Perovskites matrix elements

The SNMS depth profile (ion intensity as a function of sputter time) for the matrix elements of a Ba07Sr03TiO3 layer on a silicon substrate with Pt/Ti02/Si02 buffer layers is illustrated in Figure 9.8. Inhomogeneity of the perovskite layer was detected especially for Sr. Furthermore, an interdiffusion of matrix elements of the Ba07Sr03TiO3 layer and of the Pt barrier layer was observed. 

Depth profiles of matrix elements on Mn- and Co-perovskite layers of fuel cathodes have been measured by LA-ICP-MS in comparison to other well established surface analytical techniques (e.g., SEM-EDX).118 On perovskite layers at a spatial resolution of 100p.m a depth resolution of 100-200 nm was obtained by LA-ICP-MS. The advantages of LA-ICP-MS in comparison to other surface analytical techniques (such as XPS, AES, SIMS, SNMS, GD-OES, GDMS and SEM-EDX) are the speed, flexibility and relatively low detection limits with an easy calibration procedure. In addition, thick oxide layers can be analyzed directly and no charging effects are observed in the analysis of non-conducting thick layers. 

TABLE 5.1. Interatomic Matrix Elements for the Transition Metal Perovskite Oxides... 

Mattheiss fitted his calculated bands with LCAO bands, much as we did for tetrahedral solids in Chapter 6. We used the parameters for these tetrahedral bands to adjust the coefficients giving the matrix elements in Table 2-1, and then used those coefficients in all of the studies of. sp-bonded materials. In a similar way we shall use the results of Mattheiss s fit for the perovskites to adjust the coefficents in the expressions for sd and pd matrix elements, which will be derived in Chapter 20. These are listed in the Solid State Table and will be used wherever needed. 

A perovskite-structure system, KNiFs, which does form a multiplet structure and is an antiferromagnetic insulator, was treated by Mattheiss (1972b) in the same way other perovskites were treated he obtained the parameters for this system also, using an LCAO fit. The interatomic matrix elements he obtained,... 

To calculate the properties in terms of the perovskite gliosts, we will need a covalent energy, equal to the matrix element between a (x-oriented [Pg.457]

Matrix elements associated with the u-oriented d states and oxygen, sp hybrids that make up the perovskite ghost. 

Before making application of this formula to tlie perovskites, let us make a brief application to ionic crystals- we summarized the results of this application in Chapter 13 -and to simple tetrahedral solids. In the alkali halides, we focus upon the occupied p states in the halogen ion and calculate the chemical grip associated with interaction of the halogen ion with the alkali, v stales. These arc the same couplings that were included in the calculation of ion softening in Section 14-C. The coupling W2 of Eq. (19-29) becomes the matrix element = 1.84 h /(md ), and 2W i, is to be identified with the = 9.1 h l(nul ) used in Table 14-2. Then (Eq. 19-29) becomes... 

The unrestricted and restricted open-sheU Hartree-Fock Methods (UHF and ROHF) for crystals use a single-determinant wavefunction of type (4.40) introduced for molecules. The differences appearing are common with those examined for the RHF LCAO method use of Bloch functions for crystalline orbitals, the dependence of the Fock matrix elements on the lattice sums over the direct lattice and the Brillouin-zone summation in the density matrix calculation. The use of one-determinant approaches is the only possibility of the first-principles wavefunction-based calculations for crystals as the many-determinant wavefunction approach (used for molecules) is practically unrealizable for the periodic systems. The UHF LCAO method allowed calculation of the bulk properties of different transition-metal compounds (oxides, perovskites) the qrstems with open shells due to the transition-metal atom. We discuss the results of these calculations in Chap. 9. The point defects in crystals in many cases form the open-sheU systems and also are interesting objects for UHF LCAO calculations (see Chap. 10). 

The majority of radionuclides (>90%) generated during in-reactor burning are retained in the U oxide matrix hence, their release should be closely related to the corrosion rate of the matrix. The release of Cs and I are generally independent of the fuel corrosion rate, and the metallic elements (Mo, Ru, Tc, Rh, Pd), Xe-Kr gas bubbles, and perovskite phases ((Ba,Sr)Zr03) may only be partly controlled by the matrix corrosion rate. 

This chapter has been devoted to the piezoelectric performance of modem composites based on perovskite ferroelectric PbTiOs or its solid solutions. Modelling and effective-property predictions have been carried out for the matrix a-3 composites with stmctures shown in Figs. 1 and 7. It should be noted that elements of the hierarchical chain singledomain SC of PbTiOs - polydomain SC of PbTiOs - poled FC of modified PbTiOs are... 

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