Bleaney’s factors

Cj Bleaney s factor of lanthanide / (scaled to —100 Tr(z) trace of the magnetic susceptibility tensor... 

Spin expectation values3 (Sz) and Bleaney s factors 3 C for /f(III) free ions at 300 K, and rhombic proportionality factors0 cr lombio... 

The first numerical terms C = P2 1 + p) j / (l20(kT)2) are often referred to as Bleaney s factors and their relative values (scaled to Coy = -100) have been tabulated at 300 K for any 4f configurations including excited states contributions (table 3, Bleaney et al. (1972)). Finally, the introduction of the geometrical factors defined by eqs. (30), (31) together with C into eq. (41) gives the classical eq. (42) for the pseudo-contact shifts according to Bleaney s approach (Forsberg, 1996)... 

Magnetic anisotropies xlz (l/3)Tr/ for R = Ce-Yb except Pm, Gd (0.002 < AFj < 0.06, table 9) have been computed with eq. (58) and using five contact contributions Sfj (i = H9, H11-H14) and the geometrical G factors obtained from the crystal structures of (HHH)-[/ Co(L5)3]6+ (R = La, Lu). A qualitative good agreement (AF = 0.23) is obtained between the experimental magnetic anisotropies (scaled to -100 for Dy(III) and corrected for the variation of the crystal-field parameter near the middle of the series (vide supra), table 9) and Bleaney s factors (table 3). Further non-linear least-squares refinements of the molecular... 

A Fermi hyperfine constant for a nucleus i bJ crystal-field parameters of rank k spherical tensor operators of rank k Cj Bleaney s factor of lanthanide j (scaled to -100... 

Surprisingly, Bleaney s factors Cj determined at 300 K (table 3) are used without corrections for the treatment of the experimental NMR data recorded at 343 K. This approximation is probably justified for most i (Iir) except for / = Sm and Eu (see sect. 2.3), but the poor correlations exhibited by the vs (5j)y jCj plots might result from inadequate values... 

For homopoly metallic axial complexes, the spin expectation values and Bleaney s factors are identical for all metallic sites ((S ) = S )j and = Cj) and can be factorized out to give eq. (62) which can be linearized according to the method proposed by Reilley etal. (1975) for monometallic complexes (eqs. (63), (64), Elhabiri et al. (1999)),... 

Obviously, the use of eq. (38.6), which considers only the first term in the expansion of the Boltzmann factors, with g-tensor components weighted by unequal populations of the corresponding levels is a contradiction in terms and as could be anticipated leads to erroneous results. It is thus clear that Bleaney s theory accounts satisfactorily for the dipolar shifts in lanthanide complexes, whereas the criticisms of this theory, Horrocks et al. (1973), seem to be not well founded. We wish to emphasize that the generalized treatment of Golding and Pyykko (1973) is of course more rigorous. 

Values of (r" ) are based primarily on theoretical calculations of the 4f wave functions, for example, those of Freeman and Watson (1962) and of Judd (1963). In table 18.5 are listed the values of (/ N /), (r ), and Hfs for the tripositive rare-earth ions. Strictly speaking, correction factors differing from unity by a few percent should be applied to these (/ M /) values [Bleaney (1972)] to take account of intermediate coupling effects which arise from the admixture into the ground state (L, S, J) wave function of states of different L, S, but the same /, by the spin-orbit interaction. A table of these values is included in Bleaney (1972). 

---