Donor-Doped Case

It can now be assumed that the BaTiOj is doped with a fixed amount (y) of donor impurities D on, for example, the cation sites (D ). They are again assumed to be fixed-valent, but this time to be occupying Ba-site instead, or D, for example, Lsi . The lattice molecule may then be represented as  

As one more unknown [Dg ] is added similarly to the acceptor-doped case, one mass-conservation equation for the dopant is added to Eqs. (3)-(6) as  

In addition, the charge neutrality and site conservation conditions [Eqs. (7) and (8)] are modified, respectively, to  

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TaUe 10.1 Matrix of majority disorder types in the systems of BaTi03- The top left rectangle demarcated by thick solid lines is for the pure case this rectangle plus the rightmost column for the acceptor-doped case and the rectangle plus the bottom-most row for the donor-doped case. 

For an acceptor doped oxide the temperature dependence of the concentration of holes will be qualitatively analogous to that of electrons in the donor doped case (cf. Fig. 6.4) with the same constrictions. 

As in the case of donor doping, only one of these options will be preferred in a particular partial pressure regime, depending upon the values of the various equilibrium constants. 

Donor-doped PZTs have higher permittivities and d coefficients than acceptor-doped materials and are therefore more suitable for converting mechanical into electrical vibrations. They have higher dissipation factors than acceptor-doped materials and are therefore not as suitable for wave filters. If this were not the case, their low ageing coefficients would be an advantage. 

Returning to the n-type doping case, the total energy of the donor-defect pair is... 

In the case of Teflon the QP band structure67 is similar to that of PE (broad valence and conduction bands), but it is strongly shifted downwards due to the effect of the four negative F atoms in the unit cell. The lower limit of the conduction band lies at — 5.5 eV,67 which indicates the possibility of donor doping which could cause n-conduction in it. 

For the system of BaTi03, the equilibrium conductivity has been the most extensively documented (see, e.g.. Refs. [8, 10, 11]) over the experimentally viable range of —20 < log < 0 at elevated temperatures, although the remaining variable, OxiOj or t] has not been explicitly specified. Figure 10.6a-c shotvs the typical results for the pure [10, 12], acceptor (AlTi)-doped [13], and donor (LaBa)-doped cases [11], respectively. 

Although large amounts of potassium were inserted in the polymer (0.54 mole of K per mole of monomer) it should be noted that the final conductivity value is much lower than that attained with AsFs (500 S cm for 0.24-0.42 mole of AsFs per mole of monomer). This result might indicate that the mobility of electrons is either significantly less than that of holes or that the potassium-doped sample has a higher interparticle resistance than the AsFs-doped PPP. A less likely possibility is that the average charge transfer is less pronounced in the case of K than for AsFs. The fact that the stability of the donor-doped PPP (K or Na) was less than that of the AsFs-doped PPP could also explain why the conductivity of K-doped PPP is lower than that of AsFs-doped PPP [4,186]. 

In a manner equivalent to the above case we may construct a diagram showing the situation in the same host oxide M2O3 now donor-doped with a... 

Raman spectra have also been reported on ropes of SWCNTs doped with the alkali metals K and Rb and with the halogen Br2 [30]. It is found that the doping of CNTs with alkali metals and halogens yield Raman spectra that show spectral shifts of the modes near 1580 cm" associated with charge transfer. Upshifts in the mode frequencies are observed and are associated with the donation of electrons from the CNTs to the halogens in the case of acceptors, and downshifts are observed for electron charge transfer to the CNT from the alkali metal donors. These frequency shifts of the CNT Raman-active modes can in principle be u.sed to characterise the CNT-based intercalation compound for the amount of intercalate uptake that has occurred on the CNT wall. 

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