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

Fabrykiewicz, P.; Stękiel, M.; Sosnowska, I.; Przeniosło, R.

doi:10.1107/S2052520616017935

research papers

STRUCTURAL SCIENCE
CRYSTAL ENGINEERING
MATERIALS

ISSN: 2052-5206

Volume 73| Part 1| February 2017| Pages 27-32

https://doi.org/10.1107/S2052520616017935

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

P. Fabrykiewicz,^a M. Stękiel,^a,^b I. Sosnowska ^a and R. Przeniosło ^a ^*

^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 T_N = 950 K, have been analyzed. The integral breadths of the Bragg peaks show a hkl-dependent anisotropy, both below and above T_N. 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 T_N. 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 ), 350, 491].

Keywords: Néel temperature; high-resolution synchrotron powder diffraction; peak-broadening; ferromagnetism.

CCDC references: 1515808; 1515809

1. Introduction

Antiferromagnetic and canted weak ferromagnetic states (Néel & Pauthenet, 1952 ; Dzyaloshinsky, 1958 ; Moriya, 1960 ) as well as spin-reorientation phenomena (Morin, 1950 ) were discovered in early studies of hematite, α-Fe₂O₃ (Morrish, 1994 ). The crystal structure of α-Fe₂O₃ is of corundum-type with trigonal symmetry (Shull et al., 1951 ; Maslen et al., 1994 ; Petrás et al., 1996 ; Hill et al., 2008 ). Recent structural studies have shown that the crystal structure of α-Fe₂O₃ is monoclinic at room temperature (Przeniosło et al., 2014 ). The monoclinic symmetry of the α-Fe₂O₃ crystal structure is compatible with the canted antiferromagnetic ordering (Przeniosło et al., 2014; Stękiel et al., 2015 ), 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; Wen et al., 2005 ; Yuan et al., 2012 ) are elongated objects which grow along the [110] (hexagonal) direction, i.e. along the unique monoclinic b_m 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 ), 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 ) 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 T_N = 950 K?

Recent structural studies of other magnetic materials, e.g. BiFeO₃ (Sosnowska et al., 2012 ) and Cr₂O₃ (Stękiel et al., 2015), 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 ) favor the monoclinic space group Cc over the trigonal R3c (Sosnowska et al., 2012). The observation of small antiferromagnetic contributions perpendicular to the hexagonal [001] direction in Cr₂O₃ (Brown et al., 1999 , 2002 ) 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). 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). 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 ), assuming both rhombohedral (space group $[R\bar{3}c]$ ) and monoclinic (space group C2/c) lattices. The relation between the monoclinic lattice vectors: a⁰_m, b⁰_m and c⁰_m and the rhombohedral lattice vectors (in a hexagonal setting) a⁰_h, b⁰_h and c⁰_h is (Sosnowska et al., 2012)

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

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

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

The splitting of Wyckoff positions between $[R\bar{3}c]$ and C2/c space groups for α-Fe₂O₃ is shown in Table 1. 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). 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) 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 a⁰_m, b⁰_m, c⁰_m and $[\beta^0_{\rm m}]$ , and the final parameters are a¹_m, b¹_m, c¹_m 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, 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) 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 ) 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. a_h(T)/a_h(RT) and c_h(T)/c_h(RT) is shown in Fig. 1. These results are similar to those from Petrás et al. (1996), which also show a change of the slope of a_h(T) and c_h(T) near T_N = 950 K.

Figure 1
Temperature dependence of the relative elongation of the α-Fe₂O₃ hexagonal lattice parameters a⁰_h and c⁰_h obtained from Rietveld refinement of synchrotron radiation diffraction data. The vertical dotted line denotes the Néel temperature T_N = 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 a¹_m, b¹_m, c¹_m and $[\beta^1_{\rm m}]$ and using inverted equations (1)–(3) to obtain the pseudo-hexagonal lattice parameters: a¹_h = b¹_h, c¹_h, $[\alpha^1_{\rm h}]$ , $[\beta^1_{\rm h}]$ 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 and 3, respectively. The values of a_h and c_h at room temperature and 1053 K given in Petrás et al. (1996) agree reasonably with those given in Tables 2 and 3. The refined atomic coordinates are given in Table 4.

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 (x_m¹-x_m⁰)/x_m⁰ ×10⁶
a_m (Å)	9.61865 (38)	9.61769 (11)	100 (14)
b_m (Å)	5.03554 (11)	5.03589 (4)	−70 (9)
c_m (Å)	13.75158 (55)	13.75154 (14)	3 (13)
β_m (°)	162.404 (1)	162.403 (2)	2 (13)
a_h (Å)	5.03610 (4)	5.03589 (4)	42 (8)
b_h (Å)	5.03610 (4)	5.03589 (4)	42 (8)
c_h (Å)	13.75158 (13)	13.75154 (14)	3 (13)
α_h (°)	90.0154 (20)	90.0	171 (23)
β_h (°)	89.9846 (20)	90.0	−171 (23)
γ_h (°)	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 (x_m¹-x_m⁰)/x_m⁰ ×10⁶
a_m (Å)	9.68920 (55)	9.68845 (40)	77 (20)
b_m (Å)	5.08737 (15)	5.08774 (13)	−72 (13)
c_m (Å)	13.84868 (71)	13.84864 (57)	3 (17)
β_m (°)	162.351 (1)	162.350 (13)	−1 (19)
a_h (Å)	5.08796 (3)	5.08774 (13)	43 (14)
b_h (Å)	5.08796 (3)	5.08774 (13)	43 (14)
c_h (Å)	13.84868 (11)	13.84864 (57)	3 (17)
α_h (°)	90.0115 (18)	90.0	127 (20)
β_h (°)	89.9885 (18)	90.0	−127 (20)
γ_h (°)	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)
U_iso (Fe)	0.0033 (17)	0.0131 (28)
U_iso (O)	0.0005 (60)	0.0102 (90)

The temperature dependence of the hexagonal unit parameters' ratio c⁰_h/a⁰_h is similar to that of the monoclinic $[\beta^1_{\rm m}]$ angle as shown in Fig. 2. There is an inflection point of both c⁰_h/a⁰_h and $[\beta^1_{\rm m}]$ near T_N indicating the importance of spin-lattice coupling in α-Fe₂O₃ as shown earlier in Petrás et al. (1996). 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. (a¹_m - a⁰_m)/a⁰_m ×10⁶. There is a positive change of a_m and a negative change of b_m (both larger than the statistical errors), while the values of c_m 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. The main conclusion of this study is that the monoclinic deformation of α-Fe₂O₃ is observed both below and above T_N.

Figure 2
The temperature dependence of the ratio of the hexagonal lattice parameters c⁰_h/a⁰_h (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 T_N = 950 K.

Figure 3
Temperature dependence of the relative change of the monoclinic lattice parameters a¹_m, b¹_m, c¹_m and $[\beta^1_{\rm m}]$ of α-Fe₂O₃ (see text). The vertical dotted line denotes the Néel temperature T_N = 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 T_N) 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 ). 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. 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 T_N.

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

) and 1053 K, i.e. above T_N = 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 ), the variance $[\sigma^2]$ of 1/d²_hkl 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) and (7)]. The experimental data and the calculated peak widths with the h,k,l indices (in hexagonal setting) are shown in Fig. 5. The resulting coefficients A_i [see equation (7)] are given in Table 5. 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. 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) 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
Angular dependence of the integral breadth $[\beta_{\rm sample}(2\theta)]$ obtained for α-Fe₂O₃ at room temperature (Stękiel et al., 2015

) 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). The deformation resulting from the APB obtained with the negative A₄ coefficients (see Table 4) indicates a breaking of the trigonal symmetry. This is because $[A_4 \ne 0]$ implies a non-orthogonality between the pseudo-hexagonal axes c¹_h with a¹_h as well as c¹_h with b¹_h. 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 are shown in Table 6. 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 ) and Carra & Thole (1994 ). 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)

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 T_N. 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; Wen et al., 2005; Yuan et al., 2012). These nanowires grow along the unique monoclinic b_m 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: T_N = 950 K. Although the crystal structure of α-Fe₂O₃ nanowires is reported to be trigonal (Fu et al., 2001; Wen et al., 2005; Yuan et al., 2012), 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 ). These findings show the need for further studies of α-Fe₂O₃ in the vicinity of its Néel transition.

Supporting information

CCDC references: 1515808; 1515809

Crystal structure: contains datablocks global, I, II. DOI: https://doi.org/10.1107/S2052520616017935/dq5016sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2052520616017935/dq5016Isup2.hkl

Structure factors: contains datablock II. DOI: https://doi.org/10.1107/S2052520616017935/dq5016IIsup3.hkl

Computing details top

(I) top

Crystal data top

Fe₂O₃	β = 162.4043 (3)°
M_r = 159.7	V = 201.35 (1) Å³
Monoclinic, C2/c	Z = 4
Hall symbol: -C 2yc	F(000) = 304
a = 9.61865 (9) Å	D_x = 5.268 Mg m⁻³
b = 5.03554 (3) Å	Synchrotron radiation
c = 13.75158 (13) Å	T = 293 K

Data collection top

2θ_min = 5°, 2θ_max = 29.999°, 2θ_step = 0.001°

Refinement top

R_p = 0.097	21 parameters
R_wp = 0.129	0 restraints
R_exp = 0.094	0 constraints
R(F) = 0.032	Weighting scheme based on measured s.u.'s
43005 data points	(Δ/σ)_max = 0.025
Excluded region(s): from 30 to 100.000	Background function: 5 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Fe1	0	0	0.14473 (3)	0.0033*
O1	0	0.309 (3)	0.25	0.0005*
O2	−0.449 (2)	−0.156 (2)	−0.050 (2)	0.0005*

(II) top

Crystal data top

Fe₂O₃	β = 162.3508 (2)°
M_r = 159.7	V = 206.97 (1) Å³
Monoclinic, C2/c	Z = 4
Hall symbol: -C 2yc	F(000) = 304
a = 9.68920 (8) Å	D_x = 5.125 Mg m⁻³
b = 5.08737 (2) Å	Synchrotron radiation
c = 13.84868 (11) Å	T = 1053 K

Data collection top

2θ_min = 5°, 2θ_max = 29.999°, 2θ_step = 0.001°

Refinement top

R_p = 0.099	21 parameters
R_wp = 0.128	0 restraints
R_exp = 0.086	0 constraints
R(F) = 0.044	Weighting scheme based on measured s.u.'s
43003 data points	(Δ/σ)_max = 0.036
Excluded region(s): from 30 to 100.000	Background function: 5 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Fe1	0	0	0.14425 (3)	0.0131*
O1	0	0.313 (3)	0.25	0.0102*
O2	−0.449 (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.

References

Brown, P., Forsyth, J., Lelièvre-Berna, E. & Tasset, F. (2002). J. Phys. Condens. Matter, 14, 1957–1966. CrossRef CAS Google Scholar
Brown, P., Forsyth, J. & Tasset, F. (1999). Physica B, 267–268, 215–220. CrossRef CAS Google Scholar
Caglioti, G., Paoletti, A. & Ricci, F. (1958). Nucl. Instrum. 3, 223–228. CrossRef CAS Web of Science Google Scholar
Carra, P. & Thole, B. (1994). Rev. Mod. Phys. 66, 1509–1515. CrossRef CAS Google Scholar
Dzyaloshinsky, I. (1958). J. Phys. Chem. Solids, 4, 241–255. CrossRef CAS Web of Science Google Scholar
Finkelstein, K., Shen, Q. & Shastri, S. (1992). Phys. Rev. Lett. 69, 1612–1615. CrossRef CAS Google Scholar
Fu, Y., Chen, J. & Zhang, H. (2001). Chem. Phys. Lett. 350, 491–494. CrossRef CAS Google Scholar
Grimmer, H. (2015). Acta Cryst. A71, 143–149. Web of Science CrossRef IUCr Journals Google Scholar
Hill, A. H., Jiao, F., Bruce, P. G., Harrison, A., Kockelmann, W. & Ritter, C. (2008). Chem. Mater. 20, 4891–4899. Web of Science CrossRef CAS Google Scholar
Landau, L. & Lifschitz, E. (1969). Statistical Physics. Oxford: Pergamon Press. Google Scholar
Maslen, E. N., Streltsov, V. A., Streltsova, N. R. & Ishizawa, N. (1994). Acta Cryst. B50, 435–441. CrossRef CAS Web of Science IUCr Journals Google Scholar
Morin, F. J. (1950). Phys. Rev. 78, 819–820. CrossRef CAS Web of Science Google Scholar
Moriya, T. (1960). Phys. Rev. Lett. 4, 228–230. CrossRef CAS Web of Science Google Scholar
Morrish, A. H. (1994). Canted Antiferromagnetism: Hematite. Singapore: World Scientific. Google Scholar
Néel, L. & Pauthenet, R. (1952). C. R. Acad. Sci. 234, 2172–2174. Google Scholar
Petrás, L., Preisinger, A. & Mereiter, K. (1996). Mater. Sci. Forum, 228–231, 393–398. Google Scholar
Petříček, V., Dušek, M. & Palatinus, L. (2014). Z. Kristallogr. 229, 345–352. Google Scholar
Przeniosło, R., Fabrykiewicz, P. & Sosnowska, I. (2016). Physica B, 496, 49–56. Google Scholar
Przeniosło, R., Sosnowska, I., Stękiel, M., Wardecki, D., Fitch, A. & Jasiński, B. (2014). Physica B, 449, 72–76. Google Scholar
Roisnel, T. & Rodriguez-Carvajal, J. (2000). Mater. Sci. Forum, Proc. 7th European Powder Diffraction Conference, EPDIC, 7, 118–123. Google Scholar
Shull, C. G., Strauser, W. A. & Wollan, E. (1951). Phys. Rev. 83, 333–345. CrossRef CAS Google Scholar
Sosnowska, I., Neumaier, T. P. & Steichele, E. (1982). J. Phys. C, 15, 4835–4846. CrossRef CAS Google Scholar
Sosnowska, I., Przeniosło, R., Palewicz, A., Wardecki, D. & Fitch, A. (2012). J. Phys. Soc. Jpn, 81, 0446041–4. CrossRef Google Scholar
Stękiel, M., Przeniosło, R., Sosnowska, I., Fitch, A., Jasiński, J. B., Lussier, J. A. & Bieringer, M. (2015). Acta Cryst. B71, 203–208. Web of Science CrossRef IUCr Journals Google Scholar
Stephens, P. W. (1999). J. Appl. Cryst. 32, 281–289. Web of Science CrossRef CAS IUCr Journals Google Scholar
Wen, X., Wang, S., Ding, Y., Wang, Z. & Yang, S. (2005). J. Phys. Chem. B, 109, 215–220. CrossRef CAS Google Scholar
Williamson, G. & Hall, W. (1953). Acta Metall. 1, 22–31. CrossRef CAS Web of Science Google Scholar
Yuan, L., Wang, Y., Cai, R., Jiang, Q., Wang, J., Li, B., Sharma, A. & Zhou, G. (2012). Mater. Sci. Eng. B, 177, 327–336. CrossRef CAS Google Scholar

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Volume 73| Part 1| February 2017| Pages 27-32

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