CRYSTALLOGRAPHY

R. F. KLEVTSOVA, P. V. KLEVTSOV

GROWTH FORMS OF CRYSTALS

AND THE CRYSTAL STRUCTURE OF YCl(OH)\(_2\)

(Presented by Academician N. V. Belov, 19 XII 1964)

Crystalline yttrium hydroxychloride YCl(OH)\(_2\) was obtained, along with other solid phases, during the hydrothermal synthesis of yttrium–iron garnet crystals (\(^{1}\)). Its single crystals have the form of plates elongated in one of the directions and sometimes acquiring a needle-like form.

The relatively isometric platy crystals are the best developed; these were used for a photogoniometric study on a two-circle optical goniometer GD-1.

The results of the measurements, after their treatment on a stereographic projection, are given in Table 1. The \(z\) axis was taken as the most developed direction in the crystal, and the \(y\) axis as the direction perpendicular to the plane of the crystal plate.

Table 1

From the stereographic projection it follows that the YCl(OH)\(_2\) crystals belong to the class

\[ \frac{2}{m}\,\frac{2}{m}\,\frac{2}{m}=mmm \]

(the rhombic-dipyramidal class). The faces of the pinacoid (010) are the most developed. Along the direction [010] the unit-cell parameter should be the largest, in agreement with the parameter ratio \(a : b : c = 0.499 : 1 : 0.288\), obtained from the unit face on the stereographic projection. Along the faces of the pinacoid (100), YCl(OH)\(_2\) single crystals possess cleavage.

For X-ray structural studies, YCl(OH)\(_2\) single crystals of size \(0.2 \times 0.4 \times 0.8\ \mathrm{mm}^3\) were selected. The unit-cell parameters, obtained from rotation X-ray photographs of the crystal about the principal crystallographic directions, from zero-layer line development photographs, and also from a Debyegram taken in an RKU-114 camera, are:

\[ a = 6.21,\quad b = 12.56,\quad c = 3.62\ \text{Å} \]

(hence \(a : b : c = 0.494 : 1 : 0.288\)). With \(D_{\text{meas.}} = 3.71\ \mathrm{g/cm^3}\), the unit cell contains 4 formula units.

On an X-ray goniometer, the zero, 1st, 2nd, and 3rd layer-line developments of rotation about the \(c\) axis and the zero-layer development about the \(a\) axis were recorded. Since the absorption edge of the Y \(K_{\alpha}\)-series is very close to the wavelength

waves of Mo \(K_\alpha\) (usually used in X-ray structural studies), the photographs were taken with Ag \(K_\alpha\)—Cu \(K_\alpha\) radiation. Because of the nonspherical shape of the specimens, absorption introduced a considerable error into the estimation of intensities, especially when Cu \(K_\alpha\) radiation was used. Therefore the Cu-radiation photographs were used chiefly to determine the dimensions of the crystal unit cell, while the subsequent X-ray structural study was based on X-ray patterns taken with Ag \(K_\alpha\) radiation.

Fig. 1. Y-polyhedron formed by Cl and O(OH) atoms \(\sqrt[4]{2}\)

Analysis of the reflection intensities showed that the structure of \(\mathrm{YCl(OH)_2}\) has a pseudoperiod \(b' = b/2\).

Systematic extinctions of reflections with \(k = 2n + 1\) were observed only in the \(0kl\) zone, and reflections with \(h + l = 2n + 1\) in the \(h0l\) zone; thus the possible space groups are \(D_{2h}^{16} = Pbnm\) and \(C_{2v}^{9} = Pbn2_1\). Since optical-goniometric studies indicate the presence of a center of symmetry in the crystals in the absence of piezoelectricity, we adopted for this compound the Fedorov group \(D_{2h}^{16} = Pbnm\). The intensities of the observed reflections were estimated visually by a blackening scale with a step of \(\sqrt[4]{2}\), after which the usual method was used to obtain the arrays \(F_{hkl}^{2}\) and \(F_{hkl}\).

Table 2

The \(x\) and \(y\) coordinates of the yttrium atoms were determined from the Patterson projection \(P(uw)\). The first projections of the electron density \(\rho(xy)\) were constructed from the amplitudes \(F_{hk0}\), with signs taking into account first only the yttrium atoms, then yttrium and chlorine, and finally all atoms. The discrepancy factor calculated from the coordinates of all atoms for the \(F_{hk0}\) array at this stage was 16.9% for 87 nonzero amplitudes. To determine the \(z\) coordinate of the atoms, the Patterson projection \(P(uw)\) was used; from it it followed that all atoms are located in mirror planes \(m\). Refinement of the atomic coordinates was carried out on a large computer by the least-squares method \((^{2})\). A total of 260 nonzero amplitudes \(F_{hkl}\) were used.

Fig. 2. Character of the formation of a layer from Y-polyhedra

The finally accepted atomic coordinates are given in Table 2.

The discrepancy factor of the structure over all nonzero amplitudes \(F_{hkl}\), calculated from the refined coordinates, is 16.5% \((\sin\vartheta/\lambda \leq 0.915)\). Taking into account 102 reflections for which \(F_{\mathrm{exp}} = 0\) \((\sin\vartheta/\lambda \leq 0.60)\), the factor is 21.7% (the intensity of these reflections was taken to be equal to half the minimum observed value). The significant increase in \(R\) is explained by the large number of introduced experimental “zeros” (about 50%), arising because of the presence of a pseudoperiod in the structure.

Interatomic distances. The nearest neighbors to yttrium proved to be 8 neighbors: two Cl atoms and 6 O atoms (hydroxyl groups), which form around yttrium an octahedron—a trigonal prism with semioctahedra on two faces (Fig. 1).

The distances Y—OH in this polyhedron are: 2.30; 2.33; 2.37(2); 2.44(2) Å; Y—Cl = 2.85(2) Å.

Fig. 3. Projection of the structure of YCl(OH)₂ in coordination polyhedra onto the (001) plane

The edges of the polyhedron are OH—Cl: 3.34(2); 3.11(2); 2.99(2) Å; Cl—Cl: 3.62 Å; OH—OH: 3.62(2); 2.94(2); 2.91(2); 2.77(2); 2.70(2) Å.

The principal motif in the structure should be regarded as continuous walls of octahedra extending parallel to the (010) plane.

Fig. 4. Positions of atoms in the structure of YCl(OH)₂ (xy projection)

Within the walls the polyhedra are joined to one another in the [001] direction along the faces of the base of the prism into columns, which, in turn, in the “lateral” direction [100] are joined along the edges of the semioctahedra (Figs. 2 and 3). The entire structure as a whole consists of such layers; moreover, the first, third, fifth, etc., layers are translationally identical. The intermediate layers are displaced relative to the principal ones, being connected with them by glide planes \(n\), passing through \(1/4b\) and \(3/4b\).

The arrangement of atoms in the structure corresponds to the noted pseudoperiod \(b/2\). Indeed, from Fig. 4 it is clearly seen that for yttrium atoms there is a half-translation along the \(b\) axis, whereas the remaining, lighter atoms Cl and O are connected by the full translation—\(b\).

From consideration of the structure one should expect the presence in YCl(OH)\(_2\) crystals of a glide plane parallel to the layers (010); the direction

the slip direction \([001]\), and, accordingly, the greatest growth rate of the crystals in the \([001]\) direction, leading to the formation of needle-like crystals, can be explained by the preferential emergence in this direction of screw dislocations, which are growth centers and arise when the lattice is disturbed as a result of the incorporation of impurities, the capture of inclusions, and abrupt changes in temperature. On the growing face of the pinacoid \((010)\), a screw dislocation can apparently form only by the attachment of a three-dimensional nucleus to the stepped surface according to the mechanism proposed in \((^3)\).

Institute of Inorganic Chemistry
Siberian Branch
Academy of Sciences of the USSR

Received
20 XI 1964

REFERENCES

1. P. V. Klevtsov, R. F. Klevtsova, L. P. Sheina, Zh. strukt. khimii, 6, No. 3 (1965).
2. F. A. Brusențsev, Kristallografiya, 8, 10 (1963).
3. N. Albon, Phil. Mag., 8, No. 92, 1335 (1963).