Impedance boundary

Reflection from a Lower- or Higher-Impedance Boundary... 

When we have an impure sin e phase system, the impurities can give rise to an impurity drag effect which impedes boundary motion... 

K. S. Yee and J. S. Chen. Impedance boundary condition simulation in the FDTD/FVTD hybrid leee Transactions on Antennas and Propagation, 1997, 45, 921-925. 

M. K. Karkkainen, FDTD model of electrically thick frequency-dispersive coatings on metals and semiconductors based on surface impedance boundary conditions, IEEE Trans. Antennas Propag., vol. 53, no. 3, pp. 1174-1186, Mar. 2005. doi 10.1109/TAP.2004.842655... 

First, the impedance boundary conditions [4] for an improved modelling of small skin depth in the rod is used. 

Within the typical frequency range, between 0.5 MHz and 1 MHz for eddy current measurements, the skin depth S lies between 190 0.m and 140 0,m, which is much smaller then the rod diameter, c = 9 mm. In order model such a small skin depth a boundary layer mesh becomes necessary which create 8 elements on 390 pm with element sizes between 22-90 pm. Alternative an important feature of the model is the use of the impedance boundary condition [4], The penetration depth of the electric (E) and magnetic (H) fields into the rod is approximated using Equation 2 ... 

Impedance boundary coditions Boundary layer mesh... 

In conclusion, the model performs well within the purely inductive frequency range. Both simplifications, the impedance boundary condition on the rod and the current sheet approximation with complex material properties, were successfully applied to the FEA model in 2D as well in 3D. As a result, the total element number was reduced by a factor of 3. Consequently, the simulation model allows extensive parameter studies for several types of cracks measured with different encircling coils. 

T. Senior, Impedance boundary conditions for imperfectly conducting surfaces, Applied Scientific Research, Section B, vol. 8, no. 1, pp. 418 36, 1960. 

Botts, J., and N. Xiang. 2012. Bayesian inference for acoustic impedance boundaries in room-acoustic finite difference time-domain modeling. AIP Conference Proceedings 1443(1) 306-313. 

A resonance in the layered stracture occurs when echoes between two boundaries travel back and forth due to differences in acoustic impedances at the boundaries. For multi-layer structures a number of resonances can be observed depending on their geometry and condition. For each particular defect-free structure and given transducer we obtain a characteristic resonance pattern, an ultrasonic signature, which can be used as a reference. 

At sufficiently high frequency, the electromagnetic skin depth is several times smaller than a typical defect and induced currents flow in a thin skin at the conductor surface and the crack faces. It is profitable to develop a theoretical model dedicated to this regime. Making certain assumptions, a boundary value problem can be defined and solved relatively simply leading to rapid numerical calculation of eddy-current probe impedance changes due to a variety of surface cracks. 

For the experiments shown in Fig. 5.30 the ratio Cdi2/Cdi] is on the average 2500, very close to the ratio NG/Ntpb ( 3570)54 where N0 is the gas-exposed electrode surface area and Ntpb is the surface area of the three phase boundaries. These quantities were measured via surface titration and via SEM and the techniques described in section 5.7.2, respectively. Thus once N0 has been measured, AC Impedance spectroscopy allows for an estimation of the three-phase-boundary (tpb) length via ... 

In summary AC impedance spectroscopy provides concrete evidence for the formation of an effective electrochemical double layer over the entire gas-exposed electrode surface. The capacitance of this metal/gas double layer is of the order of 100-300 pF/cm2, comparable to that corresponding to the metal/solid electrolyte double layer. Furthermore it permits estimation of the three-phase-boundary length via Eq. 5.62 once the gas exposed electrode surface area NG is known. 

Other methods for impeding dislocation motion are the introduction of grain boundaries, and/or twin boundaries. While these impediments may increase the hardness, they are also likely to decrease the tensile strength. 

In chemical syntheses under the action of microwave irradiation the most successful applications are necessarily found to be the use of solvent-free systems [6], In these systems, microwaves interact directly with the reagents and can, therefore, drive chemical reactions more efficiently. The possible acceleration of such reactions might be optimum, because they are not moderated or impeded by solvents. Reactions on solid mineral supports and, in turn, the interaction of microwaves with the reagents on the solid phase boundary, which can substantially increase the rate of the reactions, are of particular interest [7]. 

Figure 6.7 Complex impedance of a polycrystalline ceramic sample (a) representation of the equivalent circuit of a component (b) the impedance spectrum of the equivalent circuit in (a) (c) the impedance spectrum of a typical ceramic sample. Each semicircular arc represents one component with an equivalent circuit as in (a) that at the highest frequency corresponds to the repose of the bulk, that at middle frequencies to the grain boundary response, and that at lowest frequencies to the electrodes.

A typical ceramic sample contains contributions from the bulk, the grain boundaries, and the electrode. Each of these is characterized by a semicircular arc with a maximum at RCu> = 1, where the values of resistance, capacitance, and frequency refer directly to the bulk, grain boundaries, or electrodes (Fig. 6.7c). The separation of resistance due to the bulk from that of the grain boundaries is thus easily achieved using impedance spectroscopy. 

The bulk and grain boundary conductivities of a ceramic sample can be separated using the impedance, Z, by plotting ... 

At high frequencies diffusion of the reactants to and from the electrode is not so important, because the currents are small and change sign continuously. Diffusion does, however, contribute significantly at lower frequencies solving the diffusion equation with appropriate boundary conditions shows that the resulting impedance takes the form of the Warburg impedance ... 

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