Reports of the Academy of Sciences of the USSR

1. Volume 135, No. 4

PHYSICS

A. I. ZASLAVSKII and A. G. TUTOV

STRUCTURE OF THE NEW ANTIFERROMAGNET BiFeO$_3$

(Presented by Academician A. F. Ioffe, 20 VI 1960)

In connection with the work on the search for new ferromagnetic semiconductors being carried out in the ferrites and ferroelectrics laboratory of the Institute of Semiconductors of the Academy of Sciences of the USSR, a compound of composition BiFeO$_3$, which is an antiferromagnet, was synthesized.

Polycrystalline samples of BiFeO$_3$ were prepared by the usual ceramic technology. The temperature of the preliminary firing was 750°, and of the final firing 800°. The fact that the sample was available only in powder form determined the course of the X-ray structural investigation. The powder pattern of BiFeO$_3$ was obtained in a VRS-3 camera of diameter 143 mm using Cu $K\alpha$ radiation. The interplanar spacings were corrected according to a correction curve constructed for this camera and this radiation. NH$_4$Br was used as the standard substance ($a = 4.051$ kX).

From the X-ray pattern it could be concluded that BiFeO$_3$ has a unit cell close to cubic, with a small rhombohedral distortion.

Using the hexagonal curves of T. B. Buerger ($^1$), a reliable indexing of the first 13 lines was carried out. All subsequent work on the analysis of the structure was performed in hexagonal coordinates. Complete indexing of all 54 reflections of the powder pattern was carried out with the aid of de Wolff’s scheme of $Q$ values in the reciprocal lattice ($^2$).

From the calculated parameters of the hexagonal cell ($a = 5.569 \pm 0.002$ kX; $c = 6.920 \pm 0.004$ kX) and the pycnometric density $\delta_{\mathrm{op}} = 8.31$ g/cm$^3$, the number of “molecules” of BiFeO$_3$ for the hexagonal cell was determined to be $Z = 3$. Hence the X-ray density is $\delta_X = 8.39$ g/cm$^3$. The systematic absences of reflections corresponded to the rhombohedral condition—$H + K + L = 3n$.

From the extinctions the possible space groups were established ($^3$): 146. $R3$; 148. $R\overline{3}$; 155. $R32$; 160. $R3m$ and 166. $R\overline{3}m$.

By constructing the Patterson–Harker interatomic-vector function $P(00z)$ along the direction $(0001)$, the vector $\mathbf{u} = 1/2$, corresponding to the Bi—Fe distance, was determined. In the present case this conclusion and simple crystal-chemical considerations made it possible to choose space group 166. $R\overline{3}m$. The coordinates of the ions Bi$^{3+}$, Fe$^{3+}$, and O$^{2-}$ were determined by trial and error. The experimental intensities were obtained on a URS-50I diffractometer using Cu $K\alpha$ radiation. Because of the rapid decrease of intensity with increasing diffraction angle, the intensities of only the first 26 reflections were measured. The diffractogram was recalculated with allowance for counter losses according to the formula

\[ N = N_0/(1 - \tau N_0), \]

where $N$ is the corrected number of pulses; $N_0$ is the measured number of pulses; $\tau$ is the time constant, equal to $2 \cdot 10^{-4}$ sec.

In view of the presence of groups of closely spaced reflections, their total integral intensity was determined by the weighing method. The division of the group into separate values was carried out proportionally

calculated values \(I_{HKL}\), which were calculated by the formula \(I_{HKL}=LPF^2\).

Table 1

Interplanar spacings and intensities of the BiFeO\(_3\) powder pattern

* \(hkl\)—rhombohedral indices.

Table 2

* Ionic radii were taken according to N. V. Belov and G. B. Bokii \((^5)\), with allowance for the correction for coordination number.

In view of the comparison of intensities for relatively small values \(s=\sin\vartheta/\lambda \leqslant 0.475\), no temperature correction was introduced. Nor was a dispersion correction introduced for Fe\(^{3+}\) because of the large atomic

bismuth numbers. All intensities were reduced to the 200 reflection, taken as 100. Table 1 shows good agreement between the experimental and calculated intensities. The “reliability factor”\(^{4}\)

\[ R=\sum ||F_{\rm exp}|-|F_{\rm calc}|| \big/ \sum |F_{\rm exp}| = 0.09 . \]

Passing from the hexagonal cell to the rhombohedral one, we obtain the following characteristics:

\[ a_{rh}=3.952 \pm 0.001\ \text{kX}; \qquad \alpha_{rh}=89^\circ 36' \pm 3'; \qquad Z=1. \]

The coordinates of the atoms in the rhombohedral cell are:

\[ \begin{aligned} \mathrm{Bi}^{3+}:&\quad (1a),\ 000.\\ \mathrm{Fe}^{3+}:&\quad (1b),\ \tfrac{1}{2}\ \tfrac{1}{2}\ \tfrac{1}{2}.\\ \mathrm{O}^{2-}:&\quad (3e),\ 0\ \tfrac{1}{2}\ \tfrac{1}{2};\ \tfrac{1}{2}\ 0\ \tfrac{1}{2};\ \tfrac{1}{2}\ \tfrac{1}{2}\ 0. \end{aligned} \]

Figure 1 shows the hexagonal cell of \(\mathrm{BiFeO_3}\) with the rhombohedral cell singled out. Directly from the arrangement of the ions it is seen that the structure of \(\mathrm{BiFeO_3}\) belongs to the perovskite type. The oxygen and bismuth ions together form an almost complete cubic close-packed arrangement. The coordination polyhedra are an “oxygen” cuboctahedron for bismuth and an “oxygen” octahedron for iron. The polyhedra are only slightly distorted. The most important interatomic distances in the structure are compared with the ionic radii and presented in Table 2.

Fig. 1

It is known that the geometrical criterion

\[ t=(r_A+r_O)/\sqrt{2}(r_B+r_O), \]

where \(r_A\) is the radius of ion \(A\), \(r_B\) is the radius of ion \(B\), and \(r_O\) is the radius of the oxygen ion, for compounds crystallizing in a structure of the perovskite type lies in the range from 0.8 to 1.05. In our case \(t_{\mathrm{BiFeO_3}}=0.89\).

The authors express their gratitude to E. S. Sher and L. L. Vasil’eva, who synthesized the investigated preparation, and to Prof. G. A. Smolenskii for his attention to the work.

Institute of Semiconductors
Academy of Sciences of the USSR

Received
20 VI 1960

CITED LITERATURE

1. T. Bjurström, Zs. Phys., 69, 346 (1931).
2. International Tables for X-ray Crystallography, 1952.
3. A. D. Booth, Phyl. Mag., 36, 609 (1945).
4. P. M. De Wolf, Acta Cryst., 10, 590 (1957).
5. G. B. Bokii, Introduction to Crystal Chemistry, 1954.