Comments on the Martingale Convergence Theorem Technical Report No. 21

Proofs of generality of martingale convergence theore

Magnetoelastic effects in Jahn-Teller distorted CrF2_2 and CuF2_2 studied by neutron powder diffraction

We have studied the temperature dependence of crystal and magnetic structures of the Jahn-Teller distorted transition metal difluorides CrF$_2$ and CuF$_2$ by neutron powder diffraction in the temperature range 2-280 K. The lattice parameters and the unit cell volume show magnetoelastic effects below the N\'eel temperature. The lattice strain due to the magnetostriction effect couples with the square of the order parameter of the antiferromagnetic phase transition. We also investigated the temperature dependence of the Jahn-Teller distortion which does not show any significant effect at the antiferromagnetic phase transition but increases linearly with increasing temperature for CrF$_2$ and remains almost independent of temperature in CuF$_2$. The magnitude of magnetovolume effect seems to increase with the low temperature saturated magnetic moment of the transition metal ions but the correlation is not at all perfect

Anomalous temperature-induced volume contraction in GeTe

The recent surge of interest in phase change materials GeTe, Ge$_2$Sb$_2$Te$_5$, and related compounds motivated us to revisit the structural phase transition in GeTe in more details than was done before. Rhombohedral-to-cubic ferroelectric phase transition in GeTe has been studied by high resolution neutron powder diffraction on a spallation neutron source. We determined the temperature dependence of the structural parameters in a wide temperature range extending from 309 to 973 K. Results of our studies clearly show an anomalous volume contraction of 0.6\% at the phase transition from the rhombohedral to cubic phase. In order to better understand the phase transition and the associated anomalous volume decrease in GeTe we have performed phonon calculations based on the density functional theory. Results of the present investigations are also discussed with respect to the experimental data obtained for single crystals of GeTe

Combining Molecular Dynamics with Lattice-Boltzmann: A Hybrid Method for the Simulation of (Charged) Colloidal Systems

We present a hybrid method for the simulation of colloidal systems, that combines molecular dynamics (MD) with the Lattice-Boltzmann (LB) scheme. The LB method is used as a model for the solvent in order to take into account the hydrodynamic mass and momentum transport through the solvent. The colloidal particles are propagated via MD and they are coupled to the LB fluid by viscous forces. With respect to the LB fluid, the colloids are represented by uniformly distributed points on a sphere. Each such point (with a velocity V(r) at any off-lattice position r is interacting with the neighboring eight LB nodes by a frictional force F=\xi_0(V(r)-u(r)) with \xi_0 being a friction force and u(r) being the velocity of the fluid at the position r. Thermal fluctuations are introduced in the framework of fluctuating hydrodynamics. This coupling scheme has been proposed recently for polymer systems by Ahlrichs and D"unweg [J. Chem. Phys. 111, 8225 (1999)]. We investigate several properties of a single colloidal particle in a LB fluid, namely the effective Stokes friction and long time tails in the autocorrelation functions for the translational and rotational velocity. Moreover, a charged colloidal system is considered consisting of a macroion, counterions and coions that are coupled to a LB fluid. We study the behavior of the ions in a constant electric field. In particular, an estimate of the effective charge of the macroion is yielded from the number of counterions that move with the macroion in the direction of the electric field.Comment: 37 pages, 12 figure

Stability of Ca-montmorillonite hydrates: A computer simulation study

Classic simulations are used to study interlayer structure, swelling curves, and stability of Ca-montmorillonite hydrates. For this purpose, NPzzT$ and MuPzzT ensembles are sampled for ground level and given burial conditions. For ground level conditions, a double layer hydrate having 15.0 A of basal spacing is the predominant state for relative vapor pressures (p/po) ranging in 0.6-1.0. A triple hydrate counting on 17.9 A of interlaminar distance was also found stable for p/po=1.0. For low vapor pressures, the system may produce a less hydrated but still double layer state with 13.5 A or even a single layer hydrate with 12.2 A of interlaminar distance. This depends on the established initial conditions. On the other hand, the effect of burial conditions is two sided. It was found that it enhances dehydration for all vapor pressures except for saturation, where swelling is promoted.Comment: 8 pages, 9 figure

Antiferromagnetic Order in MnO Spherical Nanoparticles

We have performed unpolarized and polarized neutron diffraction experiments on monodisperse 8 nm and 13 nm antiferromagnetic MnO nanoparticles. For the 8 nm sample, the antiferromagnetic transition temperature $T_N$ (114 K) is suppressed compared to the bulk material (119 K) while for the 13 nm sample $T_N$ (120 K) is comparable to the bulk. The neutron diffraction data of the nanoparticles is well described using the bulk MnO magnetic structure but with a substantially reduced average magnetic moment of 4.2$\pm$0.3 $\mu_B$/Mn for the 8 nm sample and 3.9$\pm$0.2 $\mu_B$/Mn for the 13 nm sample. An analysis of the polarized neutron data on both samples shows that in an individual MnO nanoparticle about 80$$ of Mn ions order. These results can be explained by a structure in which the monodisperse nanoparticles studied here have a core that behaves similar to the bulk with a surface layer which does not contribute significantly to the magnetic order.Comment: 7 pages, 5 figure