PHYSICAL CHEMISTRY

A. I. GRIGOR’EV, Yu. V. ORLOVA, V. A. SIPACHEV,
Corresponding Member of the USSR Academy of Sciences A. V. NOVOSELOVA

VIBRATIONAL SPECTRA OF ALKALI-METAL FLUOROBERYLLATES OF THE TYPE $M_2\mathrm{BeF}_4$

The crystal lattices of fluoroberyllates of the type $M_2\mathrm{BeF}_4$ are built from tetrahedral anions $\mathrm{BeF}_4^{2-}$, linked by alkali-metal cations ($^1$). A regular tetrahedron $\mathrm{BeF}_4^{2-}$ should possess four normal vibrations, two of which $(F_2)$ will be active in the absorption spectrum, and all four active in the Raman spectrum. One of the bands of the tetrahedral ion $(A_1)$, appearing in the Raman spectrum, should be strongly polarized, while the other three $(E$ and $2F_2)$ should be depolarized.

Fig. 1. Infrared absorption spectra of fluoroberyllates in the region 300–400 cm$^{-1}$ (CsI prism) (A), and in the region 400–1000 cm$^{-1}$ (KBr and NaCl prisms) (B)

The vibrational spectra of fluoroberyllates $M_2\mathrm{BeF}_4$ have not previously been studied in detail. Pecok and Sharp ($^2$) recorded the infrared spectrum of $K_2\mathrm{BeF}_4$ in the region 400–1000 cm$^{-1}$ and found an intense band near 800 cm$^{-1}$, which split into two components. They assigned it to the triply degenerate stretching vibration of $\mathrm{BeF}_4^{2-}$. Woodward attempted to record the Raman spectrum of $K_2\mathrm{BeF}_4$ in solution ($^3$). However, he did not succeed in detecting bands corresponding to the $\mathrm{BeF}_4^{2-}$ ion.*

We studied the infrared absorption spectra of $\mathrm{Li}_2\mathrm{BeF}_4$, $\mathrm{Na}_2\mathrm{BeF}_4$, $K_2\mathrm{BeF}_4$, $\mathrm{Rb}_2\mathrm{BeF}_4$, and $\mathrm{Cs}_2\mathrm{BeF}_4$ in the region 300–1000 cm$^{-1}$. The substances were recorded in the solid state as suspensions in vaseline oil. In the region 300–400 cm$^{-1}$ the spectra were recorded with an IKS-11 single-beam spectrometer with a CsI prism; in the region 400–1000 cm$^{-1}$, with an IKS-14 double-beam spectrometer with KBr and NaCl prisms. The infrared absorption spectra are shown in Fig. 1.

In addition, we investigated the Raman spectrum of solid $K_2\mathrm{BeF}_4$ using a spectrometer with gratings of the DFS-12 type. A low-pressure mercury lamp of the DRS-600 type was used as the source of the exciting line $(\lambda = 4358\ \text{Å})$. During the recording, a liquid filter with a concentrated solution of $\mathrm{KNO}_2$ was used. For recording the Raman spectrum, the following method of sample preparation was developed. Molten $K_2\mathrm{BeF}_4$ was distributed along the walls of a quartz test tube by rotating the latter, so that upon cooling—

* Obukhov-Denisov and co-workers ($^4$) likewise did not succeed in recording the Raman spectrum of glassy $\mathrm{BeF}_2$. On this basis they conclude that the Be—F bonds are predominantly ionic.

of the melt an inner cone was formed (Fig. 2). The test tube was placed with its open end toward the condenser. This method makes it possible to obtain considerably better results than when recording in conical glass cuvettes with double walls. After completion of the recording, \(\mathrm{K_2BeF_4}\) was analyzed for beryllium and silicon content. The silicon content in the specimen did not exceed \(0.1\%\); the beryllium content did not change and corresponded to that calculated for \(\mathrm{K_2BeF_4}\). The Raman spectrum of \(\mathrm{K_2BeF_4}\) is shown in Fig. 3.

Fig. 2. Schematic cross section of the cuvette with the specimen for recording the Raman spectrum of solid \(\mathrm{K_2BeF_4}\)

Fig. 3. Raman spectrum of \(\mathrm{K_2BeF_4}\)

As follows from Fig. 1, potassium fluoroberyllate has two intense bands in the absorption spectrum (\(386\ \mathrm{cm}^{-1}\) and about \(800\ \mathrm{cm}^{-1}\)). Both of these bands (\(\nu_4\) and \(\nu_3\)) should be assigned to triply degenerate vibrations (\(\mathrm{F_2}\)), the first being a deformation-vibration band and the second a stretching one. In the Raman spectrum there is a single intense band at \(560\ \mathrm{cm}^{-1}\) (Fig. 3), which without doubt should be assigned to the totally symmetric vibration (\(\mathrm{A_1}\)). In addition, in the Raman spectrum a weak \(\nu_4\) band at \(388\ \mathrm{cm}^{-1}\) is clearly observed. The other two theoretically possible bands are apparently very weakened; their intensities do not exceed the noise level. By repeated recording, a very weak triply degenerate \(\nu_3\) band is detected at \(800\ \mathrm{cm}^{-1}\). The doubly degenerate \(\nu_2\) band is located, possibly, at \(260\ \mathrm{cm}^{-1}\).

The band of the triply degenerate stretching vibration (\(\nu_3\)) in the absorption spectrum of \(\mathrm{K_2BeF_4}\) is noticeably asymmetric. In addition to the principal maximum at \(805\ \mathrm{cm}^{-1}\), it has a second maximum at \(835\ \mathrm{cm}^{-1}\). Such splitting of a triply degenerate band can apparently be explained by some lowering of the symmetry of the \(\mathrm{BeF_4^{2-}}\) ion in the crystal field: namely, from the symmetry of the group \(\mathrm{T_d}\) to the symmetry \(\mathrm{C_{3v}}\). In accordance with this, a weak band is found at \(560\ \mathrm{cm}^{-1}\), exactly corresponding to the totally symmetric band \(\nu_1\) in the Raman spectrum of \(\mathrm{K_2BeF_4}\). An analogous splitting of the frequency \(\nu_3\) probably also exists in the spectra of cesium and rubidium fluoroberyllates. These compounds also show weak bands (\(\nu_1\)) in the region of \(560\ \mathrm{cm}^{-1}\) (\(551\ \mathrm{cm}^{-1}\) for \(\mathrm{Rb_2BeF_4}\) and \(540\) for \(\mathrm{Cs_2BeF_4}\)).

The asymmetry of the \(\nu_4\) band (deformation vibration \(\mathrm{F_2}\)) in the spectra of potassium, rubidium, and cesium fluoroberyllates (Fig. 1) is not as sharply expressed as in the case of the \(\nu_3\) bands; this is possibly explained by the lower intensity of the \(\nu_4\) bands, as well as by the lower quality of recording on the single-beam spectrometer. The point group of symmetry \(\mathrm{C_{3v}}\) for the \(\mathrm{BeF_4^{2-}}\) ion is consistent with the results of X-ray determinations of the space group of the crystal lattices of fluoroberyllates. According to these determinations, the fluoroberyllates of K, Rb, and Cs are built according to the type \(\beta\)-\(\mathrm{K_2SO_4}\) (\(\mathrm{H_{16}}\)); the space group is \(\mathrm{D_{2h}^{16}}\) (\(\mathrm{Pnma}\)) and \(z = 4\) \({}^{(5-7)}\). In the case of such a space group, in the unit cell there are two groups of “sites” (special positions) with symmetry \(\mathrm{C_i}\) and multiplicity 4, and one group of sites with symmetry \(\mathrm{C_s}\) and multiplicity 4 \({}^{(8)}\). Thus, the \(\mathrm{BeF_4^{2-}}\) ions can occupy in the lattice only positions with the point group \(\mathrm{C_s}\), which is a subgroup of the group \(\mathrm{C_{3v}}\).

In the lattice of sodium fluoroberyllate there occurs, in all probability,

a more substantial distortion of the $\mathrm{BeF}_4$ tetrahedron than in the lattices of the fluoroberyllates of K, Rb, and Cs (see Fig. 1b). However, in the case of $\mathrm{Na}_2\mathrm{BeF}_4$ as well (olivine structural type, space group $D_{2h}^{16}$, $z = 4$ ($^{5,9}$)), the symmetry of the $\mathrm{BeF}_4^{2-}$ ion apparently belongs to the point group $C_{3v}$, since the $\nu_3$ band is split into only two peaks, although both are very intense.

It is interesting that in the spectrum of $\mathrm{Na}_2\mathrm{BeF}_4$ a splitting of the totally symmetric band $\nu_1$ into two bands of equal intensity is also observed (Fig. 1). Such splitting may occur as a result of Fermi resonance if, for example, the doubly degenerate vibration $\nu_2$ in this compound lies near $280\ \mathrm{cm}^{-1}$, and its overtone $2\nu_2$ near $560\ \mathrm{cm}^{-1}$, i.e., coincides with the frequency (in $\mathrm{K}_2\mathrm{BeF}_4$ $\nu_2$ is assumed to be at $260\ \mathrm{cm}^{-1}$).

In the spectrum of $\mathrm{Li}_2\mathrm{BeF}_4$ the frequency $\nu_3$ clearly shows three maxima: $785\ \mathrm{cm}^{-1}$, $809\ \mathrm{cm}^{-1}$, and $864\ \mathrm{cm}^{-1}$. Consequently, in the lithium fluoroberyllate lattice the $\mathrm{BeF}_4^{2-}$ ion has lower symmetry than in the lattices of the other fluoroberyllates, namely $C_{2v}$, $C_s$, or $C_1$.

The frequencies appearing in the spectra of fluoroberyllates $\mathrm{M}_2\mathrm{BeF}_4$ are collected in Table 1.

Table 1

Vibrational frequencies of $\mathrm{BeF}_4^{2-}$ in the spectra of fluoroberyllates of the type $\mathrm{M}_2\mathrm{BeF}_4$

In addition to the frequencies of normal vibrations considered above, several weak frequencies in the region $900$—$1000\ \mathrm{cm}^{-1}$ also appear in the IR absorption spectra of the fluoroberyllates; these are evidently overtones or combination frequencies. The most intense of them, the frequency $\nu_5$, which appears in the spectra of potassium, rubidium, and cesium fluoroberyllates, is well interpreted as the combination frequency $\nu_3 + \nu_1$.

As follows from the data of Table 1, the positions of the normal-vibration frequencies of the $\mathrm{BeF}_4^{2-}$ ion change little in going from Cs to Li.

A calculation in the simple valence-force approximation (starting from the frequency $\nu_1$) gives for the valence-force constant of the Be—F bond the value: $K_{\mathrm{Be-F}} = 3.5 \cdot 10^{-5}\ \mathrm{dyn/cm}$. This value may be compared with the corresponding values of the valence-force constants obtained by the same method for the tetrahedra $\mathrm{BF}_4^{1-}$ and $\mathrm{CF}_4$: $6.91 \cdot 10^{-5}\ \mathrm{dyn/cm}$ and $9.14 \cdot 10^{-5}\ \mathrm{dyn/cm}$, respectively ($^3$). It is noteworthy that the change in the force constants of the M—F bonds in the series beryllium—carbon occurs almost linearly with the change in the formal charge of the central atom.

Moscow State University
named after M. V. Lomonosov

Received
23 V 1963

CITED LITERATURE

1. A. V. Novoselova, Usp. khimii, 28, 33 (1959).
2. R. D. Peacock, D. W. A. Sharp, J. Chem. Soc., 1959, 2763.
3. L. A. Woodward, Trans. Farad. Soc., 54, 1271 (1958).
4. V. V. Obukhov-Denisov, T. A. Sidorov et al., ZhFKh, 34, 1622 (1960).
5. O. D. Daniel, L. Tscheischwili, Zs. Kristallogr., 103, 178 (1941); 104, 132 (1942).
6. P. L. Mukherjee, Ind. J. Phys., 18, 148 (1944).
7. N. A. Toropov, R. G. Grebenshchikov, ZhNKh, 1, 2686 (1956).
8. R. S. Halford, J. Chem. Phys., 14, 8 (1946).
9. G. S. Zhdanov, N. G. Savost’yanov, DAN, 22, 171 (1939).
10. E. Thilo, H. A. Lehman, Zs. anorg. Chem., 258, 332 (1949).