Vibrational spectra of hexaaqua complexes VIII. The

Journal of Molecular Structure 480–481 (1999) 689–693

Vibrational spectra of hexaaqua complexes VIII. The antisymmetric SO4 stretching bands in alums: LO–TO superior to correlation-field and site-group splitting Vladimir Ivanovski, Vladimir M. Petrusˇevski, Bojan Sˇoptrajanov* Institut za hemija, PMF, Univerzitet “Sv. Kiril i Metodij”, P.O. Box. 162, 91001 Skopje, Macedonia Received 27 August 1998; received in revised form 10 November 1998; accepted 10 November 1998

Abstract FT-IR spectra of RbAl(SO4)2·12H2O and KAl(SO4)2·12H2O alums were investigated in the region of the n3(SO4) mode. The spectra were analyzed at room ( ⬇ 293 K, RT) and at low temperature ( ⬇ 100 K, LT). The doublet arising from this mode, evident in the LT spectrum, could be attributed to either site-group or correlation-field splitting. In order to reveal its exact origin, isomorphous isolation of SO42⫺ ions in the corresponding selenate alums was performed. The spectra of such samples show that in the case of RbAl(SO4)2·12H2O the correlation-field splitting is dominant over the site-group splitting, while in the case of KAl(SO4)2·12H2O, both correlation and site-group splitting coexist. By means of specular reflectance spectroscopy at near normal incidence, reflection spectra were acquired and the frequencies of the LO and TO phonons were calculated. It was shown that, in terms of the corresponding, the following sequence holds in the case of RbAl(SO4)2·12H2O: LO–TO ⬎ correlation-field ⬎ site-group splitting. 䉷 1999 Elsevier Science B.V. All rights reserved. Keywords: Vibrational spectra; Hexaaquacomplexes; SO4 stretching bands; Site-group splitting; LO–TO splitting

1. Introduction Alums are double salts of the type M IM III(RO4)2·12H2O, where M I is a univalent metal/ group such as K, Na, Cs, Rb, NH4, CH3NH3, etc., M III stands for a trivalent one: Al, In, Ga, Fe, V, Cr, etc., and R represents S or Se. All alums crystallize in the cubic system, space group Pa3 (Th6), with Z 4 ([1–3] and references therein). Half of the water molecules are coordinated to M III, the other half being close to

* Corresponding author. Tel.: ⫹ 389-91-117055; fax: ⫹ 38991-226865. E-mail address: [email protected] (B. Sˇoptrajanov)

M I. The symmetry of the M I(H2O)6 and M III(H2O)6 groups is S6 and that of the RO4 groups is C3. From the structural point of view, alums are further divided into three types: a , b and g . Alums of g type differ from both a and b in the orientation of the tetrahedral anion along the C3 axes [2]. The differences between a and b types are best reflected through the geometry of the coordination polyhedron of water molecules around the univalent cation. In the case of a alums the coordination polyhedron is a distorted octahedron, while in b alums it is an almost regular hexagon. It is worth mentioning that a disorder of the sulfate group is found in many a alums, part of the SO4 groups adopting orientation as in g alums ([4–6] and references therein). Investigations concerning IR and Raman spectra

0022-2860/99/$ - see front matter 䉷 1999 Elsevier Science B.V. All rights reserved. PII: S0022-286 0(98)00832-1

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V. Ivanovski et al. / Journal of Molecular Structure 480–481 (1999) 689–693

2. Experimental

Scheme 1. Splitting of the n3(SO4) mode in the site- and unit-cell group approximations.

have been reported many times ([6–10] and references therein), different parts of the spectrum being thoroughly analyzed. In the present work, attention is paid to the region of the antisymmetric stretching vibrations of the SO4 anion and, particularly, to the true nature of the doublet band which is clearly seen at LT. Reflection studies are also included, as these give information on the LO–TO splitting which is not predicted by unit-cell group theory.

Fig. 1. IR absorption spectra of RbAl(SO4)2·12H2O in the n3 (SO42⫺) region at room temperature (RT) (a) and liquid nitrogen temperature (LNT) (b).

Single crystals of a number of alums were grown from aqueous solutions, of corresponding M2I RO4 and M2III(RO4)3 salts. The spectra were recorded on a Perkin Elmer System 2000 FT-IR interferometer, using a Graceby Specac accessory for low temperature work and Perkin Elmer specular reflectance accessory for acquiring reflection spectra at nearnormal incidence. All spectra were recorded with a 4 cm ⫺1 resolution, taking 16 (32) background and 32 (64) sample scans. The OPD velocity was 0.2 cm s ⫺1. The wavenumber accuracy is better than ^ 1 cm ⫺1. GRAMS2000 [11] and GRAMS386 [12] software packages were used for spectra acquisition and manipulations, including Kramers–Kronig transformation. The LO and TO frequencies were calculated using a computer program written in ArrayBasic [13].

3. Group-theoretical considerations When analyzing the vibrational bands in solid phase samples, one may employ at least two levels of approximation. The first one is Halford’s site symmetry method [14] in the origin of which lies the oriented-gas model. The changes in the selection rules (band splitting, IR or Raman activity etc.) are governed only by the decrease in symmetry on going from the molecular point group to its subgroup (the site-group of the molecule in the crystal). The second method, somewhat more involved, is the correlation method. It is, in a way, an extension of the site-group method. Here it is assumed that the equivalent vibrations of the molecules in the crystal (usually called identical oscillators) are further coupled. The coupling gives rise to unit-cell group modes (sometimes referred to as factor-group or Davydov splitting [15]). Let us now apply both methods/approximations to the vibrations of SO4 anions in the alum crystal and, in particular, to the triply degenerate (in the case of “free” ion) n3(SO4) modes. As seen in Scheme 1, doublets are expected in the site-group approximation, while triplets are obtained if the full correlation method is applied. If a doublet band arising from the n3(SO4) mode is


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seen in the IR spectrum, it could be ascribed to either a site-group or an incomplete correlation-field splitting. It is important to make a clear-cut distinction between these two possibilities, mostly because spectroscopists are often inclined to believe that the correlation-field can very often be neglected. This can be accomplished by the method shown later.

4. Results and discussion

Fig. 2. IR absorption spectra of isomorphously isolated RbAl(SO4)2·12H2O in RbAl(SeO4)2·12H2O in the n3 (SO42⫺) region at LNT.

Nothing but some band asymmetry is seen in the spectrum of RbAl(SO4)2·2H2O recorded at RT (Fig. 1(a)). However, band splitting is clearly observed in the LT spectrum (Fig. 1(b)). What is the nature of this doublet? Is it because of Halford’s site-group splitting, or is it a collective effect? One way to answer this question is to employ isomorphous isolation, i.e., to study the IR spectra of sulfate ions isolated in a matrix of a selenate host. Under these circumstances, the sulfate ion retains its site symmetry, its surrounding being different. As a consequence, the interactions between identical oscillators are switched off. A sample of about 5% RbAl(SO4)2·12H2O in RbAl(SeO4)2·12H2O was studied. The results are presented in Fig. 2. It can be seen that a singlet band appears, instead of the doublet in the isomorphously isolated sulfate alum. This finding is not consistent with the assumption that the doublet is a result of site-group splitting. However, it is easily explained in terms of correlationfield splitting. The disappearance of this doublet in the sample containing isomorphously isolated sulfate ions is consistent with the switched-off interactions of identical oscillators. This example clearly shows the correlation-field splitting may dominate over sitegroup one. The situation is somewhat different in the case of pure KAl(SO4)2·12H2O (Fig. 3(a)) and the sample containing isomorphously isolated sulfate ions in KAl(SeO4)2·12H2O (Fig. 3(b)). In both cases, a doublet is evident in the 1100 cm ⫺1 region 1. As the Additional bands are seen at ⬇ 1200 cm ⫺1 and at ⬇ 1060 cm ⫺1 and these could be attributed to the disordered (inverted) sulfate ions. As this splitting is rather large ( ⬇ 150 cm ⫺1), one could say that the inverted sulfate groups are more distorted than the regular ones. This will be studied in detail elsewhere [16]. 1

Fig. 3. IR absorption spectra of KAl(SO4)2·12H2O (a) and isomorphously isolated KAl(SO4)2·12H2O in KAl(SeO4)2·12H2O (b), the n3 (SO42⫺) region at LNT.

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Fig. 4. Reflection spectra (at near normal incidence) of RbAl(SO4)2·12H2O (a) and KAl(SO4)2·12H2O (b), at RT.

splitting is larger in the pure sulfate alum (Fig. 3(a)), one could say that, in this case, the site-group and the correlation-field splitting exist together. This approach was based on group-theory results

(the k 0 approximation). The weakness of this approach lies in its inability to predict a very important effect: a splitting of the triply degenerate IR active unit-cell group modes (of Fu symmetry) into a non-degenerate longitudinal optical and doubly degenerate transversal optical phonon. The splitting is a consequence of the macroscopic electrostatic field in the irradiated crystal and is usually denoted as LO–TO splitting. It is interesting to compare the latter with the site-group and correlation-field splitting. However, because of the properties of the electromagnetic field, only TO phonons may be detected in ordinary IR absorption experiments. Reflection studies, however, give additional information. The reflection spectrum gives the dependence of the coefficient of reflection of the medium, on the frequency of the external radiation (Fig. 4). By measuring the coefficient of reflection (R), and performing the Kramers–Kronig transformation [17], one may calculate the change of the phase (u ) in the reflected beam and the optical constants of the medium. These are the real (n) and the imaginary part (k), of the complex refraction index. The optical parameters are connected with the dielectric ones, that is the real 1 0 and the imaginary part 1 00 of the complex permittivity, so these two quantities can be calculated too. The dielectric parameters are important in the evaluation of the conductivity (s ) and resistivity (r ) of the medium:

s v10 1 00r ;

r

1 00r ; ⫹ 1 00r 2

v10 1 0r 2

the maxima of which give the frequencies of the transversal and longitudinal phonons in the crystal, respectively [18]. In the case of RbAl(SO4)2·12H2O and KAl(SO4)2·12H2O (Fig. 5), the difference n LO – n TO (the LO–TO splitting) is about 40–50 cm ⫺1. From the discussions here, one could say that in RbAl(SO4)2·12H2O (but also in many other alums [16]), the following sequence holds: LO–TO ⬎ correlation-field ⬎ site-group splitting: Acknowledgements

Fig. 5. Conductivity s and resistivity r at RT in the case of RbAl(SO4)2·12H2O (a,b) and KAl(SO4)212H2O (c,d) respectively.

This work was sponsored by the Ministry of Science, Republic of Macedonia and the authors are grateful for the financial support.


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