Polarisation approximation

More detailed measurements on the Pt/Fe system have covered compositions in the range 3-50 at. % Pt [81]. The 3 at. % alloy gave Hm = —1260 kG at 4-2 K and (99 keV) = -0-60(15) n.m. The value of the field is almost independent of composition within the range specified. Neutronscattering data have shown that there is no localised magnetic moment on the Pt atoms, so that the field is generated entirely by conduction-electron polarisation, approximately 0-07 unpaired conduction electrons being required per Pt atom. A similar mechanism is believed to act in the cobalt and nickel alloys [84]. 

Figure 8 Orientation of the incident X-ray beam on a single crystal giving polarisation approximately normal to the crystal surface when is small and approximately parallel with the surface when 0 is large ( ).

There is an important practical distinction between electronic and dipole polarisation whereas the former involves only movement of electrons the latter entails movement of part of or even the whole of the molecule. Molecular movements take a finite time and complete orientation as induced by an alternating current may or may not be possible depending on the frequency of the change of direction of the electric field. Thus at zero frequency the dielectric constant will be at a maximum and this will remain approximately constant until the dipole orientation time is of the same order as the reciprocal of the frequency. Dipole movement will now be limited and the dipole polarisation effect and the dielectric constant will be reduced. As the frequency further increases, the dipole polarisation effect will tend to zero and the dielectric constant will tend to be dependent only on the electronic polarisation Figure 6.3). Where there are two dipole species differing in ease of orientation there will be two points of inflection in the dielectric constant-frequency curve. 

Wetting and capillarity can be expressed in terms of dielectric polarisabilities when van der Waals forces dominate the interface interaction (no chemical bond or charge transfer) [37]. For an arbitrary material, polarisabilities can be derived from the dielectric constants (e) using the Clausius-Mossotti expression [38]. Within this approximation, the contact angle can be expressed as ... 

Using the data obtained from the silver nitrate experiments, we have derived a simple approximation to calculate the cavity polarisability as a function of diameter [22]. If we apply this model to cobalt nitrate, the derived threshold for filling is 0.8 nm [32] this result qualitatively agrees with our observations that cobalt nitrate-filled cavities are much narrower ( 2 nm) than obtained with silver nitrate (= 4 nm). 

Copper-base alloys will corrode in aerated conditions. It is, therefore, sometimes appropriate to consider cathodic protection. It becomes particularly relevant when the flow rates are high or when the design of an item causes the copper to be an anode in a galvanic cell (e.g. a copper alloy tube plate in a titanium-tubed heat exchanger). Corrosion can be controlled by polarisation to approximately — 0-6V (vs. CU/CUSO4) and may be achieved using soft iron sacrificial anodes. 

Now, when is small, the polarisation of the pipeline is approximately directly proportional to the true current density (ij) at the holidays (Section 10.7, page 10 149) in the coating. Thus... 

The operating potential of an anode material is its potential when coupled to a structure (i.e. the closed-circuit potential). Since all commercial anode materials are formulated to suffer only slight polarisation under most conditions of exposure, the operating potential approximates to the open-circuit potential. Indeed, any substantial difference (>50mV) between these two potentials will call into question the suitability of the anode in the particular environment. 

The importance of the method in corrosion testing and research has stimulated other work, and since Stern s papers appeared there have been a number of publications many of which question the validity of the concept of linear polarisation. The derivation of linearity polarisation is based on an approximation involving the difference of two exponential terms, and a number of papers have appeared that have attempted to define the range of validity of polarisation resistance measurements. Barnartt" derived an analytical expression for the deviations from linearity and concluded that it varied widely between different systems. Leroy", using mathematical and graphical methods, concluded that linearity was sufficient for the technique to be valid in many practical corrosion systems. Most authors emphasise the importance of making polarisation resistance measurements at both positive and negative overpotentials. 

Oldham and Mansfeld" approached the problem of linearity in a different way and their derivation avoids the approximation used by Stern and Geary. They conclude that although linearity is frequently achieved this is due to three possible causes (a) ohmic control due to the IR drop rather than control according to linear polarisation, (b) the similarity of the values of b, and be and (c) a predisposition by the experimenter to assume that the AE — Ai curves near must be linear. In a later paper Oldham and Mansfeld" showed that linearity of the AE — Ai curve is not essential and... 

An ideal reversible cell is characterised by an e.m.f. that remains constant irrespective of the rate of reaction in either direction, i.e. each interface constituting the cell must be so completely non-polarisable that it resists any attempt to change its potential. Although this is impossible to achieve in practice, a number of interfaces approximate to ideality providing the rate of reaction is maintained at a very low value. These reversible electrodes (or half-cells) are used as reference electrodes for determining the potential of a single electrified interface. 

The calomel electrode Hg/HgjClj, KCl approximates to an ideal non-polarisable electrode, whilst the Hg/aqueous electrolyte solution electrode approximates to an ideal polarisable electrode. The electrical behaviour of a metal/solution interface may be regarded as a capacitor and resistor in parallel (Fig. 20.23), and on the basis of this analogy it is possible to distinguish between a completely polarisable and completely non-polarisable... 

Ion chromatography (see Section 7.4). Conductivity cells can be coupled to ion chromatographic systems to provide a sensitive method for measuring ionic concentrations in the eluate. To achieve this end, special micro-conductivity cells have been developed of a flow-through pattern and placed in a thermostatted enclosure a typical cell may contain a volume of about 1.5 /iL and have a cell constant of approximately 15 cm-1. It is claimed15 that sensitivity is improved by use of a bipolar square-wave pulsed current which reduces polarisation and capacitance effects, and the changes in conductivity caused by the heating effect of the current (see Refs 16, 17). 

Barker and Jenkins45 attempted to solve the problem by application of the polarising current in a series of pulses one pulse of approximately 0.05 second duration being applied during the growth of a mercury drop, and at a fixed point near the end of the life of the drop. Two different procedures may, however, be employed (a) pulses of increasing amplitude may be superimposed upon a constant d.c. potential, or (b) pulses of constant amplitude may be applied to a steadily increasing d,c. potential. 

We used modifications of the standard solid-state CP-MAS (cross-polarisation, magic-angle spinning) experiment to allow the proton relaxation characteristics to be measured for each peak in the C spectrum. It is known that highly mobile, hydrated polymers can not be seen using either usual CP-MAS C spectrum or solution NMR (6). We found, however, that by a combination of a long-contact experiment and a delayed-contact experiment we could reconstruct a C spectrum of the cell-wall components that are normally too mobile to be visible. With these techniques we were able to determine the mobility of pectins and their approximate spatial location in comparison to cellulose. 

Fig. 9.18 Comparison of calculated time-domain spectra (NFS) and energy-domain spectra (Mossbauer absorption) for a-, b-, and c-cut single crystals of guanidinium nitroprusside. For the calculations the approximation of complete alignment of 14 parallel to the crystallographic c-axis is used. The polarisation direction of the synchrotron beam is represented by e. (Taken from [48])...

We assume that, on formation of B- XY, a fraction 5j (i = intermolecular) of an electronic charge is transferred from the electron donor atom of Z of the Lewis base B to the npz orbital of X and that similarly a fraction 5p (p = polarisation) of an electronic charge is transferred from npz of X to n pz of Y, where z is the XY internuclear axis and n and n are the valence-shell principal quantum numbers of X and Y. Within the approximations of the Townes-Dailey model [187], the nuclear quadrupole coupling constants at X and Y in the hypothetical equilibrium state of B- -XY can be shown [178] to be given by ... 

The values of Sp also behave systematically, as shown in Fig. 21, in which 5p is plotted against k for the various series B XY. It is evident that, for a given XY, Sp is an approximately linear function of k and hence of the strength of the interaction. Moreover, for a given B the order of 5p is IC1 > BrCl Br2 > CI2, which is the order of the polarisabilities of the leading atoms X in B XY and therefore seems reasonable from the definition (see earlier) of 5p. 

Why, then, is the magnetisation density used The answer is that the magnetisation density is important for certain approximations which are usually made in analysing neutron scattering experiments. In the standard polarised neutron diffraction (PND) experiment [5], only one parameter is measured - the so-called flipping ratio . It is impossible to determine a vector quantity like the magnetisation density from a single number, unless some assumptions are made. The assumptions usually made are ... 

Thus, the polarisation data, cyclic voltammetric results and the a.c. impedance measurements all suggest that, when an Ru02/TiC>2 anode exhibits a high overpotential, this is a direct consequence of the surface depletion of Ru. This is also consistent with the estimated Re values of approximately 20 Q for the failed electrodes, in contrast to the known, much higher specific resistivity of Ti02 of... 

In chlor-alkali production, EMOS should be able to determine problems with both anode coatings and membranes. The literature is replete with examples of the effect of different impurities on membranes [2] and of the analysis of different problems using polarisation curves to determine their cause [3, 4]. These analysis techniques have been incorporated into the expert system in the form of approximations of the polarisation curves. Use is made of the familiar k-factor (see Equation 8.2) or the more accurate logarithmic form of this factor (Equation 8.3) ... 

Match the main features of the rocking curve first, using plane wave calculations and a single (sigma) polarisation. It shonld be possible to fit all the main peaks accnrately in spacing and approximately in intensity. Then begin refinement to match the intensities and widths. 

---