Cation vacancy current

Next, we must develop growth equations for the two oxide layers Lx and Ln. A decomposition of layer N is required in forming layer N — 1, as required by eqn. (261), and so in this respect layer N does not differ from the inner layers. On the other hand, there is no decomposition of a layer N + 1 required to obtain the requisite oxygen, since layer N is already in contact with the gaseous oxygen phase. Thus, there is no equivalent cation vacancy current to be considered, in contrast to the other layers. Neither is there an actual cation vacancy current J l, to be considered. However, there may be oxide evaporation which must be compensated for by the net growth rate of layer N. Thus we obtain... 

Considering now oxide layer 1, there will be no decomposition of that layer required since it is in contact with the parent metal. Thus (dLj /dt)- = 0. Also, we neglect the possibility of a cation vacancy current J(jcv) due to unannihilated vacancies which diffuse into the parent metal instead of annihilating with metal atoms in the parent metal at the metal-oxide interface. Such would constitute a loss of potential oxide formation for layer 1. Another consideration is the positive contribution to the growth rate of layer 1 due to the decomposition of layer 2, so that we can write... 

Cation vacancy and anion vacancy currents can similarly lead to oxide growth. To generalize, we can state that the total oxide growth rate will be the algebraic sum of all such contributions. Mathematically, this can be written as... 

Fig. 8. Schematic diagrams of concentration profiles and the associated particle currents, (a) Cation interstitials or anion vacancies [(dC/dx)<0] and positively directed particle currents ( 0). (b) Cation vacancies or anion interstitials [(dC/dx) > 0] and negatively directed particle currents (J< 0).

Since local space-charge neutrality does not hold at the oxide interfaces, the above expression for the current is restricted to the interior zone [28] where local space charge neutrality has been found [46] to be a good approximation. This is illustrated for the case of cation vacancy (or anion interstitial) and electron-hole diffusion by Fig. 17. Thus, the domain of validity is not 0 but instead is 5 < [Pg.75]

Fig. 20. One of the interior oxide layers labeled i in a sandwich array of multilayered oxides growing by cation vacancy (cv) diffusion illustrated with the relative magnitudes of the negatively directed particle currents through layer i and the adjacent layers i — 1 and i 1.

Assuming known values for the ph qh and R cv> and assuming a known evaporation rate for the oxide, we have a set of N equations for the growth rates dL,/dt of the N layers. This formulation for cation vacancy growth is general from the standpoint that no specific coupled-currents oxidation theory has yet been invoked to evaluate the currents J/cv) through the individual layers. 

The superscript (Oxv) is an abbreviation for oxygen vacancy. Because the newly forming layer i is oxygen-rich relative to the decomposing layer — 1, an additional number of oxygen anions are required in order to utilize all of the cations released in the solid-state decomposition of layer i — 1 at xt = 0 and in the presently considered case, these are provided by a new component of the anion vacancy current generated in layer i by this phase boundary reaction. Since layer i must carry, in addition, the anion vacancy currents generated by the phase boundary reactions at Xi = 0, x2 = 0,. . . , j = 0, we have the identity... 

A recent study of potassium diffusion in KN3 indicates that cation vacancies induced by impurities dominate the diffusion process [217]. Ionic conductivity measurements also indicate that cation vacancies are responsible for the ionic current [218,219]. 

In this model, it is assumed that the total current that is detected in an external circuit upon application of a voltage is the sum of four components (1) electronic current due to the transport of electrons (e ) (2) electronic current due to the flow of electron holes (h) (3) ionic current due to the transport of anion vacancies (V<>) and (4) ionic current due to the movement of cation vacancies (V )... 

Here q is the charge on the moving species x for cation vacancies and +2 for oxygen vacancies for an oxide film of stoichiometry MO a), D is the diflnsivity, and F, R, and T have their usual meanings. The current observed in an external conductor due to the movement of the vacancies is given by Pick s first law, as applied to the metal-film interface ... 

The changes in the film material with the current density, field, and temperature at which the films are made (in dilute, aqueous solution) and the changes which occur on subsequent annealing at temperatures of up to 200 C or so, represent large proportional changes in the concentration of mobile ions, that is, according to the usual theory, in the concentration of defects (interstitial metal ions and anion and cation vacancies). However, the absolute variations in terms of numbers of defects are probably small. Thus the variations in properties, which are not directly functions of defect concentrations, such as refractive index and density, are of the order of 1 %— not large for ordinary formation conditions—whereas the variations in those properties, such as ionic conductivity, electronic conductivity, and rate of dissolution in which are directly dependent on the concentra-... 

Alternating current Angstrom Anion vacancies Magnetic induction Maximum magnetic induction Residual induction Peak energy product Elastic stiffness constant Thermal conductivity Capacitance Cation vacancies Thickness... 

Ap-type metal-deficit oxide contains metal cation vacancies. Cations diffuse in the lattice by exchange with these vacancies. Charge neutrality in the lattice is maintained by the presence of electron holes or metal cations of higher than average positive charge. Current is passed by positively charged electron holes. 

As the electric current passes through this system, the cathode (negative electrode) grows in thickness while the anode (positive electrode) shrinks. At the cathode, M+ ions are converted to M atoms, which results in growth of the cathode. From this observation, it is clear that the cations are primarily responsible for conductivity, and this is the result of a vacancy type of mechanism. In this case, the positive ion vacancies have higher mobility than do the vacancies that involve negative ions. 

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