Rate of convergence of truncated stochastic approximation procedures with moving bounds

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We study convergence and rate of convergence. Main results are supplemented with corollaries to establish various sets of sufficient conditions, with the main emphases on the parametric statistical estimation. The theory is illustrated by examples and special cases.Comment: 30 page

Initial Steps of Thermal Decomposition of Dihydroxylammonium 5,5′-bistetrazole-1,1′-diolate Crystals from Quantum Mechanics

Dihydroxylammonium 5,5?-bistetrazole-1,1?-diolate (TKX-50) is a recently synthesized energetic material (EM) with most promising performance, including high energy content, high density, low sensitivity, and low toxicity. TKX-50 forms an ionic crystal in which the unit cell contains two bistetrazole dianions {c-((NO)N3C)-[c-(CN3(NO)], formal charge of ?2} and four hydroxylammonium (NH3OH)+ cations (formal charge of +1). We report here quantum mechanics (QM)-based reaction studies to determine the atomistic reaction mechanisms for the initial decompositions of this system. First we carried out molecular dynamics simulations on the periodic TKX-50 crystal using forces from density functional based tight binding calculations (DFTB-MD), which finds that the chemistry is initiated by proton transfer from the cation to the dianion. Continuous heating of this periodic system leads eventually to dissociation of the protonated or diprotonated bistetrazole to release N2 and N2O. To refine the mechanisms observed in the periodic DFTB-MD, we carried out finite cluster quantum mechanics studies (B3LYP) for the unimolecular decomposition of the bistetrazole. We find that for the bistetrazole dianion, the reaction barrier for release of N2 is 45.1 kcal/mol, while release of N2O is 72.2 kcal/mol. However, transferring one proton to the bistetrazole dianion decreases the reaction barriers to 37.2 kcal/mol for N2 release and 59.5 kcal/mol for N2O release. Thus, we predict that the initial decompositions in TKX-50 lead to N2 release, which in turn provides the energy to drive further decompositions. On the basis of this mechanism, we suggest changes to make the system less sensitive while retaining the large energy release. This may help improve the synthesis strategy of developing high nitrogen explosives with further improved performance

An atomistic view on the Schottky barrier lowering applied to SrTiO3/Pt contacts

The interface between a metal and a semiconductor is known as Schottky contact and a key factor in semiconductor technologies. Those interfaces normally build an energetic barrier, which is responsible for the exponential current voltage dependence. Analytical models often describe the right trend for the description of the Schottky barrier height, but fail to predict the barrier properties quantitatively correct. To overcome this problem atomistic and quantum mechanical approaches are required such as the here applied density functional theory combined with the non-equilibrium Greens function method. So far, these methods have rarely been applied to wide band gap metal oxides, which leads to a lack in the understanding of oxide electronics. The presented study deals with the image force induced Schottky barrier lowering of a SrTiO3/Pt interface as a model system for wide band gap metal-oxide Schottky contacts. The Schottky barrier lowering is investigated for the case of different doping concentrations/positions and for different voltages. From a defect chemical point of view, oxygen vacancies act as donors in many metal oxides and dominate the electronic conduction in oxide electronics. Consequently, we investigated the Schottky barrier lowering induced by oxygen vacancies. The second doping mechanism is achieved in the sense of classical doping using Nb impurities, which form a conventional n-type donor. The atomistic simulation reveals the Schottky barrier lowering effect for both type of dopants. The results are compared to a standard analytical model regarding the Schottky barrier lowering