First XANES evidence of a disorder–order transition in a spinel ferrite compound: nanocrystalline ZnFe₂O₄

In situ Zn K-edge XANES experiments were performed to investigate the thermal evolution of the non-equilibrium state in nano-sized ZnFe₂O₄. The initially disordered ferrite was annealed under oxygen atmosphere and kept at temperatures of 673, 773 and 873 K. Modifications of the XANES features allowed the direct detection of the Zn local surrounding changes from O_h to T_d symmetry. Quantitative analyses of these results were performed by using the principal-component analysis approach. The ferrite inversion does not change until the activation barrier is overcome at T_a = 585 K. Above T_a, the Zn ions continuously change their environment to their normal equilibrium state. Isothermal treatments confirm that the Zn transference follows a first-order kinetic process. In addition, the thermal treatment produces a partial recrystallization that increases the average grain size from 13 to 50 nm and reduces the microstrain. The room-temperature magnetic state changes from ferrimagnetic to paramagnetic, while the blocking temperature increases after the treatment.

1. Introduction

Amongst spinel ferrites MFe₂O₄ (where M is a 3d ion), zinc ferrite has become one of the most explored compounds during recent years (see, for example, Hochepied et al., 2000; Chinnasamy et al., 2002; Hoffman et al., 2004; Stewart et al., 2007). In its normal equilibrium state, Fe³⁺ and Zn²⁺ ions are surrounded by octahedral [B] and tetrahedral (A) oxygen arrays, respectively. The equilibrium distribution can be altered by employing non-equilibrium methods of synthesis (Hoffman et al., 2004; Bohra et al., 2006; Nakashima et al., 2007a; Stewart et al., 2007) or by reducing the ZnFe₂O₄ characteristic length down to nanometric ranges (Hochepied et al., 2000; Atif et al., 2006). This implies changes in its magnetic ordering that goes from antiferro to cluster-glass to ferrimagnetic state as the inversion, i.e. the fraction of (A) sites occupied by iron, increases (Hoffman et al., 2004; Widatallah et al., 2008).

Comprehension of the underlying mechanisms that favor a non-equilibrium cation distribution is relevant not only for fundamental studies but also for possible applications when a controllable magnetic response is required. In particular, as the magnetic degradation of ferrites might limit certain purposes (Lee et al., 2006), it is also important to characterize the range of stability of the disordered ferrimagnetic state; in spite of the vast amount of published work on nanostructured ZnFe₂O₄, to our knowledge only a few studies have been performed to investigate its thermal stability (Šepelák et al., 2004; Philip et al., 2007). Šepelák et al. (2004) have studied the kinetics of disordered nanocrystalline high-energy milled ZnFe₂O₄. Through in situ X-ray diffraction (XRD) studies performed under air atmosphere, they found that the range of stability extends up to 600 K. Recently, Philip et al. (2007) also performed in situ XRD experiments on nano-sized ZnFe₂O₄. In this case the material, initially in its normal state, evolves towards a partially inverted state by heat treatment under vacuum. They also found that the cation redistribution starts at 1073 K. On the other hand, Pavese et al. (2000) had previously reported on the thermodynamic behavior of the thermally activated order–disorder transformation in bulk zinc ferrite. By using in situ neutron diffraction, they detected that an increment of the inversion parameter occurs above 800 K that smoothly increases up to 1500 K. These in situ investigations and others concerning the annealing effects on disordered ZnFe₂O₄ (Tung et al., 2002; Nakashima et al., 2007b) have provided significant information about the thermal stability of a particular distribution of cations. However, a comparison between these results may not be straightforward as different initial material has been used and, in addition, different environmental conditions or rates of heating have been employed. Thus, more studies are needed to fully understand the mechanisms involved in the second-order transition that occurs in ZnFe₂O₄ that strongly affects its magnetism.

Recently, X-ray absorption near-edge structure (XANES) experimental and ab initio simulation results on disordered ZnFe₂O₄ provided direct evidence of Zn²⁺ and Fe³⁺ transferences from equilibrium to non-equilibrium sites as the inversion increases (Stewart et al., 2007). Analogous effects were observed by Nakashima et al. (2007a) in their Fe and Zn K-edge XANES spectra of disordered ZnFe₂O₄ thin films, which were also reproduced by simulations using a first-principles method. These independent investigations provided a semi-quantitative determination of the inversion in ZnFe₂O₄, in good agreement with the inversion obtained by the extended X-ray absorption fine-structure (EXAFS) fitting analysis. These findings allowed a not always clear identification of XANES features as a function of the local structure of the compound, opening a new perspective to explore XANES as a tool to investigate the disorder ↔ order transition in spinel ferrites. For instance, XANES spectroscopy under dispersive geometry involves a shorter time for data collection when compared with EXAFS or diffraction techniques, which makes it appropriate for kinetics studies. It also represents an alternative to the diffraction in situ experiments performed on nanocrystalline ZnFe₂O₄, whose results are characterized by broad reflection lines that, added to thermal effects, might make it difficult to obtain reliable structural and inversion parameters during a treatment.

We present here an investigation of the thermal stability of partially inverted nano-sized ZnFe₂O₄ by employing, for the first time, in situ time-resolved XANES experiments. We will demonstrate that the thermal evolution of Zn K-edge XANES spectra allows us to follow the thermally activated relocation of zinc ions towards their equilibrium positions. This study is complemented by performing ex situ X-ray diffraction, XANES, EXAFS and magnetic measurements.

2. Experiment

Partially inverted ZnFe₂O₄ nanoferrite (degree of inversion determined by EXAFS analysis, c = 0.4, average grain size D = 13 nm) was obtained by milling hydrothermally prepared nanocrystalline ZnFe₂O₄ (c = 0.2, D = 6 nm). Details of sample preparation can be found elsewhere (Stewart et al., 2007). In situ XANES spectra at the Zn K-edge (9659 eV) were collected in transmission mode using the D06A-DXAS beamline at LNLS (Laboratório Nacional de Luz Síncrotron) in Campinas, Brazil. A curved crystal monochromator selects a bandwidth of hundreds of eV around absorption edges, according to the Bragg angle and radius of curvature. Details of the experimental set-up of the beamline have been published elsewhere (Tolentino et al., 2005). The XANES experiments were performed in a controlled-atmosphere cell (Meneses et al., 2006), heating the inverted zinc ferrite sample at a rate of 10 K min⁻¹ in an oxygen flow from ambient temperature up to 673 K for 60 min (step X), 773 K for 60 min (step Y) and 873 K for 120 min (step Z). Afterwards the furnace was switched off and the sample was allowed to cool down inside the cell under oxygen flow. The data analysis was performed by subtracting a linear background and rescaling the absorbance by normalizing the difference between the baseline and the post-edge absorption in a region approximately 300 eV behind the edge. A Fortran program was used (Fernández-García et al., 1995) to analyze the XANES data using principal-component factor analysis.

XANES and EXAFS ex situ spectra (Zn and Fe K-edges) of the sample before and after the treatment were collected at room temperature in transmission mode using a Si(111) monochromator with a slit aperture of 0.3 mm at the XAFS-1 beamline of the LNLS. The χ(k) EXAFS signal was extracted using the Athena program and analyzed using the Arthemis program (Ravel & Newville, 2005).

XRD patterns at room temperature were taken using a Philips PW 1710 diffractometer (Cu Kα radiation with λ = 1.5406 Å). XRD data were collected at room temperature in the 20° ≤ 2θ ≤ 120° range, with 0.02° step width and counting rate of 10 s per step. Magnetic measurements were carried out using a SQUID magnetometer (Quantum Design) and an AC susceptometer (Lakeshore).

3. Results and discussion

3.1. X-ray absorption results

X-ray absorption near-edge spectra at the Zn K-edge are a sign of the electronic transition from the zinc 1s core level to unoccupied p-type states. Zn K-edge XANES of normal spinel ZnFe₂O₄ consists of three resolved peaks, A, B and C (Fig. 1), at around 9664, 9668 and 9672 eV, respectively, a shoulder at around 9677 eV (peak D), plus additional structure at higher energies (peak E) (Waychunas et al., 2003; Stewart et al., 2007). These features were adequately reproduced by means of ab initio calculations using the FEFF8.2 code (Ankudinov et al., 1998) considering the electron scattering from the ligand shell surrounding the Zn absorber (Stewart et al., 2007).

Figure 1 Ex situ Zn K-edge XANES spectra taken at room temperature of nano-sized ZnFe2O4 before and after the thermal treatment.

Experimentally, we found that as ZnFe₂O₄ becomes partially inverted the intensity of the second peak B [labelled A1 in Stewart et al. (2007)] progressively increases and the shoulder D weakens (line A2). These trends were also confirmed by our calculation results. Indeed, the theoretical spectra generated by assuming a weighted sum of the spectrum with Zn at its equilibrium tetrahedral sites plus the spectrum corresponding to Zn substitutional to the Fe atoms at octahedral sites are in very good agreement with our experimental findings (Stewart et al., 2007). In particular, the B peak is a signature of the white line corresponding to Zn substitutional to Fe in the spinel structure, whose theoretical spectrum is also characterized by the almost absence of peak D (Waychunas et al., 2003; Stewart et al., 2007). These effects of inversion on the Zn K-edge XANES were later corroborated by Nakashima et al. (2007) in their study about ZnFe₂O₄ thin films with a disordered cation distribution. Moreover, they reproduced the features of the ZnFe₂O₄ XANES spectra at Zn and Fe K-edges throughout simulations using first-principles calculations based on density functional theory. Their results also showed that the middle peak contribution increases when Zn²⁺ at octahedral sites is considered while the peak at D corresponds to an electronic transition that involves Zn sites with T_d symmetry.

To investigate the thermal stability of partially inverted ZnFe₂O₄ we have performed in situ XANES experiments at the Zn K-edge. Owing to its initial inversion (c = 0.4), XANES spectra taken before the treatment show the enhancement of peak B and the almost absence of the shoulder D when compared with the spectrum of normal ZnFe₂O₄ (Stewart et al., 2007).

We observe that, as nanocrystalline disordered ZnFe₂O₄ is annealed, a progressive recovering of the normal spinel XANES features takes place, i.e. the middle peak B decreases and the shoulder D becomes more noticeable after annealing. This tendency can be visualized through color contour curves of the absorption spectra, as shown in Fig. 2. Indeed, we distinguish an initial state with a white line centralized at about 9668 eV, while the final state clearly shows the four features A, B, C and D that characterize XANES of normal ZnFe₂O₄ (see also Fig. 1). This trend is reversed to the behavior observed as the inversion increases (Stewart et al., 2007). Therefore, considering the previous results, we assign this change as an indication that the Zn local environment is changing from O_h to T_d symmetry with the treatment.

Figure 2 Color contour map of the absorption spectra recorded under in situ conditions. The annealing temperatures at steps X, Y and Z are indicated at the top. The heating rate was kept to 10 K min^−1. The blue region indicates the pre-edge contribution while the dark red region represents the position of the white line. The discontinuity of the white line between spectra 40 and 47 is due to intensity saturation.

To further characterize the thermally activated disorder–order transition we performed a principal-component analysis (PCA). PCA consists of a statistical methodology applied on a set of normalized energy calibrated spectra (Malinowski & Howery, 1980), which has become an important tool for the recognition of components using XANES data provided the presence of clearly dissimilar features of each individual species. Thus, taking into account the different features that distinguish Zn K-edge XANES of partially inverted from normal ZnFe₂O₄, we generated the spectra as a linear combination of these two components to roughly estimate the proportion of each site by using this approach. Table 1 shows the calculated eigenvalues with their respective variance, the percentage significance level (%SL) and the IND, an empirical function used to help in deciding the number of components (Malinowski & Howery, 1980). Assuming a 5% test level for %SL, the PCA would indicate the presence of two principal components in the thermal treatment. However, the IND function suggests that a seventh principal component could be present (Table 1). However, the lack of importance of this possible component can be tested visually by examining the abstract row matrix in Fig. 3. Indeed, it can be seen that the first two factors (1 and 2) represent most of the signal while the third and subsequent are mainly dominated by noise and low-frequency background components. On the other hand, Table 1 points out the very low contributions to the variance made by eigenvalues higher than the second one. Consequently, the number of principal components has been fixed at two. Fig. 4 shows the result of PCA by considering some selected spectra. The result of this analysis shows that the inversion does not change on heating until the activation barrier is overcome at about T_a = 585 K (Figs. 2 and 4). Above T_a the Zn ions continuously change their local environment to an equilibrium state along the maximum temperature studied (step Z, T_max = 873 K) and continue along the equilibrium pathway on cooling.

Table 1
Eigenvalues from the PCA, their variance, the percentage significance level (%SL) and the IND, the empirical function used to determine the number of components (n)

n	Eigenvalue	Variance†	%SL	IND × 10^−4
1	1697.7	99.966	0.0	0.740
2	0.53851	0.032	0.0	0.217
3	0.013794	0.001	6.06	0.202
4	0.0091835		5.51	0.185
5	0.0057103		5.24	0.168
6	0.0030411		7.10	0.158
7	0.0009242		25.78	0.175
8	0.0007361		27.32	0.199
9	0.00054870		30.84	0.234
10	0.00033881		40.32	0.294

†Variances lower than 10⁻³ are not reported.

Figure 3 Abstract component matrix for the selected spectra at the Zn K-edge.

Figure 4 Thermal dependence of the inversion c obtained by performing a PCA of the data.

After the activation barrier is surmounted, the inversion during heating (10 K min⁻¹) decreases following a linear behavior with time, c/c_i = 1 − αt, where α = 1.4 × 10⁻³ s⁻¹ and c_i is the initial inversion. A relaxation process towards equilibrium is also observed at each isotherm. Fig. 5 shows the time dependency of the relative degree of inversion c/c₀ when the ferrite sample remains at the isotherm T = 873 K (c₀ is the initial inversion at the beginning of step Z). Following the assumption made by Šepelák et al. (2004) to analyze their in situ XRD data, we supposed a relaxation towards a normal spinel configuration controlled by a kinetic process obeying an exponential law. Fitting c/c₀ versus time data by using the function c/c₀ = exp[k(t − t₀)] gives a rate constant k ≃ 0.01 min⁻¹ and an induction time t₀ ≃ 20 min.

Figure 5 Isothermal kinetics of the Zn transference in nano-sized ZnFe2O4 at T = 873 K (step Z). The solid line corresponds to the fitting considering an exponential law.

Fourier transforms (FTs) of the k³χ(k) EXAFS signal at Zn and Fe K-edges without phase correction for the sample after the thermal treatment are shown in Fig. 6, while fit results are summarized in Table 2. From the FTs of the Zn K-edge spectra we observe an almost disappearance of the peak corresponding to Zn octahedrally coordinated at R ≃ 2.95 Å, which was clearly visible in the FTs corresponding to the sample before the treatment (Stewart et al., 2007). Furthermore, these FTs resemble those of bulk ZnFe₂O₄ (Stewart et al., 2007). This is in accordance with the thermally activated Zn[B] → Zn(A) transference illustrated by the present XANES studies. From these EXAFS data we found that after completing the treatment the inversion parameter c ≃ 0.05, i.e. almost the same inversion that we estimated for bulk ZnFe₂O₄.

Table 2
EXAFS Fe and Zn K-edge fitted parameters for ZnFe₂O₄ after thermal treatment

N is the coordination number, R is the distance from the central atom, σ² is the Debye–Waller factor and E₀ is the energy shift.

Edge	Shell	N	R (Å)	σ^2 × 10^−2 (Å^2)	E0 (eV)
K-Fe	O	5.9 ± 0.6	2.01 ± 0.01	0.6 ± 0.1	−7.4 ± 0.6
	Fe	5.9 ± 0.6	2.989 ± 0.004	0.6 ± 0.06	−7.4 ± 0.6
	O	2 ± 0.2	3.49 ± 0.01	0.95 ± 0.09	−7.4 ± 0.6
	Zn	5.9 ± 0.6	3.51 ± 0.01	0.95 ± 0.09	−7.4 ± 0.6
K-Zn	O	3.8 ± 0.4	2.003 ± 0.007	0.4 ± 0.3	4 ± 1
	Fe	11 ± 1	3.54 ± 0.04	1.0 ± 0.2	4 ± 1
	O	11 ± 1	3.57 ± 0.04	1.0 ± 0.2	4 ± 1
	Zn	3.7 ± 0.3	3.69 ± 0.04	1.0 ± 0.2	4 ± 1

Figure 6 Fourier transforms of k^3χ(k) EXAFS data at the Zn and Fe K-edges taken ex situ for nanocrystalline ZnFe2O4 after completing the thermal treatment following the steps X, Y and Z. The solid lines are the fitting results corresponding to the parameters shown in Table 2.

3.2. Thermally induced structural and magnetic changes in ZnFe₂O₄ nanoparticles

The XRD pattern of the thermally treated zinc ferrite only showed the peaks belonging to ZnFe₂O₄ (see inset of Fig. 7) with narrowed linewidths when compared with those before the treatment (Fig. 7). Considering the corrected integral breadth, β, of the most intense reflection (311), we estimated, by means of Scherrer's equation, the average grain size (D). Also, from the relation β = 4(Δd/d)tanθ we found the average microstrain level, ∊ = Δd/d. The results show that D has grown to 50 nm and ∊ has decreased by 40%. Furthermore, the cell parameter changes from a = 8.435 to 8.439 Å. This lattice dilation might be associated with the evolution towards a less disordered state owing to more Zn²⁺ with higher radius than Fe³⁺ occupying A sites after the calcinations (a = 8.441 Å for normal bulk ZnFe₂O₄).

Figure 7 A region of the X-ray diffraction patterns of ZnFe2O4 before and after treatment and of bulk ZnFe2O4. Inset: whole X-ray diffraction pattern of ZnFe2O4 after completing treatment through steps X, Y and Z.

Fig. 8 shows magnetization versus applied magnetic field (M–H) before and after the treatment. M–H of initial inverted ferrite shows a sigmoidal shape with a high magnetization owing to its ferrimagnetic state. This state comes from the occupancy of Fe³⁺ at both B and A sites that promotes the action of J_AB superexchange interactions that give rise to the ferrimagnetic ordering. After the treatment, the ferrimagnetic state at room temperature is almost eradicated (Fig. 8), as can be observed by the almost disappearance of the sigmoidal shape and the linear increment of M for all values of the field. This indicates that, in addition to the Zn²⁺ redistribution as observed by the Zn K-edge XANES, Fe³⁺ ions are also changing their local environment from T_d to O_h symmetry or are being transferred to occupy their equilibrium position.

Figure 8 Magnetization versus applied magnetic field curves taken at room temperature for ZnFe2O4 before and after treatment.

Fig. 9 shows the in-phase component of the AC susceptibility, χ. We observe that, after the annealing, the χ maximum has shifted towards lower temperatures by about 170 K. The temperature at which the maximum occurs is associated with the blocking temperature, T_B, of the particle moments. Considering the Brown–Néel model, the anisotropy energy E_a for independent moments is related to T_B as E_a = k_BT_Bln(τ/τ₀), where τ₀ is a factor in the range 10⁻⁹–10⁻¹² s, and k_B is Boltzmann's constant. When assuming a uniaxial anisotropy, E_a = K_effV, where K_eff is the anisotropy constant and V is the volume of the magnetic particles. Therefore, the decrease of T_B can be associated with a reduction of the apparent magnetic size or a decrease of K_eff owing to a reduction of the surface anisotropy (Tung et al., 2002). Indeed, thermal activated relocations of type Zn²⁺[B] → Zn²⁺(A) and Fe³⁺(A) → Fe³⁺[B] suggest that pathways Fe[B]—O— Fe(A) become less probable. This would also imply a reduction in the magnetic cluster sizes and the consequent decrease in T_B.

Figure 9 Thermal dependence of the low-field in-phase component of the AC-susceptibility (χ) of ZnFe2O4 before (a) and after (b) treatment.

3.3. Comments about the disorder–order transition in nano-sized ZnFe₂O₄

Our results relating to the thermal stability of the dis­ordered state in nano-sized ZnFe₂O₄ show a good agreement with those reported by Šepelák et al. (2004). We can infer that, independent of whether the annealing is performed under air or oxygen flow, the stability of the non-equilibrium cation extends up to 585–600 K. Thus, probably owing to its metastable character, the disorder → order transition activates at a lower temperature than the order → disorder transition (Pavese et al., 2000; Philip et al., 2007). However, some questions remain unanswered regarding the mechanism involved in these transitions. Usually they are depicted as a movement or redistribution of cations between the spinel interstitial sites. However, it is uncertain whether there is a hopping of cations or the transition involves a rearrangement of oxygen atoms that mainly affects the surface layer. It seems that to generate the order → disorder change the creation of oxygen vacancies is necessary (Pavese et al., 2000; Philip et al., 2007). On the other hand, milling ZnFe₂O₄ always causes an inversion enhancement, independent of whether the particle/grain sizes decrease (Hoffman et al., 2004) or increase (Stewart et al., 2007). This would imply that milling not only affects the surface but involves the whole particle, causing an accumulation of defects that favors a non-equilibrium distribution of cations. When the thermal treatment is performed in such a way that the material has oxygen available, it stabilizes in its normal state (Šepelák et al., 2004; Philip et al., 2007). Thus, all these results would point out that the oxygen mobility is playing an important role, but more investigations are required to interpret the configuration changes in spinel compounds that strongly influence their physical properties.

4. Conclusions

By means of Zn K-edge in situ XANES experiments we were able to directly observe the zinc transference from non-equilibrium octahedral positions to equilibrium tetrahedral ones within the spinel structure of ferrimagnetic ZnFe₂O₄ nanoparticles. We found that the activation of the disorder–order transition takes place above 585 K and intensifies with temperature. Isothermal treatments showed that the Zn transference follows a first-order kinetic process. Additional results indicate that the thermal treatment produces a partial recrystallization that increases the average grain size from 13 to 50 nm and reduces the microstrain. Once the activation barrier is overcome, the cation configuration (Fe and Zn) moves towards equilibrium and consequently the spontaneous magnetization of the initial ferrimagnetic state starts to be erased. Finally, these results demonstrate the feasibility of XANES spectroscopy to gain insight into the order ↔ disorder transitions in Zn-containing spinel compounds.