Copper vacancy concentration

K the copper thermal difihisivity DqC = 2.11-10 mVs for T=543K according and y is about 0.3 J/m for pure copper and depends on the CEC content for the case of Ni and others additional impurities the actual single vacancy concentration, Cvi, is estimated by it s steady state value, Cvst, ... 

The steady state does not involve the movement of ions. These are blocked by the ion blocking electrode, graphite. Moreover, the concentration of species available for migration [interstitial copper and copper vacancies in the case of CuCl) is much larger than that of the electron holes. Consequently, on application of E, the relative conoentration of electron holes is greatly affected while the concentration of copper ions is virtually unaffected. Hence [d x + /d x) = and because no ions move, [8cl)/8x) == 0 as shown in the diagram. Further details are available in reference 8. 

The values of the equilibrium constant may be computed from Eq. (8). Burton has shown that vacancy formation entropies in cubic metals range from 3.6 to 5.2 e.u. For the case of copper, a value of 3.8 e.u. was computed. The energy of vacancy formation has been estimated to be about 23 kcal/mole. Thus at 1000°K, Ky for copper is found to be 6 x 10 from Eq. (8). Assuming [1 ] ci 1, this value would also correspond to the vacancy concentration according to Eq. (13). 

Your supervisor suggests that the total copper concentration will be reduced if Si is doped with phosphorus. Write defect equilibria equations for the incorporation of each of these species to examine the effect of phosphorus doping on each type of Cu impurity. At what concentration of P will you get the minimum total Cu concentration. By how much will the amount of Cu be reduced over intrinsic Si Assume that the silicon vacancy concentration does not change with impurity concentration. 

In terms of formal point defect terminology, it is possible to think of each silver or copper ion creating an instantaneous interstitial defect and a vacancy, Ag and VAg, or Cu and Vcu as it jumps between two tetrahedral sites. This is equivalent to a high and dynamic concentration of cation Frenkel defects that continuously form and are eliminated. For this to occur, the formation energy of these notional defects must be close to zero. 

For example, at 1200°K — F(2) must be greater than 0.24 eV in order that the two correction terms differ by less than 10%. However, for the small defect concentrations of interest here (e.g. c,w6x 10-5 for Fv — 1.0 eV in copper) the correction due to the vacancy-pair term is unimportant for much smaller values of — Fl2) so that differences are not practically very important. The terms of order (c°)3 are more difficult to compare and the numerical values depend on the relative magnitudes of Fw and F((123 ), as can be seen by noting that the sum of products of /-functions in Bs is equivalent to... 

In deriving Eq. (36), and hence Eq. (38), it was assumed that the induction time is dominated by the time required to accumulate a critical areal concentration of cation vacancies (i.e., the formation time of the vacancy condensate). However, as evident from Fig. 33, the induction time may exceed the vacancy condensation time by the amount required for the film to dissolve locally and rupture. We previously lumped these effects into the relaxation time, r, and for the pitting of metals such as iron, copper, nickel, and stainless steels, which form very thin barrier layers, this approximation appears to be reasonable, in that Eq. (36) accounts for the experimental data very well. It is possible, however, to envision a case where the time... 

Abstract The Lifshitz - Slezov theory is applied to study the metastable states of the matrix damage clusters, MA, and the copper enriched clusters, CEC, in neutron irradiated steels. It was found that under irradiation conditions the CE Cs are at the Ostwald stage for a neutron fluence of about 0.0002 dpa. The time dependence of number density, MDn, is determined by summarizing all differential equations of the master equation for MA with neglecting of dimmers concentration in comparison with concentration of the single vacancies and subtraction of the number CEC that replace the MA, namely vacancy clusters, due to the diffusivity of copper and other impurity atoms to them. For binary Fe-0.3wt%Cu under neutron irradiation with dose 0.026, 0.051, 0.10 and 0.19 dpa the volume content of the precipitates from the SANS experiment is found to be about 0.229, 0.280, 0.237 and 0.300 vol% respectively. The volume fraction of CEC, in these samples is 0.195 vol% and the calculated volume fraction ofMA is 0.034, 0.085, 0.042 and 0.105 vol% for doses 0.026, 0.051, 0.10 and 0.19 dpa respectively. 

In this study samples were prepared which contained controlled concentrations of both anion and cation vacancies. All samples were prepared by dissolving copper (S-9 s Aesar Chemical Co.) and La203 (4-9 s Aesar Chemical Co.) in 1 1 dilute nitric acid. The solution was evaporated on a hot plate to dryness, then placed in a furnace,... 

From Eq. (11.3), it is apparent that higher partial pressures of oxygen for p-type semiconductors must be accompanied by higher concentrations of vacancies and holes at the 02-oxide interface. Hence, copper oxidizes at higher rates the higher the oxygen pressure, in accord with prediction [25]. 

That is, the concentration of cation vacancies is proportional to the eighth root of the partial pressure of oxygen in the case of the above mentioned ideal conditions. Now, in CU2O the transport number of the electronic charge carriers is one, and the diffusion of copper ions via vacancies is rate-determining. Thus, if local defect equilibrium is assumed, it follows from eq. (8-14) that the component diffusion coefficient varies as p l according to the equation ... 

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