Abstract Generated abstract
The paper reports a single-crystal X-ray determination of the structure of orthorhombic gamma-Na2BeF4, undertaken because this compound was expected to model gamma-Ca2SiO4 and direct structural data had been lacking. Using limited zero-level diffraction photographs, Patterson analysis, and comparison with the gamma-Ca2SiO4 motif, the authors determined atomic coordinates in the acentric space group Pn21a and obtained discrepancy factors of about 11 to 13 percent. The structure is described as an olivine-type arrangement based on close-packed fluorine double layers, with Na occupying half of the octahedral voids and Be occupying one quarter of the tetrahedral voids. Unlike related compounds with larger alkali cations, Na remains six-coordinated, and two distinct types of Na octahedra are identified.
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CRYSTALLOGRAPHY
G. G. Guseinov, V. V. Ilyukhin, Academician N. V. Belov
CRYSTAL STRUCTURE OF Na ORTHOFLUOROBERYLLATE
\(\gamma\)-\(\mathrm{Na_2BeF_4}\)
Recently in our laboratory \((^{1,2})\) the structures of the alkali orthofluoroberyllates \(\mathrm{K_2BeF_4}\) and \(\mathrm{Rb_2BeF_4}\) were solved, and it was shown that both can indeed serve, according to Goldschmidt–Fersman \((^{3,4})\), as model structures for orthosilicate \(\mathrm{Ba_2SiO_4}\), the K compound being quite close, while the Rb compound is somewhat distorted. In the solved structures—very probably in \(\mathrm{Ba_2SiO_4}\) and presumably in \(\mathrm{Sr_2SiO_4}\)*—an olivine-like \((\mathrm{Mg_2SiO_4})\) motif is well expressed, but with considerable deviations—distortions associated with the “large size” of the cations K and Rb, and also Ba, in comparison with Mg. As for the Ca orthosilicate of analogous formula, namely \(\mathrm{Ca_2SiO_4}\), three modifications are known for it, one of which—larnite, \(\gamma\)-\(\mathrm{Ca_2SiO_4}\)—repeats the olivine structure especially accurately: Ca in it is located in octahedra, and the environment of each \(\mathrm{O^{2-}}\) anion strictly corresponds to the olivine environment, despite the increase in the size of the Ca octahedron with the standard dimensions of the \([\mathrm{SiO_4}]\) tetrahedron.
In accordance with this, solving the structure of \(\gamma\)-\(\mathrm{Na_2BeF_4}\) is of interest; as Table 1 shows (the ionic radii of “parallel” atoms are given according to Goldschmidt and, in parentheses, according to Ahrens; the latter have better justified themselves in comparing \(\mathrm{Ba_2SiO_4}\) with the models \(\mathrm{K_2BeF_4}\) and \(\mathrm{Rb_2BeF_4}\)), it should be a perfect model of the structure of Ca orthosilicate.
Table 1
| \(\mathrm{Na^+}\) | \(\mathrm{Be^{2+}}\) | \(\mathrm{F^-}\) | \(\mathrm{Ca^{2+}}\) | \(\mathrm{Si^{4+}}\) | \(\mathrm{O^{2-}}\) |
|---|---|---|---|---|---|
| 0.98(0.97) | 0.35(0.34) | 1.33(1.33) | 1.04(0.99) | 0.39(0.42) | 1.32(1.32) |
The absence of direct structural data for \(\gamma\)-\(\mathrm{Na_2BeF_4}\) is connected with the great difficulty of obtaining single-crystal samples. It should be noted, however, that on the basis of Debyegrams, using the closeness of the unit-cell parameters, the authors \((^6)\) came to the conclusion that the structure of \(\gamma\)-\(\mathrm{Na_2BeF_4}\) is built according to the olivine type. We obtained the possibility of directly solving the structure thanks to the kindness of B. P. Sobolev and Yu. P. Dikov, who placed at our disposal single crystals of Na orthoberyllate—the product of hydrothermal synthesis. Of the three modifications \((\gamma-, \delta-, x)\) of \(\mathrm{Na_2BeF_4}\), the rhombic \(\gamma\)-phase seemed the most promising with respect to model connection with larnite (\(\delta\) is trigonal and \(x\) is monoclinic). Among the large mass of crystalline \(\gamma\)-\(\mathrm{Na_2BeF_4}\), it was nevertheless possible to isolate only one crystallite, of tenths-of-a-millimeter dimensions, suitable for single-crystal photography. With Laue class \(mmm\), the cell parameters \(a = 10.181\ \text{Å}\), \(b = 5.61\ \text{Å}\), \(c = 4.447\ \text{Å}\) do not agree with previously published data \((^{6-8})\). A density of 2.48 corresponds to a content in the cell of \(Z = 4\) formula units. The X-ray group \(mmm\, Pn{-}a\), following from systematic absences, covers two Fedorov groups: \(Pnma\) and \(Pn2_1a\), of which the acentric \(Pn2_1a\) was chosen,
* Infrared spectral data do not allow the structures of \(\mathrm{Sr_2SiO_4}\) and \(\mathrm{Ba_2SiO_4}\) to be fully identified \((^5)\).
since in the final result it made it possible to reduce the discrepancy factor \(R\) to a significantly better value.
In the reduced symmetry, the first relatively significant difference from \(\gamma\)-Ca\(_2\)SiO\(_4\) appeared; this seemed interesting to us in connection with the previously noted “fundamental” asymmetry of the tetrahedral Be atoms as compared with Si \((^9)\). At the same time, lowering the symmetry led to an increase in the number of structural parameters (20 in \(\gamma\)-Na\(_2\)BeF\(_4\), as compared with 9 in the olivine structure of \(\gamma\)-Ca\(_2\)SiO\(_4\)).
For the initial determination of the structure, it proved sufficient to have two zero-level photographs \(hk0\) and \(h0l\) with intensities measured from blackening marks (interval \(\sqrt[4]{2}\), Mo \(K_\alpha\) radiation, \((\sin\theta/\lambda)_{\max}=0.84\) and \(1.02\ \text{\AA}^{-1}\) on the two photographs).
An attempt to determine the signs of the structure amplitudes by direct methods gave no results because of the small number of independent reflections (in the orthorhombic structure there are, a priori, half as many of them as in the monoclinic one). The solution was found from analysis of Patterson maps, supported by the expected rough analogy with the motif of \(\gamma\)-Ca\(_2\)SiO\(_4\). The latter was important in distinguishing Na atoms from (isoelectronic in the ionic state) F atoms. The principal points were the fixing of two Na atoms, first in the acentric projection \(hk0\) and then in the centrosymmetric \(h0l\), followed by further determination of the F atoms up to the identification of the lightest atom, Be. The final discrepancy factors were: \(R_{hk0}=11.2\%\) \((B=0.35)\) and \(R_{h0l}=12.6\%\) \((B=0.5)\).
Fig. 1. Crystal structure of \(\gamma\)-Na\(_2\)BeF\(_4\) on the (001) plane
Fig. 2. Crystal structure of \(\gamma\)-Na\(_2\)BeF\(_4\) in polyhedra
The adopted coordinates are given in Table 2.
The interatomic distances corresponding to these coordinates are:
Be—F \(=1.46\)–\(1.55\ \text{\AA}\), with edges of the Be tetrahedron F—F \(=2.48\)–\(2.57\ \text{\AA}\).
Table 2
| Atoms | \(x/a\) | \(y/b\) | \(z/c\) | Atoms | \(x/a\) | \(y/b\) | \(z/c\) |
|---|---|---|---|---|---|---|---|
| Na\(_{\mathrm{I}}\) | 0.000 | 0.002 | 0.020 | F\(_{\mathrm{II}}\) | 0.158 | 0.473 | 0.749 |
| Na\(_{\mathrm{II}}\) | 0.233 | 0.748 | 0.503 | F\(_{\mathrm{III}}\) | 0.083 | 0.259 | 0.276 |
| Be | 0.172 | 0.238 | 0.646 | F\(_{\mathrm{IV}}\) | 0.059 | 0.732 | 0.750 |
| F\(_{\mathrm{I}}\) | 0.158 | 0.033 | 0.751 |
The Na—F distances are close to the mean value \((\mathrm{Na}—\mathrm{F} = 2.08—2.18\ \text{Å})\), \(2.13\ \text{Å}\).
It is convenient to compare the structures of orthofluoroberyllates \(\mathrm{Na_2BeF_4}\) with Ca-orthosilicates, since between \(\mathrm{Ca_2SiO_4}\) and artificial \(\mathrm{Na_2BeF_4}\) there exists (according to the literature data) isotypism in all modifications \((^8)\).
With such a consideration, for \(\gamma\)-\(\mathrm{Na_2BeF_4}\) (Fig. 1) we arrive at the classical description of the olivine structure \((^{10-12})\). The basis of the structure of \(\gamma\)-\(\mathrm{Na_2BeF_4}\) is a closest double-layer packing of F atoms, in which \(1/2\) of the octahedral voids are occupied by Na and \(1/4\) of the tetrahedral voids by Be.
Fig. 3. Ribbons of \(\mathrm{Na_1}\) (a) and \(\mathrm{Na_2}\) (b) in the structure of \(\gamma\)-\(\mathrm{Na_2BeF_4}\).
It is clear that the very similar structural parameters of \([\mathrm{SiO_4}]\) and \([\mathrm{BeF_4}]\) should not cause any special changes in the structural motif, but the replacement of Mg (0.74) by the comparatively large Na (0.98) would seem, to some extent, to have had to affect the general structural motif in \(\gamma\)-\(\mathrm{Na_2BeF_4}\). However, in contrast to larger cations (K, Rb, Cs, ...), which require an increase in coordination numbers (up to 9), in the structure of \(\gamma\)-\(\mathrm{Na_2BeF_4}\) the coordination number of the large Na remains equal to 6. Possibly for this reason, no “defects” characteristic of olivine are observed in the structure of \(\gamma\)-\(\mathrm{Na_2BeF_4}\) (as is evidenced by the F—F distances).
In the structure, two types of Na-octahedra are clearly distinguished (Fig. 2). Octahedra of \(\mathrm{Na_I}\) are situated as if isolated at the beginning and at \(1/2a\), being joined by \([\mathrm{BeF_4}]\)-tetrahedra (Fig. 3a), and play a cementing role between ribbons of \(\mathrm{Na_{II}}\) octahedra running parallel to the \(c\) axis (Fig. 3b).
Institute of Crystallography
Academy of Sciences of the USSR
Received
3 IV 1965
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