Scaling law of Wolff cluster surface energy

We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension $1 < d_f \le 3$ in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of Wolff cluster and are able to establish a new scaling relation. It enables us to introduce a new exponent associated to the surface energy of Wolff cluster. Finally, this new exponent is linked to a dynamical exponent via an inequality.Comment: 12 pages, 3 figures. To appear in PR

Determination of Parabolic Rate Constants from a Local Analysis of Mass-Gain Curves

A method is proposed to allow a more accurate evaluation of thermogravimetric data to identify diffusion or partial diffusion control of scaling kinetics. This method is based on the fitting of mass-gain data to a parabola over a short time interval. The translation of the time interval over the entire test time period provides an actual instantaneous parabolic rate constant independently of any transient stage or simultaneous reaction steps. The usefulness and limitations of this procedure are illustrated from oxidation tests performed on several metallic materials (pure nickel, single-crystal superalloys, and NbTi-Al alloy)

Multi-Sample Thermobalance for Rapid Cyclic Oxidation Under Controlled Atmosphere

When testing the resistance to oxidation of high temperature materials, the cyclic oxidation test is used as a reference because it integrates isothermal oxidation kinetics, oxide scale adherence, mechanical stresses, metallic alloy and oxide mechanical behavior and their evolution with time, in conditions close to the actual conditions of use. To fill the gap between the measurements of physical data (oxidation kinetics, interfacial energy, oxide toughness, growth stresses, coefficients of thermal expansion, mechanical properties of the alloy under the oxide scale,...) and the cyclic oxidation test, comprehensive scientific work is necessary, but also technological development and understanding of the practice of the cyclic oxidation test. This paper presents a new experimental tool, which allows the simultaneous measurement of the mass of several samples placed in the same controlled atmosphere during fast thermal cycles. This multi-sample thermobalance is described, in association with the description of the measurement methodology (i.e. “cyclic thermogravimetry”). First tests of performance of the apparatus are given, including heating and cooling rates and continuous Samass measurements for a P91 alloy

Continuous Thermogravimetry under Cyclic Conditions

Thermogravimetry during cyclic oxidation of metallic alloys is described. A methodology is given in order to determine the Net Mass Gain, the GrossMass Gain, the total mass of spalled oxide, the rate of metal consumption and the average oxide scale thickness as a function of the number of cycles. The fraction of oxide scale which spalls at each cycle can be also calculated, and the parabolic constant can be estimated at each cycle. Two examples are given: the cyclic oxidation of a NiAl single crystal in flowing oxygen at 1150xC, and the cyclic oxidation of alloy P91 at 800xC in laboratory air. Advantages and disadvantages of this technique are discussed in regards to classical interrupted tests in crucibles. Thermogravimetry during cyclic oxidation appears to be a powerful tool in order to model and quantify the cyclic oxidation test which is of great interest in order to qualify the resistance of materials to oxidation in conditions close to their actual use, but a specific aspparatus need to be developed in order to obtain data in an efficient and economical manner. A new apparatus designed for this purpose is described briefly

Dynamical transport properties of NbSe3_3 with simultaneous sliding of both charge density waves

Measurements of the nonlinear conductivity in NbSe$_3$ when the high-T and the low-T charge-density waves (CDWs) are simultaneously sliding have been performed. It is shown that the threshold electric field, $E_{t1}$, for depinning the high-T CDW increases 4 - 5 times at the temperature at which the low-T CDW is formed, indicating the strong pinning effect resulting from the interaction between both CDWs. Under application of a radio-frequency (rf) field, Shapiro steps are never observed simultaneously for both CDWs. At the electric field less then one for high-T CDW sliding only Sapiro steps for low-T CDW were observed, and at higher field only Shapiro steps for high-T CDW exist.Comment: 5 pages, 6 figures, accepted in PR

Numerical simulation of cyclic oxidation kinetics with automatic fitting of experimental data

This paper proposes a model, based on a Monte Carlo method, to assess cyclic oxidation tests. The numerical code fits automatically the experimental net mass change curves. Oxidation kinetics are identified as well as the relationship between spalling and local oxide thickness or time. The modelling is applied to cyclic oxidation of NiPtAl single crystals at 1150 °C in dry air

Effect of Cycle Frequency on High Temperature Oxidation Behavior of Alumina-forming Coatings Used for Industrial Gas Turbine Blades

Oxidation kinetics of platinum modified aluminide and overlay coatings on nickel base superalloys were investigated. Isothermal oxidation tests were carried out at 1050°C in synthetic air. Cyclic oxidation tests were performed with 2 cycle frequencies : - Short term cycles : 1h dwells at 1050°C in synthetic air ×1800 cycles - Long term cycles : 300h dwells at 1050°C in laboratory air × 6 cycles (experiment planned to totalize at least 10 000 hours at high temperature) The mass gain curves point out a large effect of the cycle frequency at 1050°C for overlay NiCoCrAlYTa coating whereas the effect is less significant for Pt-modified nickel aluminide coating. Scanning electron microscopy combined with energy dispersive X-ray spectroscopy was used to evaluate the effect of cycle frequency on microstructural evolution. A simple statistical spalling model [1,2], assuming that the parabolic rate constant kp and the spalling probability p are constant, is tentatively applied and discussed in view of the microstructural evolution complexity

Investigations on the Diffusion of Oxygen in Nickel at 1000°C by SIMS Analysis

High-purity polycrystalline nickel foils have been oxidized at 1000°C in laboratory air before being analyzed in secondary ion mass spectrometry to locally measure the oxygen content in solid solution. The values obtained in metallic grains are surprisingly the same before and after the oxidation treatments (between 5 and 10 atom ppm) and they are much lower than the ones predicted from the literature solubility and diffusion coefficient data at 1000°C. It is shown that this discrepancy could have its origins in the purity level of the samples but also in the exclusive oxygen diffusion in nickel grain boundaries. This last assumption is supported by the occurrence of nickel oxide particles on the walls of voids located in grain boundaries

Quantification of growth kinetics and adherence of oxide scales formed on Ni-based superalloys at high temperature

Cyclic and isothermal oxidation behaviors of first and fourth-generation superalloys AM1 and MCNG were investigated to evaluate the ability of the scratch test to quantify the adhesion of multi-layered oxide scales. Effects of sulfur content and of scale thickness were studied independently. Available models lead to large discrepancies in the calculated work of adhesion values with the evaluation of the residual stress being the largest source of error. Nevertheless, models can assess the effect of sulfur content and the scratch test can be used to correlate the long-term cyclic oxidation behavior and the adhesion of oxide scales

Correlations between Growth Kinetics and Microstructure for Scales Formed by High-Temperature Oxidation of Pure Nickel. II. Growth Kinetics

The oxidation kinetics of high-purity nickel were studied between 500 and 1200°C, in pure oxygen at atmospheric pressure, for aûerage oxide-scale thicknesses of 1, 5, 10, and 30 μm. In the oûerall temperature range studied, a decrease in the parabolic rate constant kp with increasing scale thickness was observed. Depending on temperature and oxide-scale thickness, growth kinetics can be interpreted as a mixture of parabolic- and cubic-growth kinetics. Possible correlations between growth kinetics and microstructures of the oxide scales were inûestigated. From this set of experimental data, oxidation-kinetics models were tested. In particular, the effect of grain-boundary diffusion on NiO-growth kinetics was discussed. The correlations between growth kinetics and oxide microstructures appear to be more complex than usually reported