Physicochemical processes and thermochemical parameters of GdFeO₃ formation from amorphous hydroxides: decisive role of carbonate impurities

Abstract

The mechanism of formation of nanocrystalline gadolinium orthoferrite (GdFeO₃) during the heat treatment of gadolinium and iron(III) hydroxides synthesized by ultrasound-assisted co-precipitation was studied. The obtained samples were investigated by energy-dispersive X-ray spectroscopy, simultaneous thermal analysis via coupled differential scanning calorimetry and thermogravimetric analysis (DSC–TGA), powder X-ray diffraction (PXRD) and Fourier-transform infrared (FTIR) spectroscopy. The DSC–TGA results confirm that the formation of GdFeO₃ occurs after the complete decomposition of gadolinium oxycarbonate derivatives. The PXRD results indicate that GdFeO₃ is formed as a result of the reaction of amorphous iron(III) oxide (am-Fe₂O₃) at temperatures of 675–700 °C with amorphous gadolinium oxide (am-Gd₂O₃) (primary carbonate-independent pathway) and at temperatures of 725–775 °C with cubic gadolinium oxide (c-Gd₂O₃) transformed from the hexagonal gadolinium oxide (h-Gd₂O₃) which results from the decomposition of gadolinium oxycarbonate derivatives at temperatures of 675–725 °C (secondary carbonate-dependent pathway). The FTIR results are consistent with the assumption that gadolinium oxycarbonate derivatives decompose with the formation of h-Gd₂O₃ in the last-mentioned temperature range. The enthalpy of the reaction of formation of nanocrystalline GdFeO₃ defined from the DSC–TGA data is equal to − 16.89 ± 0.36 kJ mol⁻¹. The activation energy for the formation of nanocrystalline GdFeO₃ obtained from the DSC data is equal to 1193.62 ± 112.05 kJ mol⁻¹, 1202.27 ± 112.06 kJ mol⁻¹ and 1151.08 ± 106.53 kJ mol⁻¹ according to the Kissinger, Augis–Bennett/Boswell and Flynn–Wall–Ozawa methods, respectively. Also, based on the DSC data, the true onset temperature of the formation of nanocrystalline GdFeO₃ was found to be ~ 756 °C.

Introduction

Rare-earth orthoferrites (REFeO₃, where RE is a rare-earth element: Sc, Y, La–Lu) are a class of chemical compounds with an orthorhombic perovskite structure that have been actively studied due to their magnetic, optical and electrical properties [1,2,3,4,5,6,7]. One of these compounds is gadolinium orthoferrite (GdFeO₃) which has been proposed for various applications such as catalysis [8], photocatalysis [9], electrocatalysis [10], luminescence [11], gas sensing [12] and as a contrast agent for magnetic resonance imaging (MRI) [13,14,15,16]. In the synthesis of GdFeO₃ nanocrystals, various methods have been employed, including co-precipitation [17], hydrothermal method [18], solution combustion [19], sol–gel [20], microwave method [21], sonochemical method [22] and using heterobimetallic [23] and metal–organic [24] precursors. The co-precipitation method, which we preferred in our previous works [25,26,27,28,29,30], makes it possible to synthesize nanocrystalline GdFeO₃ with minimal foreign chemical impurities since the co-precipitated gadolinium and iron(III) hydroxides are dehydrated during heat treatment with the formation of the corresponding oxides, which then form the compound of interest. However, due to the active sorption of carbon oxide (CO₂) from the ambient air into the reagent solutions during their preparation or onto the surface of co-precipitated hydroxides during their washing and drying, gadolinium carbonate can be formed. Such partial carbonatization of co-precipitated hydroxides may lead to sample inhomogeneity in terms of phase composition, and as a result, to the formation of another phase along with GdFeO₃ after heat treatment [25, 26, 30]. Therefore, it is of scientific and practical interest to study and understand the role of carbonates in the formation mechanism of nanocrystalline GdFeO₃ by co-precipitation.

In the literature, several publications have investigated the mechanism of formation of GdFeO₃ nanocrystals by the co-precipitation method [31,32,33]. Prakash et al. [31] investigated the formation of nanocrystalline GdFeO₃ by sintering a synthesized sample of co-precipitated hydroxides at temperatures of 600–1200 °C. They found that gadolinium oxide (Gd₂O₃) was present in the sintered products up to a temperature of 1000 °C, above which single-phase GdFeO₃ nanocrystals were obtained; therefore, they consider the temperature of 1200 °C to be optimal for sintering. The authors reported the presence of carbonates in the synthesized sample, but they did not indicate their role in the formation of GdFeO₃. Tugova and Karpov [32] studied the mechanism of formation of nanocrystalline GdFeO₃ upon the calcination of co-precipitated hydroxides at temperatures of 500–900 °C. They established that the products heat treated at temperatures of 500–600 °C contain gadolinium dioxymonocarbonate (Gd₂O₂CO₃) which decomposes at temperatures of 600–700 °C to form cubic Gd₂O₃, and starting from a temperature of 700 °C, GdFeO₃ is formed. Based on these results, they concluded that the formation of GdFeO₃ nanocrystals occurs through two mechanisms: the first mechanism is related to the simultaneous dehydration of co-precipitated hydroxides, while the other is associated with both dehydration and decarbonation, which leads to an increase in the temperature of GdFeO₃ synthesis. The work of Popkov et al. [33] confirmed the results of the previous one [32] that the formation of GdFeO₃ nanocrystals proceeds via two routes: from the co-precipitated hydroxides along the main route and from the products of partial carbonatization along the side one.

In this paper, we continue the work of the aforementioned colleagues, focus on simultaneous thermal analysis of the precursor and study in detail the mechanism of formation of GdFeO₃ nanocrystals synthesized employing the ultrasound-assisted co-precipitation method, which apparently, maintains sample homogeneity by enhancing diffusion and mixing processes [30]. The content of carbonates in the products of heat treatment of the synthesized sample of co-precipitated hydroxides at different temperatures is estimated. In addition, the true onset temperature of the formation of nanocrystalline GdFeO₃ is found, and the enthalpy and the activation energy for this formation reaction are also defined.

Materials and methods

Synthesis of samples

In this work, gadolinium and iron(III) hydroxides were synthesized by direct co-precipitation accompanied by ultrasonication. After that, samples of the obtained co-precipitated hydroxides were heated at different temperatures in the air.

An aqueous solution of stoichiometric amounts of gadolinium nitrate hexahydrate “Gd(NO₃)₃·6H₂O” (puriss., 99.9%) and iron(III) nitrate nonahydrate “Fe(NO₃)₃·9H₂O” (pur., 98.00%) with a concentration of 0.01 mol L⁻¹ for each salt was used as a source of gadolinium and iron(III) ions. An aqueous solution of sodium hydroxide (NaOH) (p.a.) with a concentration of 1 mol L⁻¹ was used as a precipitating medium. Gadolinium and iron(III) nitrates react with sodium hydroxide to form water-soluble sodium nitrate (NaNO₃) and a precipitate of gadolinium hydroxide “Gd(OH)₃” and iron(III) hydroxide “Fe(OH)₃” (exchange reaction). The equation for this reaction can be written as follows:

Gd(NO₃)₃(aq) + Fe(NO₃)₃(aq) + 6NaOH(aq) = Gd(OH)₃(s) + Fe(OH)₃(s) + 6NaNO₃(aq).

Co-precipitation of gadolinium and iron(III) hydroxides

For the synthesis of co-precipitated hydroxides, 100 mL of 1 mol L⁻¹ sodium hydroxide solution was added dropwise to 100 mL of 0.01 mol L⁻¹ gadolinium and iron(III) nitrates solution, which was constantly stirred with a magnetic stirrer and irradiated with ultrasound by immersing the ultrasonic horn of a ‘‘Venpan type UD-20 automatic’’ ultrasonic disintegrator into it throughout the entire co-precipitation process. The synthesis was repeated two more times, each time with 100 mL of each reagent solution. Then, the resulting precipitates with the supernatants from the three syntheses were mixed using a magnetic stirrer. After settling, most of the supernatant was decanted, and the co-precipitated hydroxides were separated from the remainder by centrifugation. Thereafter, the obtained precipitate was washed three times with distilled water to remove residual sodium hydroxide and sodium nitrate. The washed co-precipitated hydroxides were separated from water by centrifugation and then dried at a temperature of 45 °C.

Heat treatment of co-precipitated hydroxides

Samples of the synthesized co-precipitated hydroxides with a mass of about 50 mg were heated at different temperatures in the range of 650–850 °C with an interval of 25 °C (650, 675, 700, 725, 750, 775, 800, 825 and 850 °C) for 4 h in the air.

Characterization of co-precipitated hydroxides

Energy-dispersive X-ray spectroscopy

The content of gadolinium and iron in the synthesized sample of co-precipitated hydroxides was determined by energy-dispersive X-ray spectroscopy (EDXS) using a “TESCAN VEGA3” scanning electron microscope (TESCAN ORSAY HOLDING, Brno-Kohoutovice, Czech Republic) with an accelerating voltage of 30.0 kV coupled with an “x-act” silicon drift detector (Oxford Instruments, Abingdon, Oxfordshire, UK).

Differential scanning calorimetry and thermogravimetric analysis

The synthesized sample of co-precipitated hydroxides was investigated by differential scanning calorimetry and thermogravimetric analysis (DSC–TGA) using a “NETZSCH STA 449 F3” simultaneous thermal analyzer (NETZSCH-Gerätebau GmbH, Selb, Germany) up to 900 °C at three different heating rates (10, 20 and 30 °C min⁻¹) in an inert atmosphere of argon. The sample masses were 11.160, 11.568 and 11.183 mg at heating rates of 10, 20 and 30 °C min⁻¹, respectively. The DSC and TGA curves of the reference substances (potassium chromate “K₂CrO₄” and barium carbonate “BaCO₃”) were obtained using the same simultaneous thermal analyzer at the same three heating rates. The sample mass of K₂CrO₄ was 15.677 mg at a heating rate of 10 °C min⁻¹ and 16.130 mg at heating rates of 20 and 30 °C min⁻¹, while the sample mass of BaCO₃ was 11.933 mg at all heating rates. All measurements were carried out in platinum crucibles (DSC/TG pan Pt). The processing of the DSC–TGA data was carried out using the “NETZSCH Proteus Thermal Analysis” software.

Characterization of heat-treated products

Powder X-ray diffraction

The powder X-ray diffraction (PXRD) patterns were recorded using a ‘‘Rigaku SmartLab 3’’ diffractometer (Rigaku Corporation, Tokyo, Japan) in the Bragg angle range of 15–61° at a scan speed of 0.2 deg min⁻¹ and a step width of 0.01°. The processing of the PXRD data was carried out using the ‘‘SmartLab Studio II’’ software. The mass fractions of the crystalline phases were estimated by the Rietveld refinement method using the crystal structure data of the Inorganic Crystal Structure Database (ICSD) structures with the identifiers of ICSD 27278, ICSD 162247 and ICSD 150677 for orthorhombic GdFeO₃, hexagonal Gd₂O₃ and cubic Gd₂O₃, correspondently. The relative mass fractions of the X-ray amorphous phases in the products that underwent heat treatment at temperatures up to 775 °C were estimated by normalizing the obtained diffractograms of these products, determining the integrated intensity of the amorphous halo on the normalized diffraction patterns in the Bragg angle range of ~ 15.2–27.2° and recalculating the resulting values as percentages of the maximum. The estimated results of mass fractions of the X-ray amorphous and crystalline phases in each heat-treated product were combined by subtracting the integrated intensity of the amorphous halo from 100% and recalculating the mass fractions of crystalline phases as fractions of the obtained value.

Fourier-transform infrared spectroscopy

The Fourier-transform infrared (FTIR) spectra in the wavenumber range of 400–4000 cm⁻¹ were obtained by Kubelka–Munk transformation of diffuse reflectance data acquired using a “Bruker INVENIO-S” FTIR spectrometer (Bruker Optics, Ettlingen, Germany) with a “PIKE” diffuse reflectance attachment (PIKE Technologies, Madison, WI, USA). The relative mass percentages of gadolinium oxycarbonate derivatives in the products that underwent heat treatment at temperatures up to 800 °C were estimated by normalizing the obtained FTIR spectra of these products, determining the integrated intensity of the asymmetric and symmetric stretching vibrations of carbonate groups (CO ²⁻₃ ) on the normalized FTIR spectra in the wavenumber range of ~ 1260–1625 cm⁻¹ and recalculating the resulting values as percentages of the maximum.

Results and discussion

Energy-dispersive X-ray spectroscopy

According to the EDX spectrum presented in Fig. 1, the synthesized sample of co-precipitated hydroxides is practically chemically pure. The carbon detected in the investigated sample is related to the presence of carbonate groups, the appearance of which, as we mentioned earlier, is a consequence of the active sorption of CO₂ from the ambient air into the reagent solutions during their preparation or onto the surface of co-precipitated hydroxides during their washing and drying. Based on the EDXS results, the atomic ratio of gadolinium to iron (Gd:Fe) is (49.92 ± 0.03)%:(50.08 ± 0.03)%; therefore, the average Gd:Fe atomic ratio is about 1.000:1.003, which is very close to the atomic ratio of 1:1 in GdFeO₃, i.e., the content of gadolinium and iron in the synthesized sample corresponds to the stoichiometry of the compound of interest. It is worth noting that the Gd:Fe atomic ratio is preserved during the synthesis since neither gadolinium nor iron is included in the composition of compounds that are volatile during the heat treatment of co-precipitated hydroxides.

Fig. 1

EDX spectrum of the co-precipitated hydroxides. The inset (pie chart) shows the average Gd:Fe atomic ratio in the sample

Differential scanning calorimetry and thermogravimetric analysis

As was shown earlier [25, 27, 29, 33], upon heat treatment, gadolinium and iron(III) hydroxides undergo a series of physicochemical processes before forming GdFeO₃. The DSC and TGA curves of the synthesized sample of co-precipitated hydroxides at different heating rates (10–30 °C min⁻¹) are presented in Fig. 2a and b, respectively. The first derivatives of the TGA curves (the DTG curves) are presented in supplementary Fig. S1. On the obtained DSC curves (Fig. 2a), 7 thermal effects can be detected: 6 endothermic (effects indicated by downward pointing arrows 1–6) and one exothermic (effect indicated by upward pointing arrow 8), whereas on the presented DTG curves (Fig. S1), 7 endothermic effects are observed (effects 1–7). These effects are associated with the evaporation of the physically adsorbed water on the sample surface (endothermic effect 1: ~ 53–63 °C by DSC, ~ 51–58 °C by DTG); the dehydration of iron(III) hydroxide to form iron(III) oxide (endothermic effect 2: ~ 126–163 °C by DSC, ~ 132–156 °C by DTG); the dehydration of gadolinium hydroxide in three stages: firstly to form gadolinium oxide sesquihydrate (endothermic effect 3: ~ 226–247 °C by DSC, ~ 223–246 °C by DTG), secondly to form gadolinium oxyhydroxide (endothermic effect 4: ~ 294–319 °C by DSC, ~ 299–322 °C by DTG), and thirdly, to gadolinium oxide (endothermic effect 6: ~ 414–452 °C by DSC, ~ 420–442 °C by DTG); the first stage of decomposition of gadolinium carbonate to form an oxycarbonate derivative (endothermic effect 5: ~ 371–384 °C by DSC, ~ 369–392 °C by DTG); the last stage of decomposition of gadolinium oxycarbonate derivative to form gadolinium oxide (endothermic effect 7: ~ 756–758 °C by DTG), and finally, the formation of gadolinium orthoferrite from gadolinium and iron(III) oxides (exothermic effect 8: ~ 764–772 °C by DSC). All these results are summarized in Table 1. As can be seen from Table 1, the temperatures of the maximum thermal and mass loss effects generally tend to increase with increasing heating rate. According to the TGA curves (Fig. 2b), the total mass loss is about 21.69%, 21.75% and 20.58% at a heating rate of 10, 20 and 30 °C min⁻¹, correspondently. These mass losses are related to the release of water (effects 1–4 and 6) and CO₂ (effects 5 and 7). The results obtained are in good agreement with the previous ones [32, 33], which confirm that the formation of GdFeO₃ occurs after the mass loss is completed, i.e., after the complete decomposition of gadolinium oxycarbonate derivatives.

Fig. 2

DSC (a) and TGA (b) curves of the co-precipitated hydroxides at different heating rates. The inset in (b) shows the exothermic effect of GdFeO₃ formation (t is the temperature, t_max is the temperature of the maximum thermal effect). The arrows pointing down indicate endothermic effects (effects 1–6), while the arrows pointing up indicate exothermic effects (effect 8)

Table 1 Thermal (DSC) and mass loss (DTG) effects of the co-precipitated hydroxides at different heating rates

Enthalpy of the reaction of formation of nanocrystalline GdFeO₃

To found the enthalpy of formation of nanocrystalline GdFeO₃ based on the DSC–TGA results, two reference substances were used: K₂CrO₄ and BaCO₃. Potassium chromate and barium carbonate undergo certain physicochemical transformations at temperatures below and above the formation temperature of GdFeO₃, respectively. According to the data used to calibrate the thermal analyzer, at a heating rate of 10 °C min⁻¹, K₂CrO₄ transforms from orthorhombic to hexagonal form in an endothermic process [34] at a temperature of 668.0 °C with an enthalpy of 35.000 J g⁻¹, while BaCO₃ melts in an endothermic process at a temperature of 808.0 °C with an enthalpy of 94.900 J g⁻¹.

At each heating rate (β), the onset temperature (t_onset) and peak area (A) of the endothermic effects of the reference substances and the exothermic effect of GdFeO₃ formation were determined from the DSC curves, whereas the values of sample mass at each onset temperature (m_onset) were determined from the TGA curves. Peak areas in µV °C were calculated from their values in µV s given by the software using the heating rate according to Eq. 1.

$$A \left[\mathrm{\upmu V }^\circ \mathrm{C}\right]=A \left[\mathrm{\upmu V \,s}\right]\cdot \frac{\beta \left[^\circ \mathrm{C }\,{\mathrm{min}}^{-1}\right]}{60 \left[\mathrm{s }\,{\mathrm{min}}^{-1}\right]}$$

(1)

Then, the “specific” peak areas (A*) were calculated by dividing the obtained peak areas by the corresponding sample masses at onset temperature as shown in Eq. 2.

$${A}^{*} \left[\mathrm{\upmu V }^\circ \mathrm{C }\,{\mathrm{mg}}^{-1}\right]=\frac{A \left[\mathrm{\upmu V }^\circ \mathrm{C}\right]}{{m}_{\mathrm{onset}} \left[\mathrm{mg}\right]}$$

(2)

After that, the known enthalpy values associated with the endothermic effects of the reference substances were divided by the corresponding “specific” peak areas as shown in Eq. 3.

$$\Delta H/{A}^{*} \left[\mathrm{J }{\mathrm{\upmu V}}^{-1} \,{^\circ \mathrm{C}}^{-1}\right]=\frac{\Delta H \left[\mathrm{J }{\mathrm{g}}^{-1}\right]\cdot {10}^{-3} \left[\mathrm{g }\,{\mathrm{mg}}^{-1}\right]}{{A}^{*} \left[\mathrm{\upmu V }\,^\circ \mathrm{C }\,{\mathrm{mg}}^{-1}\right]}$$

(3)

Then, the resulting values of ΔH/A* were plotted as a function of t_onset at each heating rate (Fig. 3), where each dependence is a straight line drawn between two reference points: one for K₂CrO₄ and the other for BaCO₃.

Fig. 3

Dependences of the ratio of enthalpy to the “specific” peak area on the onset temperature of the thermal effect in the temperature range ~ 663–805 °C at different heating rates

Based on the equations of the straight lines obtained, the values of ΔH/A* for GdFeO₃ at each heating rate were calculated using the corresponding onset temperatures of the exothermic effect of GdFeO₃ formation. All these data are summarized in Table 2.

Table 2 DSC–TGA data used in the estimation of the enthalpy of the reaction of formation of nanocrystalline GdFeO₃

Thereafter, multiplying the resulting values of ΔH/A* for GdFeO₃ at each heating rate by the corresponding “specific” peak areas calculated earlier by Eq. 2, the enthalpy of the reaction of formation of nanocrystalline GdFeO₃ can be estimated (Eq. 4).

$$\Delta H \left[\mathrm{J }\,{\mathrm{g}}^{-1}\right]=\Delta H/{A}^{*} \left[\mathrm{J }{\mathrm{\upmu V}}\,^{-1} {^\circ \mathrm{C}}^{-1}\right]\cdot {A}^{*} \left[\mathrm{\upmu V }\,^\circ \mathrm{C }{\mathrm{mg}}^{-1}\right]\cdot {10}^{3} \left[\mathrm{mg }\,{\mathrm{g}}^{-1}\right]$$

(4)

According to Eq. 4, the enthalpy of the reaction of formation of nanocrystalline GdFeO₃ is in the range from about − 63.36 to − 66.54 J g⁻¹ or from about − 16.54 to − 17.37 kJ mol⁻¹. In other words, it is approximately equal to − 64.67 ± 1.36 J g⁻¹ or − 16.89 ± 0.36 kJ mol⁻¹. This value is much less than the enthalpy of formation of GdFeO₃ at 298.15 K (− 1351.432 ± 8.368 kJ mol⁻¹ [35]), which can be explained by the fact that the standard enthalpy of formation corresponds to the formation of GdFeO₃ from its constituent elements (Gd, Fe and O) in their standard states, while in this work, the enthalpy of formation of GdFeO₃ from gadolinium and iron(III) oxides was estimated. Furthermore, the calculated value does not correspond to bulk GdFeO₃, but to nanosized GdFeO₃; therefore, it should be smaller.

Activation energy for the formation of nanocrystalline GdFeO₃

To estimate the activation energy for the formation of nanocrystalline GdFeO₃ based on the DSC data, three kinetic methods were applied: the Kissinger method [36], the Augis–Bennett/Boswell method [37, 38] and the Flynn–Wall–Ozawa (FWO) method [39, 40]. These non-isothermal kinetic methods depend on the relationship between the heating rate and the absolute temperature at which the reaction reaches its maximum value [41]. The mathematical formulas for these methods can be written as shown in Eqs. 5–7.

Kissinger method

$$\mathrm{ln}\left(\frac{\beta }{{T}_{\mathrm{max}}^{2}}\right)=-\frac{{E}_{\mathrm{a}}}{R{T}_{\mathrm{max}}}+\mathrm{ln}\left(\frac{AR}{{E}_{\mathrm{a}}}\right)$$

(5)

Augis–Bennett/Boswell method

$$\mathrm{ln}\left(\frac{\beta }{{T}_{\mathrm{max}}}\right)=-\frac{{E}_{\mathrm{a}}}{R{T}_{\mathrm{max}}}+\mathrm{const}.$$

(6)

Flynn–Wall–Ozawa method

$$\left.\begin{array}{c}\mathrm{log}\;\beta =-0.4567\frac{{E}_{\mathrm{a}}}{R{T}_{\mathrm{max}}}+\text{const}.\\ \mathrm{ln}\;\beta =-1.052\frac{{E}_{\mathrm{a}}}{R{T}_{\mathrm{max}}}+\text{const}.\end{array}\right\}$$

(7)

In these equations, β is the heating rate, T_max is the absolute temperature at which the reaction reaches its maximum value, i.e., the peak of the thermal effect (in our work, T_max is the absolute temperature of the maximum exothermic effect of GdFeO₃ formation on the corresponding DSC curve), E_a is the activation energy, A is the pre-exponential factor and R is the molar gas constant.

Based on the Kissinger method (Eq. 5), plotting ln(β/T ²_max ) against 1/T_max results in a straight line with a slope of − E_a/R and a y-intercept of ln(AR/E_a). Similarly, in accordance with the Augis–Bennett/Boswell method (Eq. 6), plotting ln(β/T_max) versus 1/T_max gives a straight line with a slope of − E_a/R, whereas according to the FWO method (Eq. 7), plotting of ln β against 1/T_max gives a straight line with a slope of − 1.052E_a/R. Figure 4 shows these straight lines obtained using the previously determined temperatures of the maximum exothermic effect of GdFeO₃ formation on the DSC curves at different heating rates (Table 1, effect 8). In the first two methods, the activation energy for the formation of nanocrystalline GdFeO₃ can be calculated by multiplying the resulting slopes by − R, while in the third method, the obtained slope should be multiplied by − R and divided by 1.052. The DSC data used and the calculation results are summarized in Table 3.

Fig. 4

Dependences of ln(β/T ²_max ) (Kissinger method), ln(β/T_max) (Augis–Bennett/Boswell method) and ln β (FWO method) on the reciprocal absolute temperature of the maximum exothermic effect of GdFeO₃ formation on the DSC curves. R² is the coefficient of determination

Table 3 DSC data used in the estimation of activation energy for the formation of nanocrystalline GdFeO₃ and the results obtained

According to the calculation results, the activation energy for the formation of nanocrystalline GdFeO₃ is approximately equal to 1193.62 ± 112.05 kJ mol⁻¹, 1202.27 ± 112.06 kJ mol⁻¹ and 1151.08 ± 106.53 kJ mol⁻¹ based on the Kissinger, Augis–Bennett/Boswell and FWO methods, correspondently, which are quite close. The relative standard error of the estimated values ranges from about 9.25 to 9.39%. This high value of activation energy is due to the high temperature required for the complete decomposition of gadolinium oxycarbonate derivatives before the formation of GdFeO₃, as discussed earlier (See Section “Differential scanning calorimetry and thermogravimetric analysis”). In accordance with the Kissinger method, the pre-exponential factor has an average value of about 1.62 × 10⁶⁰ min⁻¹.

True onset temperature of the formation of nanocrystalline GdFeO₃

The values of the onset temperature of the exothermic effect of GdFeO₃ formation previously determined from the DSC curves (Table 2) are found to be about 759, 765 and 768 °C at a heating rate of 10, 20 and 30 °C min⁻¹, respectively. Therefore, the temperature at which nanocrystalline GdFeO₃ begins to form increases with increasing heating rate. To found the true onset temperature of the formation of nanocrystalline GdFeO₃, i.e., at a heating rate of 0 °C min⁻¹, the dependence of t_onset on β was plotted, and as a result, a straight line was obtained (Fig. 5). By extrapolating the resulting straight line to the y-axis (where β = 0 °C min⁻¹), the true onset temperature of the formation of nanocrystalline GdFeO₃ was found to be about 756 °C, which is quite close to the temperature of 750 °C used in our previous works [25,26,27,28,29,30].

Fig. 5

Dependence of the onset temperature of the formation of nanocrystalline GdFeO₃ on the heating rate

Powder X-ray diffraction

The diffractograms of the products of heat treatment of the co-precipitated gadolinium and iron(III) hydroxides in the temperature range of 650–850 °C for 4 h are presented in Fig. 6. According to these diffraction patterns, the heat-treated product obtained at a temperature of 650 °C is X-ray amorphous, whereas the products that underwent heat treatment at a temperature of 800 °C and higher are pure-phase crystalline samples and consist of orthorhombic gadolinium orthoferrite (o-GdFeO₃) (ICSD 27278, space group 62: Pbnm). On the other hand, the X-ray phase analysis of the heat-treated products obtained in the temperature range of 675–775 °C shows that, in addition to o-GdFeO₃, they also contain other crystalline phases that, apparently, can be associated with hexagonal gadolinium oxide (h-Gd₂O₃) (ICSD 162247, space group 164: P-3m1) and cubic gadolinium oxide (c-Gd₂O₃) (ICSD 150677, space group 206: Ia-3). Along with these three crystalline phases, the last-mentioned products also contain X-ray amorphous phases, as seen from the amorphous halo in the Bragg angle range of ~ 15.2–27.2°. These phases include amorphous iron(III) oxide (am-Fe₂O₃), amorphous gadolinium oxide (am-Gd₂O₃) and/or amorphous gadolinium oxycarbonate derivatives “am-Gd₂O_3-x(CO₃)_x”. The estimated results of mass fractions of the X-ray amorphous and crystalline phases in all heat-treated products are presented in Fig. 7.

Fig. 6

Powder X-ray diffraction patterns of the heat-treated products of the co-precipitated hydroxides. The peak bars indicate the positions of the reflections of the ICSD structures used in the Rietveld refinement. The Miller indices presented belong to o-GdFeO₃

Fig. 7

Mass fractions of the X-ray amorphous phases “am-Fe₂O₃, am-Gd₂O_3, am-Gd₂O_3-x(CO₃)_x” and crystalline phases (o-GdFeO₃, h-Gd₂O₃, c-Gd₂O₃) in the heat-treated products of the co-precipitated hydroxides

In accordance with Fig. 7, with an increase in the treatment temperature from 650 to 700 °C, the mass fraction of X-ray amorphous phases sharply decreases (from 100% at 650 to ~ 31% at 700 °C), while the mass fraction of o-GdFeO₃ sharply increases (from 0 at 650 to ~ 61% at 700 °C). This can be explained by the formation of o-GdFeO₃ as a result of the reaction of am-Fe₂O₃ and am-Gd₂O₃ at temperatures of 675–700 °C. This primary pathway of GdFeO₃ formation is independent of the decomposition of gadolinium oxycarbonate derivatives.

On the other hand, the mass fractions of h-Gd₂O₃ and c-Gd₂O₃ progressively increase with an increase in the treatment temperature up to 725 °C (reaching a maximum of ~ 13% for h-Gd₂O₃ and ~ 1.5% for c-Gd₂O₃), above which they begin to decrease gradually and completely disappear at a temperature of 800 °C. It is well known that under normal conditions, gadolinium oxide may exist in cubic (C-type, space group 206: Ia-3) or monoclinic (B-type, space group 12: C2/m) forms, whereas the hexagonal form (A-type, space group 164: P-3m1), at ambient pressure, is only stable at very high temperatures (more than 2443 K/ ~ 2170 °C) [42, 43]. However, the formation of h-Gd₂O₃ in the products heat treated in the temperature range of 675–775 °C is most likely related to the presence of gadolinium oxycarbonate derivatives, which, if they were crystalline, could have a hexagonal form that is more stable than other crystalline forms, e.g., the hexagonal form of Gd₂O₂CO₃ is more stable than its tetragonal and monoclinic forms [44]. Based on this assumption and the results obtained, in the temperature range of 675–725 °C, gadolinium oxycarbonate derivatives progressively decompose with the formation of CO₂ and h-Gd₂O₃, which then transforms to the form stable in the synthesis conditions, c-Gd₂O₃, which, at temperatures of 725–775 °C, reacts with am-Fe₂O₃ to form o-GdFeO₃. This is the secondary pathway of GdFeO₃ formation that depends on the decomposition of gadolinium oxycarbonate derivatives. It should be noted that the formation of o-GdFeO₃ as a result of the reaction of am-Fe₂O₃ and h-Gd₂O₃, i.e., without the transformation of h-Gd₂O₃ to c-Gd₂O₃, may be possible, but there is no clear evidence for this, especially since the mass fraction of c-Gd₂O₃ is less than the mass fraction of h-Gd₂O₃ in all heat-treated products containing both of these phases, which indicates that the GdFeO₃ formation along this pathway occurs with the participation of c-Gd₂O₃ consumed. Besides, since the last stage of decomposition of gadolinium oxycarbonate derivatives proceeds at a temperature of ~ 756–758, as follows from the DTG curves (Table 1, effect 7), h-Gd₂O₃ can be formed even above the temperature of 725 °C; however, we cannot observe this on the diffractograms of the products heat treated at temperatures of 750–775 °C, most likely because above the temperature of 725 °C, h-Gd₂O₃ transforms to c-Gd₂O₃ which then reacts with am-Fe₂O₃ faster than h-Gd₂O₃ is produced from the decomposition of gadolinium oxycarbonates derivatives. Similarly, the GdFeO₃ formation along this pathway can begin below the temperature of 725 °C, but in this case, the reaction of c-Gd₂O₃ (and perhaps h-Gd₂O₃) with am-Fe₂O₃ is slower than the production of h-Gd₂O₃ from the decomposition of gadolinium oxycarbonate derivatives. The obtained results are in good agreement with the results of DSC, according to which the exothermic effect of GdFeO₃ formation is observed at a temperature of ~ 764–772 °C (Table 1, effect 8).

Figure 8 illustrates the proposed mechanism for the formation of nanocrystalline GdFeO₃ synthesized, i.e., by ultrasound-assisted co-precipitation, as follows from the DSC–TGA and PXRD data.

Fig. 8

Mechanism of formation of nanocrystalline GdFeO₃ via heat treatment of co-precipitated hydroxides

Fourier-transform infrared spectroscopy

The FTIR spectra of the products of heat treatment of the synthesized sample of co-precipitated gadolinium and iron(III) hydroxides in the temperature range of 650–850 °C for 4 h are presented in Fig. 9. The wavenumbers of the absorption bands that correspond to the main vibrations in the obtained FTIR spectra of the products that underwent heat treatment in the temperature range of 650–775 °C and their assignment are summarized in Table 4.

Fig. 9

FTIR spectra of the heat-treated products of the co-precipitated hydroxides (M = Gd³⁺, Fe³⁺). The absorption bands corresponding to atmospheric CO₂ in the wavenumber range of ~ 2275–2400 cm⁻¹ were omitted to facilitate comparison

Table 4 Assignment of the absorption bands corresponding to the main vibrations in the FTIR spectra of the products heat treated up to 775 °C

The broad absorption band in the region of high wavenumbers centered at ~ 3256–3385 cm⁻¹ (band 1) is a consequence of the overlapping of asymmetric and symmetric stretching vibrations of water “ν(H₂O)”, which is physically adsorbed on the surface of the samples during their storage and/or preparation for investigation [28]. The absorption band of the bending vibration of physically adsorbed water “δ(H₂O)” is observed at ~ 1636–1637 cm⁻¹ (band 2). The bands observed at ~ 1507–1508 cm⁻¹ (band 3) and at ~ 1391–1398 cm⁻¹ (band 4) can be attributed to the asymmetric “ν_as(CO₃²⁻)” and symmetric “ν_s(CO₃²⁻)” stretching vibrations of carbonate groups, respectively, whereas the bands observed at ~ 1045–1088 cm⁻¹ (band 5), at ~ 849–859 cm⁻¹ (band 6) and at ~ 664–670 cm⁻¹ (band 7) may be assigned to the symmetric stretching vibration of the C–O bond “ν_s(C–O)”, the out-of-plane bending “π(CO₃²⁻)” and rocking “ρ(CO₃²⁻)” vibrations of carbonate groups, correspondently [45]. The band observed at ~ 564–570 cm⁻¹ (band 8) can be attributed to the stretching vibrations of the Gd–O bond “ν(Gd–O)” and the Fe–O bond “ν(Fe–O)” in the Gd–O–Fe and Fe–O–Fe systems [46], while the band observed at ~ 435–444 cm⁻¹ (band 9) may be assigned to the O–Fe–O bending vibration “δ(O–Fe–O)” in octahedral FeO₆ groups [31]. The last-mentioned absorption band (band 9) is practically absent in the FTIR spectrum of the product heat treated at a temperature of 650 °C, which is X-ray amorphous as followed from the PXRD results (see Section “Powder X-ray diffraction”).

As can be seen from Fig. 9, the intensity of the asymmetric and symmetric stretching vibrations of carbonate groups (Table 4, bands 3 and 4) on the normalized FTIR spectra in the wavenumber range of ~ 1260–1625 cm⁻¹ gradually decreases with an increase in heating temperature to become practically negligible at a temperature of 800 °C. The relative mass percentages of gadolinium oxycarbonate derivatives in the products that underwent heat treatment at temperatures up to 800 °C, estimated based on the integrated intensity of these vibrations, are presented in Fig. 10. The mass fractions of h-Gd₂O₃ in these heat-treated products, previously estimated using the PXRD data, were recalculated as percentages of the maximum and presented in the same figure for comparison.

Fig. 10

Relative mass percentages of gadolinium oxycarbonate derivatives in the products heat treated at temperatures up to 800 °C according to the FTIR data (purple) and relative mass fractions of h-Gd₂O₃ in these products as followed from the PXRD results (orange). “Relative (rel.)” here means that the values are calculated relative to the maximum

The results presented in Fig. 10 are in good agreement with our assumption that gadolinium oxycarbonate derivatives progressively decompose with the formation of h-Gd₂O₃ up to the temperature of 725 °C, above which the mass fraction of h-Gd₂O₃ begins to decrease due to the formation of o-GdFeO₃ along with the secondary pathway, i.e., with the participation of c-Gd₂O₃ (see Section “Powder X-ray diffraction”). Above the temperature of 725 °C, gadolinium oxycarbonate derivatives continue to decompose gradually, but, as we discussed earlier, h-Gd₂O₃ then transforms to c-Gd₂O₃ which reacts with am-Fe₂O₃ faster than h-Gd₂O₃ is produced; therefore, we observe not an increase but a decrease in the mass fraction of h-Gd₂O₃. At a temperature of 800 °C, h-Gd₂O₃ completely disappears and gadolinium oxycarbonate derivatives become practically negligible.

Carbonate content in gadolinium oxycarbonate derivatives

To estimate the carbonate content in gadolinium oxycarbonate derivatives, i.e., to estimate the values of x in the formula Gd₂O_3-x(CO₃)_x at different temperatures, we used the TGA data at temperatures of 700, 725 and 750 °C at different heating rates (10–30 °C min⁻¹) as well as the PXRD data for the products that underwent heat treatment at these temperatures, which include only am-Fe₂O₃ and am-Gd₂O_3-x(CO₃)_x as amorphous phases. As discussed earlier, at temperatures of 675–700 °C, am-Fe₂O₃ reacts with am-Gd₂O₃ to form o-GdFeO₃ along the primary pathway (see Section “Powder X-ray diffraction”); therefore, the product heat treated at a temperature of 675 °C still contains am-Gd₂O₃, the presence of which complicates the calculation (the unnormalized diffraction pattern of this product shown in Fig. S2 confirms that, at a treatment temperature of 675 °C, o-GdFeO₃ is not fully crystallized in comparison with the products heat treated at higher temperatures). As for the product heat treated at a temperature of 775 °C, the relative mass percentage of gadolinium oxycarbonate derivatives is rather small (Fig. 10), which may also affect the calculation results.

According to the EDXS results, the average Gd:Fe atomic ratio is about 1.000:1.003, which is maintained during heat treatment (see Section “Energy-dispersive X-ray spectroscopy”); therefore, the average Gd:Fe molar ratio can be considered equal to 1:1 in all heat-treated products, which means that the amounts in moles (n) of gadolinium and iron are equal (Eq. 8).

$${n}_{\mathrm{Gd}}={n}_{\mathrm{Fe}}$$

(8)

The amounts in moles of gadolinium and iron in the selected heat-treated products can be determined from Eqs. 9 and 10, respectively.

$${n}_{\mathrm{Gd}}={n}_{o-{\mathrm{GdFeO}}_{3}}+2{n}_{h-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}+2{n}_{c-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}+2{n}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}$$

(9)

$${n}_{\mathrm{Fe}}={n}_{o-{\mathrm{GdFeO}}_{3}}+2{n}_{am-{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}$$

(10)

Substituting Eqs. 9 and 10 in Eq. 8 and rearranging, we can determine the amount in moles of Gd₂O_3-x(CO₃)_x (Eq. 11).oxycarbonate derivatives, one mole

$${n}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}={n}_{am-{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}-{n}_{h-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}-{n}_{c-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}$$

(11)

Since the amount of a substance in moles is equal to its mass (m) divided by its molar mass (M), Eq. 11 can be written as shown in Eq. 12.

$$\frac{{m}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}}{{M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}}=\frac{{m}_{am-{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}}{{M}_{{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}}-\frac{{m}_{h-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}}{{M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}}-\frac{{m}_{c-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}}{{M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}}$$

(12)

The molar mass of gadolinium oxycarbonate derivatives can be determined as a function of x from Eq. 13.

$${M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}={M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}+x\cdot {M}_{{\mathrm{CO}}_{2}}$$

(13)

Dividing both sides of Eq. 12 by the mass of the sample at a temperature of t (m_t) and considering that the mass of a phase divided by the sample mass at a certain temperature is equal to the mass fraction of that phase (w) at that temperature, Eq. 12 is converted to Eq. 14.

$$\frac{{w}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}}{{M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}+x\cdot {M}_{{\mathrm{CO}}_{2}}}=\frac{{w}_{am-{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}}{{M}_{{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}}-\frac{{w}_{h-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}}{{M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}}-\frac{{w}_{c-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}}{{M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}}$$

(14)

The mass fraction of am-Fe₂O₃ in the selected samples can be determined from the estimated mass fraction of amorphous phases (w_amorph) by subtracting the mass fraction of the other amorphous phase, Gd₂O_3-x(CO₃)_x, as shown in Eq. 15.

$${w}_{am-{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}={w}_{\mathrm{amorph}}-{w}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}$$

(15)

Substituting Eq. 15 in Eq. 14 and rearranging, we can determine the mass fraction of gadolinium oxycarbonate derivatives in the investigated samples as a function of x (Eq. 16).

$${w}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}=\frac{\left[{w}_{\mathrm{amorph}}\cdot {M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}-\left({w}_{h-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}+{w}_{c-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}\right)\cdot {M}_{{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}\right]\cdot ({M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}+x\cdot {M}_{{\mathrm{CO}}_{2}})}{{M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}\cdot \left({M}_{{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}+{M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}+x\cdot {M}_{{\mathrm{CO}}_{2}}\right)}$$

(16)

In accordance with the decomposition equation for gadolinium oxycarbonate derivatives, one mole of Gd₂O_3-x(CO₃)_x decomposes with the release of x mole of CO₂, and a mass of m(Gd₂O_3-x(CO₃)_x) decomposes with the release of a mass of m(CO₂); therefore, using chemical arithmetic, we can write Eq. 17.

$${m}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}\cdot x\cdot {M}_{{\mathrm{CO}}_{2}}={m}_{{\mathrm{CO}}_{2}}\cdot {M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}$$

(17)

Since the mass of Gd₂O_3-x(CO₃)_x at a certain temperature, as mentioned above, is equal to its mass fraction multiplied by the sample mass at that temperature, Eq. 17 can be written as shown in Eq. 18.

$${w}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3-x}{\left({\mathrm{CO}}_{3}\right)}_{x}}\cdot {m}_{t}\cdot x\cdot {M}_{{\mathrm{CO}}_{2}}={m}_{{\mathrm{CO}}_{2}}\cdot \left({M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}+x\cdot {M}_{{\mathrm{CO}}_{2}}\right)$$

(18)

Substituting Eq. 16 in Eq. 18, rearranging and solving for x, we obtain the required equation (Eq. 19).

$$x=\frac{{m}_{{\mathrm{CO}}_{2}}\cdot {M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}\cdot \left({M}_{{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}+{M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}\right)}{{M}_{{\mathrm{CO}}_{2}}\cdot \left[{M}_{{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}\cdot \left({m}_{t}\cdot {w}_{\mathrm{amorph}}-{m}_{{\mathrm{CO}}_{2}}\right)-{m}_{t}\cdot {M}_{{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}}\cdot \left({w}_{h-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}+{w}_{c-{\mathrm{Gd}}_{2}{\mathrm{O}}_{3}}\right)\right]}$$

(19)

Using Eq. 19, the carbonate content in gadolinium oxycarbonate derivatives in the investigated samples can be estimated. At different heating rates (10–30 °C min⁻¹), the sample mass at a temperature of t (m_t), where t = 700, 725 and 750 °C, was determined from the TGA curves (Fig. 2b). In addition, the mass of CO₂ included in the sample at a temperature of t “m(CO₂)”, i.e., its mass that will be released upon the complete decomposition of gadolinium oxycarbonate derivatives in this sample, was also determined using the TGA data as the difference between the sample mass at each temperature (m_t) and the sample mass at the end (completion) of mass loss on the TGA curve (m_end). The mass fractions of the amorphous phases (w_amorph), h-Gd₂O₃ “w(h-Gd₂O₃)” and c-Gd₂O₃ “w(c-Gd₂O₃)” at each investigated temperature were previously estimated based on the PXRD data (Fig. 7). The TGA and PXRD data used and the calculation results are summarized in Table 5. The dependences of x in Gd₂O_3-x(CO₃)_x on temperature at different heating rates are presented in Fig. 11.

Table 5 TGA and PXRD data used in the estimation of carbonate content in gadolinium oxycarbonate derivatives and the results obtained

Fig. 11

Dependences of x in the formula of gadolinium oxycarbonate derivatives “Gd₂O_3-x(CO₃)_x” on temperature (t) at different heating rates. The inset shows the extrapolation of these dependences to the temperature range in which the obtained DSC and DTG curves showed the first stage of gadolinium carbonate decomposition with the formation of an oxycarbonate derivative. R² is the coefficient of determination

As follows from Fig. 11, the obtained dependences can be described by linear equations with coefficients of determination in the range of 0.9363–0.9999. The extrapolation of these dependences to the temperature of 775 °C shows that x at this temperature is estimated at ~ 0.00–0.22 with an average value of ~ 0.12, which is in good agreement with the PXRD and FTIR results. On the other hand, extrapolating the resulting dependences to the temperature range in which the obtained DSC and DTG curves showed the first stage of gadolinium carbonate decomposition with the formation of an oxycarbonate derivative (Table 1, effect 5), the x value in this derivative may be estimated at ~ 1.56–2.33 with an average value of ~ 1.91. This result is very close to the literature data [33], according to which, at a temperature of ~ 363–370 °C, gadolinium carbonate “Gd₂(CO₃)₃” decomposes to gadolinium monooxydicarbonate “Gd₂O(CO₃)₂” with the release of CO₂.

Conclusions

In this work, a complex and detailed experimental investigation of the mechanism of formation of GdFeO₃ nanocrystals was performed, which shows that the co-precipitated gadolinium and iron(III) hydroxides upon heat treatment undergo a series of physicochemical processes including the dehydration to the corresponding oxides and the decomposition of gadolinium oxycarbonate derivatives prior to the formation of GdFeO₃. The PXRD results indicated that the GdFeO₃ formation occurs via two pathways: a primary carbonate-independent pathway involving am-Gd₂O₃ and a secondary carbonate-dependent pathway involving h-Gd₂O₃ and c-Gd₂O₃. The FTIR results showed that gadolinium oxycarbonate derivatives gradually decompose with increasing heating temperature to become practically negligible at a temperature of 800 °C. The resulting linear equations for the dependence of x in Gd₂O_3-x(CO₃)_x on temperature predict that gadolinium carbonate at a temperature of ~ 266–426 °C decomposes to Gd₂O(CO₃)₂ which, at a temperature of ~ 553–601 °C, decomposes to Gd₂O₂CO₃, which, in turn, decomposes to Gd₂O₃ at a temperature of ~ 776–839 °C.