Computing hysteresis points of nonlinear equations depending on two parameters

A direct method is described for computing a hysteresis point (double turning point) corresponding to a cusp point of a system ofn nonlinear equations inn variables depending on two parameters. By addition of two equations a minimally extended system ofn+2 nonlinear equations is constructed for which the hysteresis point is an isolated solution. An efficient implementation of Newton's method is presented not requiring evaluations of second derivatives of the original problem. Two numerical examples show the efficiency of theQ-quadratically convergent method.     

Characterization and electrochemical properties of CF4 plasma-treated boron-doped diamond surfaces

The effect of CF₄ plasma etching on diamond surfaces, with respect to treatment time, was investigated using scanning electron microscopy (SEM), Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), and electrochemical measurements. SEM observations and Raman spectra indicated an increase in surface roughening on a scale of 10–20 nm, and an increase in crystal defect density was apparent with treatment time in the range of 10 s to 30 min. In contrast, alteration of the diamond surface terminations from oxygen to fluorine was found to be rather rapid, with saturation of the F/C atomic ratio estimated from XPS analysis after treatment durations of 1 min and more. The redox kinetics of Fe(CN)₆^3−/4− was also found to be significantly modified after 10 s of CF₄ plasma treatment. This behavior shows that C–F terminations predominantly affect the redox kinetics compared to the effect on the surface roughness and crystal defects. The double-layer capacitance (C_dl) of the electrolyte/CF₄ plasma-treated boron-doped diamond interface was found to show a minimum value at 1 min of treatment. These results indicate that a short-duration CF₄ plasma treatment is effective for the fabrication of fluorine-terminated diamond surfaces without undesirable surface damage.