Ionic Interactions in Lanthanide Halides Z. Akdeniz, Z. Çiçek, and M. P. Tosia Department of Physics, University of Istanbul, Istanbul, Turkey and Abdus Salam International Centre for Theoretical Physics, 1-34014 Trieste, Italy a INFM and Classe di Scienze, Scuola Normale Superiore, 1-56126 Pisa, Italy Reprint requests to Prof. M. P. T.; Fax: +39-050-563513; E-mail: [email protected] Z. Naturforsch. 55 a, 861-866 (2000); received September 27, 2000 We determine a model of the ionic interactions in RX3 compounds (where R is a metal in the rare-earth series from La to Lu and X = CI, Br or I) by an analysis of data on the static and dynamic structure of their molecular monomers. The potential energy function that we adopt is patterned after earlier work on Aluminium trichloride [Z. Akdeniz and M. P. Tosi, Z. Naturforsch. 54a, 180 (1999)], but includes as an essential element the electric polarizability of the trivalent metal ion to account for a pyramidal shape of RX3 molecules. From data referring mostly to trihalides of elements at the ends and in the middle of the rare-earth series (/. e. LaX3, GdX3 and LuX3), we propose systematic variations for the effective valence, ionic radius and electric polarizability of the metal ions across the series. As a first application of our results we predict the structure of the Dy2Cl6 and Dy2Br6 molecular dimers and demonstrate by comparison with electron diffraction data that lanthanide-ion polarizability plays a quantitative role also in this state of tetrahedral-like coordination. Key words: Ionic Clusters; Molten Salts. 1. Introduction a number of years a matter of controversy. Although the majority of the data supports slightly pyramidal Industrial and technical applications have moti- shapes for RX3 gaseous molecules, the question as to vated interest in rare-earth halides for a number of which of these are planar (D3h symmetry) and which years. Great attention has been given to their vapours are pyramidal (C3v symmetry) does not seem to be and to the volatile vapour complexes that are formed fully settled experimentally [1]. The assignment of with complexing agents such as the alkali halides vibrational frequencies on the basis of C3v symmetry or the Al trihalides, in view of a series of poten- [1] yields relatively low values for the frequency of tial applications related to new energy sources, en- the u2 mode, indicating that these molecules are quite ergy conservation, and recycling or separation pro- floppy. cesses [ 1 ]. The extraction and processing of rare-earth On the theoretical side, extended Hiickel calcula- metals are based on molten-salt technologies, giv- tions by Myers et al. [5] predicted a pyramidal config- ing incentive to current efforts at determining ther- uration for all these molecules, with the X-R-X bond modynamic and structural properties of rare-earth angle increasing both across the lanthanide series and halide melts by both experimental and simulational across the halogen series from 91° in LaF3 to 119° methods [2], in Lul3. Attention has also been drawn to the role In attempting to develop a refined model for the of ionic polarizabilities in determining the molecular ionic interactions in rare-earth halides it seems natural shape [6]. Within a simple ionic model the distortion to follow the approach developed by two of us [3] for of an RX3 molecule from a planar to a pyramidal Al chlorides and alkali chloroaluminates: that is, to shape is driven by the energy gain from electric po- start by examining the static and dynamic structure larization of the rare-earth ion: a pyramidal shape is of the simplest molecular units, which are the RX3 then favoured by a high polarizability of the rare-earth monomers. As evidenced in the work of Molnär and ion and by a short X-R bond length. This prediction Hargittai [4], the shape of these molecules has been for is in accord with the trends revealed by the molecu- 0932-0784 / 2000 / 0900-1100 $ 06.00 © Verlag der Zeitschrift für Naturforschung, Tübingen • www.znaturforsch.com 862 Z. Akdeniz et al. • Ionic Interactions in Lanthanide Halides lar orbital calculations of Myers et al. [5]. However, 2. Interionic Force Model and Evaluation of for quantitative purposes the available value of the Model Parameters lanthanide-ion polarizability obtained by Pauling [7] is likely to be much too low. The rare-earth ions do not Following our earlier study of the Al-based chlo- seem to have been considered in the re-assessments rides [3], the microscopic model that we use for lan- of the Pauling polarizability scale due to Tessman, thanide halide clusters incorporates the Born model Kahn and Shockley [8] and to later workers [9]. The of cohesion [10] and the shell model for vibrational work of these authors led to a very sizable increase of motions and crystal defects [11]. Electron-shell de- the polarizability over the Pauling values for all other formability is described through (i) effective valences positive ions, and in particular to an increase by about Zi subject to overall charge compensation; (ii) the a factor of two for the doubly charged alkaline-earth electric and overlap polarizabilities of the halogens ions. (denoted by a\ and as, respectively); and (iii) the electric polarizability OR of the lanthanide ions. Over- Therefore, our first task in the present work is to lap repulsions of exponential form involve ionic radii obtain a new estimate for the electric polarizability of Ri and stiffness parameters p . Van der Waals dipole- the lanthanide ions. We focus for this purpose on those x dipole interactions are included for the halogens. gaseous RX3 molecules for which electron diffraction data are available to provide evidence for a pyramidal For convenience we report here the form of the shape and a value for the X-R-X bond angle. These potential energy [/({r^}, {Pj}) as a function of the mainly are the chloride, bromide and iodide of La, bond vectors r^ and of the electric dipole moments pz carried by the ions. This is Gd and Lu (excepting Lal3), and their study presents two evident advantages: (i) these elements are at the beginning, in the middle and at the end of the rare- f({r«}, b,}) = E +*«ovi) - earth series, so that their inclusion in the analysis i<j Tij facilitates an assessment of trends ; and (ii) the elec- c tron distribution in the f-shell of these elements in the + t/p ;i({rlj},{pj)+t/shell({rl,},{pj).(l) isolated state is spherically symmetrical, thus exclud- ing that f-shell anisotropy may be relevant in driving The overlap repulsive energy in (1) is taken in the a pyramidal distortion as discussed by Molnär and Busing form [12] Hargittai [4]. In view of the presumable uncertainties in the mea- #ij(r) = f(Pi + Pj) exp[(i?i + Rj - r)/(pi + Pj)l (2) sured pyramidal bond angles, our main aim is the as- The reader is referred to our earlier work [3] for ex- sessment of trends in the ionic-model parameters for pressions of the classical polarization energy and the trivalent ions across the rare-earth series, rather of the shell deformation energy Usht\\. than their individual values in each system. These A very helpful aspect of the model (1) is that trans- parameters are the electric polarizability, the effec- ferability of the parameters describing the halogen tive valence and the ionic radius entering the core ions and direct proportionality between the charac- repulsion. In Sect. 2, after a brief reminder of the teristic radius RR and the hardness parameter pR of essence of our model as developed in [3], we list the the metal ion are approximately valid. We expect input values of the other model parameters and the (and, as we shall see below, find) that the rare-earth available evidence on bond lengths, bond angles and compounds of present interest are rather highly ionic vibrational mode frequencies in each of the gaseous molecules that we have taken into consideration. The Table 1. Input of interionic force parameters for rare-earth trends of the model parameters for the lanthanide ions trihalidesa. across the series of rare-earth trihalides are presented X 2 2 R 3 3 5 2 and discussed in Sect. 3. A first test of our results / (e /Ä ) r'PR ax(A ) as (A ) Cx (eÄ / ) is reported in Sect. 4, by giving a prediction of the CI 0.05 18.6 3.00 0.83 5.50 structure of the Dy chloride and bromide dimers and Br 0.05 18.6 4.17 1.2 7.17 comparing it with evidence from electron diffraction I 0.05 18.6 6.29 1.7 10.1 experiments. Finally, Sect. 5 ends the paper with a a The polarizability ax is taken from [9], the other parameters brief summary and outlook. from [13]. Z. Akdeniz et al. • Ionic Interactions in Lanthanide Halides 863 Table 2. Bond lengths rRX (Ä), bonds angles ZX-R-X (de- Table 2 also includes the values that we have ob- -1 grees) and vibrational frequencies (cm ) of selected RX3 tained for the other vibrational frequencies of these d molecules . molecules. It should be noted that many of the mode Molecule R ZX-R-X U frequencies reported in the literature are mere esti- RX "1 2 "3 mates and that there is a very appreciable spread in 14,22 LaCl3' ' 2.56 116.5 336.8 52.1 332.5 72.6 the frequencies from different experiments and differ- 333 26 63 1 LaBr,' -^] 2.74 115.5 190 35 220 47 ent sources, as discussed for instance by Koväcs et al.