UDC 548.736.626

CRYSTALLOGRAPHY

M. A. SIMONOV, Yu. K. EGOROV-TISMENKO, Academician N. V. BELOV

CRYSTAL STRUCTURE OF Na, Cd SILICATE

\(\mathrm{Na_2CdSi_2O_6 = Na_6Cd_3[Si_6O_{18}]}\)

The objects of investigation were samples of crystals of a synthetic Na, Cd silicate (“phase \(K\)”) in the system \(\mathrm{Na_2O—CdO—SiO_2}\), obtained* in the laboratory of hydrothermal synthesis of the Institute of Crystallography, Academy of Sciences of the USSR \((^{1})\). The chemical composition of phase \(K\), according to the analysis of V. S. Bykova, G. A. Arapova, and Yu. S. Nesterova (\(\mathrm{SiO_2}\)—37.47%; \(\mathrm{CdO}\)—42.88%; \(\mathrm{Na_2O}\)—19.3%; \(\Sigma = 99.65\%\)), may be expressed by the approximate formula \(\mathrm{Na_2Cd[Si_2O_6]}\), with the metasilicate ratio \(\mathrm{Si:O = 1:3}\).

The parameters of the pseudotetragonal cell (Laue class \(mmm\)) of phase \(K\):

\[ a = 10.40 \pm 0.05\ \text{\AA}, \quad b = 10.40 \pm 0.05\ \text{\AA}, \quad c = 7.45 \pm 0.03\ \text{\AA}\quad (c = {}^{1}/_{2}c) \]

were established from rotation x-ray photographs (Mo radiation). Along the short \(c\) axis there is a distinctly expressed pseudoperiod \(c' = {}^{1}/_{2}c\).

The experimental intensity material consisted of reflections with the nets \(hk0\), \(hk2\), \(hk3\), \(hk4\), \(hk6\), \(h0l\), \(h1l\), and \(0kl\)** \((\max \sin\vartheta/\lambda = 0.8)\). The intensities of the reflections were estimated visually by comparison with a standard blackening scale with a step \(\sqrt{2}\); the standards were obtained in a Weissenberg x-ray goniometer using the 440 reflection.

The syngony \(mmm\) fixed from the Laue photographs was once again confirmed by the symmetry of the obtained nets.

Absence of integral extinctions excludes nonprimitivity of the lattice, but the disappearance of a considerable part of the \(hkl\) reflections with \(h+k=2n+1\) and the weakness of those retained indicate pseudocentering of the face \((001)\), just as the pseudoperiod \(c' = {}^{1}/_{2}c\) weakened all \(hkl\) reflections with \(l=2n+1\).

Fig. 1. Na, Cd metasilicate (phase \(K\)). Pseudotetragonal projection of the structure on the plane \(xy\). In addition to tetrahedra, polyhedra around Cd are singled out. Spheres are Na cations.

The only systematic extinctions remaining were in the \(hk0\) zone \((h+k=2n+1)\), which leads to the x-ray group \(P--n\), i.e., to two space groups \(D_{2h}^{13}=Pmmn\) and \(C_{2v}^{7}=Pm2_1n\) \((P2_1mn)\). In view of the absence of a center of symmetry (presence of a piezoelectric effect), only the hemimorphic space group \(C_{2v}^{7}=Pm2_1n\) \((P2_1mn)\) is possible. Analysis of the pater-

* Within very narrow concentration limits the dimensions of the crystallites, somewhat elongated along \([001]\), are \(\sim 0.1\) mm.

** The missing \(hk1\) and \(hk5\) were not recorded because of the pseudoperiod.

son projections and the first calculations for localizing the Cd atoms in the \(xy\) projection confirmed that, with a pseudotetragonal setting—choice of axes—the space group of phase \(K\) is \(C_{2v}^{7}=Pm2_1n\).

At a specific gravity \(d=3.82\), a cell of the indicated dimensions contains \(Z=6\) formula units of \(\mathrm{Na_2CdSi_2O_6}\). The atoms are distributed over two types of crystallographic positions: fourfold general positions and single twofold special positions on mirror planes \(m\).

The presence in the cell of 6 Cd atoms, with multiplicity 4 for the general positions, made it possible, already from the Patterson projections \(uv\), \(uw\), to determine the coordinates of the Cd atoms; from these, in the \(xy\) projection, through a series of electron-density syntheses, it was possible to localize the Si and Na atoms and part of the oxygen atoms.

However, the pseudoperiod along the \(c\) axis with the pseudo-centered \(xy\) face, as well as the large number of overlaps in all projections, made their interpretation difficult. In the subsequent structural analysis, the main role was played by three-dimensional complete and difference Fourier syntheses. The structural model obtained was refined by the method of successive approximations, since the presence of a pseudoperiod, with a relatively small number of independent nonzero reflections, substantially impeded effective refinement of the atomic coordinates by the least-squares method. All calculations were performed at the Computing Center of Moscow University on a BESM-4 machine, using programs developed by B. L. Tarnopol’skii and V. I. Andrianov \((^{2})\). The final coordinates of the basis atoms (53 parameters) of phase \(K\) are given in Table 1. The discrepancy factor for these coordinates is \(R_{hkl}=11.5\%\). The averaged constant of isotropic thermal

Fig. 2. Na, Cd metasilicate. Principal architectural rods of the structure—ribbons of Cd, Na octahedra in the \(yz\) projection

Table 1

\(\mathrm{Na_2CdSi_2O_6}\) (phase \(K\)). Coordinates of the basis atoms

oscillations practically became zero (\(B = 0.03\) Å), which should be considered a direct consequence of neglecting absorption.

The structural motif of the pseudotetragonal phase \(K\) is most clearly seen in the basal projection \(xy\) (Fig. 1), with the oxygen tetrahedra around Si and part of the Cd octahedra singled out; the Na atoms are shown as spheres. The basis of the structure consists of ribbons of Cd, Na octahedra, infinite along \(c\) (Fig. 2), located at the levels \(x = 0\) and \(x = \tfrac{1}{2}\). The ribbons, repeated translationally along \(b\), are connected with one another by a silicic-oxygen radical—the group \([\mathrm{Si}_6\mathrm{O}_{18}]\), which also cements the ribbons located at different levels.

Fig. 3. Na, Cd metasilicate. Six-membered (pseudotetragonal) rings in axonometry. The upper and two lower ones are connected by a glide plane

The island radical with formula \([\mathrm{Si}_6\mathrm{O}_{18}]\) is a six-membered ring, similar to lovozerite rings \((^3,\,^4)\): the ring may be described as two parallel diorthogroups \(\mathrm{Si}_2\mathrm{O}_7\), elongated along the \(c\) axis and linked on one side above, and on the other side below, by single \(\mathrm{SiO}_4\) tetrahedra situated in the symmetry planes (Figs. 1 and 3)*.

In Fig. 4, in the \(xz\) projection, four types of Na polyhedra are shown. Two Na cations (\(\mathrm{Na}_2, \mathrm{Na}_3\)) have six neighbors at distances of 2.24–2.87 Å. The nearest neighbors of \(\mathrm{Na}_1\) are seven O atoms at distances of 2.20–2.75 Å. \(\mathrm{Na}_4\) is in eightfold coordination (2.2–2.75 Å).

In the arrangement of Cd, Na, Si polyhedra, two levels are clearly distinguished (\(+\) and \(-\) zigzags of the ribbon of Cd octahedra) along the \(c\) axis, which creates the noted pseudoperiod \(c' = \tfrac{1}{2}c\). The Cd atoms are, moreover, arranged according to the \(C\)-law, producing pseudocentering of the face (001).

Fig. 4. Na, Cd metasilicate. Four types of Na polyhedra in the \(xz\) projection

With a satisfactory balance of valence forces, the interatomic distances lie within the limits:

\[ \begin{aligned} \mathrm{Si} - \mathrm{O} &= 1.52\text{--}1.69\ \text{Å} &&\text{for } \mathrm{O} - \mathrm{O} = 2.51\text{--}2.79\ \text{Å},\\ \mathrm{Na} - \mathrm{O} &= 2.2\text{--}2.87\ \text{Å} &&\text{for } \mathrm{O} - \mathrm{O} = 2.62\text{--}4.97\ \text{Å},\\ \mathrm{Cd} - \mathrm{O} &= 2.0\text{--}2.79\ \text{Å} &&\text{for } \mathrm{O} - \mathrm{O} = 2.77\text{--}4.4\ \text{Å}. \end{aligned} \]

* In projection along the pseudotetragonal axis, the ring appears four-membered, resembling a single-story four-membered ring of baotite \((^5)\) and a two-story four-membered ring in ecanite \((^6)\), and therefore our ring may be characterized as a compromise one, with two two-story links and two single-story links.

The distances from the bridging atoms in the radical \([\mathrm{Si}_6\mathrm{O}_{18}]\) to the central Si atoms are somewhat increased (1.64–1.67 Å) compared with the average (1.62 Å). The shared edges of the Cd octahedra are shortened to 2.77 Å. The shared edge of the \(\mathrm{Na}_4\) eight-vertex polyhedron with the \(\mathrm{Si}_4\) tetrahedron is also shortened, to 2.64 Å.

On the basis of the structure obtained for phase \(K\), its expanded formula should be written as \(\mathrm{Na}_6\mathrm{Cd}_3[\mathrm{Si}_6\mathrm{O}_{18}]\). The unit cell contains two such units (\(Z' = 2\)).

Comparison of the solved structure, which has the gross formula \(\mathrm{Na}_2\mathrm{CdSi}_2\mathrm{O}_6\), with the structure of \(\mathrm{Na}_2\mathrm{ZnSi}_2\mathrm{O}_6\) (phase \(C'\), \(M\)) demonstrates that complete replacement of Zn atoms, which usually prefer tetrahedral coordination \((^{7})\), by Cd atoms leads to a complete rearrangement of the structure, in particular to the replacement of infinite metachains by a ring-type metaradical \((^{8})\).

Moscow State University
named after M. V. Lomonosov

Received
22 III 1967

REFERENCES

\(^{1}\) M. A. Simonov, O. K. Melnikov, B. N. Litvin, in: Collected Articles, Hydrothermal Synthesis, “Nauka,” 1967.
\(^{2}\) B. L. Tarnopol’skii, V. I. Andrianov, ZhSKh, 4, 3, 434 (1963).
\(^{3}\) N. V. Belov, Crystal Chemistry of Silicates with Large Cations, Publishing House of the Academy of Sciences of the USSR, 1961.
\(^{4}\) V. V. Ilyukhin, N. V. Belov, DAN, 131, No. 1, 176 (1960); Crystallography, 5, No. 2 (1960).
\(^{5}\) V. I. Simonov, Crystallography, 5, 544 (1960).
\(^{6}\) V. I. Mokeeva, N. I. Golovastikov, DAN, 165, No. 6 (1965).
\(^{7}\) N. V. Belov, E. A. Pobedimskaya, Mineralogical Collection, Lviv University, 20, 326 (1966).
\(^{8}\) M. A. Simonov, N. V. Belov, DAN, 164, No. 2 (1965).