Conductivity partial

The relative contributions of ions, electrons and positive holes to the conductivity is described drrough the transport number which is related to a partial conductivity defined by... 

Here, tg = 1 and Iq2- is negligible, and thus the rate of oxidation is determined by the partial conductivity due to the Ni2+ ions. 

At high temperature, the conductivity was found to increase linearly with temperature and the observed high-temperature MR was positive. In fact, by fitting the data using a simple two-band model] 17] the authors obtained the theoretical curve in Fig. 4 (a). The fitting parameters showed that the ratio Op/ct, where Op and are the partial conductivities of holes and electrons, respectively, decreases with increasing tern-... 

If there is more than one type of carrier, i.e. electrons and positive holes, as in MWCNT, the contribution of each type of carrier should be taken into account. In that case, the total electrical conductivity is given by the sum of the partial conductivities. 

A similar process occurs if we electrolyze the phase sequence AX/AY, using A-metal electrodes. AX and AY are immiscible ionic crystals. This time we focus on the AX/AY interface. Since there is always a finite electronic partial conductivity and the very small transference numbers te (AX) and te (AY) are normally different, the AX side of the AX/AY interface serves either as an anode (oxidizing) or as a cathode (reducing). The difference (te(AY)-te(AX)) is proportional to the anodic (cathodic) current in AX. The cathodic interface is expected to obtain similar morphologies as have been described for the A-metal cathode in the previous paragraph. It is immobile as long as Dx,Dymorphological instability is therefore due to the A precipitates which cause the perturbations. 

While partial conduction currents are driven by the gradients in the respective electrochemical potentials (according to Eq. (3)), the external voltage that we measure is determined by the difference of the electrons electrochemical potentials (/ieon) or Fermi-levels (//(,on/Nm) at both terminals... 

We will see that in the steady state of the blocking cells, we can extract partial conductivities, and from the transients chemical diffusion coefficients (and/or interfacial rate constants). Cell 7 combines electronic with ionic electrodes here a steady state does not occur but the cell can be used to titrate the sample, i.e., to precisely tune stoichiometry. Cell 1 is an equilibrium cell which allows the determination of total conductivity, dielectric constant or boundary parameters as a function of state parameters. In contrast to cell 1, cell 2 exhibits a chemical gradient, and can be used to e.g., derive partial conductivities. If these oxygen potentials are made of phase mixtures212 (e.g., AO, A or AB03, B203, A) and if MO is a solid electrolyte, thermodynamic formation data can be extracted for the electrode phases. 

For intermediate time resolutions (of the order of r ) the bulk capacitor has become impermeable, and the boundary circuit is relevant for the time dependence (second term in Eq. (64)) term 1 is constant, while term 3 is still zero. Finally in the long-time regime, at t rs, the stoichiometric polarization occurs while both bulk and boundary responses constitute the initial voltage jump from U= 0 to 11 = If (/ , + R ) note that both corresponding capacitors are completely impermeable, i.e., terms 1 and 2 are constant. In the steady state (f rs) all the capacitors block, and R + Kon 316 obtained as the stationary resistance value. Obviously time-resolved dc experiments allow the partial conductivities and the capacitances to be measured together with the chemical diffusion coefficient (ts ccl/Cf). The switching-off behavior is analogous. 

In the case of the asymmetrical cell considered, the voltage variation leads to an one-sided extension of the P0 range, and the detailed evaluation of the correct voltage relation contains easily extractable information on partial conductivities. This is obtained as follows If the Pq2 dependence is a power law (cr oc PtN), Eq. (66) directly leads to... 

Figure 42. Steady-state results of a Wagner-Hebb polarization of Y-doped Z1O2 or TI1O2 with the aid of the cell 0N2, Pt YSZ or YST air, Pt (left, current-voltage curve for Tho.9Yo.1Ch 95 (YST), right partial conductivities for Zro.9Yo.1O1.95 (YSZ)).232 Reprinted from L.D. Burke, H. Rickert, and R. Steiner, Z Phys. Chem. N.F., 74 (1971) 146-167. Copyright 1971 with permission from Oldenbourg Verlagsgruppe.

Figure 43. Temperature dependence of total and partial conductivities of (a) bulk and (b) grain boundary111 in a 0.016 wt% Fe-doped SrTi03 bicrystal at about 2.0 Pa oxygen. The lower electronic and the much lower ionic grain boundary values are due to Mott-Schottky layer (see Part I, Section V).233 Reprinted from X. Guo, J. Fleig and J. Maier, J. Electrochem. Soc., 148 (2001) J50-J53. Copyright 2001 with permission from The Electrochemical Society, Inc.

The steady-state result (Eq. (77)) can be directly used to separate ionic and electronic conductivities the disadvantage of the technique is that it presupposes gas-separation. If not special measures are taken, it becomes unreliable for the ionic transport number less than 1%. Thus, this method well complements the Wagner-Hebb method which is very sensitive to small transference numbers. The partial conductivities of PbO shown in Figure 48 have been de-convoluted by the emf technique just described.3... 

Figure 48. The concentration cell experiment together with impedance spectroscopy allows one to separate ionic (

As the oxygen partial pressure ratio, and hence A/u0, is known, the ambipolar conductivity is readily determined from the flux. This knowledge can be further used to calculate the partial conductivities, and by knowing Ef from the transient (i.e., by also evaluating the delay time231) to derive the thermodynamic factor (i.e., the chemical capacitance). 

As described in Section II.2 variants of the permeation techniques use systems in which electronic and ionic pathways are locally separated, e.g., an ion conductor which is internally short-circuited by percolating metallic inclusions (or materials in which grain boundary and bulk possess different conductivity types (e.g., nano- Ce02)). In all these cases the permeation flux is determined by the lowest partial conductivity. 

In this equation, Oei and Oion are the partial conductivities of oxygen ions and electrons, respectively, and F is Faraday s constant. 

A Partially Conductive and a Partially Semiconductive Ceramic.. 182 7.5 Materials Contrasts in the SFM Non-Contact Mode. 185... 

The following sections will give an overview of our experiments with some partially conducting and some semi-conducting samples, measured either in the contact mode (Sect. 7.5) to obtain ohmic and capacitive currents or in the non-contact mode (Sect. 7.6) to get information about the distribution of surface charges. 

Historically, this method was suggested by Wagner [i] following the work by Hebb [ii], who first proposed to use ion- or electron-blocking electrodes for the determination of partial conductivities in a 4-probe arrange-... 

The first equation shows that the flux of -> charge carriers in an electrochemical system is proportional to the partial conductivity and thermodynamic driving force, namely the electrochemical potential gradient (see Onsager equation). When the chemical potential of... 

The charge carrier may be electronic (either electrons, e, or holes, h) or atomic (cation or anion defects). Each of the partial conductivities is given by the expression ... 

Figure 2.11. Partial conductivities of Ce02. at I atm. of oxygen partial pressure (—) CCO2. 99.9% purity (...) CeOj.j 99.99% purity (-----------) CcOj. single crystal 99.9% purity.

It is obvious that a highly permeable membrane material must exhibit large con-ductivies for both ionic and electronic charge carriers. Partial conductivities of various, so-called mixed ionic electronic conductors (MIEC), as calculated or directly obtained from Refs. 9-21, are presented in Figure 2. 

Figure 2 Ionic and electronic partial conductivities of selected mixed conducting oxides with various Crystal structures YSZ(10 m/o TiOi), (xdfZrQjTtQj)20y," SrFeCog Of at 1000°C, Ceafido,202.s > La 2 r 2 n02, r FeO, s > ...

The concentration of electrons increases with decreasing oxygen partial pressure, while the concentration of electron holes decreases. The above results are summarized in Figure 8, showing the partial conductivities of oxygen ions, electrons and electron holes in YSZ as a function of oxygen partial pressure. ... 

Poly(vinyl alcohol) is typically obtained by alcoholysis of poly(vinyl esters), for example from polyfvinyl acetate) and methanol in the presence of NaOH. The process can be completed or only partially conducted. In this latter case a copolymer (alcohol/ester) is obtained. Other synthetic procedures are used, most of them also based on the hydrolysis of poly(vinyl esters). Poly(vinyl alcohol) is typically used in the atactic form, but isotactic or syndiotactic poly(vinyl alcohols) also are known. 

Evaluation of oj from Eq. (10.10) requires that data exist for the partial conductivities Ojon and Oei as a fimction of oxygen partial pressure between the limits of the integral. In what follows, some special relations for either prevailing electronic or ionic conduction are discussed. 

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