Crystal Fields at RareEarth Ions
Abstract
The object of this paper is to find out why the calculated rareearth crystalfield parameters do not agree with those determined experimentally. As is well known, in explaining the 4f spectra in the rareearth compounds, one needs relatively few crystalfield constants, V_{n}^{m}'s. These V_{n}^{m}'s have been measured for many rareearth ions in LaCl_{3}, ethylsulfates and other lattices. One can study the V_{n}^{m}'s in a given lattice as the nuclear charge is varied (starting from Ce, Z=58 to Yb, Z=70). For a given n and m one finds that the V_{n}^{m}'s vs Z vary fairly smoothly. However, when the crystal fields are calculated using an ionic model one cannot get good agreement with the V_{n}^{m}'s. In general, neither the magnitude nor the Z dependence of the V_{n}^{m}'s can be reproduced. The calculated crystalfield parameters are written as: (1αn)<r^{n}>Anm, where α_{n} is the shielding factor (the outer 5s^{2}p^{6} electrons to some extent shield the inner 4f electrons from the crystal field), <r^{n}> is the expectation value of r^{n} over the 4f electrons, and A_{n}^{m} is a lattice sum over the charges in the lattice that produce the crystal field. To try to determine why the agreement is bad, the effect of the lattice in altering the values of α_{n} and <r^{n}> was calculated. However, the principle trouble appears to come from the A_{n}^{m} values. Anm∝∼1/R^{n+1}, where R is the distance between the rareearth ion and the charges in the lattice that produce the crystal fields. For the important n=4 and 6 lattice sums one gets very rapid convergence. The A_{n}^{m} sums are usually calculated assuming the lattice can be replaced by point charges, point dipoles, etc., at the nucleus of the ions surrounding the rareearth ions. Thus, R is taken as the various internuclear distances. However, for lattice sums that depend on such high powers of R, one must consider the extended nature of the charge distribution of the ions surrounding the rare earths. Another way of stating the trouble is: Since the distance between the observer (rareearth ion) and the charge distribution is not large compared to the extent of the charge distribution it is not a good approximation to replace the charge distribution by point moments. From numerical examples it is easy to see, for n=4 and 6, that most of the contribution to the A_{n}^{m} sums comes from the parts of the surrounding ions that are closest to the rareearth ions. Thus it becomes difficult to calculate the A_{n}^{m}'s accurately. However, using this idea, agreement is obtained with the dependence of the V_{n}^{m}'s on Z and some of the interrelationships between the different n terms.
For the lattices usually used as hosts one cannot calculate the A_{2}^{0} sum because of its sensitivity to the xray data and charge distribution parameters. However, by using nuclear quadrupole resonance data to eliminate calculating the actual lattice sum, one gets good agreement between the measured V_{2}^{0}'s and (1α2)<r^{2}>A20.
 Publication:

Journal of Chemical Physics
 Pub Date:
 January 1965
 DOI:
 10.1063/1.1695703
 Bibcode:
 1965JChPh..42..377B