Effective moments

The effective moment of inertia / and the friction coefficient / could easily be estimated. The force constant k associated with the relative motion of the lobes was determined from an empirical energy function. To do so, the molecule was opened in a step-wise fashion by manipulating the hinge region and each resulting structure was energy minimized. Then, the interaction energy between the two domains was measured, and plotted versus 0. 

Magnetic Properties. The magnetic susceptibilities of the ferrous and ferric porphyrazines 11,13, and 16a-d are reported in Table IV. For 11, which is a square-planar d6 system, the effective moment of 3.82 is consistent with a... 

Five isotopomers of Sia were studied in Ref (20), and are labeled as follows Si- Si- Si (I) Si- Si- Si (II) Si- Si- Si (III) Si- "Si- Si (IV) Si- Si- °Si (V). Rotational constants for each (both corrected and uncorrected for vibration-rotation interaction) can be found towards the bottom of Table I. Structures obtained by various refinement procedures are collected in Table II. Two distinct fitting procedures were used. In the first, the structures were refined against all three rotational constants A, B and C while only A and C were used in the second procedure. Since truly planar nuclear configurations have only two independent moments of inertia (A = / - 4 - 7. = 0), use of B (or C) involves a redundancy if the other is included. In practice, however, vibration-rotation effects spoil the exact proportionality between rotational constants and reciprocal moments of inertia and values of A calculated from effective moments of inertia determined from the Aq, Bq and Co constants do not vanish. Hence refining effective (ro) structures against all three is not without merit. Ao is called the inertial defect and amounts to ca. 0.4 amu for all five isotopomers. After correcting by the calculated vibration-rotation interactions, the inertial defect is reduced by an order of magnitude in all cases. 

Curium metal was found to be antiferromagnetic Its Curie-WeiB behaviour above the Neel point is in good agreement with the localized picture (pett = 8 Pb as in Gd metal). In the case of Bk, again the Curie-WeiB law gives the expected effective moment value ... 

Then, curium metal is antiferromagnetic and its paramagnetic effective moment definitively supports the picture of a localized 5 f configuration the same is true for what is known about berkelium and californium metals ... 

The effective and ordered moments in a cubic crystal field were also calculated using the obtained gj values and the wave functions given by Lea, Leask and WolP In the case of the Tg quadruplet the magnetic moment is anisotropic and depends upon the crystal field parameter x. The effective moment is space averaged and given as a function x ° The value of the ordered moment along (001) is given as a function of x also. 

Within L-S coupling the ground state multiplet is leading to an effective moment Heff = 3.38 Xb (see Table 3) which is slightly higher than the experimental value Peff = 3.2 Pb thus J mixing is small and the ground state is essentially H4 (Chan and Lam ... 

At the beginning of this section we said that a localized picture is very often the best starting point for U, Np and Pu compounds. Is there any clear-cut criterion to direct us in the way of itinerant magnetism Good experimental evidence seems to be - a reduced ordered moment (in particular when it is incompatible with the effective moment in the crystal field scheme ) and - a large electronic specific heat (> 10 mJ/mol K ) and - a reduced magnetic entropy at the transition ( RLn2)... 

Table 8. Bare ( ) and corrected values for the constant susceptibility and the effective moment of plutonium monopnictides...

Fig. 8. Angular distribution of the 4f charge density of lanthanide atoms for Jz = J (effective moment parallel to the z-axis). After Thole in Coehoom (1990). In Ce, Pr, Nd, Tb, Dy, Ho the charge density is oblate (aj < 0), in Pm, Sm. Er, Tm, Yb it is prolate (aj > 0). In Gd, Lu (L = 0), the charge density has spherical symmetry.

We see from (4.104) that, although the vibrational quantum number is not changing, the frequency of a pure-rotational transition depends on the vibrational quantum number of the molecule undergoing the transition. (Recall that vibration changes the effective moment of inertia, and thus affects the rotational energies.) For a collection of diatomic molecules at temperature T, the relative populations of the energy levels are given by the Boltzmann distribution law the ratio of the number of molecules with vibrational quantum number v to the number with vibrational quantum number zero is... 

The fifth term in (4.67) represents an interaction between vibration and rotation, and ae is called a vibration-rotation coupling constant. [Do not confuse ae with a in (4.26).] As the vibrational quantum number increases, the average internuclear distance increases, because of the anharmonicity of the potential-energy curve (Fig. 4.4). This increases the effective moment of inertia, and therefore decreases the rotational energy. We can define a mean rotational constant Bv for states with vibrational quantum number v by... 

In 1939 Klemm and Doll [276] prepared all the halides of divalent europium and studied the magnetic characteristics of these compounds. The magnetic susceptibilities (X g) and effective moments of the fluoride, chloride, bromide and iodide are tabulated in Table 15. Except for the... 

Table 15. The magnetic susceptibilities (xg) and effective moments of europous halides [276]...

The manifold of energy levels for small J then has the appearance shown in Fig. 7. In higher approximation it would be necessary to take account of centrifugal distortion which causes the effective moments of inertia to increase slightly with J. For highly asymmetric tops the evaluation of the energy levels is difficult but approximate values can be interpolated from published tables (Erlandsson, 1956 King ef al., 1943, 1949). 

I is the effective moment of inertia of a dipole (we consider here a linear molecule), determined by the relation (149). The spectral function L(z), calculated for thermal equilibrium, is linearly related to the spectrum C° of the dipolar autocorrelation function (ACF) C°(f) (VIG, p. 137 GT, p. 152) as... 

It should be noted that relation (2.51) is valid within the sudden approximation. However, the relaxation of heavy particle impurities typically involves motion that is slow compared with vibrations of the host lattice (i.e., the tunneling takes place in the adiabatic limit). The net effect of the adiabatic approximation is to renormalize the effective moment of inertia of the particle. This approach was used, for example, to describe vacancy diffusion in light metals. The evolution of the rate constant from Arrhenius behavior to the low-temperature plateau was described within the framework of one-dimensional tunneling of a... 

NdRu4Sbi2 is metallic and undergoes some type of magnetic transition near 1.3 K. The magnetic susceptibility follows a Curie-Weiss law above 50 K with an effective moment of 3.45/u.b and a Weiss temperature of -28 K. Crystal fields likely effect the susceptibility and magnetic interactions for temperatures below 50 K. Low temperature heat capacity data confirm the bulk nature of the magnetic transition (Takeda and Ishikawa, 2000b). 

EuFe4Pj2 is metallic and orders ferromagnetically for temperatures below 100 K (Grandjean et al., 1984). The effective moment, as determined from the high temperature magnetic sus-... 

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