Beyond power laws: Universality in the average avalanche shape

We report the measurement of multivariable scaling functions for the temporal average shape of Barkhausen noise avalanches, and show that they are consistent with the predictions of simple mean-field theories. We bypass the confounding factors of time-retarded interactions (eddy currents) by measuring thin permal- loy films, and bypass thresholding effects and amplifier distortions by applying Wiener deconvolution. We find experimental shapes that are approximately symmetric, and track the evolution of the scaling function. We solve a mean- field theory for the magnetization dynamics and calculate the form of the scaling function in the presence of a demagnetizing field and a finite field ramp-rate, yielding quantitative agreement with the experiment.Comment: 13 pages, 14 figure

Revealing the true impact of interstitial and substitutional nitrogen doping in TiO2 on photoelectrochemical applications

Application of photocatalysts that strongly absorb within the visible range is a common strategy to improve the efficiency of photoelectrochemical (PEC) systems; this may translate to high photocurrents, but it is not always the case. Here, we show that nitrogen doping enhances visible light absorption of TiO2; however, it does not necessarily result in improved PEC performance. Depending on the applied external potential, N-doping can improve, or degrade, PEC performance either under water oxidation conditions or via hole scavenging (Na2S/Na2SO3). In this work, we developed a holistic approach to evaluate the true impact of N doping in TiO2 on PEC performance. Interstitial and substitutional N doping are experimentally explored for the first time through a simple and novel PEC approach which complemented X-ray photoelectron analyses. Using this approach, we show that interstitial N doping of anatase TiO2 dominates up to 400 °C and substitutional doping up to ca. 600 °C, without rutile formation. This reveals that the bottleneck for doping higher N-concentrations in TiO2 is the direct transformation to thermodynamically favorable N-rich phases, such as TiN/Ti2N at 700 °C, inhibiting the formation of rutile phase. Transmission electron microscopy revealed that N doping proceeds mainly from the inner to the outer tube walls via nitridation and follows a preferential pathway from interstitial to substitutional doping. Direct PEC experimental evidence on visible light activation of N doped TiO2, and the location of interband states, showed acceptor levels of 1.0 eV for substitutional and 0.7 eV for interstitial doping above the TiO2 valence band maximum. In addition, due to O vacancies and Ti3+ species, donor levels below the conduction band minimum were also created. These levels act as trapping/recombination centers for charge carriers and, therefore, the gain in the visible range due to N doping does not translate to an improved PEC performance by these structural defects. Ultimately, we show that whilst there is a benefit of visible light absorption through N doping in TiO2, the PEC performance of the samples only surpasses pristine TiO2 at relatively high biasing (>0.3 V vs. Ag/AgCl)