UDC 549.76

CRYSTALLOGRAPHY

V. P. GOLOVACHEV, É. A. KUZ’MIN, Yu. A. KHARITONOV,
Academician N. V. BELOV

CRYSTAL STRUCTURE OF POTASSIUM TETRACHROMATE $K_2Cr_4O_{13}$

In recent years, in a number of silicates, phosphates, etc., isolated triortho groups $[Z_3O_{10}]$ have been demonstrated by X-ray methods $({}^{1-3})$, and this has aroused interest in the radicals $[Z_4O_{13}]$, for which two chemically difficult-to-distinguish configurations are possible (Fig. 1A and 1B)*.

In the first X-ray study of K tetrachromate $({}^{4})$, for monoclinic crystals of $K_2Cr_4O_{13}$ it was established that: $a = 7.50$, $b = 8.55$, $c = 9.47$ Å; $\beta = 92^\circ$, $Z = 2$**. It was pointed out that tetrachromate is thermodynamically unstable even at ordinary temperature, but that the decomposition reaction proceeds slowly, and this makes X-ray investigation possible.

Fig. 1. Island (terminal) radicals of 4 tetrahedra: A and B—with formula $[Z_4O_{13}]$, V and G—with metaformula $[Z_4O_{12}]$

For the present analysis, crystals of $K_2Cr_4O_{13}$ were grown from an aqueous solution by the method described in $({}^{5})$. Two specimens, $0.1 \times 0.2 \times 0.2\ \mathrm{mm}^3$ and $0.2 \times 0.2 \times 0.4\ \mathrm{mm}^3$, coated with a protective cellulose film, gave a good diffraction pattern. The unit-cell parameters were obtained from rotation and zero-layer Weissenberg photographs (RGNS goniometer, equi-inclination method): $a = 8.71$, $b = 7.55$, $c = 9.37$ Å; $\beta = 93^\circ$.

The three-dimensional experimental material for the X-ray structural analysis consisted of 550 nonzero reflections $h0l - h6l$ and $0kl - 1kl$

* But clearly differing from radicals also with 4 tetrahedra but with formula $[Z_4O_{12}]$ (Fig. 1V and 1G).

** The parameters differ from those established by us by a somewhat incomprehensible interchange of $a$ and $b$.

(Mo radiation, \(\max \sin \vartheta/\lambda = 0.7\ \text{Å}^{-1}\)). The intensities of the reflections were estimated on the \(V^2\) blackening-mark scale, using multiple exposures for strong reflections. After introduction of the \(LP\) factor, no absorption correction was introduced. With Laue symmetry \(2/m\), the extinctions \(l = 2n - 1\) in the \(h0l\) zone make possible two Fedorov groups: \(C_s^2 = Pc\) and \(C_{2h}^4 = P2/c\).

Most of the peaks of the three-dimensional Patterson function constructed from the experimental data were concentrated in four sections parallel to the \(xz\) plane. This indicated a pseudosymmetric arrangement of the heavy Cr and K atoms and considerably complicated the solution of the structure. Using the symmetry and a new method of representing the Patterson function in the form of a system of segments\({}^{6}\), it was possible to localize the chromium and potassium atoms within the acentric group \(Pc\). The lighter O atoms were fixed in a cycle of three-dimensional syntheses of the electron density \(\rho(xyz)\). The value of the discrepancy factor achieved (for all atoms) was 20%. Least-squares refinement reduced \(R_{hkl}\) to 10.8%. The coordinates of the basis atoms (55 independent positional parameters) are given in Table 1. The temperature correction common to all atoms is \(B = 1.3\ \text{Å}^{-2}\).

Fig. 2. Structure of K tetrachromate \(\mathrm{K_2Cr_4O_{13}}\). The spheres show the parallel \(c\) axes of the crystallographically independent columns of \(\mathrm{K_1}\) and \(\mathrm{K_2}\). Between them, two tetragroups \([\mathrm{Cr_4O_{13}}]\), related by the glide plane \(c\) (parallel to the plane of the drawing), are shown.

Complete solution of the structure did not confirm the idea of the radical \(\mathrm{Cr_4O_{13}}\) as a member of the series \(ZO_4 — Z_2O_7 — Z_3O_{10} — Z_4O_{13} — Z_5O_{16}\) (terminating in a zunyite five-membered unit), but neither is there a strictly linear configuration.

Table 1

\(\mathrm{K_2Cr_4O_{13}}\). Coordinates of the basis atoms

The 4 independent Cr atoms form, in the direction of the \(a\) axis, a radical of two corners with 4 Cr tetrahedra. The tetragroup \([\mathrm{Cr_4O_{13}}]^{2-}\) may be represented as a trioorthogroup \(\mathrm{Cr_3O_{10}}\) elongated by 1 tetrahedron (more precisely, by one umbrella molecule \(\mathrm{CrO_3}\)). The idea of con-

condensation of two diortho groups \(\mathrm{Cr_2O_7}\), as is seen from Fig. 2 and is indirectly confirmed by the easier preparation of \([\mathrm{Cr_4O_{13}}]^{2-}\), rather than \([\mathrm{Cr_3O_{10}}]^{2-}\), from the corresponding bichromates.

Among the Cr—O distances, 6 bridging ones are distinguished:

\[ \mathrm{Cr_4 - O_6}=1.91,\qquad \mathrm{Cr_1 - O_6}=1.83,\qquad \mathrm{Cr_1 - O_9}=1.75, \]

\[ \mathrm{Cr_2 - O_9}=1.96,\qquad \mathrm{Cr_2 - O_2}=1.70,\qquad \mathrm{Cr_3 - O_2}=1.84\ \text{\AA}. \]

They are substantially longer than the remaining Cr—O distances, which are equal: in the first tetrahedron, 1.56 and 1.51 Å; in the second, 1.61 and 1.63 Å; in the third, 1.63, 1.54, and 1.69 Å; in the fourth, 1.61, 1.77, and 1.64 Å. The angles \(\mathrm{Cr_1 - O_9 - Cr_2}\) are \(128^\circ\), \(\mathrm{Cr_2 - O_2 - Cr_3}\) \(144^\circ\), and \(\mathrm{Cr_4 - O_6 - Cr_1}\) \(110^\circ\). The two independent K cations are characterized by a large coordination number—11—but by very compact and almost identical polyhedra. The mean distances \(\mathrm{K_1 - O}=3.00\) Å and \(\mathrm{K_2 - O}=3.03\) Å are exceptionally close; moreover, the next K—O distances, which are not included in the first coordination sphere, 3.88 and 4.52 Å, respectively, are clearly not bonded to K.

Fig. 3. \(\mathrm{K_2Cr_4O_{13}}\), \(xy\) projection. Two tetragroups \([\mathrm{Cr_4O_{13}}]\) are shown; they are connected by a plane perpendicular to the plane of the drawing—the glide plane \(c\).

The potassium 11-vertex polyhedra are very large, but do not form a three-dimensional framework. Each type of K-polyhedron is built up into its own infinite chain (Fig. 2), which is “stretched” along its own glide plane \(c\), perpendicular to the \(y\) axis, at the level \(\sim 0\) for the \(\mathrm{K_2}\)-polyhedra and \(\sim b/2\) for the \(\mathrm{K_1}\)-polyhedra. The two kinds of K chains are combined into infinite layers of large 11-vertex polyhedra. The layers are parallel to the plane (100) and are connected to one another by the \(\mathrm{Cr_4O_{13}}\) tetragroups. The two tetragroups per cell, at the levels \(\sim b/4\) and \(\sim 3b/4\), are linked to one another by the same \(c\) planes (Fig. 3).

Gorky Research Physicotechnical Institute
at N. I. Lobachevsky Gorky State University

Institute of Crystallography
Academy of Sciences of the USSR
Moscow

Received
26 II 1970

CITED LITERATURE

1. M. A. Simonov, Yu. K. Egorov-Tismenko, N. V. Belov, DAN, 175, No. 1 (1947).
2. M. A. Simonov, Yu. K. Egorov-Tismenko, N. V. Belov, DAN, 179, No. 6 (1968).
3. G. Donnay, R. Allmann, Acta Crystallogr., B24, 845 (1968).
4. V. I. Spitsyn, N. S. Afonskii, V. I. Tsirel’nikov, ZhNKh, 5, No. 7, 1505 (1960).
5. Guide to Preparative Chemistry, ed. by Brauer, IL, 1956, p. 776.
6. E. A. Kuz’min, V. P. Golovachev, N. V. Belov, DAN, 192, No. 1 (1970).