Brownian motion on the Sierpinski carpet

We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpinski carpet that is invariant with respect to the local symmetries of the carpet. Consequently for each such fractal the law of Brownian motion is uniquely determined and the Laplacian is well defined

Tunneling splitting of magnetic levels in Fe8 detected by 1H NMR cross relaxation

Measurements of proton NMR and the spin lattice relaxation rate 1/T1 in the octanuclear iron (III) cluster [Fe8(N3C6H15)6O2(OH)12][Br8 9H2O], in short Fe8, have been performed at 1.5 K in a powder sample aligned along the main anisotropy z axis, as a function of a transverse magnetic field (i.e., perpendicular to the main easy axis z). A big enhancement of 1/T1 is observed over a wide range of fields (2.5-5 T), which can be attributed to the tunneling dynamics; in fact, when the tunneling splitting of the pairwise degenerate m=+-10 states of the Fe8 molecule becomes equal to the proton Larmor frequency a very effective spin lattice relaxation channel for the nuclei is opened. The experimental results are explained satisfactorily by considering the distribution of tunneling splitting resulting from the distribution of the angles in the hard xy plane for the aligned powder, and the results of the direct diagonalization of the model Hamiltonian.Comment: J. Appl. Phys., in pres

Screening procedure for structurally and electronically matched contact layers for high-performance solar cells: hybrid perovskites

The rapid progress in performance of solar cells based on hybrid halide perovskites means that devices based on these materials have reached a stage where research interest can now focus on development of robust technology. One of the key questions relating to these (and indeed any) devices is their lifetime and stability which in turn is often influenced by the quality of interfaces and junctions within the device. In this study we present a methodology which allows screening for mechanically stable, electronically suitable interface combinations – applying the technique to screen 175 common semiconductors for viability as electron and hole extracting contacts for CH3NH3PbI3. The screening method can be applied to any semiconductor junction problem and relies on easily obtained experimental or theoretical information – electron affinity, ionisation potential, lattice parameters and crystal structure. From the screening we rank the candidates according to a figure of merit, which accounts for band alignment and chemical/mechanical stability of the interface. Our screening predicts stable interfaces with commonly applied electron extraction layers such as TiO2 and ZnO as well giving insight into the optimal polymorphs, surfaces and morphologies for achieving good quality contacts. Finally we also predict potentially effective new hole and electron extraction layers, namely Cu2O, FeO, SiC, GaN, and ZnTe