Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Raman microscopy of the molybdate minerals koechlinite, iriginite and lindgrenite

A series of molybdate bearing minerals including wulfenite, powellite, lindgrenite and iriginite have been analysed by Raman microscopy. These minerals are closely related and often have related paragenesis. Raman microscopy enables the selection of individual crystals of these minerals for spectroscopic analysis even though several of the minerals can be found in the same matrix because of the paragenetic relationships between the minerals. The molybdenum bearing minerals lindgrenite, iriginite and koechlinite were studied by scanning electron microscopy and compositionally analysed by EDX methods using an electron probe before Raman spectroscopic analyses. The Raman spectra are assigned according to factor group analysis and related to the structure of the minerals. These minerals have characteristically different Raman spectra.