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Deformations of the α-Fe2O3 rhombohedral lattice across the Néel temperature

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aFaculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland, and bInstitute of Geosciences, Goethe University, D-60438 Frankfurt am Main, Germany
*Correspondence e-mail: radek@fuw.edu.pl

Edited by M. de Boissieu, SIMaP, France (Received 15 July 2016; accepted 8 November 2016; online 23 January 2017)

High-resolution synchrotron radiation powder diffraction patterns of α-Fe2O3 measured between room temperature and 1100 K, i.e. above the Néel temperature TN = 950 K, have been analyzed. The integral breadths of the Bragg peaks show a hkl-dependent anisotropy, both below and above TN. This anisotropy can be quantitatively described by using a statistical peak-broadening model [Stephens (1999). J. Appl. Cryst. 32, 281]. Model calculations show that the rhombohedral α-Fe2O3 lattice is deformed and the deformation leads to a monoclinic lattice with the unique monoclinic axis along the hexagonal [110] direction both below and above TN. The monoclinic symmetry of bulk α-Fe2O3 is compatible with α-Fe2O3 nanowire growth along the [110] direction reported in Fu et al. [Chem. Phys. Lett. (2001[Fu, Y., Chen, J. & Zhang, H. (2001). Chem. Phys. Lett. 350, 491-494.]), 350, 491].

1. Introduction

Antiferromagnetic and canted weak ferromagnetic states (Néel & Pauthenet, 1952[Néel, L. & Pauthenet, R. (1952). C. R. Acad. Sci. 234, 2172-2174.]; Dzyaloshinsky, 1958[Dzyaloshinsky, I. (1958). J. Phys. Chem. Solids, 4, 241-255.]; Moriya, 1960[Moriya, T. (1960). Phys. Rev. Lett. 4, 228-230.]) as well as spin-reorientation phenomena (Morin, 1950[Morin, F. J. (1950). Phys. Rev. 78, 819-820.]) were discovered in early studies of hematite, α-Fe2O3 (Morrish, 1994[Morrish, A. H. (1994). Canted Antiferromagnetism: Hematite. Singapore: World Scientific.]). The crystal structure of α-Fe2O3 is of corundum-type with trigonal symmetry (Shull et al., 1951[Shull, C. G., Strauser, W. A. & Wollan, E. (1951). Phys. Rev. 83, 333-345.]; Maslen et al., 1994[Maslen, E. N., Streltsov, V. A., Streltsova, N. R. & Ishizawa, N. (1994). Acta Cryst. B50, 435-441.]; Petrás et al., 1996[Petrás, L., Preisinger, A. & Mereiter, K. (1996). Mater. Sci. Forum, 228-231, 393-398.]; Hill et al., 2008[Hill, A. H., Jiao, F., Bruce, P. G., Harrison, A., Kockelmann, W. & Ritter, C. (2008). Chem. Mater. 20, 4891-4899.]). Recent structural studies have shown that the crystal structure of α-Fe2O3 is monoclinic at room temperature (Przeniosło et al., 2014[Przeniosło, R., Sosnowska, I., Stękiel, M., Wardecki, D., Fitch, A. & Jasiński, B. (2014). Physica B, 449, 72-76.]). The monoclinic symmetry of the α-Fe2O3 crystal structure is compatible with the canted antiferromagnetic ordering (Przeniosło et al., 2014[Przeniosło, R., Sosnowska, I., Stękiel, M., Wardecki, D., Fitch, A. & Jasiński, B. (2014). Physica B, 449, 72-76.]; Stękiel et al., 2015[Stękiel, M., Przeniosło, R., Sosnowska, I., Fitch, A., Jasiński, J. B., Lussier, J. A. & Bieringer, M. (2015). Acta Cryst. B71, 203-208.]), while the trigonal corundum-type crystal structure is not. There are also other arguments supporting the hypothesis of a monoclinic symmetry of the α-Fe2O3 crystal structure. The α-Fe2O3 nanowires and nanobelts (Fu et al., 2001[Fu, Y., Chen, J. & Zhang, H. (2001). Chem. Phys. Lett. 350, 491-494.]; Wen et al., 2005[Wen, X., Wang, S., Ding, Y., Wang, Z. & Yang, S. (2005). J. Phys. Chem. B, 109, 215-220.]; Yuan et al., 2012[Yuan, L., Wang, Y., Cai, R., Jiang, Q., Wang, J., Li, B., Sharma, A. & Zhou, G. (2012). Mater. Sci. Eng. B, 177, 327-336.]) are elongated objects which grow along the [110] (hexagonal) direction, i.e. along the unique monoclinic bm axis. The choice of the [110] growth direction indirectly points to a possible breaking of the threefold rotation symmetry of the α-Fe2O3 crystal structure.

It is often assumed, see e.g. Grimmer (2015[Grimmer, H. (2015). Acta Cryst. A71, 143-149.]), that the small monoclinic distortions of the crystal structure of α-Fe2O3 observed at room temperature are due to the magnetic ordering. This idea is in agreement with the Landau description of phase transitions (Landau & Lifschitz, 1969[Landau, L. & Lifschitz, E. (1969). Statistical Physics. Oxford: Pergamon Press.]) assuming that the symmetry of the paramagnetic phase (at high temperature) and the symmetry of the magnetically ordered phase (at low temperature) should show a group–subgroup relation. The paper is motivated by the following question. Does the crystal structure symmetry of α-Fe2O3 change around the magnetic phase transition at TN = 950 K?

Recent structural studies of other magnetic materials, e.g. BiFeO3 (Sosnowska et al., 2012[Sosnowska, I., Przeniosło, R., Palewicz, A., Wardecki, D. & Fitch, A. (2012). J. Phys. Soc. Jpn, 81, 0446041-4.]) and Cr2O3 (Stękiel et al., 2015[Stękiel, M., Przeniosło, R., Sosnowska, I., Fitch, A., Jasiński, J. B., Lussier, J. A. & Bieringer, M. (2015). Acta Cryst. B71, 203-208.]), have also shown monoclinic deformations of the rhombohedral lattice. In the case of BiFeO3 the magnetic moments modulation directed along the hexagonal [110] direction (Sosnowska et al., 1982[Sosnowska, I., Neumaier, T. P. & Steichele, E. (1982). J. Phys. C, 15, 4835-4846.]) favor the monoclinic space group Cc over the trigonal R3c (Sosnowska et al., 2012[Sosnowska, I., Przeniosło, R., Palewicz, A., Wardecki, D. & Fitch, A. (2012). J. Phys. Soc. Jpn, 81, 0446041-4.]). The observation of small antiferromagnetic contributions perpendicular to the hexagonal [001] direction in Cr2O3 (Brown et al., 1999[Brown, P., Forsyth, J. & Tasset, F. (1999). Physica B, 267-268, 215-220.], 2002[Brown, P., Forsyth, J., Lelièvre-Berna, E. & Tasset, F. (2002). J. Phys. Condens. Matter, 14, 1957-1966.]) also favor the monoclinic symmetry over the trigonal one.

2. Experimental

High-resolution synchrotron radiation diffraction measurements were performed with a synthetic commercial α-Fe2O3 powder sample provided by Aldrich. The measurements were performed at the ESRF beamline ID22 operating at the wavelength 0.40086 Å, as described in Stękiel et al. (2015[Stękiel, M., Przeniosło, R., Sosnowska, I., Fitch, A., Jasiński, J. B., Lussier, J. A. & Bieringer, M. (2015). Acta Cryst. B71, 203-208.]). Synchrotron radiation diffraction measurements were performed with α-Fe2O3 at several temperature steps by warming from room temperature to 1053 K. After reaching every temperature step by the hot-air blower sensor there was a 12 min waiting time before thermal equilibration. Synchrotron radiation powder diffraction measurements with α-Fe2O3 took 30 min at every temperature step. The angular range was 5 < 2θ < 30° corresponding to 0.218 < s < 1.291 Å−1, where [s = 2 \sin(\theta)/\lambda], covering 80 Bragg reflections of the trigonal crystal structure of α-Fe2O3. Polycrystalline powder samples were sealed in 0.5 mm diameter borosilicate capillaries. The capillaries were rotated in order to reduce potential texture effects. The synchrotron radiation powder diffraction patterns of α-Fe2O3 were analyzed by the Rietveld method asuming the corundum-type crystal structure (space group [R\bar{3}c]) and the distorted monoclinc crystal structure (space group C2/c) as described in Przeniosło et al. (2014[Przeniosło, R., Sosnowska, I., Stękiel, M., Wardecki, D., Fitch, A. & Jasiński, B. (2014). Physica B, 449, 72-76.]). The hexagonal setting of the space group [R\bar{3}c] will be used in the present paper.

3. Results

3.1. Monoclinic crystal structure model

The synchrotron radiation diffraction patterns of α-Fe2O3 were analyzed by the Rietveld method using JANA2006 (Petříček et al., 2014[Petříček, V., Dušek, M. & Palatinus, L. (2014). Z. Kristallogr. 229, 345-352.]), assuming both rhombohedral (space group [R\bar{3}c]) and monoclinic (space group C2/c) lattices. The relation between the monoclinic lattice vectors: a0m, b0m and c0m and the rhombohedral lattice vectors (in a hexagonal setting) a0h, b0h and c0h is (Sosnowska et al., 2012[Sosnowska, I., Przeniosło, R., Palewicz, A., Wardecki, D. & Fitch, A. (2012). J. Phys. Soc. Jpn, 81, 0446041-4.])

[{\bf a}^0_{\rm m} = - {{1} \over {3}} {\bf a}^0_{\rm h} + {{1} \over {3}} {\bf b}^0_{\rm h} - {{2} \over {3}} {\bf c}^0_{\rm h}, \eqno(1)]

[{\bf b}^0_{\rm m} = - {\bf a}^0_{\rm h} - {\bf b}^0_{\rm h}, \eqno(2)]

[{\bf c}^0_{\rm m} = {\bf c}^0_{\rm h}. \eqno(3)]

The splitting of Wyckoff positions between [R\bar{3}c] and C2/c space groups for α-Fe2O3 is shown in Table 1[link]. There is only one positional parameter for oxygen ions x(O) in the trigonal structure model of α-Fe2O3. The present paper describes a study of the Bragg peak shapes which give information about the lattice deformations.

Table 1
Splitting of the Wyckoff positions between the [R\bar{3}c] (hexagonal setting) and the C2/c (monoclinic) space groups for α-Fe2O3

C2/c (equiv.) shows the monoclinic coordinates which are obtained from the rhombohedral ones by using transformation (1)–(3)[link][link][link]. The last column shows which coordinates are free in C2/c.

Ion [R\bar{3}c] C2/c (equiv.) C2/c (general)
Fe 12c (0, 0, z0) 8f (0, 0,z0) (0,0,z)
O 18e [(x_0,0, {{1} \over {4}})] 8f [ (-{{3} \over {2}}x_0, -{{1} \over {2}}x_0, {{1} \over {4}}-x_0)] (x,y,z)
O 18e [ (\bar{x}_0,\bar{x}_0,{{1} \over {4}})] 4e [ (0,x_0,{{1} \over {4}})] [(0,y,{{1} \over {4}})]

The index `0' in equations (1)–(3)[link][link][link] means that both the hexagonal and monoclinic lattice vectors correspond to the rhombohedral lattice, while the index `1' refers to the monoclinic lattice (distorted with regard to the rhombohedral one), also called a pseudo-hexagonal lattice.

For the Rietveld refinement asssuming the monoclinic space group C2/c the starting values of the lattice parameters are a0m, b0m, c0m and [\beta^0_{\rm m}], and the final parameters are a1m, b1m, c1m and [\beta^1_{\rm m}]. The oxygen atomic coordinates obtained with the trigonal structure were transformed to the monoclinic lattice, as given in Table 1[link], and these were the starting values for the refinements of the monoclinic model. The oxygen coordinates of (4e) and (8f) positions (shown in Table 1[link]) were free in the Rietveld fits with the monoclinic structure model. Isotropic atomic displacement parameters for Fe and O ions were refined both in the trigonal and monoclinic models. The isotropic peak width dependence from Caglioti et al. (1958[Caglioti, G., Paoletti, A. & Ricci, F. (1958). Nucl. Instrum. 3, 223-228.]) was assumed

[FWHM^2(\theta) = U\tan^2(\theta)+V\tan(\theta) + W. \eqno(4)]

The temperature dependence of the relative elongation of the hexagonal unit-cell parameters of α-Fe2O3, i.e. ah(T)/ah(RT) and ch(T)/ch(RT) is shown in Fig. 1[link]. These results are similar to those from Petrás et al. (1996[Petrás, L., Preisinger, A. & Mereiter, K. (1996). Mater. Sci. Forum, 228-231, 393-398.]), which also show a change of the slope of ah(T) and ch(T) near TN = 950 K.

[Figure 1]
Figure 1
Temperature dependence of the relative elongation of the α-Fe2O3 hexagonal lattice parameters a0h and c0h obtained from Rietveld refinement of synchrotron radiation diffraction data. The vertical dotted line denotes the Néel temperature TN = 950 K.

The monoclinic unit cell is difficult to visualize and in order to show its main properties a transformation to the pseudo-hexagonal axes was performed. This was done by taking a1m, b1m, c1m and [\beta^1_{\rm m}] and using inverted equations (1)–(3)[link][link][link] to obtain the pseudo-hexagonal lattice parameters: a1h = b1h, c1h, [\alpha^1_{\rm h}], [\beta^1_{\rm h}] and [\gamma^1_{\rm h}]. Please note that in the pseudo-hexagonal lattice it is possible that [\alpha^1_{\rm h} \ne 90^\circ] or [\beta^1_{\rm h} \ne 90^\circ] or [\gamma^1_{\rm h} \ne 120^\circ]. The values of the lattice parameters for α-Fe2O3 at room temperature and 1053 K are given in Tables 2[link] and 3[link], respectively. The values of ah and ch at room temperature and 1053 K given in Petrás et al. (1996[Petrás, L., Preisinger, A. & Mereiter, K. (1996). Mater. Sci. Forum, 228-231, 393-398.]) agree reasonably with those given in Tables 2[link] and 3[link]. The refined atomic coordinates are given in Table 4[link].

Table 2
Structural parameters for α-Fe2O3 obtained at 293 K for the monoclinic model and the trigonal model (see text)

The last column gives the relative change of each parameter.

Parameter Monoclinic (index 1) pseudo-hexagonal Trigonal (index 0) hexagonal Relative change (xm1-xm0)/xm0 ×106
am (Å) 9.61865 (38) 9.61769 (11) 100 (14)
bm (Å) 5.03554 (11) 5.03589 (4) −70 (9)
cm (Å) 13.75158 (55) 13.75154 (14) 3 (13)
βm (°) 162.404 (1) 162.403 (2) 2 (13)
ah (Å) 5.03610 (4) 5.03589 (4) 42 (8)
bh (Å) 5.03610 (4) 5.03589 (4) 42 (8)
ch (Å) 13.75158 (13) 13.75154 (14) 3 (13)
αh (°) 90.0154 (20) 90.0 171 (23)
βh (°) 89.9846 (20) 90.0 −171 (23)
γh (°) 120.0073 (6) 120.0 61 (5)

Table 3
Structural parameters for α-Fe2O3 obtained at 1053 K for the monoclinic model and the trigonal model (see text)

The last column gives the relative change of each parameter.

Parameter Monoclinic (index 1) pseudo-hexagonal Trigonal (index 0) hexagonal Relative change (xm1-xm0)/xm0 ×106
am (Å) 9.68920 (55) 9.68845 (40) 77 (20)
bm (Å) 5.08737 (15) 5.08774 (13) −72 (13)
cm (Å) 13.84868 (71) 13.84864 (57) 3 (17)
βm (°) 162.351 (1) 162.350 (13) −1 (19)
ah (Å) 5.08796 (3) 5.08774 (13) 43 (14)
bh (Å) 5.08796 (3) 5.08774 (13) 43 (14)
ch (Å) 13.84868 (11) 13.84864 (57) 3 (17)
αh (°) 90.0115 (18) 90.0 127 (20)
βh (°) 89.9885 (18) 90.0 −127 (20)
γh (°) 120.0077 (4) 120.0 64 (4)

Table 4
Atomic coordinates and isotropic displacement parameters obtained from Rietveld refinement for α-Fe2O3 by assuming the monoclinic structure model at 293 K and 1053 K

  293 K 1053 K
z(Fe) (8f) 0.14473 (3) 0.14425 (3)
y(O) (4e) 0.309 (3) 0.313 (3)
x(O) (8f) −0.449 (2) −0.449 (3)
y(O) (8f) −0.156 (2) −0.155 (3)
z(O) (8f) −0.050 (2) −0.049 (2)
Uiso (Fe) 0.0033 (17) 0.0131 (28)
Uiso (O) 0.0005 (60) 0.0102 (90)

The temperature dependence of the hexagonal unit parameters' ratio c0h/a0h is similar to that of the monoclinic [\beta^1_{\rm m}] angle as shown in Fig. 2[link]. There is an inflection point of both c0h/a0h and [\beta^1_{\rm m}] near TN indicating the importance of spin-lattice coupling in α-Fe2O3 as shown earlier in Petrás et al. (1996[Petrás, L., Preisinger, A. & Mereiter, K. (1996). Mater. Sci. Forum, 228-231, 393-398.]). The relative size of the monoclinic deformation is estimated by calculating the relative change of the monoclinic unit-cell parameters with regard to the trigonal ones, e.g. (a1m - a0m)/a0m ×106. There is a positive change of am and a negative change of bm (both larger than the statistical errors), while the values of cm and [\beta_{\rm m}] do not change within errors. The temperature dependence of the relative changes of the α-Fe2O3 monoclinic lattice parameters is shown in Fig. 3[link]. The main conclusion of this study is that the monoclinic deformation of α-Fe2O3 is observed both below and above TN.

[Figure 2]
Figure 2
The temperature dependence of the ratio of the hexagonal lattice parameters c0h/a0h (left scale) is compared with the temperature dependence of the monoclinic angle [\beta^1_{\rm m}] (right scale). The vertical dotted line denotes the Néel temperature TN = 950 K.
[Figure 3]
Figure 3
Temperature dependence of the relative change of the monoclinic lattice parameters a1m, b1m, c1m and [\beta^1_{\rm m}] of α-Fe2O3 (see text). The vertical dotted line denotes the Néel temperature TN = 950 K.

3.2. Anisotropic peak-broadening model assuming trigonal symmetry `on average'

The synchrotron radiation diffraction patterns of α-Fe2O3 measured at room temperature and 1053 K (i.e. above TN) were analysed by fitting a pseudo-Voigt profile to the observed Bragg peaks (i.e. model-independent analysis) using WinPlotr (Roisnel & Rodriguez-Carvajal, 2000[Roisnel, T. & Rodriguez-Carvajal, J. (2000). Mater. Sci. Forum, Proc. 7th European Powder Diffraction Conference, EPDIC, 7, 118-123.]).

The integral breadth, denoted as [\beta_{\rm obs}(2\theta)] was used as a measure of the Bragg peak widths as in Williamson & Hall (1953[Williamson, G. & Hall, W. (1953). Acta Metall. 1, 22-31.]). The instrumental contribution was estimated with the LaB6 standard. The integral breadths obtained from the LaB6 diffraction pattern were refined with a fourth-order polynomial function [\beta_{\rm LaB_6}(2\theta)]. The sample contribution to the integral breadth, [\beta_{\rm sample}(2\theta)] was calculated as

[\beta_{\rm sample}(2\theta) = \{ \beta^2_{\rm obs}(2\theta)-\beta^2_{\rm LaB_6}(2\theta) \}^{1/2}. \eqno(5)]

This formula works for Gaussian peak shape but as the instrumental contribution to [\beta_{\rm obs}] is smooth and the use of similar fomulae, e.g. [\beta_{\rm sample}(2\theta) = \beta_{\rm obs}(2\theta)-\beta_{\rm LaB_6}(2\theta)], leads to the same type of hkl-dependent anisotropy of [\beta_{\rm sample}(2\theta)]. The experimental [\beta_{\rm sample}(2\theta)] values obtained for α-Fe2O3 at room temperature and 1053 K are shown in Fig. 4[link]. The lines are shown as a guide-to-the-eye. The β values observed for 1053 K are smaller than those observed at room temperature, probably because of the crystallite growth process at elevated temperatures. Similar sets of local maxima and minima of [\beta_{\rm sample}(2\theta)] are observed both at room temperature and 1053 K. This model independent observation confirms that the deformations of the α-Fe2O3 rhombohedral lattice are present both below and above TN.

[Figure 4]
Figure 4
Angular dependence of the experimental values of the integral breadth [\beta_{\rm sample}(2\theta)] obtained for α-Fe2O3 at room temperature (Stękiel et al., 2015[Stękiel, M., Przeniosło, R., Sosnowska, I., Fitch, A., Jasiński, J. B., Lussier, J. A. & Bieringer, M. (2015). Acta Cryst. B71, 203-208.]) and 1053 K, i.e. above TN = 950 K. The error bars were omitted for clarity and the lines are given as a guide-to-the-eye.

In the anisotropic peak broadening (APB) model described in Stephens (1999[Stephens, P. W. (1999). J. Appl. Cryst. 32, 281-289.]), the variance [\sigma^2] of 1/d2hkl is calculated as:

[\sigma^2(1/d^{2}_{hkl}) = \sum_{i = 1}^{4} A_i W_{i}(h,k,l), \eqno(6)]

with the following invariant polynomials (for the assumed Laue class [\bar{3}m]): W1 = (h2+hk+k2)2, W2 = (h2+hk+k2) l2, W3 = l4 and W4 = (3h3-3k3+(k-h)3)l.

The calculated integral breadths [\beta_{sample}(2 \theta)] are given as

[\eqalignno{\beta_{\rm sample}(\theta) &\,=\, {{B_0} \over {\cos\theta}} \cr & + \left\{ A_0 + A_1{{W_1} \over {Q^4}} + A_2{{W_2} \over {Q^4}} + A_3{{W_3} \over {Q^4}} + A_4{{W_4} \over {Q^4}} \right\}^{1/2} \tan\theta .\cr &&(7)}]

B0 gives the crystallite size contribution, A0 gives the average (isotropic) microstrain-type contribution, while the coeffcients A1,A2,A3,A4 describe the anisotropic broadening contributions. The [\beta(2\theta)] dependence observed for α-Fe2O3 at room temperature and 1053 K was refined using the APB model [equations (5)[link] and (7)[link]]. The experimental data and the calculated peak widths with the h,k,l indices (in hexagonal setting) are shown in Fig. 5[link]. The resulting coefficients Ai [see equation (7)[link]] are given in Table 5[link]. The coefficients A1 and A3 give values smaller than their statistical errors. Setting A1 = A3 = 0 did not change the fit quality in a significant way. It is interesting to note that the coefficient [ A_4\,\lt\,0]. With positive l, the polynomial W4 = (3h3-3k3+(k-h)3)l gives positive values for [h\,\gt\, k] and negative for [h\,\lt\, k]. The contribution of W4 with the negative coefficient A4 explain the `reversed' behaviour of the widths of the broad (0,2,4) and the narrow (2,0,2) Bragg peaks, see Fig. 5[link]. The polynomial W4 gives zero for (h,h,l) so the behaviour of the widths of e.g. (1,1,3), (1,1,6) Bragg peaks is described with the positive coefficient of the polynomial W2 = (h2+hk+k2) l2.

Table 5
Values of the refined parameters and their statistical accuracies obtained with the anisotropic peak-broadening model using equation (7)[link] applied to α-Fe2O3 at 293 and 1053 K

  α-Fe2O3 (room temperature) α-Fe2O3 (1053 K)
B0 0.0043 (2) 0.0032 (2)
A0 4.72 (08) ×10-3 2.84 (39) ×10-3
A2 1.36 (13) ×10-6 8.39 (65) ×10-7
A4 −2.13 (16) ×10-6 −1.36 (76) ×10-6
[Figure 5]
Figure 5
Angular dependence of the integral breadth [\beta_{\rm sample}(2\theta)] obtained for α-Fe2O3 at room temperature (Stękiel et al., 2015[Stękiel, M., Przeniosło, R., Sosnowska, I., Fitch, A., Jasiński, J. B., Lussier, J. A. & Bieringer, M. (2015). Acta Cryst. B71, 203-208.]) and 1053 K. The experimental values are shown with solid symbols and error bars, while results of the refinement with the APB model are shown with solid lines. The Bragg peak indices in the right panels are given for the hexagonal setting of the space group [R\bar{3}c].

4. Discussion

The present paper shows that the high-resolution synchrotron radiation diffraction patterns of α-Fe2O3 can be described by assuming either (i) a monoclinic symmetry of the crystal structure or alternatively (ii) a statistically described deformation of the rhombohedral lattice (so-called APB model; Stephens, 1999[Stephens, P. W. (1999). J. Appl. Cryst. 32, 281-289.]). The deformation resulting from the APB obtained with the negative A4 coefficients (see Table 4[link]) indicates a breaking of the trigonal symmetry. This is because [A_4 \ne 0] implies a non-orthogonality between the pseudo-hexagonal axes c1h with a1h as well as c1h with b1h. In this case the threefold rotation axis is absent in the symmetry of the crystal structure of α-Fe2O3.

The proposed monoclinic crystal structure (space group C2/c) leads to Bragg peaks that are forbidden in the rhombohedral structure (space group [R\bar{3}c]). The intensities of 25 such forbidden Bragg peaks calculated using the structural parameters from Tables 2–4[link][link][link] are shown in Table 6[link]. The Bragg peaks allowed in the monoclinic model but forbidden in the rhombohedral model are numbered from 1 to 25. A few representative Bragg peaks allowed in the rhombohedral model are also shown. The most intense rhombohedral Bragg peak (104)h has a total intensity of 2 ×106, while the most intense forbidden peaks have intensities of about 500. A measurement of weak reflections (i.e. 4000 times weaker than the most intense reflection) was not possible at the high-resolution synchrotron radiation diffraction beamline ID22, i.e. they are too weak compared with the background fluctuations in the experimental data. The present data gives no hint on the possible temperature dependence of these forbidden reflections. The forbidden reflections due to the monoclinic deformations discussed above should not be confused with the forbidden hexagonal (003)h and (009)h reflections studied by resonant synchrotron scattering in hematite, see e.g. Finkelstein et al. (1992[Finkelstein, K., Shen, Q. & Shastri, S. (1992). Phys. Rev. Lett. 69, 1612-1615.]) and Carra & Thole (1994[Carra, P. & Thole, B. (1994). Rev. Mod. Phys. 66, 1509-1515.]). The monoclinic Bragg peaks [(\bar{2}03)_{\rm m}] [equivalent to (003)h] and [(\bar{6}09)_{\rm m}] [equivalent to (009)h] are also both forbidden in the space group C2/c.

Table 6
List of Bragg peak intensities calculated for the monoclinic α-Fe2O3 crystal structure model for 293 and 1053 K (parameters from Table 4[link])

The first column gives the peak number (for peaks forbidden in the rhombohedral model) or the hexagonal indices (for peaks allowed in the rhombohedral model). Columns 2–4 give the monoclinic indices, columns 5–6 and 7–8 give the d-spacings and intensities calculated for 293 and 1053 K, respectively.

1 2 3 4 5 6 7 8
No. h k l d(293 K) (Å) I(293 K) d(1053 K) (Å) I(1053 K)
1 −1 1 1 4.157220 538.4 4.198735 478.5
(012)h −2 0 2 3.683574 212434.0 3.717948 198030.1
(012)h −1 1 2 3.682504 368969.3 3.717051 350127.5
(104)h −3 1 4 2.700070 1355721.9 2.722419 1352078.9
(104)h -2 0 4 2.699572 664717.6 2.722078 640748.8
(110)h 1 1 0 2.518051 995831.4 2.543982 947777.1
(110)h 0 2 0 2.517771 482353.1 2.543684 476386.6
2 −3 1 5 2.326172 10.7 2.344772 127.6
(006)h −4 0 6 2.291931 33734.0 2.308114 27871.0
3 0 2 1 2.153576 241.8 2.175587 473.4
4 −5 1 7 1.791271 79.7 1.804867 10.6
5 −4 2 5 1.708799 193.2 1.724219 127.5
6 −4 2 7 1.459420 15.8 1.471864 112.4
7 −3 3 3 1.385740 15.1 1.399578 5.1
8 −1 3 3 1.385616 13.6 1.399484 4.7
9 −7 1 11 1.201693 0.5 1.210484 10.1
10 −2 4 1 1.086870 26.6 1.098033 11.3
11 −8 2 11 1.084616 42.9 1.093121 9.3
12 −7 3 9 1.053271 4.8 1.062471 1.4
13 −5 3 9 1.053107 3.5 1.062348 1.0
14 −9 1 13 1.028041 12.8 1.035474 0.2
15 −2 4 5 1.013482 14.4 1.023481 9.3
16 −6 4 7 0.953360 18.9 0.962430 4.7
17 −8 2 13 0.951677 0.2 0.958996 16.2
18 1 5 1 0.870456 37.2 0.879408 49.6
19 −5 5 5 0.831444 42.4 0.839747 34.8
20 −3 5 7 0.797129 18.2 0.804920 35.6
21 −11 1 17 0.795328 0.8 0.801035 1.7
22 −11 3 15 0.775499 1.5 0.781672 0.3
23 −9 3 15 0.775390 0.9 0.781590 0.2
24 −10 4 13 0.759260 9.5 0.765794 1.2
25 −12 2 17 0.758450 14.7 0.764091 0.9

The most important conclusion from this study is that the crystal structure of α-Fe2O3 is monoclinic both below and above TN. The monoclinic symmetry may be related with the magnetic properties of α-Fe2O3. These observations should be compared with the oxidation of iron which leads to the formation of α-Fe2O3 nanowires (Fu et al., 2001[Fu, Y., Chen, J. & Zhang, H. (2001). Chem. Phys. Lett. 350, 491-494.]; Wen et al., 2005[Wen, X., Wang, S., Ding, Y., Wang, Z. & Yang, S. (2005). J. Phys. Chem. B, 109, 215-220.]; Yuan et al., 2012[Yuan, L., Wang, Y., Cai, R., Jiang, Q., Wang, J., Li, B., Sharma, A. & Zhou, G. (2012). Mater. Sci. Eng. B, 177, 327-336.]). These nanowires grow along the unique monoclinic bm axis, i.e. hexagonal [110] direction and the whole process occurs at temperatures from 873 to 1073 K, i.e. both below and above the bulk α-Fe2O3: TN = 950 K. Although the crystal structure of α-Fe2O3 nanowires is reported to be trigonal (Fu et al., 2001[Fu, Y., Chen, J. & Zhang, H. (2001). Chem. Phys. Lett. 350, 491-494.]; Wen et al., 2005[Wen, X., Wang, S., Ding, Y., Wang, Z. & Yang, S. (2005). J. Phys. Chem. B, 109, 215-220.]; Yuan et al., 2012[Yuan, L., Wang, Y., Cai, R., Jiang, Q., Wang, J., Li, B., Sharma, A. & Zhou, G. (2012). Mater. Sci. Eng. B, 177, 327-336.]), the growth direction anisotropy points towards the monoclinic symmetry hypothesis for nanowires as well. On the other hand, the monoclinic symmetry can also be unrelated with the magnetic properties; a recent study has shown similar monoclinic crystal structure symmetry in the nonmagnetic calcite, CaCO3 (Przeniosło et al., 2016[Przeniosło, R., Fabrykiewicz, P. & Sosnowska, I. (2016). Physica B, 496, 49-56.]). These findings show the need for further studies of α-Fe2O3 in the vicinity of its Néel transition.

Supporting information


Computing details top

(I) top
Crystal data top
Fe2O3β = 162.4043 (3)°
Mr = 159.7V = 201.35 (1) Å3
Monoclinic, C2/cZ = 4
Hall symbol: -C 2ycF(000) = 304
a = 9.61865 (9) ÅDx = 5.268 Mg m3
b = 5.03554 (3) ÅSynchrotron radiation
c = 13.75158 (13) ÅT = 293 K
Data collection top
2θmin = 5°, 2θmax = 29.999°, 2θstep = 0.001°
Refinement top
Rp = 0.09721 parameters
Rwp = 0.1290 restraints
Rexp = 0.0940 constraints
R(F) = 0.032Weighting scheme based on measured s.u.'s
43005 data points(Δ/σ)max = 0.025
Excluded region(s): from 30 to 100.000Background function: 5 Legendre polynoms
Profile function: Pseudo-VoigtPreferred orientation correction: none
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Fe1000.14473 (3)0.0033*
O100.309 (3)0.250.0005*
O20.449 (2)0.156 (2)0.050 (2)0.0005*
(II) top
Crystal data top
Fe2O3β = 162.3508 (2)°
Mr = 159.7V = 206.97 (1) Å3
Monoclinic, C2/cZ = 4
Hall symbol: -C 2ycF(000) = 304
a = 9.68920 (8) ÅDx = 5.125 Mg m3
b = 5.08737 (2) ÅSynchrotron radiation
c = 13.84868 (11) ÅT = 1053 K
Data collection top
2θmin = 5°, 2θmax = 29.999°, 2θstep = 0.001°
Refinement top
Rp = 0.09921 parameters
Rwp = 0.1280 restraints
Rexp = 0.0860 constraints
R(F) = 0.044Weighting scheme based on measured s.u.'s
43003 data points(Δ/σ)max = 0.036
Excluded region(s): from 30 to 100.000Background function: 5 Legendre polynoms
Profile function: Pseudo-VoigtPreferred orientation correction: none
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Fe1000.14425 (3)0.0131*
O100.313 (3)0.250.0102*
O20.449 (3)0.155 (3)0.049 (2)0.0102*
 

Acknowledgements

Thanks are due to A. Fitch for support during the measurements at ESRF. Thanks are due to the Ministry of Science and Higher Education (Poland) for funding access to the ESRF facilities.

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