- Email: [email protected]
Variable temperature powder neutron diffraction study of the Verwey transition in magnetite Fe3O4
Solid State Sciences 2 (2000) 747– 753
www.elsevier.com/locate/ssscie
Variable temperature powder neutron diffraction study of the Verwey transition in magnetite Fe3O4 Jon P. Wright, Anthony M.T. Bell 1, J. Paul Attfield * Department of Chemistry, Uni6ersity of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK Received 8 March 2000; accepted 25 July 2000 Dedicated to Professor J.M. Ho¨nig on the occasion of his 75th birthday
Abstract Neutron powder diffraction data have been collected from a sample of polycrystalline Fe3O4. High resolution data collected at 60 K are fitted using a simple rhombohedral distortion of the cubic unit cell. This model accounts for all of the peak splittings that occur upon cooling through the Verwey transition temperature (TV). Lower resolution data collected between 2 and 280 K are fitted using the same model, which gives TV = 11095 K. These data show a change in the thermal expansion due to the softening of phonons above TV and a change in crystallite extinction arising from twinning at the transition. © 2000 E´ditions scientifiques et me´dicales Elsevier SAS. All rights reserved. Keywords: Magnetite; Verwey transition; Variable temperature study; Powder neutron diffraction; Crystal structure of Fe3O4
1. Introduction The mineral magnetite is one of the oldest known magnetic materials. Below the Curie temperature of 860 K, the iron cation spins order ferrimagnetically, giving a bulk magnetisation. Magnetite adopts the inverse cubic spinel crystal structure and is formulated as Fe3 + [Fe3 + Fe2 + ]O4. Fe3 + occupies the tetrahedral sites and Fe2 + and Fe3 + are distributed equally over the octahedral sites. The octahedral sites are identical at room temperature due to rapid electron hopping between Fe2 + and Fe3 + ions. Upon cooling, the resistivity of magnetite increases * Correspondence and reprints. Tel.: + 1-223-336332; fax: + 1223-336362. E-mail address: [email protected] (J.P. Attfield). 1 Present address: Inorganic Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QR, UK.
sharply at the Verwey transition at TV ca. 120 K [1,2], which is believed to be a charge ordering of the Fe2 + and Fe3 + states. The original model for the charge ordered structure of Verwey et al. [2] was thought to have been confirmed by a single crystal neutron diffraction experiment [3], although this experiment was later found to be flawed by multiple scattering effects [4] and no definitive model has since been identified. The difficulty of understanding the Verwey transition has been exacerbated by variations in sample stoichiometry. It was not properly appreciated until the 1980’s that the careful control of sample composition is crucial for obtaining reproducible results [5]. Magnetite can be non-stoichiometric according to the formula Fe3-3l O4 and TV is suppressed with increasing l\ 0. The transition changes from first to second order when l \0.0039 and at l= 0.0117, the magnetite –haematite phase boundary is reached.
1293-2558/00/$ - see front matter © 2000 E´ditions scientifiques et me´dicales Elsevier SAS. All rights reserved. PII: S1293-2558(00)01107-9
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
748
Despite many attempts, no conclusive study of the low temperature structure has emerged. Both rhombohedral [6,7] and orthorhombic [8] distortions of the cubic spinel cell were reported for the low temperature phase. Although the original Verwey model has an underlying orthorhombic symmetry, subsequent work showed that the structural distortion is essentially rhombohedral [9]. Furthermore, the observation of superstructure reflections indexed as (h, k, l+1/2) on the cubic cell [10] are not predicted by the Verwey model. The low temperature space group and supercell were established as monoclinic Cc; 2a × 2a × 2a, where a is the cubic spinel cell parameter from a neutron study of a partially detwinned single crystal [11]. However, the observation of a magnetoelectric effect indicates that the symmetry may be triclinic P1( . The only published refinement [12] of the low temperature structure used a reduced cell and two orthorhombic space groups that are incompatible with the metric tensor. Although these refined models included several inequivalent octahedral sites, no evidence for charge ordering was found. Large, good quality crystals of stoichiometric magnetite can be grown, but single crystal studies below TV are plagued by extinction, multiple scattering and twinning effects. These problems are less Table 1 Crystal structure parameters for Fe3O4 in the cubic phase and two settings of space group R3( m a Atom
Wyck
x
y
z
Cubic space group Fd3( m, ac = 8.3970(1) A, , u= 0.050(2) Fe(1) 8a 1/8 1/8 1/8 Fe(2) 16d 1/2 1/2 1/2 O 32e 1/4+u 1/4+u 1/4+u Space group F3( m, a non-standard setting of R3( m in which the axes coincide with the Fd3( m axes, a= ac, h= 90 ° Fe(1) 8c 1/8 1/8 1/8 Fe(2a) 4c 1/2 1/2 1/2 Fe(2b) 12e 1/4 3/4 0 O(a) 8c 1/4+u 1/4+u 1/4+u O(b) 24h 3/4-u% 1/2+u¦ 1/2+u¦ Space group R3( m (hexagonal axes), ar = ac/ 2, cr = 3ac Fe(1) 6c 0 0 1/8 Fe(2a) 3b 0 0 1/2 Fe(2b) 9e 1/2 0 0 O(a) 6c 0 0 1/4+u O(b) 18h 4u%/3+1/6 −4u%/3–1/6 1/12–u¦/3 a
u =u% =u¦ if pseudo-cubic symmetry is preserved.
severe in powder diffraction experiments and modern synchrotron X-ray and neutron diffractometers offer high count rates and resolution that may be sufficient for the study of the low temperature structure. To investigate the feasibility of this, we report preliminary powder neutron diffraction studies of Fe3O4 above and below TV.
2. Experimental A powder sample of Fe3O4 was prepared by mixing and pelleting stoichiometric amounts of Fe metal and Fe2O3, which were heated in an evacuated, sealed silica tube for a total of 84 h at 1273 K and quenched to room temperature. The sintered product was hand-ground to a powder. Neutron diffraction data were recorded at the Institute Laue et Langevin, Grenoble. High resolution data were collected using the D2b instrument with a 35% collimation and a wavelength of 1.59432 A, . The sample was mounted in a cryostat and patterns were recorded with 0B 2qB 162.5° with a step of 0.05° at temperatures of 130 and 60 K. A variable temperature study was also performed on the high flux instrument D20 which uses a fixed bank of 1600 counters covering 0B2q B 160° in 0.1° steps. Patterns were recorded at 2 K; from 10 to 80 K in 10 K steps; from 80 to 140 K in 5 K steps; and from 140 to 280 K in 10 K steps, at a wavelength of 2.41 A, for 15 min per pattern. Rietveld fits to the D2b data were carried out using the GSAS program [13] and the D20 data were fitted using the PRODD [14] program, which is based on the Cambridge Crystallographic Subroutine Library [15].
3. Results Fig. 1(a) shows a Rietveld fit to the 60 K D2b pattern of magnetite using a rhombohedrally distorted spinel cell (Tables 1 and 2). This gives a good fit to the peak splittings that are clearly observed at high angles. The number of refineable positional parameters in the R3( m symmetry model is four with two different octahedral sites in a 1:3 ratio, compared to only one parameter and octahedral site in the cubic Fd3( m model. Although the peak positions are described well by the rhombohedral distortion, there are several intensity mismatches, particularly at
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
749
Fig. 1. Powder neutron diffraction profiles of Fe3O4 from instrument D2b. (a) Rietveld fit of the rhombohedral model to 60 K data. (b) Comparison of 60 and 130 K patterns showing superstructure peaks in the low temperature profile.
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
750
Table 2 Refined parameters from the D2b data at 60 K in space group R3( m (Rp = 7.6%, Rwp = 10.5%) Cell parameters: a= 5.92767 (5)A, , c =14.5699 (2)A, [Equivalent to a= 8.39265 (7)A, , h = 89.8682 (5)° in F3( m setting] Fe site moment= 4.03(2) mB Atom
x
y
z
Fe(1) Fe(2a) Fe(2b) O(a) O(b)
0 0 1/2 0 0.1732(1)
0 0 0 0 0.8268
0.1250 1/2 0 0.2549(1) 0.0817(3)
Bond Length (A, )
Bond Angle (°)
Fe(1)O(a) 1.893(6) (×1) O(a)Fe(1)O(b) 109.5(1) (×3) Fe(1)O(b) 1.887(2) (×3) O(b)Fe(1)O(b) 109.4(1) (×3) Fe(2a)O(b) 2.058(3) (×6) O(b)Fe(2a)O(b) 180 (×3) 87.5(1) (×6) 92.5(1) (×6) Fe(2b)O(a) 2.058(3) (×2) O(a)Fe(2b)O(a) 180 Fe(2b)O(b) 2.058(2) (×4) O(a)Fe(2b)O(b) 87.8(4) (×4) 92.2(4) (×4) O(b)Fe(2b)O(b) 180 (×2) 87.5(4) (×2) 92.5(2) (×2)
low angle. The fit was not significantly improved by lowering the symmetry of the model further and may reflect systematic errors in the diffraction intensities arising from granularity or extinction; the latter effect is seen in the D20 study below. The atomic parameters were fixed at their ideal cubic phase values, the isotropic factor for all atoms was fixed at zero and the magnetic moments on the Fe sites were constrained to have the same magnitude, in order to obtain a stable and physically realistic refinement. Comparison of the 60 and 130 K D2b patterns (Fig. 1b) reveals many superstructure peaks at 60 K, confirming that the true cell is larger and of lower symmetry than rhombohedral below TV. These have peak heights of B 50 counts in comparison to ca. 12 000 counts for most intense fundamental reflection. These peaks can be indexed using the monoclinic supercell reported previously [11]. The variable temperature D20 data are shown in Fig. 2(a). There is a large increase in the height of the diffraction peaks on cooling below TV, as shown in the contour plot in Fig. 2(b), although the peak
splittings and broadenings resulting from the lattice distortion would be expected to lead to a reduction in the peak heights. This is evidence of a decrease in the mosaic size of the crystallites as they twin on cooling through the transition, leading to a reduction in extinction effects. Sequential Rietveld fits to the D20 data were carried out using the cubic Fd3( m model above TV and a rhombohedral F3( m (non-standard setting of R3( m) model below the transition. The cell constants, atomic parameters and an extinction coefficient [16] were varied in the refinements. TV was found to be 11095 K. Although the lattice distortion is only evidenced by a slight broadening of the diffraction peaks, the refined h=89.875(6)° for the D20 pattern at 60 K does not differ significantly from the value of h= 89.8682(5)° obtained from the fit to more highly resolved D2b data, showing that the cell parameters derived from D20 fits are reliable. The thermal variations of the cell constants, volume, octahedral and tetrahedral site moments and extinction coefficient are shown in Figs. 3–6.
4. Discussion The good fit to the high angle part of the 60 K D2b pattern in Fig. 1 verifies that the lattice distortion accompanying the Verwey transition in magnetite is rhombohedral to a good approximation. This splits the octahedral sites into two inequivalent sets, although the ratio of the site multiplicities (3:1) is not compatible with a 1:1 charge ordered arrangement. It has not been possible to refine the rhombohedral or lower symmetry structures with these data because of systematic intensity errors arising from granularity or extinction effects. However, it is clear that the peaks arising from the previously reported superstructure are resolvable by powder neutron diffraction, although their intensities are B0.5% of the maximum intensity. This demonstrates that the superstructure should be amenable to refinement in future experiments. The highly perfect nature of the cubic magnetite structure leads to unusually severe extinction, as observed in Fig. 2. Refinement of the secondary extinction parameter in the D20 fits shows (Fig. 6) that the mosaic block size is almost halved by the twinning that occurs on cooling through the Verwey transition. Magnetite samples will clearly need to be
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
Fig. 2. (a) Surface plot of the variable temperature D20 study of Fe3O4. (b) Contour plot of the (400) peak.
751
752
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
Fig. 5. Refined magnetic moments (tetrahedral Fe(1) moment, squares; octahedral Fe(2a) and Fe(2b) moment, circles) from the D20 experiment on Fe3O4.
Fig. 3. Thermal variation of the unit cell parameters of Fe3O4, a and h refined from the D20 data.
ground finely in order to minimise extinction effects in future powder diffraction experiments. The rhombohedral angle h, which is a good approximant to the order parameter for the Verwey transition, shows a sharp discontinuous change at TV (Fig. 3) as expected for this abrupt first order transition. The thermal variation in the a parameter (Fig. 3) and the cell volume (Fig. 4) show several new features. Below TV the volume is almost constant with only a slight positive expansion. The cell contracts on warming through the transition, in keeping with the loss of Fe2 + /Fe3 + order above the transi-
Fig. 4. Thermal variation of the unit cell volume of Fe3O4.
tion. Above TV, the volume increases in a quadratic manner, but the expansion only becomes strongly positive above ca. 140 K. This is consistent with a strong electron –phonon coupling that only becomes activated above the Verwey transition when delocalisation of charge carriers becomes possible. The role of volume effects [17] has recently been acknowledged as being of importance in explaining the influence of pressure [18] and composition [5] on the Verwey transition and phonon softening above TV has been studied by diffuse neutron scattering [19]. The refined octahedral and tetrahedral site magnetic moments (Fig. 5) show no discontinuity through the Verwey transition, except for some slight variations due to refinement instabilities close
Fig. 6. Thermal variation of the refined extinction coefficient from the D20 experiment on Fe3O4.
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
to TV. This confirms that no significant magnetic reorganisation occurs at the transition. In conclusion, this study demonstrates that the distortion of the magnetite structure below the Verwey transition is primarily rhombohedral. This is not in keeping with the orthorhombic charge ordering models originally proposed by Verwey. The unique rhombohedral axis coincides with the 3-fold or pseudo 3-fold axes of the FeO6 octahedra, so that the lattice distortion may result from a magnetoelastic coupling (cf. Fe1-x O) or a Jahn-Teller distortion, associated with the localisation of orbitally degenerate Fe2 + states at the transition, rather than being primarily driven by Fe2 + /Fe3 + charge ordering. A refinement of the monoclinic superstructure is needed to resolve the charge ordering issue. These experiments have shown that powder neutron data with sufficient counting statistics and resolution can be obtained, but extinction remains a problem in this case. The variable temperature experiment shows that magnetite has almost no net thermal expansion until above ca. 140 K, showing that polaronic or other phonon assisted motion of the carriers states occurs above the Verwey transition.
Acknowledgements We thank Dr M.A.G. Aranda, Dr A. Hewat, Dr P.G. Radaelli and Dr A.J. Wright for assistance with the collection of neutron data and EPSRC for the provision of neutron beam time and studentships for
753
J.P.W. and A.M.T.B. J.P.W. and A.M.T.B. respectively thank the Rutherford Appleton and Daresbury Laboratories for CASE support.
References [1] E.J.W. Verwey, P.W. Haayman, Physica (Utrecht) 8 (1941) 979. [2] E.J.W. Verwey, P.W. Haayman, F.C. Romeijan, J. Chem. Phys. 15 (1947) 181. [3] W.C. Hamilton, Phys. Rev. 110 (1958) 1050. [4] G. Shirane, S. Chikazumi, J. Akimitsu, K. Chiba, M. Matsui, Y. Fuji, J. Phys. Soc. Jpn. 47 (1975) 1779. [5] J.M. Honig, J. Alloys Compounds 229 (1995) 24. [6] N.C. Toombs, H.P. Rooksby, Acta Cryst. 4 (1951) 474. [7] H.P. Rooksby, B.T.M. Willis, Acta Cryst. 6 (1953) 565. [8] S.C. Abrahams, B.A. Calhoun, Acta Cryst. 6 (1953) 105. [9] L.J. Vieland, Acta Cryst. A31 (1975) 753. [10] E.J. Samuelsen, E.J. Bleeker, L. Dobrzynski, T. Riste, J. Appl. Phys. 39 (1968) 1114. [11] M. Iizumi, G. Shirane, Sol. State Commun. 17 (1975) 433. [12] M. Iizumi, T.F. Koetzle, G. Shirane, S. Chikazumi, M. Matsui, S. Todo, Acta Cryst. B38 (1982) 2121. [13] AC Larson, RB Von Dreele, Los Alamos National Laboratory Report No. LA-UR-86-784, (1994). [14] JP Wright, JB Forsyth, in preparation. [15] J.C. Matthewman, P. Thompson, P.J. Brown, J. Appl. Cryst. 15 (1982) 167. [16] T.M. Sabine, Aust. J. Phys. 38 (1985) 507. [17] J.H.V.J. Brabers, F. Walz, H. Kronmu¨ller, J. Phys: Condens. Matter 11 (1999) 3679. [18] G.K. Rozenberg, G.R. Hearne, M.P. Pasternak, P.A. Metcalf, J.M. Honig, Phys. Rev. B. 53 (1996) 6482. [19] K. Siratori, Y. Ishii, Y. Morii, S. Funakashi, S. Todo, A. Yanase, J. Phys. Soc. Jpn. 67 (1998) 2818.
www.elsevier.com/locate/ssscie
Variable temperature powder neutron diffraction study of the Verwey transition in magnetite Fe3O4 Jon P. Wright, Anthony M.T. Bell 1, J. Paul Attfield * Department of Chemistry, Uni6ersity of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK Received 8 March 2000; accepted 25 July 2000 Dedicated to Professor J.M. Ho¨nig on the occasion of his 75th birthday
Abstract Neutron powder diffraction data have been collected from a sample of polycrystalline Fe3O4. High resolution data collected at 60 K are fitted using a simple rhombohedral distortion of the cubic unit cell. This model accounts for all of the peak splittings that occur upon cooling through the Verwey transition temperature (TV). Lower resolution data collected between 2 and 280 K are fitted using the same model, which gives TV = 11095 K. These data show a change in the thermal expansion due to the softening of phonons above TV and a change in crystallite extinction arising from twinning at the transition. © 2000 E´ditions scientifiques et me´dicales Elsevier SAS. All rights reserved. Keywords: Magnetite; Verwey transition; Variable temperature study; Powder neutron diffraction; Crystal structure of Fe3O4
1. Introduction The mineral magnetite is one of the oldest known magnetic materials. Below the Curie temperature of 860 K, the iron cation spins order ferrimagnetically, giving a bulk magnetisation. Magnetite adopts the inverse cubic spinel crystal structure and is formulated as Fe3 + [Fe3 + Fe2 + ]O4. Fe3 + occupies the tetrahedral sites and Fe2 + and Fe3 + are distributed equally over the octahedral sites. The octahedral sites are identical at room temperature due to rapid electron hopping between Fe2 + and Fe3 + ions. Upon cooling, the resistivity of magnetite increases * Correspondence and reprints. Tel.: + 1-223-336332; fax: + 1223-336362. E-mail address: [email protected] (J.P. Attfield). 1 Present address: Inorganic Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QR, UK.
sharply at the Verwey transition at TV ca. 120 K [1,2], which is believed to be a charge ordering of the Fe2 + and Fe3 + states. The original model for the charge ordered structure of Verwey et al. [2] was thought to have been confirmed by a single crystal neutron diffraction experiment [3], although this experiment was later found to be flawed by multiple scattering effects [4] and no definitive model has since been identified. The difficulty of understanding the Verwey transition has been exacerbated by variations in sample stoichiometry. It was not properly appreciated until the 1980’s that the careful control of sample composition is crucial for obtaining reproducible results [5]. Magnetite can be non-stoichiometric according to the formula Fe3-3l O4 and TV is suppressed with increasing l\ 0. The transition changes from first to second order when l \0.0039 and at l= 0.0117, the magnetite –haematite phase boundary is reached.
1293-2558/00/$ - see front matter © 2000 E´ditions scientifiques et me´dicales Elsevier SAS. All rights reserved. PII: S1293-2558(00)01107-9
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
748
Despite many attempts, no conclusive study of the low temperature structure has emerged. Both rhombohedral [6,7] and orthorhombic [8] distortions of the cubic spinel cell were reported for the low temperature phase. Although the original Verwey model has an underlying orthorhombic symmetry, subsequent work showed that the structural distortion is essentially rhombohedral [9]. Furthermore, the observation of superstructure reflections indexed as (h, k, l+1/2) on the cubic cell [10] are not predicted by the Verwey model. The low temperature space group and supercell were established as monoclinic Cc; 2a × 2a × 2a, where a is the cubic spinel cell parameter from a neutron study of a partially detwinned single crystal [11]. However, the observation of a magnetoelectric effect indicates that the symmetry may be triclinic P1( . The only published refinement [12] of the low temperature structure used a reduced cell and two orthorhombic space groups that are incompatible with the metric tensor. Although these refined models included several inequivalent octahedral sites, no evidence for charge ordering was found. Large, good quality crystals of stoichiometric magnetite can be grown, but single crystal studies below TV are plagued by extinction, multiple scattering and twinning effects. These problems are less Table 1 Crystal structure parameters for Fe3O4 in the cubic phase and two settings of space group R3( m a Atom
Wyck
x
y
z
Cubic space group Fd3( m, ac = 8.3970(1) A, , u= 0.050(2) Fe(1) 8a 1/8 1/8 1/8 Fe(2) 16d 1/2 1/2 1/2 O 32e 1/4+u 1/4+u 1/4+u Space group F3( m, a non-standard setting of R3( m in which the axes coincide with the Fd3( m axes, a= ac, h= 90 ° Fe(1) 8c 1/8 1/8 1/8 Fe(2a) 4c 1/2 1/2 1/2 Fe(2b) 12e 1/4 3/4 0 O(a) 8c 1/4+u 1/4+u 1/4+u O(b) 24h 3/4-u% 1/2+u¦ 1/2+u¦ Space group R3( m (hexagonal axes), ar = ac/ 2, cr = 3ac Fe(1) 6c 0 0 1/8 Fe(2a) 3b 0 0 1/2 Fe(2b) 9e 1/2 0 0 O(a) 6c 0 0 1/4+u O(b) 18h 4u%/3+1/6 −4u%/3–1/6 1/12–u¦/3 a
u =u% =u¦ if pseudo-cubic symmetry is preserved.
severe in powder diffraction experiments and modern synchrotron X-ray and neutron diffractometers offer high count rates and resolution that may be sufficient for the study of the low temperature structure. To investigate the feasibility of this, we report preliminary powder neutron diffraction studies of Fe3O4 above and below TV.
2. Experimental A powder sample of Fe3O4 was prepared by mixing and pelleting stoichiometric amounts of Fe metal and Fe2O3, which were heated in an evacuated, sealed silica tube for a total of 84 h at 1273 K and quenched to room temperature. The sintered product was hand-ground to a powder. Neutron diffraction data were recorded at the Institute Laue et Langevin, Grenoble. High resolution data were collected using the D2b instrument with a 35% collimation and a wavelength of 1.59432 A, . The sample was mounted in a cryostat and patterns were recorded with 0B 2qB 162.5° with a step of 0.05° at temperatures of 130 and 60 K. A variable temperature study was also performed on the high flux instrument D20 which uses a fixed bank of 1600 counters covering 0B2q B 160° in 0.1° steps. Patterns were recorded at 2 K; from 10 to 80 K in 10 K steps; from 80 to 140 K in 5 K steps; and from 140 to 280 K in 10 K steps, at a wavelength of 2.41 A, for 15 min per pattern. Rietveld fits to the D2b data were carried out using the GSAS program [13] and the D20 data were fitted using the PRODD [14] program, which is based on the Cambridge Crystallographic Subroutine Library [15].
3. Results Fig. 1(a) shows a Rietveld fit to the 60 K D2b pattern of magnetite using a rhombohedrally distorted spinel cell (Tables 1 and 2). This gives a good fit to the peak splittings that are clearly observed at high angles. The number of refineable positional parameters in the R3( m symmetry model is four with two different octahedral sites in a 1:3 ratio, compared to only one parameter and octahedral site in the cubic Fd3( m model. Although the peak positions are described well by the rhombohedral distortion, there are several intensity mismatches, particularly at
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
749
Fig. 1. Powder neutron diffraction profiles of Fe3O4 from instrument D2b. (a) Rietveld fit of the rhombohedral model to 60 K data. (b) Comparison of 60 and 130 K patterns showing superstructure peaks in the low temperature profile.
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
750
Table 2 Refined parameters from the D2b data at 60 K in space group R3( m (Rp = 7.6%, Rwp = 10.5%) Cell parameters: a= 5.92767 (5)A, , c =14.5699 (2)A, [Equivalent to a= 8.39265 (7)A, , h = 89.8682 (5)° in F3( m setting] Fe site moment= 4.03(2) mB Atom
x
y
z
Fe(1) Fe(2a) Fe(2b) O(a) O(b)
0 0 1/2 0 0.1732(1)
0 0 0 0 0.8268
0.1250 1/2 0 0.2549(1) 0.0817(3)
Bond Length (A, )
Bond Angle (°)
Fe(1)O(a) 1.893(6) (×1) O(a)Fe(1)O(b) 109.5(1) (×3) Fe(1)O(b) 1.887(2) (×3) O(b)Fe(1)O(b) 109.4(1) (×3) Fe(2a)O(b) 2.058(3) (×6) O(b)Fe(2a)O(b) 180 (×3) 87.5(1) (×6) 92.5(1) (×6) Fe(2b)O(a) 2.058(3) (×2) O(a)Fe(2b)O(a) 180 Fe(2b)O(b) 2.058(2) (×4) O(a)Fe(2b)O(b) 87.8(4) (×4) 92.2(4) (×4) O(b)Fe(2b)O(b) 180 (×2) 87.5(4) (×2) 92.5(2) (×2)
low angle. The fit was not significantly improved by lowering the symmetry of the model further and may reflect systematic errors in the diffraction intensities arising from granularity or extinction; the latter effect is seen in the D20 study below. The atomic parameters were fixed at their ideal cubic phase values, the isotropic factor for all atoms was fixed at zero and the magnetic moments on the Fe sites were constrained to have the same magnitude, in order to obtain a stable and physically realistic refinement. Comparison of the 60 and 130 K D2b patterns (Fig. 1b) reveals many superstructure peaks at 60 K, confirming that the true cell is larger and of lower symmetry than rhombohedral below TV. These have peak heights of B 50 counts in comparison to ca. 12 000 counts for most intense fundamental reflection. These peaks can be indexed using the monoclinic supercell reported previously [11]. The variable temperature D20 data are shown in Fig. 2(a). There is a large increase in the height of the diffraction peaks on cooling below TV, as shown in the contour plot in Fig. 2(b), although the peak
splittings and broadenings resulting from the lattice distortion would be expected to lead to a reduction in the peak heights. This is evidence of a decrease in the mosaic size of the crystallites as they twin on cooling through the transition, leading to a reduction in extinction effects. Sequential Rietveld fits to the D20 data were carried out using the cubic Fd3( m model above TV and a rhombohedral F3( m (non-standard setting of R3( m) model below the transition. The cell constants, atomic parameters and an extinction coefficient [16] were varied in the refinements. TV was found to be 11095 K. Although the lattice distortion is only evidenced by a slight broadening of the diffraction peaks, the refined h=89.875(6)° for the D20 pattern at 60 K does not differ significantly from the value of h= 89.8682(5)° obtained from the fit to more highly resolved D2b data, showing that the cell parameters derived from D20 fits are reliable. The thermal variations of the cell constants, volume, octahedral and tetrahedral site moments and extinction coefficient are shown in Figs. 3–6.
4. Discussion The good fit to the high angle part of the 60 K D2b pattern in Fig. 1 verifies that the lattice distortion accompanying the Verwey transition in magnetite is rhombohedral to a good approximation. This splits the octahedral sites into two inequivalent sets, although the ratio of the site multiplicities (3:1) is not compatible with a 1:1 charge ordered arrangement. It has not been possible to refine the rhombohedral or lower symmetry structures with these data because of systematic intensity errors arising from granularity or extinction effects. However, it is clear that the peaks arising from the previously reported superstructure are resolvable by powder neutron diffraction, although their intensities are B0.5% of the maximum intensity. This demonstrates that the superstructure should be amenable to refinement in future experiments. The highly perfect nature of the cubic magnetite structure leads to unusually severe extinction, as observed in Fig. 2. Refinement of the secondary extinction parameter in the D20 fits shows (Fig. 6) that the mosaic block size is almost halved by the twinning that occurs on cooling through the Verwey transition. Magnetite samples will clearly need to be
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
Fig. 2. (a) Surface plot of the variable temperature D20 study of Fe3O4. (b) Contour plot of the (400) peak.
751
752
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
Fig. 5. Refined magnetic moments (tetrahedral Fe(1) moment, squares; octahedral Fe(2a) and Fe(2b) moment, circles) from the D20 experiment on Fe3O4.
Fig. 3. Thermal variation of the unit cell parameters of Fe3O4, a and h refined from the D20 data.
ground finely in order to minimise extinction effects in future powder diffraction experiments. The rhombohedral angle h, which is a good approximant to the order parameter for the Verwey transition, shows a sharp discontinuous change at TV (Fig. 3) as expected for this abrupt first order transition. The thermal variation in the a parameter (Fig. 3) and the cell volume (Fig. 4) show several new features. Below TV the volume is almost constant with only a slight positive expansion. The cell contracts on warming through the transition, in keeping with the loss of Fe2 + /Fe3 + order above the transi-
Fig. 4. Thermal variation of the unit cell volume of Fe3O4.
tion. Above TV, the volume increases in a quadratic manner, but the expansion only becomes strongly positive above ca. 140 K. This is consistent with a strong electron –phonon coupling that only becomes activated above the Verwey transition when delocalisation of charge carriers becomes possible. The role of volume effects [17] has recently been acknowledged as being of importance in explaining the influence of pressure [18] and composition [5] on the Verwey transition and phonon softening above TV has been studied by diffuse neutron scattering [19]. The refined octahedral and tetrahedral site magnetic moments (Fig. 5) show no discontinuity through the Verwey transition, except for some slight variations due to refinement instabilities close
Fig. 6. Thermal variation of the refined extinction coefficient from the D20 experiment on Fe3O4.
J.P. Wright et al. / Solid State Sciences 2 (2000) 747–753
to TV. This confirms that no significant magnetic reorganisation occurs at the transition. In conclusion, this study demonstrates that the distortion of the magnetite structure below the Verwey transition is primarily rhombohedral. This is not in keeping with the orthorhombic charge ordering models originally proposed by Verwey. The unique rhombohedral axis coincides with the 3-fold or pseudo 3-fold axes of the FeO6 octahedra, so that the lattice distortion may result from a magnetoelastic coupling (cf. Fe1-x O) or a Jahn-Teller distortion, associated with the localisation of orbitally degenerate Fe2 + states at the transition, rather than being primarily driven by Fe2 + /Fe3 + charge ordering. A refinement of the monoclinic superstructure is needed to resolve the charge ordering issue. These experiments have shown that powder neutron data with sufficient counting statistics and resolution can be obtained, but extinction remains a problem in this case. The variable temperature experiment shows that magnetite has almost no net thermal expansion until above ca. 140 K, showing that polaronic or other phonon assisted motion of the carriers states occurs above the Verwey transition.
Acknowledgements We thank Dr M.A.G. Aranda, Dr A. Hewat, Dr P.G. Radaelli and Dr A.J. Wright for assistance with the collection of neutron data and EPSRC for the provision of neutron beam time and studentships for
753
J.P.W. and A.M.T.B. J.P.W. and A.M.T.B. respectively thank the Rutherford Appleton and Daresbury Laboratories for CASE support.
References [1] E.J.W. Verwey, P.W. Haayman, Physica (Utrecht) 8 (1941) 979. [2] E.J.W. Verwey, P.W. Haayman, F.C. Romeijan, J. Chem. Phys. 15 (1947) 181. [3] W.C. Hamilton, Phys. Rev. 110 (1958) 1050. [4] G. Shirane, S. Chikazumi, J. Akimitsu, K. Chiba, M. Matsui, Y. Fuji, J. Phys. Soc. Jpn. 47 (1975) 1779. [5] J.M. Honig, J. Alloys Compounds 229 (1995) 24. [6] N.C. Toombs, H.P. Rooksby, Acta Cryst. 4 (1951) 474. [7] H.P. Rooksby, B.T.M. Willis, Acta Cryst. 6 (1953) 565. [8] S.C. Abrahams, B.A. Calhoun, Acta Cryst. 6 (1953) 105. [9] L.J. Vieland, Acta Cryst. A31 (1975) 753. [10] E.J. Samuelsen, E.J. Bleeker, L. Dobrzynski, T. Riste, J. Appl. Phys. 39 (1968) 1114. [11] M. Iizumi, G. Shirane, Sol. State Commun. 17 (1975) 433. [12] M. Iizumi, T.F. Koetzle, G. Shirane, S. Chikazumi, M. Matsui, S. Todo, Acta Cryst. B38 (1982) 2121. [13] AC Larson, RB Von Dreele, Los Alamos National Laboratory Report No. LA-UR-86-784, (1994). [14] JP Wright, JB Forsyth, in preparation. [15] J.C. Matthewman, P. Thompson, P.J. Brown, J. Appl. Cryst. 15 (1982) 167. [16] T.M. Sabine, Aust. J. Phys. 38 (1985) 507. [17] J.H.V.J. Brabers, F. Walz, H. Kronmu¨ller, J. Phys: Condens. Matter 11 (1999) 3679. [18] G.K. Rozenberg, G.R. Hearne, M.P. Pasternak, P.A. Metcalf, J.M. Honig, Phys. Rev. B. 53 (1996) 6482. [19] K. Siratori, Y. Ishii, Y. Morii, S. Funakashi, S. Todo, A. Yanase, J. Phys. Soc. Jpn. 67 (1998) 2818.