The effects of temperature on μeff

   So far, we have ignored the effects of temperature on μ_eff. If a complex obeys the Curie Law (equation 1.2), then μ_eff is independent of temperature; this follows from a combination of equations 1.1 and 1.2.

                    (1.1)

                                       (1.2)

 where C = Curie constant; T = temperature in K.   However, the Curie Law is rarely obeyed and so it is essential to state the temperature at which a value of μ_eff has been measured. For second and third row d-block metal ions in particular, quoting only a room temperature value of μ_eff is usually meaningless; when spin–orbit coupling is large, μ_effis highly dependent on T.

Fig. 1.1 Kotani plot for a t_2g⁴ configuration; λ is the spin– orbit coupling constant. Typical values of μ_eff(298 K) for Cr(II), Mn(III), Ru(IV) and Os(IV) are indicated on the curve.

For a given electronic configuration, the influence of temperature on μ_effcan be seen from a Kotani plot of μ_eff  against kT/λ where k is the Boltzmann constant, T is the temperature in K, and λ is the spin–orbit coupling constant. Remember that λ is small for first row metal ions, is large for a second row metal ion, and is even larger for a third row ion. Figure 1.1 shows a Kotani plot for a t₂g⁴ configuration; four points are indicated on the curve and correspond to typical values of μ_eff(298 K) for complexes of Cr(II) and Mn(III) from the first row, and Ru(IV) and Os(IV) from the second and third rows respectively. Points to note from these data are:

• since the points corresponding to μ_eff(298 K) for the first row metal ions lie on the near-horizontal part of the curve, changing the temperature has little effect on μ_eff;
• since the points relating to μ_eff(298 K) for the heavier metal ions lie on parts of the curve with steep gradients, μ_eff is sensitive to changes in temperature; this is especially true for Os(IV).