J. Chern. SOC., Faraday Trans. I, 1989, 85(3), 493-501 X-Ray Diffraction and Raman Spectral Analysis of Molten CdCl, Yoshiki Takagi,* Noriko Itoh? and Tetsur6 Nakamura Research Laboratory of Engineering Materials, Tokyo Institute of Technology, Nagatsuta-cho 4259, Midori-ku, Yokohama 227, Japan The structure of molten CdCl, has been investigated by X-ray diffraction and Raman spectral analysis. The tetrahedral configuration (CdCI,) was confirmed from the first and second peaks of the radial distribution function. Crystalline MCl,(M = Mg, Mn, Fe, Co, Ni and Cd) has a CdC1,-type layer structure.' In which C1 atoms are close-packed f.c.c., a layer of M atoms alternates with every two Cl layers and every M atom has six nearest-neighbour CI atoms in octahedral coordination. For molten MCI,-ACl systems where A is an alkali metal, many workers have suggested that tetrahedral complex MCIi- ions exist predominantly in ACI-rich In molten MgCI,, MnCl,, FeCI,6 and COCI,~, MCI, in a tetrahedral configuration has been suggested to occur, as shown by the enthalpy of mixing.In this paper the radial distribution function (r.d.f.) of molten CdCI, is obtained, and a structural model of the molten state is proposed by considering the geometrical orientation of the ions. The coordination states of molten CdCI, have also been studied by Raman spectroscopy. To date, the Cd-Cl stretching frequencies in the crystalline, molten and solution states have been reported. However, as shown in table 1, various assignments have been made. For instance, Bues' made an assignment on the basis of a 4-coordinated Cd2+ ion, while Clarke et al.' based their assignment and 6-coordination state by reference to previous data.'" Both assignments are reasonable from the viewpoint of selection rules.Ex per imen tal The experimental procedures and analysis of the observed intensities are identical to those described previously. 11, l2 Cadmium chloride (99.9 O/O, Rare Metallic Co.) was dried in vacuo at 473 K for a few days. The anhydrous cadmium chloride was melted at 923 K in a silica glass tube, purified by bubbling dry HCI over it for 1 h and then sealed in a silica glass tube (fig. 1) following evacuation. The X-ray measurements were made using parafocusing reflection geometry. Mo K2 radiation was used and the beam was monochromatized by use of a curved graphite single crystal mounted in the diffracted beam.The correction for background, polarization, absorption and Compton scattering were applied to the observed data and were scaled to the independent scattering factor for the stoichiometric unit using the method of Krogh-Moe13 and N ~ r m a n . ' ~ The radial distribution function D(r), average correlation function G(r) and reduced intensity function Si(S) were calculated using methods reported previously. l l . l2 Parameters used in the calculation are given in table 2. Japan. t Present address: Tokyo Metropolitan Institute of Technology, 6-6 Asahigaoka, Hino, Tokyo 191, 493Table 1. Raman shifts of CdCl, solid molten salt Raman shift/cm-' T/"C assignment Raman shift / cm-I T/ "C assignment ref. no.2 ref. no. $ 242 hexagonal 2 % 1 $ 213 20 A , of tetragonal CdCIt- 1 212+5 580-650 A, of tetragonal CdCli- in layer lattice 3 - - 3 205 & 3 233 & 3 - 23 5 25 } A , , of triply shared CdC1;- 4 215 > 600 essentially CdC1;- 4 2 z 3 229" 580" associated with low net coordinated Cd2+ in disordered ionic melt B 239 room - this work 229 580, - this work K. temp. 760 & 5 Tanemo tob 210-217 580, 605 a Not observed but extrapolated to 580 "C. A member of staff in our laboratory.Y. Takagi, N . Itoh and T. Nakamura h diffracted beam Fig. 1. X-Ray diffraction cell for volatile sample. Table 2. Parameters used in the calculation of the r.d.f. temperature/K 923 DJstoichiornetric unit A-3 0.011 067 effective electron number : K C d 48.580 0 16.810 0 12.00 K, I Srnax/A-l 495 incident beam The Raman spectra were recorded on a JEOL spectrometer with 514.5 nm excitation '(ca.300 mW) by an argon-ion laser (Spectra Physics). Results and Discussion X-Ray Diffraction The correlation function G(r) and the radial distribution function D(r) are shown in fig. 2. The function D(r)/r is also shown in fig. 2. The first peak in D(r) in fig. 2 evidently corresponds to, the nearest-neighbour interaction of Cd-C1 pairs. The nearest Cd-Cl distance, 2.42 A, in the molten state is slightly shorter than that in the crystalline state. The number of chlorine atoms around each cadmium species wa; calculated from the first peak assuming a Gaussian distribution centred at 2.42 A. The observed number of chlorine atoms which are nearest to cadmium is 3.9, and decreases markedly on melting in comparison with the number for the crystalline state, which is 6.0.The second and third peaks of the correlation function G(r) are due to the contribution of the nearest Cl-Cl and Cd-Cd ion pairs, respectively. The numbers and distances of these ion pairs obtained by analysis of the radial distribution function are listed in table 3. Raman Spectra We observed a single polarized band at 239 cm-l for the solid CdCl, (fig. 3). This Raman shift is in good agreement with the previous values of 242,15 and 235 cm-'.' When the CdCI, was heated to 853 and 1033 K, a single polarized band was observed at 229 cm-l (fig. 3). This Raman shift is apparently different from the previous values~9*1s of ca.212 cm-', rather it is same as the Raman shifts of solid CdCl,.g.16 A different Raman spectrum was obtained in our laboratory, although the experimental procedure was the496 Structure of Molten CdC1, Fig. 2. Radial 9 8 7 5 6 4 * 5 2 4 3 2 1 0 2 n A 1 u 0 distribution 1 2 3 4 6 6 7 8 9 1 0 l I A I I I I I I I I 4 3 4 5 6 7 8 9 1 0 r/A function D(r), correlation function G(r) and function CdCl, at 923 K. Table 3. Average distance,, ,,/A, root mean square displacement, ( Arij)H, and coordination number, n,,, for i-j pairs i-j pair T i , <Ari,>: nij Cd-Cl 2.42 0.055 3.90 Cd-Cd 4.88 1.32 3.6 Cl-Cl 3.80 0.294 10.88 10.9 Cd-Cl 5.56 - 1 I I I I I I I l I I I (d n 229 (4 239 P 400 300 200 100 400 300 200 100 400 300 200 100 wavenumber/cm-' of molten Fig. 3. The normal (n) and polarized (p) Raman spectra of CdCl,: (a) solid, (b) 853 K and (c) 1038 K.Y.Takagi, N . Itoh and T. Nakamura 497 Table 4. The observed frequencies, v, of the local vibration of tetrahedral CdC1,2- molten salt solution selection ~ mode rule vlcrn-l state ref. vlcm-' state ref. a, R," pol. 256f3 CdCI,..uCsCI 4 (x = 2,3,4.3) 253+3 CdCl,.xKCl 4 (-u = 2,3,4.3) 250 & 2 CdCI, . xLiC1 4 (x = 2,3,4.3) 259 CdCI,..yKCI 6 (x = 1,2) f, R, depol. - - - 264 (Et,N),CdCI, in 13 HCI 26 1 (Et,N),CdCI, in 13 CH,NO, 260 (Et,N),CdCI, in 13 CH,,CN 258 (Et,N),CdCI,, 13 tetra-n- butyl phosphate 28 I (Et,N),CdCl,, in 13 CH,CN (Et,N),CdCI,, 13 tetra-n-butyl _______- ~~ - .- - ' I Raman. Table 5. GF matrix for tetrahedral CdCIi- 1 I G(a,) = -(1 +3cos 109.4")+- m(.d MCI I I G(f,) = - (1 - cos 109.4") + - mcd %I '(a,) = If, + ? f r , l m, is the mass of atom X.same. The Raman shift observed at 2 10-2 17 cm-I by Tanemoto agreed with the reported l6 This suggests that the coordination state is not so simple nor so regular at long range. The Raman shifts due to CdC1;- local structure are 260 cm-' (a,) and 281 cm-' (f2),9917*18 as shown in table 4. The existence of the CdC1;- ion is supported also by measurements of electrical conductivity," viscosity2" and surface tension.'' Table 4 shows that the a, frequencies are the same, although the circumstances are changed from the molten state to the various organic solutions. This means that the force constants obtained from the CdCIi- unit have universal values for various CdCl:-,-" unit structures, if the bond length is same.Thus the force constants of CdCIt- were determined by the GF method22 using the generalized force field as given by V is the potential energy, f, and f,, are the force constants and Ar is the change in the Cd-CI bond distance from the equilibrium position. The block matrices of G and F are498 Structure of Molten CdCI, Table 6. The stretching frequencies of CdC12,-" (n = 2, 3 and 6) ~ observed calculated unit point state of ref. structure group mode the sample no. vlcrn-' vlcm-' CdCl, D,, v,(Ci) TBP"/KCI s o h 13 280 248 CdCI, D,, v,(ai) TBP"/KCl s o h 13 265 254 v,(e') TBP"/KCI s o h 13 287 - ;E; ( i f bond angle - c,, Vlb,) - v3(e) - 281 = 110" - - CdC1;- 0, v,(A,,) solid 2,4, this work 237 + 2 265 a Extract from KCI aqueous solution to the tri-n-butyl phosphate soh tion.Fig. 4. (a) and (b) Corner-shared and (c) edge-shared models of bitetrahedra. shown in table 5. Thus f, = 1.225 x 10, N m-' and f,, = 0.0624 x lo2 N m-' were obtained. The value of f, + 3f,, ( = 1.412 x 10, N m-') corresponds to f = 47t2cm,, v: (1.41 x 10, N m-') calculated by Davies and Long.ls The values off, andf,, of CdCIi- were used to calculate the stretching frequencies of possible unit structures such as CdCl,, CdCl; and CdCli-. The v1 and v3 frequencies calculated for planar or bent CdCI, agreed with the observed values, as seen in table 6. However, v1 frequencies calculated for the respective CdCl, and CdCli- species did not agree with the observed values. This is because the Cd-CI bond distance is unchanged in the case of CdCl,, but becomes short in the case of CdCl,, and becomes long in the case of CdCIt-, compared with CdCli-.If we assume that molten CdC1, contains all or some species of CdCI,, CdCl;, CdC1,2- and CdC1,4- unit structures, the peak frequency of the Raman band synthesized by superposing the Raman bands of the unit structures is at least 237 cm-l. The peak frequency of 213 or 229 cm-' in table 3 cannot be reproduced by such a superposition.Y. Takagi, N . Itoh and T. Nakamura 12 0 140 160 180 a/" Fig. 5.fb values plotted against the bent angle a used in the present calculations. Table 7. Description of the normal coordinates (normalizing factors omitted) 499 - Q , Q2 Q3 Q4 Q5 QG Q, - Qa - 1 1 1 1 1 1 1 1 - 1 - 1 - 1 3 - 1 - 1 - 1 3 1 1 1 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 3 1 1 1 - 3 - 1 - 1 2 0 - 1 - 1 2 0 1 - 1 0 0 1 - 1 0 0 - 1 - 1 2 0 1 1 - 2 0 - 1 - 1 0 0 - 1 1 0 0 The isolated CdC12,-" unit structure exists only in systems containing two or more components. In the glassy state the calculation should be carried out for the bridged structures. It seems difficult for the octahedral unit structure to have various bridge angles.Rather, the tetrahedral unit structure is more suited to have flexible bridge angles. Therefore the stretching frequencies were calculated using a CdC1,-Cl-CdCl, model. A generalized configuration is illustrated in fig. 4. The CdCli- at one side retains symmetry and the bridge angle between bonds rs and rs, a, has values ranging from 109.4 to 180". If a = 180°, CdCl, units at both sides are related by an eclipsed or staggered configuration.The potential energy, 5, is given by (2) & = v, + fb Ar8 Ars. We have already determinedf, = 1.225 x 10, andf,, = 0.0624 x 10, N m-', but not the value of fb. Thus an assumption was introduced that fb =A, if a = 109.4", fb = 0 if a = 180°, and fb varies with a as shown in fig. 5. The normal coordinates are given in table 7. The calculated frequencies are shown in table 8. The same values were obtained from the staggered and eclipsed configurations. As the Q, and the Q, modes are totally symmetric, the Raman-scattering intensity is most strong among modes Q,-Q,. The value of v, is independent of a, but v2 shifts to lower frequencies as the bridge angle becomes wider. If the v, and Y , bands overlap and give rise to a single band, the peak frequencies appear between 270 and 132 cm-'.For example, the Raman shifts observedv1 0 0 Table 8. Symmetry of the modes and the calculated frequencies, vralrd(crn-') of Cd,CI;- ~~ Cd-C1-Cd bridge conformations Q, Q 2 Q3 Q4 Q5 QG Q, Qfl linear D3d (staggered) (eclipsed) Dm CS a = 109.4" 'calrd 120" 130" 140" 150" 160" 170" A', A, R 267 R, i.r. 270 268 268 267 267 267 267 4 A, R 132 R, i.r. 239 213 196 I69 159 142 130 E" E" 1.r. i.r. A," p2" i.r. 1.r. I?. A," A," E' E' E" E" 1.r. i.r. R, i.r. R, i.r. R R 5 % % B Z B, A2 inactive R, i.r. R 4 B, A, cp 266 358 28 I 28 1 28 1 28 1 R, i.r. R, i.r. R, i.r. 264 302 28 1 28 1 all vibrations are R and i.r. active $ 265 325 28 1 28 1 B 265 332 28 1 28 1 p 3 265 357 28 1 28 1 265 350 28 1 28 1 266 363 28 1 28 1 266 373 28 1 28 1Y.Takagi, N . Itoh and T. Nakamura 50 1 at 213 and 229 cm-' coincided with the calculated frequencies: if the oscillator strengths of modes Q, and Q, are equal, ( v , + v,)/2 = 21 3 cm-' for a = 150" and (v, + vJ/2 = 232 cm-' for a = 130", respectively. On the other hand, the depolarized Raman shift observed at 281 cm-I for CdC1,2- coincided with the calculated frequency v 5 , v ~ , vi or v8. These were independent of the bridge angle and of the unit structure. The calculation of normal frequencies should also be made for the edge-shared model, CdCl,. Assuming that ( a ) the molecular symmetry is DZh, (h) the CdCl, CI,Cd unit remains a regular tetrahedron and (c) the Cd-CI bond distance is equal to that of the isolated CdC1;- unit, the frequencies of the totally symmetric modes (Alg) are 275 and 230 cm-l.As the Cd-Cl bond used for bridging is longer than the terminal Cd-CI bond, the A,, frequencies will become lower in wavenumber that 275 or 230 cm-'. Also, a simple expression for the potential energy such as eqn (2) seems insufficient to treat such a complex structure as the edge-shared model. The number of chlorine atoms around each cadmium atom was 3.9, and the ratio of the nearest Cl-C1 and nearest Cd-CI distances was close to the value 1.63 [i.e. (8/3)2]. Thus the existence of [CdCl,] tetrahedral units in the melt was confirmed by analysis of the radial distribution function. The result is consistent with the Raman spectral study reported in the present work./cl \ \c1/ The computations were carried out on an M-180 and VAX8600 computer at the Nagatsuta Branch of the Computer Centre of the Tokyo Institute of Technology. References 1 R. W. G. Wyckoff, Crystal Structures (Interscience, New York, 1960), vol. 1, p. 272. 2 K. Tanemoto and T. Nakamura, Chem. Lett., 1975, 4, 351. 3 A. S. Kucharski and S. N. Flengas, J. Elecrrochem. Soc., 1974, 121, 1298. 4 G. N. Papatheodorou and 0. J. Kleppa, J. Inorg. Nucl. Chem., 1971, 33, 1298. 5 B. R. Sundheim and M. Kukk, Discuss. Faraduy SOC., 1961, 32, 49. 6 G. N. Papatheodorou and 0. J. Kleppa, J. Inorg. Chem., 1971, 33, 1249. 7 W. 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