The Critical Current Density

We plot in figure 2 the angular dependence of the critical current density JJJd, Jd is the critical current density when a magnetic field is applied parallel to the film surface. We note that JcI is independent of the angle 9. The solid circles are the experimental data obtained for YBa2Cu307.8 thin film at 10 T and 60 K. For comparison, the solid curve presents the theoretical values given by [8] 

As can be seen, in this experimental condition, the theoretical curve proposed by the intrinsic pinning model of Tachiki and Takahachi are in good agreement with our experimental data. 

The experimental values obtained at 60 K, in an applied magnetic field of 0.6 T are plotted in figure 3. For comparison, with the theoretical values the solid line presents the intrinsic pinning model values using Jcl = 6.07x106 A/cm2 and Jc2 = 2.3xl06 A/cm2. 

The concordance between the two curves is less good than in the case where the applied magnetic field is 10 T especially for angles close of 90°. 

At low temperature, flux lines preferentially penetrate into the weakly superconducting layers cause they are stabilized the most when they are at the weakly superconducting layers, since the loss of the superconducting energy due to the inclusion of the flux lines is least in this case. 

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Initially, the curve conforms to the Tafel equation and curve AB which is referred to as the active region, corresponds with the reaction Fe- Fe (aq). At B there is a departure from linearity that b omes more pronounced ns the potential is increased, and at a potential C the current decreases to a very small value. The current density and potential at which the transition occurs are referred to as the critical current density, and the passivation potential Fpp, respectively. In this connection it should be noted that whereas is determined from the active to passive transition, the Flade potential Ef is determined from the passive to active transition... 

Fig. 1.41 Schematic anodic polarisation curves for a passivatable metal showing the effect of a passivating agent that has no specific cathodic action, but forms a sparingly soluble salt with the metal cation, a without the passivating agent, b with the passivating agent. The passive current density, the active/passive transition and the critical current density are all lowered in b. The effect of the cathodic reaction c, is to render the metal active in case a, and passive...

The ease with which stainless steels can passivate then increases with the level of chromium within the alloy and so materials with higher chromium content are more passive (i.e. conduct a lower passive current density) and passivate more readily (i.e. the critical current density is lower and the active/passive transition is lower in potential). They are also passive in more aggressive solutions the pitting potential is higher. 

In the case of the stainless steels, or other readily passivated metals, the rapid reduction of dissolved oxygen on the freely exposed surface will be sufficient to exceed the critical current density so that the metal will become passive with a potential greater than whereas the metal within the crevice will be active with a potential less than. The passivation of the freely exposed surface will be facilitated by the rise in pH resulting from oxygen reduction, whilst passivation within the crevice will be impeded by the high concentration of Cl ions (which increases the critical current density for passivation) and by the H ions (which increases the passivation potential E, see Section 1.4). 

For many metals the critical current density for passivation (/ ,) increases with increasing pH of the solution ... 

In de-aerated 10sulphuric acid (Fig. 3.45) the active dissolution of the austenitic irons occurs at more noble potentials than that of the ferritic irons due to the ennobling effect of nickel in the matrix. This indicates that the austenitic irons should show lower rates of attack when corroding in the active state such as in dilute mineral acids. The current density maximum in the active region, i.e. the critical current density (/ ii) for the austenitic irons tends to decrease with increasing chromium and silicon content. Also the current densities in the passive region are lower for the austenitic irons... 

The significance of the Flade potential Ef, passivation potential pp, critical current density /pn, passive current density, etc. have been considered in some detail in Sections 1.4 and 1.5 and will not therefore be considered in the present section. It is sufficient to note that in order to produce passivation (a) the critical current density must be exceeded and b) the potential must then be maintained in the passive region and not allowed to fall into the active region or rise into the transpassive region. It follows that although a high current density may be required to cause passivation ) only a small current density is required to maintain it, and that in the passive region the corrosion rate corresponds to the passive current density (/p, ). 

Fig. 10,54 Potentiostatic anodic polarisation curves for mild steel in 10% sulphuric acid. Note the magnitude of the critical current density which is lO -lO A/m this creates a problem in practical anodic protection since very high currents are required to exceed icu. and therefore...

Example 5 A stainless steel pipe is to be used to convey an aerated reducing acid at high velocity. If the concentration of dissolved Oj is 10 mol dm (10 mol cm ) calculate whether or not the steel will corrode when (a) the acid is static, (b) the acid is moving at high velocity. Assume that the critical current density for passivation of the steel in the acid is 200/iAcm the thickness of the diffusion layer is 0-05 cm when the acid is static and 0-005 cm when the acid flows at a high velocity assume the diffusion coeffi-... 

In acidic electrolytes with fluoride, silicon is stable at OCP, while electrochemical dissolution takes place for anodic potentials. For anodic current densities below the critical current density JPS PS is formed and the electrolyte-electrode interface is found to be Si-H covered. Species active in the dissolution process are HF, (HF)2 and HF2. A dissolution reaction proposed for this regime is ... 

The critical current density /PS, easily identified by the first anodic peak in the current voltage plot, is shown for p-type samples of different crystal orientation in Fig. 4.9. Note that JPS is largest for silicon electrodes of (100) crystal orientation, independently of the electrolyte concentration used (inset of Fig. 4.9). This indicates that the dissolution process has an anisotropic component [Le9]. 

The formation of luminescent PS requires HF to be present in the electrolyte, while the presence of water is not essential [Pr7]. The intensity as well as the peak energy of the PL emission increases with the PS formation current density J for a fixed electrolyte concentration. If various electrolytes are compared, the ratio between formation current density J and the critical current density JPS is more relevant than the absolute value of J. Because the porosity itself depends on J/JPS, in many studies... 

Figure II. Schematic anodic polarization curves at a fixed temperature. Determination of either transpassive potential ( ,) or pitting potential ( p and repassivation potential ( ,) at the critical current density (/ ). t rcvis the current density at which the scan is reversed. ...

For the usual dc measurement the constant dc current source should be capable of providing currents in the range 0.1-10 mA for a typical bar of 1 mm square cross-section, 1 cm length, and a resistivity at 100 K of 50 pOhm-cm the voltage measured for a 1 mA current source would be 1 / V. Since even for a typical low value of the critical current density, 100 A/cm2, the measurement current would be 1000 times less and thus have essentially no effect on the measurement. However, the measurement of 1 / V to a precision of 1% already requires care to assure that noise and thermal voltages are reduced well below this value. Currents of similar value are used for measurements in thin films. 

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