Lanthanum calculations

Hardness can also be calculated by summation of the individually deterrnined alkaline earths by means of atomic absorption analysis. Basic samples must be acidified, and lanthanum chloride must be added to minimise interferences from phosphate, sulfate, and aluminum. An ion-selective electrode that utilizes ahquid ion exchanger is also available for hardness measurement however, this electrode is susceptible to interferences from other dissolved metal ions. 

B3N6] A [BN3] and N (Fig. 8.11). Band-structure calculations performed for La3(B3N5) revealed a band gap in the order of 4 eV. The corresponding nitridoborate oxide La5(BN3)Og [30] is also salt-Hke, owing the typical nitridoborate structure pattern regarding the environment of the [BN3] ion with lanthanum... 

Based on the results of our band-structure calculations we assume that the metal-like properties of lanthanum nitridoborates are related by B-B interactions between adjacent BNx units in structures. 

With respect to CO oxidation an activity order similar to that described above for CH4 combustion has been obtained. A specific activity enhancement is observed for Lai Co 1-973 that has provided a 10% conversion of CO already at 393 K, 60 K below the temperature required by LalMnl-973. This behavior is in line with literature reports on CO oxidation over lanthanum metallates with perovskite structures [17] indicating LaCoOs as the most active system. As in the case of CH4 combustion, calcination at 1373 K of LalMnl has resulted in a significant decrease of the catalytic activity. Indeed the activity of LalMnl-1373 is similar to those of Mn-substituted hexaaluminates calcined at 1573 K. Dififerently from the results of CH4 combustion tests no stability problems have been evidenced under reaction conditions for LalMnl-1373 possibly due to the low temperature range of CO oxidation experiments. Similar apparent activation energies have been calculated for all the investigated systems, ranging from 13 to 15 Kcal/mole, i.e almost 10 Kcal/mole lower than those calculated for CH4 oxidation. 

Figure 8.15 Calculated composition versus oxygen stoichiometry curves for Lai- SrjCoCb-s. [The two experimental points are taken from data in A. N. Petrov, V. A. Cherepanov, and A. Y. Zuev, Thermodynamics, Defect Structure and Charge Transfer in Doped Lanthanum Cobaltites An Overview, J. Solid State Electrochem., 10, 517-537 (2006).]...

The removal of the radical electron corresponds to the first oxidation process. The resulting cation should be diamagnetic. The first reduction is relatively easy, because filling of the HOMO leads to the closed shell species La Cg2T Theoretical calculations predicted that the location of the lanthanum within the cage is off-center, which allows a stronger interaction with carbon atoms of the fullerene sphere [81- 3]. 

A numerical model to simulate the lattice expansion behavior of the doped lanthanum chromites under a cell operating condition has been proposed, and the deformation of the lanthanum chromite interconnectors has been calculated [33], In the model, the sample deformation is calculated from the profile of the oxygen vacancy concentration in the interconnector. Under a practical cell operation, the oxygen vacancy concentration in the interconnector distributes unevenly from the air side to the fuel side. The distribution of the oxygen vacancy concentration in the interconnector depends on both the temperature distribution in the interconnector and the profile of the oxygen partial pressure at the interconnector surface. Here, a numerical model calculation for the expansion behavior of the LaCrC>3 interconnector under a practical cell operation is carried out, and the uneven distribution of... 

Fig. 5.1. Enthalpies of formation AH 1, for barium and lanthanum fluorides and iodides experimental values for BaX2 and LaX3, otherwise calculated values as explained in text.

The ionic radius can also affect the rate of ion exchange. An example of this is shown in the work of Sharma et al., (1970), who studied the rate of exchange of La3+, Tb3+, and Lu3+ in HC1 using a flow system (Fig. 5.6). Calculated D values are shown in Table 5.4, along with data on ion size. Lanthanum has the largest ionic crystal radius, while Lu3+ has the smallest. The hydrated size of the ions is in the order Lu3+ > Tb3+ > La3+. 

Positronium (Ps) annihilation probability in the nanovoids of the samples in initial state is found to be 11.13 %, whereas the mean nanovoid radii for the crystalline and liquid-crystalline samples are 0.33 and 0.28 nm, respectively. After dissolution of Cgo fullerenes probability of Ps annihilation in nanovoids is decreased by the factor of 2.7. The general spectrum of lanthanum laurate initial pattern is presented in the Fig. 1. The calculated parameters of the investigated patterns are resulted in the Table 1. 

TABLE 1. Parameters of ACAP spectra and the calculated sizes of nanovoids in lanthanum laurate patterns... 

Lanthanum to nitrogen bonds are present in the mixed COT complexes [242]. Cerium(IV) forming stable complexes with COT, Ce(COT)2 is characterized. Self-consistent field calculations showed [243] the ground state of cerocene to be almost entirely 4/ corresponding to the formula Ce3+(COT -5)2 rather than Ce4+(COT2)2 The methyl substituent in COT stabilizes the Ce(IV) complex which has a non-linear Cg-Ce-Cg angle of 176°. The two COT substituents are not staggered, and they are equidistant from cerium. 

The eight-coordinate tetrakis(diethyldithiocarbamate) lanthanide complexes are isomor-phous and the lanthanum complex has a quasi-tetrahedral configuration of the four CS2 chelate groups. The transition frequencies and dipole strengths of these complexes available over the accessible f-f manifold allowed the extraction of the Judd-Ofelt intensity parameters Qx for k = 2, 4, 6 by standard least squares methods [112,113]. The values of observed Qx and calculated Q, values are given in Table 8.10. The three components of f2() are... 

Thulium with f12 configuration has a ground state 3 6- It resembles Pr3+ with f2 configuration except for the reversal of ground level multiplets. The energy levels of Tm3+ in lanthanum ethyl sulphate nonahydrate matrix have been calculated and observed using the best fit parameters [179] A (r2) 129.8 cm-1 A (r4) — 71.0 cm 1 A°(r6) — 28.6 cm A66(r6) 432.8 cm-. ... 

He(I) photoelectron spectra of lanthanum tris-yS -diketonate complexes have been studied and the spectra interpreted on the basis of quantum chemical calculations of ground and ionized states by X -DV and ab initio methods [54]. The comparative analysis of the photoelectron spectra of Sc, and Lu tris-acetylacetonates showed that substitution of one oxygen atom by NH group shifts the two pairs of n and n orbitals to a different extent. The IE (ionization energy) values for (e) and 7T3 (ai) orbitals decreased by 0.8-1.0 eV. The n and n+ molecular orbital two pair bands showed a weak shift of 0.1 eV or less. 

If the BVS rule is not satisfied (i.e. when the BVS are not very near to the formal charges for the ions) this may indicate metastability. In LaNiOa.s, for example, BVS calculations give a lanthanum valence of -1-2.63 and valences of -1-2.20 and -1-2.13 for the octahedral and square planar nickel cations, respectively. Although the Ni cation prefers square planar coordination, this oxide readily takes up oxygen upon heating in undergoing a stmctural transition to the perovskite LaNiOs, where the BVS are -1-3.05 and -1-3.01 for lanthanum and nickel, respectively (Alonso et al., 1997). The following worked example illustrates how to use Eqs. 3.20 and 3.21 with Table 3.7. 

If the values of the parameters used in the calculation are compared, the determining factor is the much lower value of I4 for cerium (3547 kJ/mol compared with 4819 kJ/mol for La) due to the fact that the fourth electron is being removed from a different shell (nearer the nucleus) in the case of lanthanum. 

Question 2.3 Assuming lattice energies for CeFs and Cep4 of —4915 and —8391 kJ/mol respectively, and using the same enthalpy of atomization and electron affinity for fluorine as in the lanthanum examples (Section 2.9.1.), calculate A7/f for Cep3 and Cep4. Take an enthalpy of atomization of 398 kJ/mol for cerium (Table 2.6). Use ionization energies from Table 2.2. 

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