are suitable for such an application. The direct application of complex potentials is described with the aid of examples, taking into account a problem in potential theory, the case of periodic cuts, and an elasticity problem for a nonhomogeneous plane. The reduction to singular integral equations is discussed along with the numerical solution of singular integral equations of the first kind, integral equations with generalized Cauchy kernels, and singular integral equations of the second kind.

Determination of molybdenum–oxygen bond distances and bond orders by Raman spectroscopy

Abstract: A correlation is developed for relating Raman stretching frequencies of molybdenum–oxygen (MoO) bonds to their respective bond distances in molybdenum oxide compounds. MoO bond orders are also related to stretching frequencies. The MoO correlation is expected to offer invaluable insight into the structures of molybdate species in chemical systems which are not amenable to analysis by diffraction or other spectroscopic techniques. In the present study, the correlation is used to predict stretching frequencies for perfect MoO4 and MoO6 structures, and to determine MoO bond distances of the MoO6 octahedron in Ba2CaMoO6 as well as the dehydrated surface molybdate species in MoO3/Al2O3.

Mapping surface plasmons at the nanometre scale with an electron beam

Abstract: The optical response from metal nanoparticles and nanostructures is dominated by surface plasmon generation and is critically dependent on the local structure and geometry. Electron energy-loss spectroscopy (EELS), combined with recent developments in spectrum imaging and data processing, has been used to observe the energy and distribution of surface plasmons excited by fast electrons. The energy of the plasmon responses is consistent with the optical response and with calculations. For gold and silver rods and ellipsoids, longitudinal, transverse and distinct cluster modes were readily identified and mapped. The spatial resolution of the presented maps is one order of magnitude better than that achievable with scanning near-field optical microscopy (SNOM)-based techniques.