Analytical critical current density

Critical care analytes, measuring, 24 55 Critical cooling rate, of steel, 23 283 Critical current density, 23 821-823, 825 optimization of, 23 829 in PIT conductors, 23 833-834 temperature and field dependence of, 23 847-848... 

Current density and the type of primary ion have a critical effect on SIMS analyses. High current densities are desirable for rapid profiling and high-sensitivity analysis, whereas low current densities are chosen when the analyte layer is thin or when using static SIMS. Exotic polyatomic ion sources are an area of active research today Re04 [104], SF5+ [105], SF6 , NO, CF3+, C, and many others [106,107], have been reported to provide exceptional enhancement of secondary ion yields and ultrashallow depth profiling. However, the most heavily used ion sources today are the hollow cathode duoplasmatron (Fig. 4.31) [108], the thermal... 

While the general features of several of the models are similar, the particular analytical expressions, wherever available, vary widely depending upon the details of a given model. In what follows, some of the equations from the work of Tanner et al for composite cathodes are given to illustrate the role of various parameters [27]. In the low current density limit, over which the Butler-Volmer equation can be linearised, the effective charge transfer or the polarisation resistance (activation polarisation only) for cathode interlayer thickness greater than the critical thickness can be given by [22]... 

It is generally accepted that for atomic liquids far from the critical point, the microscopic or nisation is dominated by the repulsive intoactions between the atoms. The longer range attractive forces serve only to maintain the high density of the liquid phase and the temperature acts only as a mechanism with which to vary the density. With this in mind, the hard sphere fluid has become the standard starting point for liquid state themies in which the attractive forces can be introduced, fin example, via a van der Waals approach. Hard sphere systems have been studied extensively using computer simulation, with the numerical data determined for the equation of state used as a substitute for an exactly solvable model for the liquid phase. This is in contrast to the gas and solid phases, for which the ideal gas and harmonic solid provide analytic models, respectively. Indeed, the lack of an analytic model for the liquid phase has meant that many of the current theories rely substantially on the insight obtained from the earliest simulations of the hard sphere fluid [1]. 

---