4f-electron

Uranium is the fourth element of the actinide (SJ series. In the actinide series the electrons are more effectively shielded by the Is and 7p electrons relative to the 4f electrons (shielded by 6s, 6p) in the lanthanide (4p series. Thus, there is a greater spatial extension of 5f orbitals for actinides than 4f orbitals for lanthanides. This results in a small energy difference between and 5/ 6d7s electronic configurations, and a wider range of oxidation states is... 

A contraction resulting from the filling of the 4f electron shell is of course not exceptional. Similar contractions occur in each row of the periodic table and, in the d block for instance, the ionic radii decrease by 20.5 pm from Sc to Cu , and by 15 pm from Y to Ag . The importance of the lanthanide contraction arises from its consequences ... 

Figure 1.1 shows that the stability sequence revealed by chemical reactions and chemical synthesis corresponds to thermodynamic stabilities. An explanation requires a theory that will explain both. To get it we apply the theory of atomic spectra [9]. The energy of the 4f electrons in an ion with the configuration [Xe]4P, F(4P), can be written [nU+E Q-p(4f )] where U, a negative quantity, is the energy of each 4f electron in the field of the positively charged xenon core, and Frep(4P) represents the repulsion between the n 4f electrons. In Table 1.1, rep(4P) is expressed as a function of the Racah parameters and E. The... 

The second class of reaction is that of processes in which the 4f electrons are conserved. The obvious examples are the complexing reactions of tripositive lanthanide ions. Here the irregularities due to changes in inter-electronic repulsion almost entirely disappear. We then get the slight smooth energy change whose consequences were so familiar to 19 century chemists, who struggled vdth the separation problem. 

In many cases, lanthanide reactions can either be assigned exclusively to one of these two classes, or they show deviations that the classification makes understandable. In Fig. 1.2, we plot the values of AH for the complexing of the tripositive aqueous ions by EDTA (aq), a reaction in which the 4f electrons are conserved. The irregularities are negligible at the chosen scale. Also shown are the values of AH (MCl3,s) which refer to ... 

Here, for nearly all of the elements, the number of 4f electrons in the metallic state and in the trichloride is the same, so we expect a largely smooth energy... 

The principle introduced above is best exploited by classifying lanthanide compounds not by oxidation state, but by the number of 4f electrons at the metal site. For example, the reaction... 

These difficulhes show that the descriphon nearly smooth for the energies of inter-conversion of tri-f compounds is a confession of inadequacy. But other kinds of reaction in which the 4f electrons are conserved suggest that it may be possible to refine nearly smooth into something more precise. To this we now turn. 

Very often, the tetrad effect is not clearly discernible in the energies of processes in which 4f electrons are conserved. It may, for example, be obscured by irregularities caused by structural variations in either reactants or products. This is especially likely given the willingness of lanthanide ions to adopt a variety of coordination geometries. There is, however, no doubt that tetrad-like patterns are often observed. But does Table 1.2 provide a convincing explanation of what is seen ... 

Imagine a thoroughly convincing test of the explanation. We begin with a reaction in which the 4f electrons are conserved. In the sequence La Lu, each... 

In the lanthanide series, the equivalent values are much reduced by the retreat of the 4f electrons into the xenon core. This is so whether we consider processes that involve the condensation of gaseous ions, or conventional reactions. Table 1.3 includes data for the change... 

The divalent rare-earth ion Eu has the 4f electronic configuration at the ground states and the 4f 5d electronic configuration at the excited states. The broadband absorption and luminescence of Eu are due to 4f - 4 f 5d transitions. The emission of Eu is very strongly dependent on the host lattice. It can vary from the ultraviolet to the red region of the electromagnetic spectrum. Furthermore, the 4f-5d transition of Eu decays relatively fast, less than a few microseconds [33]. 

C07-0070. List all the valid sets of quantum numbers for a 4f electron. 

Apart from d- and 4f-based magnetic systems, the physical properties of actinides can be classified to be intermediate between the lanthanides and d-electron metals. 5f-electron states form bands whose width lies in between those of d- and 4f-electron states. On the other hand, the spin-orbit interaction increases as a function of atomic number and is the largest for actinides. Therefore, one can see direct similarity between the light actinides, up to plutonium, and the transition metals on one side, and the heavy actinides and 4f elements on the other side. In general, the presence or absence of magnetic order in actinides depends on the shortest distance between 5f atoms (Hill limit). 

Fig. 2.19. Temperature dependence of the amplitudes of coherent phonons of Gd(0001) and Tb(0001). On the right axis, and Ap show the square of calculated spontaneous magnetization given by the Brillouin function with Jq =7/2 and =6/2 representing the magnetic moment of 4f electrons. From [59]...

Trivalent lanthanide cations have luminescent properties which are used in a number of applications. The luminescence of the lanthanide ions is unique in that it is long-lasting (up to more than a millisecond) and consists of very sharp bands. Lanthanide emission, in contrast to other long-lived emission processes, is not particularly sensitive to quenching by oxygen because the 4f electrons found within the inner electron core... 

Moreover, the analysis of the optical spectra of transition metal and rare earth ions is very illnstrative, as they present qnite different features due to their particular electronic configurations transition metal ions have optically active unfilled outer 3d shells, while rare earth ions have unfilled optically active 4f electrons screened by outer electroiuc filled shells. Because of these unfilled shells, both kind of ion are usually called paramagnetic ions. 

The rare earth (RE) ions most commonly used for applications as phosphors, lasers, and amplifiers are the so-called lanthanide ions. Lanthanide ions are formed by ionization of a nnmber of atoms located in periodic table after lanthanum from the cerium atom (atomic number 58), which has an onter electronic configuration 5s 5p 5d 4f 6s, to the ytterbium atom (atomic number 70), with an outer electronic configuration 5s 5p 4f " 6s. These atoms are nsnally incorporated in crystals as divalent or trivalent cations. In trivalent ions 5d, 6s, and some 4f electrons are removed and so (RE) + ions deal with transitions between electronic energy sublevels of the 4f" electroiuc configuration. Divalent lanthanide ions contain one more f electron (for instance, the Eu + ion has the same electronic configuration as the Gd + ion, the next element in the periodic table) but, at variance with trivalent ions, they tand use to show f d interconfigurational optical transitions. This aspect leads to quite different spectroscopic properties between divalent and trivalent ions, and so we will discuss them separately. 

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