Structural and Magnetic Characterization of Mechanically Alloyed (Fe₂O₃)_1−x(Al₂O₃)_x Solid Solutions via Pulsed Neutron Powder Diffraction

Abstract

Neutron powder diffraction experiments were carried out to characterize mechanochemically synthesized (Fe₂O₃)_1−x(Al₂O₃)_x solid solutions with corundum-type structure, focusing on their lattice and magnetic structures with varying temperature and composition. The neutron diffraction experiments for (Fe₂O₃)_0.5(Al₂O₃)_0.5 in the temperature range between 4 K and 300 K reveal that no significant structural phase transition occurred. The behavior of temperature variation of lattice parameters is different from α-Fe₂O₃ and α-Al₂O₃ and reveals the thermal expansion coefficients of α_a = 5.76(2) × 10⁻⁶ K⁻¹ and α_c = 6.19(5) × 10⁻⁶ K⁻¹ between 200 K and 300 K. The room temperature neutron diffraction of (Fe₂O₃)_1−x(Al₂O₃)_x shows a linear decrease in lattice parameters with the aluminum substitution, following Vegard’s law, along with a decrease in the magnetic moment, indicating the dilution effect on spin interactions. With the increase in the aluminum substitution from x = 0 to 0.5, the deduced magnetic moment decreases from 2.224 μ_B to 0.862 μ_B.

1. Introduction

Corundum-type structured α-Fe₂O₃ (hematite) is a promising candidate anode material for lithium-ion batteries (LIBs), though significant volume changes during its conversion reaction restrict its cycle performance [1,2,3,4,5]. Using α-Al₂O₃ (corundum) to stabilize the crystal structure of α-Fe₂O₃ by forming a solid solution seems an appropriate means of addressing this limitation. However, the solid solution ranges between them in the equilibrium phase diagram are considerably limited around the end-number compositions [6,7]. Despite extensive efforts to extend the solid solution range, the wide range of the intermediate composition (0.3 < x < 0.75) for (Fe₂O₃)_1−x(Al₂O₃)_x exhibits two-phase coexistence [8,9,10,11]. In recent years, we have innovatively synthesized the entire compositional range (0 ≤ x ≤ 1) of the corundum-type solid solution through the mechanical alloying method starting from a mixture of γ-Fe₂O₃ and γ-Al₂O₃ [12]. X-ray diffraction confirmed that the compositional dependence of lattice parameters of the obtained solid solutions agrees with Vegard’s law assuming JCPDS data of α-Fe₂O₃ (33-664) and α-Al₂O₃ (46-1212) [12,13]. In the charge–discharge tests of (Fe₂O₃)_1−x(Al₂O₃)_x as electrode materials, the solid solutions exhibited good cycle performance in the compositional range of 0.33 ≤ x ≤ 0.45 [12].

In previous work, we carried out transmission electron microscopy (TEM), extended X-ray absorption fine structure (EXAFS), and Mössbauer spectroscopy experiments to clarify the atomic level solid solution formation and the cation distribution in samples with x = 0 − 0.67 [14]. The TEM experiments showed that the typical particle size of the solid solutions was 10–20 nm, with lattice spacings consistent with those calculated with Vegard’s law. The EXAFS measurements showed that the radial distribution of Fe-Fe distance decreased monotonously with the increase in aluminum substitution, while the Fe-O distance did not significantly. Through room-temperature Mössbauer spectroscopy, with the increase in the aluminum substitution, the spectra gradually shifted from a sextet pattern (weak ferromagnetism) into a doublet (paramagnetism) due to the dilution of the Fe-Fe spin interaction. To further understand the thermodynamic behavior of the (Fe₂O₃)_1−x(Al₂O₃)_x solid solutions, low-temperature heat capacities have been measured [15]. While the obtained heat capacities of the solid solutions showed a similar trend of temperature dependence with pure α-Fe₂O₃ and α-Al₂O₃ [16], the measured values are slightly higher than their weighted averages, and a heat capacity anomaly was observed below 25 K.

To investigate the detailed structural information of the mechanically alloyed (Fe₂O₃)_1−x(Al₂O₃)_x solid solution, we conducted time-of-flight (TOF) neutron powder diffraction experiments in the present study. Neutron diffraction provides precise atomic positions including oxygen ions [17,18] and also probes the magnetic structure due to the neutron spin interactions, which matches the investigation of a new type of solid solution with spin interactions [19]. In this study, we employed the neutron powder diffraction technique to clarify the structural and magnetic properties of the (Fe₂O₃)_1−x(Al₂O₃)_x solid solution with varying temperature and composition.

2. Materials and Methods

(Fe₂O₃)_1−x(Al₂O₃)_x solid solutions were synthesized through high-energy ball milling, as described in the previous studies [12,14,15]. Stoichiometric mixtures of γ-Fe₂O₃ (Sigma Aldrich, St. Louis, MO, USA, 99+%) and γ-Al₂O₃ (Strem Chem., Newburyport, MA, USA, 96%) powders were loaded into a 20 mL volume silicon nitride (Si₃N₄) milling vessel, along with ten silicon nitride milling balls in 10 mm diameter. No solvents were used during the process. The milling was conducted in air under atmospheric pressure using a planetary ball milling machine (Fritsch, Idar-Oberstein, Germany, Premium Line P-7) operated at 800 rpm in segmented intervals for a total milling time of 240 min (12 cycles of 20 min of operation with 40 min of cooling).

The neutron powder diffraction experiments were carried out using the special environment neutron diffraction instrument (BL09 SPICA) at the Japan Proton Accelerator Research Complex (J-PARC) in Tokai, Japan [20]. The instrument features a top-loading 4 K cryostat with a measurement range from 4 K to 300 K. About 1 g of synthesized (Fe₂O₃)_1−x(Al₂O₃)_x solid solution powder with x = 0.5 was loaded into a vanadium sample holder, which was sealed under helium gas conditions. The diffraction data were collected at room temperature for 3 h, 200 K for 2.5 h, 100 K for 2.5 h, 20 K for 4.5 h, and 4 K for 4.5 h through the BS (Back Scattering) bank for d = 0.3–4.0 Å and QA (Quasi Axial) bank for d = 0.4–5.0 Å. BS and QA detectors are positioned at different scattering angles, with BS located at high angles for high-resolution structural analysis and QA at intermediate angles offering balanced resolution and intensity, making it suitable for detecting magnetic scattering. Compositional dependence was also investigated using x = 0, 0.20, 0.40, and 0.50. We selected these compositions based on the Mössbauer spectroscopy results [14], which show a transition from a sextet to a doublet within this range. The diffracted data were collected at room temperature for 3 h. Lattice information was mainly obtained from the BS bank data, while the magnetic information was from the QA bank. The lattice and magnetic structures were refined by the Rietveld method using Z-Rietveld software (ver. 2.0.0) [21]. For the crystal structure analysis of the solid solutions, the space group was selected as R$\overline{3}$c of hematite lattice, placing Fe and Al at the identical 12c and O at the 16e sites.

3. Results and Discussion

3.1. Temperature Dependences of the Structure of (Fe₂O₃)_0.5(Al₂O₃)_0.5

Figure 1a shows the temperature dependence of the neutron diffraction patterns of (Fe₂O₃)_0.5(Al₂O₃)_0.5 detected at the BS bank. As depicted in Figure 1a, only slight shifts in peak due to the thermal expansion with no observable structural phase transition were observed from room temperature down to 4 K. While our previous calorimetric investigation [15] suggested anomalous behavior below 25 K, apparent structural change was not detected in the present neutron diffraction experiment.

Figure 1b shows the neutron diffraction patterns of (Fe₂O₃)_0.5(Al₂O₃)_0.5 collected at the QA bank. Relatively large peaks around d ~ 4.1 Å and 4.5 Å attributed to the 101 and 003 magnetic reflections, respectively, are observed. Since these reflections have been reported for hematite [22], we suggest that the spin arrangement of the iron sublattices in the solid solution is related to that of pure α-Fe₂O₃. In addition, the intensities of the 101 and 003 magnetic reflections seem to decrease gradually with the increase in temperature, while other peaks do not.

Figure 2a–e represent the Rietveld refined neutron diffraction patterns of (Fe₂O₃)_0.5(Al₂O₃)_0.5 collected at 4 K, 20 K, 100 K, 200 K, and room temperature by the BS bank. A small number of diffraction peaks for silicon nitride (Si₃N₄) contamination of the milling vessel were also included in the analysis as the second phase. To evaluate the possibility of remaining starting materials, the Rietveld refinement was examined, assuming the coexistence of γ-Fe₂O₃ and γ-Al₂O₃. However, the calculated mass fractions of the γ-phases were less than 0.1%, so the analysis was conducted assuming a corundum-type solid solution with a minimal amount of Si₃N₄. Although the peak profiles were broadened due to the milled sample, and lower d-spacing peaks overlapped considerably, profile fitting could be performed with rather small R_wp. From the lattice and magnetic reflections, the propagation vector was obtained as k = (0, 0, 0), indicating that the periodicity of the magnetic structure aligns with the lattice structure without any additional modulation. Through the analysis of the magnetic diffraction peaks detected in the QA bank, the magnetic moments |M| were obtained as 1.293 μ_B and 1.189 μ_B at 4 K and room temperature, respectively. This slight improvement in |M| with the decrease in temperature might be due to the restricted thermal fluctuations of magnetic spins at low temperatures, although the contribution is much smaller in comparison with the effect of aluminum substitution as described later.

Table 1. Structure parameters of mechanically alloyed (Fe₂O₃)_0.5(Al₂O₃)_0.5 refined from the BS bank data.

Temperature (K)	Atom	Site	g	x	y	z	Biso (Å2)
4	Fe/Al	12c	1	0	0	0.14729(2)	0.810(1)
	O	18e	1	0.31477(5)	0	0.25	0.939(1)
		a = 4.91009(4) Å, c = 13.39012(17) Å, Rwp = 2.4458%
20	Fe/Al	12c	1	0	0	0.14620(2)	0.772(3)
	O	18e	1	0.30777(6)	0	0.25	0.763(4)
		a = 4.90967(4) Å, c = 13.39059(16) Å, Rwp = 2.3661%
100	Fe/Al	12c	1	0	0	0.14731(3)	0.830(4)
	O	18e	1	0.31149(8)	0	0.25	0.832(4)
		a = 4.91040(5) Å, c = 13.3916(2) Å, Rwp = 2.5226%
200	Fe/Al	12c	1	0	0	0.14667(2)	0.776(4)
	O	18e	1	0.30910(7)	0	0.25	0.743(3)
		a = 4.91233(4) Å, c = 13.3960(2) Å, Rwp = 2.0989%
R.T.	Fe/Al	12c	1	0	0	0.14738(2)	0.858(4)
	O	18e	1	0.30858(6)	0	0.25	0.745(3)
		a = 4.91514(3) Å, c = 13.4041(2) Å, Rwp = 2.4458%

Space group: $R\overline{3}c$ (hexagonal lattice); g: occupancy; x, y, z: fractional coordinates; B_iso: atomic displacement factor.

summarizes the structural parameters of (Fe₂O₃)_0.5(Al₂O₃)_0.5 at various temperatures obtained from the Rietveld refinement. Some selected interatomic distances are also listed in

Table 2. Temperature dependences of the selected Fe-O and Fe-Fe distances in (Fe₂O₃)_0.5(Al₂O₃)_0.5 evaluated from Table 1, and superscripts i–iv indicate the corresponding ions in Figure 3.

Temperature (K)	(Fe/Al)i–Oi (Å)	(Fe/Al)ii–Oii (Å)	(Fe/Al)i–(Fe/Al)ii (Å)	(Fe/Al)ii–(Fe/Al)iii (Å)	(Fe/Al)i–(Fe/Al)iv (Å)
4	2.0689(3)	1.8894(2)	2.7506(5)	3.9445(5)	3.3121(3)
20	2.0531(3)	1.8995(2)	2.7800(5)	3.9153(5)	3.2969(3)
100	2.0568(4)	1.8974(3)	2.7504(9)	3.9454(9)	3.3126(5)
200	2.0533(3)	1.9009(2)	2.7687(6)	3.9293(6)	3.3049(3)
R.T.	2.0476(3)	1.9069(2)	2.7511(6)	3.9510(6)	3.3168(3)

, for which the atomic labels are available in the structural model in Figure 3.

Figure 4a shows the temperature dependence of the lattice parameters of (Fe₂O₃)_0.5(Al₂O₃)_0.5. Both a and c increase with temperature. Although the lattice parameters of α-Fe₂O₃ and α-Al₂O₃ are simultaneously plotted in Figure 4b, the compositional dependence is too significant for direct comparison. To compare the thermal evolutions, the lattice parameters were normalized by each room temperature value and plotted in Figure 4c. Assuming the linear thermal expansion coefficient,

$$\alpha ={\displaystyle \frac{1}{l_0}}·{\displaystyle \frac{\mathsf{\Delta }l}{\mathsf{\Delta }T}}$$

the α_a and α_c of (Fe₂O₃)_0.5(Al₂O₃)_0.5 were evaluated, where l₀ is the lattice parameter at the lower temperature side, and Δl/ΔT represents the average temperature gradient of the lattice parameters for the given temperature range.

Table 3. The calculated thermal expansion coefficients of (Fe₂O₃)_0.5(Al₂O₃)_0.5.

	Temperature (K)	$\mathit{\alpha }$a (10−6 K−1)	$\mathit{\alpha }$c (10−6 K−1)
(Fe2O3)0.5(Al2O3)0.5	4–100	0.66(2)	1.15(3)
	200–300	5.76(2)	6.19(5)
α-Fe2O3 [24]	2–77	1.90	1.53
	150–293	1.44	1.05
α-Al2O3 [25,26]	2–100	1.50	1.89
	200–300	1.05	1.77

shows the thermal expansion coefficients of (Fe₂O₃)_0.5(Al₂O₃)_0.5 compared with α-Fe₂O₃ and α-Al₂O₃. As expected from Figure 4c, α obtained in the temperature range 4–100 K is lower than that in 200–300 K. The difference in the trend among normalized lattice parameters for (Fe₂O₃)_0.5(Al₂O₃)_0.5, α-Fe₂O₃, and α-Al₂O₃ in Figure 4c is possibly due to lattice distortion induced during the mechanical alloying process or the cation mixing effect.

The previous calorimetric investigation revealed the higher heat capacity for mechanically alloyed (Fe₂O₃)_0.5(Al₂O₃)_0.5 in comparison with the averaged one of pure α-Fe₂O₃ and α-Al₂O₃, indicating the lower Debye temperature Θ_D [15]. Ruffa [27] suggested the relationship between α and Θ_D as $\alpha \left(T\right)={\displaystyle \frac{3k}{2aD{r}_D}}{\left({\displaystyle \frac{T}{{\Theta }_D}}\right)}^{3}g(x_D)$ for the cubic lattice assuming Morse potential, where k is the Boltzmann constant, and a, $r_D$, and D are the lattice parameters, nearest-neighbor distance, and dissociation energy of morse potential, respectively. $x_D$ means ${\Theta }_D/T$, and $g\left(x_D\right)$ is described as $g\left(x_D\right)={\int }_0^{x_D}{\displaystyle \frac{x^4{e}^{x}dx}{{(e^x-1)}^2}}$. Since the cubed term ${\left({\displaystyle \frac{T}{{\Theta }_D}}\right)}^3$ is strongly attributed to α, i.e., a smaller Θ_D results in a larger α, the previous heat capacity result is qualitatively consistent with the larger thermal expansion coefficient.

3.2. Compositional Dependence of the Structure of (Fe₂O₃)_1−x(Al₂O₃)_x

Figure 5 shows the neutron diffraction patterns of (Fe₂O₃)_1−x(Al₂O₃)_x (x = 0 − 0.5) collected at room temperature through the (a) BS and (b) QA banks. From the diffraction patterns of the BS bank, the overall peaks shift toward lower d-spacings as the x-value increases, indicating a reduction in lattice constants. For the QA bank, the intensity of magnetic reflections around d ~ 4.1 Å and 4.5 Å decreases significantly with the increase in aluminum substitution. This should be due to the dilution of magnetic iron ions by non-magnetic aluminum ions, which weakens the spin–spin interactions. Through the Rietveld refinement, lattice structure information for (Fe₂O₃)_1−x(Al₂O₃)_x (x = 0, 0.2, 0.4, and 0.5) was obtained and is listed in

Table 4. Structure parameters of (Fe₂O₃)_1–x(Al₂O₃)_x (x = 0, 0.2, 0.4 and 0.5) at room temperature.

Composition	Atom	Site	g	x	y	z	Biso (Å2)
x = 0	Fe/Al	12c	1	0	0	0.145556(8)	0.937(1)
	O	18e	1	0.30992(4)	0	0.25	0.610(2)
		a = b = 5.025556(17) Å, c = 13.73302(9) Å, Rwp = 3.6910%
x = 0.2	Fe/Al	12c	1	0	0	0.14723(1)	0.870(1)
	O	18e	1	0.30862(4)	0	0.25	0.636(2)
		a = b = 4.98646(2) Å, c = 13.61093(10) Å, Rwp = 2.6605%
x = 0.4	Fe/Al	12c	1	0	0	0.146591(13)	0.915(2)
	O	18e	1	0.31000(5)	0	0.25	0.774(3)
		a = b = 4.93405(3) Å, c = 13.45815(14) Å, Rwp = 2.0553%
x = 0.5	Fe/Al	12c	1	0	0	0.14738(2)	0.858(4)
	O	18e	1	0.30858(6)	0	0.25	0.745(3)
		a = b = 4.91514(3) Å, c = 13.4041(2) Å, Rwp = 2.4458%

Space group: $R\overline{3}c$ (hexagonal lattice); g: occupancy; x, y, z: fractional coordinates; B_iso: atomic displacement factor.

. Some selected Fe-O and Fe-Fe bond lengths are shown in

Table 5. Compositional dependences of the Fe-O distances and Fe-Fe distances in the (Fe₂O₃)_1–x(Al₂O₃)_x at room temperature evaluated using Table 4, and superscripts i–iv indicate the corresponding ions in Figure 3.

x-Value	(Fe/Al)i–Oi (Å)	(Fe/Al)ii–Oii (Å)	(Fe/Al)i–(Fe/Al)ii (Å)	(Fe/Al)ii–(Fe/Al)iii (Å)	(Fe/Al)i–(Fe/Al)iv (Å)
0	2.1174(2)	1.9358(1)	2.8687(3)	3.9978(3)	3.3674(1)
0.2	2.0942(2)	1.9240(1)	2.8163(3)	3.9891(3)	3.3539(1)
0.4	2.0679(3)	1.9059(2)	2.7834(4)	3.9457(4)	3.3187(2)
0.5	2.0476(3)	1.9069(2)	2.7511(6)	3.9510(6)	3.3168(2)

, indicating that increasing aluminum substitution results in a reduction in Fe-O and Fe-Fe bond lengths.

Figure 6 plots the compositional dependences of the lattice parameters for (Fe₂O₃)_1−x(Al₂O₃)_x, showing that both lattice parameters a and c decrease linearly with the aluminum concentration. These lattice parameters agree well with the previous X-ray diffraction results [12], which are depicted by closed symbols. This behavior should be ascribed to the smaller ionic radius of aluminum (0.535 Å) compared to that of iron (0.645 Å) [28,29]. Hence, we suggest that replacing iron ions with smaller aluminum ions reduces the distance between oxygen ions, leading to lattice contraction. Since the Fe-O or Fe-Fe distances vary with the concentration of aluminum, the excellent cycle performance for 0.33 ≤ x ≤ 0.45 [12] is not due to the structural characteristics but the electrochemical properties such as conductivity or equilibrium potential.

Figure 7 shows the compositional variation of the magnetic moment |M| of (Fe₂O₃)_1−x(Al₂O₃)_x calculated with the data at the QA bank. For the sample of x = 0 obtained by milling γ-Fe₂O₃, the magnetic moment |M| is deduced to be 2.224 μ_B, whereas that of α-Fe₂O₃ at 300 K is 4.118(6) μ_B in the MAGNDATA database [30]. This discrepancy might be due to the smaller particle size and possibly the introduced micro-strain as well as poorer crystallinity caused by the mechanical alloying process. Nanoparticle-sized materials often exhibit characteristic behaviors [31,32]. A higher surface ratio with lower coordination numbers results in the reduction in surface exchange interactions and the magnetic moment [33,34]. As the aluminum substitution increases, the magnetic moment continuously decreases. The partial substitution of aluminum with iron reduces the spin–spin interactions, allowing the magnetic state of (Fe₂O₃)_1−x(Al₂O₃)_x to shift from weak ferromagnetism to a rather paramagnetic state. This behavior is consistent with the previous Mössbauer measurements, showing gradual change in spectra from sextet into doublet profiles [14]. Further comparison with Mössbauer spectroscopy requires simulation, including iron dispersion and spin interaction, which should be conducted in future work.

4. Conclusions

The lattice and magnetic structures of mechanically alloyed (Fe₂O₃)_1−x(Al₂O₃)_x solid solutions were investigated by TOF neutron powder diffraction with temperature and compositional variation. No observable structural phase transition was detected in the neutron diffraction patterns of (Fe₂O₃)_0.5(Al₂O₃)_0.5 from 4 K to room temperature, except for a slight shift due to the thermal expansion. The temperature dependence of the normalized lattice parameters is quite different from that of α-Fe₂O₃ and α-Al₂O₃, presumably due to lattice distortion or the Fe/Al mixing effect. On the other hand, the lattice parameters of the (Fe₂O₃)_1−x(Al₂O₃)_x solid solution decrease linearly with the increase in the aluminum concentration at room temperature, as observed in the previous X-ray diffraction experiment. The deduced magnetic moment of (Fe₂O₃)_1−x(Al₂O₃)_x also decreases with the increase in aluminum substitution due to the reduction in magnetic interaction, as expected from the previous Mössbauer spectroscopy investigation. In addition, the change in the interatomic distances, especially for Fe–Fe, which governs the exchange interactions, should be considered. This investigation would provide essential information on the structure of newly synthesized (Fe₂O₃)_1−x(Al₂O₃)_x solid solutions.