Values of CFSE

Draw energy level diagrams to represent a high-spin electronic configuration. Confirm that the diagram is consistent with a value of CFSE = 0.4A ct. 

Since the splitting parameter in the tetrahedral field is smaller than in the octahedral field, the tetrahedral field is always a weak field, Aptetrahedral field, the highest values of CFSE correspond to d and d configurations. Figure 3.9 presents the comparative crystal field splitting of d orbitals of the central ion in complexes of geometry tetrahedral, octahedral, tetragonal, and square-planar. 

Table 1.19 Lattice energy and CFSE for selected spinel compounds. Values of U, E, and from Ottonello (1986). CFSE values calculated with values proposed by McClure (1957). Data in kJ/mole x = degree of inversion.

Somewhat better data are available for the enthalpies of hydration of transition metal ions. Although this enthalpy is measured at (or more property, extrapolated to) infinite dilution, only six water molecules enter the coordination sphere of the metal ion lo form an octahedral aqua complex. The enthalpy of hydration is thus closely related to the enthalpy of formation of the hexaaqua complex. If the values of for the +2 and +3 ions of the first transition elements (except Sc2, which is unstable) are plotted as a function of atomic number, curves much like those in Fig. 11.14 are obtained. If one subtracts the predicted CFSE from the experimental enthalpies, the resulting points lie very nearly on a straight line from Ca2 lo Zn2 and from Sc to Fe3 (the +3 oxidation state is unstable in water for Ihe remainder of the first transition series). Many thermodynamic data for coordination compounds follow this pattern of a douUe-hunped curve, which can be accounted for by variations in CFSE with d orbital configuration. 

The crystal field spectra and derived A0 and CFSE parameters for several garnets containing octahedrally coordinated trivalent transition metal ions are summarized in table 5.3. The values of A0 and CFSE reflect the variations of metal-oxygen distances in the garnet structures. 

For the pseudo-tetragonally elongated Ml octahedral site in the olivine structure, an alternative method for obtaining the CFSE of Fe2+ ions in this site is to evaluate the ligand field splitting parameters in the equatorial plane and along the axial direction using eqs (3.14) to (3.16). The crystal field spectral data for the fayalite Ml site (see fig. 5.11a) yield values for 10 Dq(m) and 10 Dq(eq) of 8,172 cm-1 and 9,327 cm-1, respectively. The mean 10 Dq value of 8,942 cm-1 and the CFSE of 4,133 cm-1 compare favourably with A0 = 8,830 cm-1 and CFSE = 4,250 cm-1 for Fe2+ in the fayalite Ml sites determined by the baricentric method (fig. 5.11a). 

The value of A, and hence the calculated CFSE, for Ni2+ ions in the olivine Ml sites appears to be anomalously high compared to values acquired in other octahedral sites in oxide structures, including bunsenite and MgO (table 5.1), Ni2Si04 spinel ( 5.4.3), and other phases listed later (table 5.19). The dis-crepency results from incorrect assignments of bands i and j listed in table 5.4... 

The polarized spectra of staurolite, Fe2Al9Si4023(0H), accomodating tetrahe-drally coordinated Fe2+ ions (point symmetry Cm mean Fe-0 = 200.8 pm) and consisting of absorption bands spanning the 5,000 to 7,000 cm-1 region (Bancroft and Bums, 1967a Dickson and Smith, 1976), are illustrated in fig. 4.6 and discussed in 4.4.3. These bands completely mask any contributions from Fe2+ ions that might be present in centrosymmetric octahedral sites in the staurolite structure. The A, and CFSE parameters of tetrahedral Fe2+ ions in staurolite are estimated to be about 5,300 cm-1 and 3,700 cm-1, respectively. The spectra of the cobaltian staurolite, lusakite, illustrated in fig 4.7, indicates that tetrahedrally coordinated Co2+ ions have A, and CFSE values of about 6,500 cm-1 and 7,800 cm-1, respectively. 

The optical spectra of blue tourmalines have attracted considerable attention focused mainly on assignments of Fe2+ —> Fe3+ IVCT bands, positions of crystal field bands for Fe2+ ions expected to be located in two different octahedral sites, and intensification mechanisms of these crystal field bands (e.g., Faye et al., 1968., 1974 Wilkins et al., 1969 Bums, 1972a Smith, 1977, 1978a Mattson and Rossman, 1984,1987b). Curve-resolved spectra yielded two sets of paired bands (Faye et al., 1974). One set at 14,500 cm-1 and 9,500 cm-1 assigned to Fe2+ in the Al or c-site (point group Q mean Al-O = 192.9 pm) yielded A0 and CFSE values of about 11,000 cm-1 and 4,900 cm-1, respectively. The second set of bands at 13,200 cm-1 and 7,900 cm-1 attributed to Fe2+ in the Mg or b-site (point group Cm mean Fe-O = 202.5 pm) provided A0 and CFSE values of approximately 10,000 cm 1 and 4,500 cm-1, respectively. 

Chloritoid. Optical spectra of chloritoids, again studied mainly on account of the Fe2+ —> Fe3+ IVCT band at 16,300 cm-1 (Faye et al., 1968 H lenius et al., 1981), also contain features assignable to CF transitions in Fe2+ ions. These cations are located in the M1B positions in brucite layers which are surrounded by four OH" ions and two trans- non-bridging oxygens belonging to isolated [Si04] tetrahedra in silicate layers in the chloritoid structure. The two absorption bands at 10,900 cm-1 and 8,000 cm-1 yield approximate values of A0 = 9,000 cm-1 and CFSE = 4,050 cm-1, respectively, for the Fe2+ ions. 

The values of Fe2+ CFSE s that are derived throughout this chapter by assuming baricentric splittings of t2g and eg orbitals in low-symmetry or distorted sites are listed in table 5.16 (see also fig. 7.6). For minerals hosted by Al3+ ions, the CFSE values are seen to decrease in the order... 

The CFSE values of Ni2+-bearing minerals summarized earlier in table 5.19 decrease in the order... 

Consider two phases a and /J containing octahedral sites available for cation occupancy. The distribution of cations between these sites will depend on the relative values of the CFSE for the two sites. If CFSE > CFSE 1, then the Nemst distribution coefficient, D, expressing the concentration ratio of transition element, M, between the two phases... 

A large negative value of AEa implies that a cation gains stability by forming an activated complex with pentagonal bipyramidal or square pyramidal symmetry. On this basis, cations such as Fe2+, Co2+, Ti3+, and V3+, as well as the 3d5 cations with zero CFSE, are predicted to show rapid reaction rates of substitution or leaching from a crystal structure. 

A The general trend to more exothermic values with increasing atomic number is attributable to the decrease in ionic radius across the period because, as the anion-cation separation becomes smaller, the lattice enthalpy increases (equation 3.3). Superimposed on this trend is the effect of CFSE values. These are small in comparison to the overall magnitude of A// , but nonetheless have a significant effect. The double dip in the plot may be accounted for in terms of the variation in high-spin CFSE values across the first-row d-block. as shown in Figure 6.3. This shows respective CFSE contributions to of -(YsfA j for Ti-", -(V Aq for... 

A This involves comparing 0Dq with the pairing energy (PE) to determine that the complex is low spin. The crystal field splitting diagram shows the electron configuration from which the value of the CFSE can be calculated ... 

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