Effects of Oxygen Partial Pressure and Tolerance Factor on Phase Selection of DyMnO₃

Abstract

The equilibrium crystal structure of LnMnO₃ (Ln: lanthanide) is known to be orthorhombic when larger ions from La³⁺ to Dy³⁺ are used as Ln³⁺, and hexagonal when smaller ions from Ho³⁺ to Lu³⁺ are used. Research indicates that the hexagonal phase forms when the tolerance factor, expressed as functions of radii of the constituent ions, is less than 0.840. In this study, we attempted to induce oxygen deficiency in DyMnO₃ through solidification at low oxygen partial pressure using an aerodynamic levitator. The objective was to decrease the tolerance factor by reducing the valence of manganese ions and thereby increasing their ionic radius. The results showed an increase in oxygen deficiency as the oxygen partial pressure decreased. Based on the assumption that the manganese ions’ valence decreased due to an increase in oxygen deficiency, the corresponding tolerance factor evaluated from the average ionic radii of manganese and oxygen also decreased. This decrease promoted the formation of the hexagonal phase, similar to the effect observed when the ionic radius of Ln³⁺ is reduced.

 

This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 87 (2023) 226–230. The abstract and figure captions are modified.

1. Introduction

The crystal structure of stable rare-earth manganese oxides, represented by the molecular formula LnMnO₃ (Ln: Lanthanoid), exhibits two distinct forms.¹⁾ For relatively larger Ln element ionic radii, spanning from La³⁺ to Dy³⁺, the crystal structure is orthorhombic LnMnO₃ (o-LnMnO₃, space group: Pbnm). However, when the ionic radius of the Ln is relatively smaller, ranging from Ho³⁺ to Lu³⁺, the crystal structure is hexagonal LnMnO₃ (h-LnMnO₃, space group: P6₃cm). Kumar et al.²⁾ observed a two-phase structure composed of o-DyMnO₃ and h-DyMnO₃ in a DyMnO₃ sample solidified from the undercooled melt in an oxygen gas atmosphere using an aerodynamic levitation furnace (ADL). They also detected oxygen deficiency in the sample displaying the two-phase structure. Harikrishnan et al.³⁾ reported that the crystal growth of DyMnO₃ using the floating zone method resulted in the formation of o-DyMnO₃ in both air and oxygen gas atmospheres, while h-DyMnO₃ was formed in an argon gas atmosphere. These findings suggest oxygen potential differences play a role in phase selection during DyMnO₃ solidification.

In an ABO₃ sample—where A represents rare earth or alkaline earth elements, B represents transition metals, and O signifies an oxygen atom—the tolerance factor (TF) serves as a useful criterion for phase selection. TF is defined as⁴⁾

  

\begin{equation} \mathit{TF} = \frac{r_{\text{A}} + r_{\text{O}}}{\sqrt{2} (r_{\text{B}} + r_{\text{O}})} \end{equation} (1)

where r_A, r_B, and r_O are the ionic radii of A³⁺, B³⁺, and O²⁻, respectively. The stable phase is an orthorhombic perovskite-type structure when TF > 0.8, and an ilmenite-type structure when TF < 0.8. For hexagonal ABO₃ oxides, it has been reported that the criteria for the formation of the P6₃/mmc phase, which is the high-temperature phase of the P6₃cm phase, is TF < 0.86.^5,6) In the EuFeO₃ system, with a calculated TF of 0.861 results in the hexagonal phase (h-EuFeO₃) is formed through a double recalescence event during undercooling solidification. In a SmFeO₃ system, where the calculated TF exceeds 0.864, only the orthorhombic phase (o-SmFeO₃) forms from the undercooled melt, with no double recalescence detected.⁶⁾

Since the ionic radius of Mn³⁺ matches that of Fe³⁺, according to Shannon,⁷⁾ the phase selection criterion using the TF for the LnFeO₃ system likely applies to the LnMnO₃ system as well. Table 1 illustrates the constituent phases of various LnMnO₃ samples solidified from the undercooled melt, as reported by Kumar et al.,²⁾ as a function of the TF, assuming a coordination number of 7 for Ln³⁺. The assumed ionic radii for Mn³⁺ and O²⁻ are 0.0580 nm and 0.1380 nm, respectively. The h-LnMnO₃ phase forms when the TF is <0.840, while the o-LnMnO₃ phase forms when the TF is ≥0.840. This outcome confirms that a decrease in TF leads to the formation of h-LnMnO₃. Our primary focus here is that the TF decreases if the radius of the Mn ion (r_Mn) can be increased, similar to the effect of a decrease in the ionic radius of Ln³⁺ (r_Ln).

Table 1 Relationship between the phase constitution of solidified LnMnO₃,²⁾ the ionic radii of Ln³⁺, and the tolerance factor (TF) when the coordination number (CN) of Ln³⁺ is defined as 7. The radii of Mn³⁺ and O²⁻ are defined as 0.0580 nm (CN = 5) and 0.1380 nm, respectively.

When considering the oxygen potential in the formation of DyMnO₃(s), the following chemical equilibrium⁸⁾ should be considered:

  

\begin{equation} \text{2Dy$_{2}$O$_{3}$(s)} + \text{4MnO(s)} + \text{O$_{2}$(g)} \leftrightarrows \text{4DyMnO$_{3}$(s)} \end{equation} (2)

  

\begin{equation} \Delta G^{\circ} = -534400 + 224\ T\ [\text{J${\cdot}$mol$^{-1}$}] \end{equation} (3)

Here, ΔG° signifies the standard Gibbs energy change for the reaction. Above the equilibrium temperature, a reduction in oxygen potential shifts the chemical equilibrium to the left, reducing Mn³⁺ to Mn²⁺. Assuming eq. (3) concerning ΔG° can be applied at temperatures above the liquidus line of DyMnO₃, it is likely that DyMnO₃(s) rapidly solidified from the melt under low oxygen potentials would contain both Mn³⁺ and Mn²⁺. In this scenario, an oxygen deficiency would occur in the solidified sample, corresponding to the presence of Mn²⁺, to maintain electrical neutrality. As a result, the TF decreases due to the larger ionic radius of Mn²⁺ (0.0750 nm, CN = 5) compared to Mn³⁺ (0.0580 nm, CN = 5). This could potentially promote the formation of h-DyMnO₃, similar to when smaller Ln³⁺ ions are used.

In this study, we examined the relationship between oxygen deficiency and the constituent phases of DyMnO₃ samples solidified under various oxygen partial pressures ($P_{\text{O}_{2}}$). We also investigated the content of Mn²⁺ in the samples to calculate the TF as a function of the mean radius value for the Mn ion. The objective was to clarify whether the calculated TF, which varies depending on the Mn²⁺ content in the DyMnO₃ sample, could serve as a criterion for phase selection, similar to the TF calculated simply as a function of radii for Ln³⁺. It’s worth noting that for the cation reduction reaction, we only considered Mn³⁺ → Mn²⁺, as the standard Gibbs energy for the formation of Dy₂O₃ (−372.5 kJ·mol⁻¹) is lower than that of Mn₂O₃ (−191.3 kJ·mol⁻¹).^9–12)

2. Experimental Procedure

Dy₂O₃ and Mn₂O₃ powders, each with a purity of 99.9 mass% or higher, were weighed in a 1:1 molar ratio (162 mg and 68 mg, respectively) and thoroughly mixed using an agate mortar. The mixed powder was melted on a copper hearth through irradiation with a semiconductor laser to form a DyMnO₃ ingot. This ingot was then crushed and re-melted on the copper hearth to homogenize the sample composition and to form a 2-mm-diameter spherical sample (approximately 20 mg in weight).

This spherical sample was placed on a nozzle of the ADL and levitated by a jet of Ar–O₂ mixture gas, injected from the bottom at a flow rate of approximately 600 mL/min using mass flow controllers (MC-3102L-NC, LINTEC Corp.). The $P_{\text{O}_{2}}$ of the gas was varied between 1 and 1 × 10⁵ Pa. The levitated sample was heated and melted by irradiating it with a semiconductor laser beam from above. It was then cooled by shutting off the laser and allowed to solidify rapidly from the undercooled melt.

The solidification behavior and surface morphology of the sample were monitored at 2000 frames/sec using a high-speed video camera (FASTCAM MC-MP, Photron Ltd.). The temperature history of the sample was recorded at a sampling rate of 2000 Hz using a monochromatic pyrometer with a 1.0 mm spot diameter (FTK9-P600A, JAPANSENSOR Corp.). We set the emissivity to 0.9 under the assumption that the emissivity of molten DyMnO₃ is equivalent to that of LnFeO₃¹³⁾ and remains consistent in the solid state.

The mass change of the solidified sample during heating to 1200 K and cooling to room temperature was examined in a high-purity oxygen gas atmosphere using a thermogravimetric-differential thermal analyzer (TG-DTA, TG-DTA2200S Mac Science Co., Ltd.). The surface morphology of the solidified sample was observed using a confocal laser scanning microscope (LSM, OPTELICS H1200, Lasertec Corp.). The constituent phases of the as-solidified samples were identified by powdered X-ray diffraction (XRD, Miniflex600, Rigaku Corp.) using CuK_α radiation at room temperature. The TF was calculated from the relationship between the oxygen deficiency rate and the constituent phase of the solidified sample. A list of nomenclatures used throughout this study is provided in Table 2.

Table 2 Nomenclature list.

3. Experimental Results

Figure 1 presents the typical thermal gravimetric analysis (TGA) curves of samples solidified under conditions of $P_{\text{O}_{2}} \approx 1 \times 10^{5}$ Pa (solid line) and $P_{\text{O}_{2}} \approx 1$ Pa (dashed line). The analysis was conducted in high-purity oxygen gas at $P_{\text{O}_{2}} \approx 1 \times 10^{5}$ Pa. The mass of the sample solidified under $P_{\text{O}_{2}} \approx 1 \times 10^{5}$ Pa increases with temperature, plateaus around 1200 K, and then remains constant during the subsequent cooling stage. These results suggest that the mass increase during heating is due to an irreversible reaction. In contrast, the sample solidified under $P_{\text{O}_{2}} \approx 1$ Pa shows a noticeably larger mass increase during heating compared to the sample solidified under $P_{\text{O}_{2}} \approx 1 \times 10^{5}$ Pa. This observation aligns with our prediction that oxygen deficiency is induced in DyMnO₃ samples solidified under low oxygen pressure. The mass increase during heating can be attributed to the absorption of atmospheric oxygen to compensate for the oxygen deficiency in the sample. Even in samples solidified under a high-purity oxygen gas atmosphere ($P_{\text{O}_{2}} \approx 1 \times 10^{5}$ Pa), some oxygen deficiency appears to be present.

Fig. 1

TGA curves of DyMnO₃ samples solidified at $P_{\text{O}_{2}}$ of 1 Pa (dashed line) and 1 × 10⁵ Pa (solid line) under a high purity oxygen gas at $P_{\text{O}_{2}}$ of 1 × 10⁵ Pa flowing at a rate of 50 mL/min.

Figures 2 and 3 exhibit typical XRD patterns and LSM images of surface morphologies for the DyMnO₃ samples solidified under various $P_{\text{O}_{2}}$ conditions, respectively. The XRD pattern of the sample solidified at $P_{\text{O}_{2}} \approx 1 \times 10^{5}$ Pa (Fig. 2(a)) shows diffraction peaks of h-DyMnO₃ () and o-DyMnO₃ (□) phases. The surface morphology of the corresponding sample (Fig. 3(a)) is reminiscent of so-called faceted dendrites. Kumar et al. reported²⁾ that the faceted surface indicates the formation of h-DyMnO₃ with crystal anisotropy, whereas the dendrites suggest the formation of o-DyMnO₃.

Fig. 2

XRD patterns of DyMnO₃ samples solidified under various $P_{\text{O}_{2}}$ conditions.

Fig. 3

Surface morphology of DyMnO₃ samples solidified under various $P_{\text{O}_{2}}$ conditions as observed by confocal laser scanning microscopy.

As the $P_{\text{O}_{2}}$ during sample solidification decreases, the intensity of the diffraction peak of o-DyMnO₃ decreases. As a result, the XRD pattern of the sample solidified at $P_{\text{O}_{2}} \approx 3 \times 10^{3}$ Pa primarily reveals the diffraction peaks of h-DyMnO₃ (Fig. 2(c)). Furthermore, this sample, solidified at $P_{\text{O}_{2}} \approx 3 \times 10^{3}$ Pa, displays only a faceted surface, with no evidence of dendrites (Fig. 3(c)).

Further decrease in $P_{\text{O}_{2}}$ during sample solidification leads to the formation of cubic Dy₂O₃ (c-Dy₂O₃, space group: $Ia\bar{3}$) (◇) and cubic MnO (c-MnO, space group: $Fm\bar{3}m$) (○). This outcome aligns with our hypothesis that a decrease in oxygen potential shifts the chemical equilibrium for DyMnO₃ formation, as per eq. (2), to the left, reducing Mn³⁺ to Mn²⁺.

4. Discussion

As previously stated, oxygen deficiency was induced in the DyMnO₃ sample by lowering the oxygen partial pressure of the atmospheric gas during solidification. This decrease in oxygen partial pressure promoted the formation of h-DyMnO₃ while inhibiting the formation of o-DyMnO₃. Furthermore, when the oxygen partial pressure was reduced, c-MnO and c-Dy₂O₃ were formed, confirming that some Mn³⁺ was reduced to Mn²⁺. In this section, based on these experimental results, we will evaluate the TF for DyMnO₃ samples in which some Mn³⁺ was reduced to Mn²⁺ due to the oxygen deficiency. Moreover, we will discuss the relationship between the TF and phase selection of DyMnO₃ samples.

When some Mn³⁺ is reduced to Mn²⁺ in the DyMnO₃ samples under low oxygen partial pressure, it is necessary to assess the fraction of Mn²⁺ induced in h-DyMnO₃ to determine the mean radius of the manganese ions, $\bar{r}_{\text{Mn}}$. The fraction of Mn²⁺ induced in h-DyMnO₃ can be calculated from the oxygen deficiency ratio of h-DyMnO₃. If we assume that c-MnO and c-Dy₂O₃ are stoichiometric, we can relate the oxygen deficiency ratio of the entire sample evaluated by TGA (ε), the oxygen deficiency ratio of h-DyMnO₃ (ε_h), and the mole fraction of c-MnO (x) through the following chemical reaction:

  

\begin{align} & \text{Dy$^{3+}$Mn$_{(1 - 2 \times 3\varepsilon)}^{3+}$Mn$_{(2 \times 3\varepsilon)}^{2+}$O$_{3(1 - \varepsilon)}^{2-}$} \\ &\quad =\text{($1 - x$)Dy$^{3+}$Mn$_{(1 - 2 \times 3\varepsilon_{h})}^{3+}$Mn$_{(2 \times 3\varepsilon_{h})}^{2+}$O$_{3(1 - \varepsilon_{h})}^{2-}$} \\ &\qquad+ x\left(\text{Mn$^{2+}$O} + \frac{1}{2}\text{Dy$_{2}$O$_{3}$}\right) \end{align} (4)

Since the molar number of oxygen on both sides of eq. (4) is equal, ε_h can be expressed as

  

\begin{equation} \varepsilon_{h} = \frac{3\varepsilon - 0.5x}{3(1 - x)} \end{equation} (5)

Furthermore, if ε_h is known, the $\bar{r}_{\text{Mn}}$ for h-DyMnO₃ containing oxygen deficiency can be expressed as

  

\begin{equation} \bar{r}_{\text{Mn}} = (1 - 2 \times 3\varepsilon_{h})r_{\text{Mn}^{3+}} + (2\times 3\varepsilon_{h})r_{\text{Mn}^{2+}} \end{equation} (6)

Therefore, once the value of x is obtained, we can calculate the TF of the DyMnO₃ samples in which some Mn³⁺ is reduced to Mn²⁺ due to oxygen deficiency. Moreover, understanding the relationship between the ratio of intensities of diffraction peaks of h-DyMnO₃ (I_h) and c-MnO (I_c), as well as their quantity ratio, allows us to estimate the value of x from the results shown in Fig. 2. We prepared artificial mixtures of h-DyMnO₃, c-MnO, and c-Dy₂O₃ powders with an arbitrary x value, thoroughly mixed using an agate mortar. The XRD patterns of these mixtures were then obtained as shown in Fig. 4. The intensity of the diffraction peak of c-MnO increases with the x value. The I_c/I_h of $(01\bar{1})$ for c-MnO and $(2\bar{1}1)$ for h-DyMnO₃, obtained from Fig. 4, is plotted as a function of the x value in Fig. 5. Using Fig. 5 as a calibration curve, and assuming that the effects of mixing and oxygen deficiency were negligible in the XRD patterns of the artificial mixtures, the I_c/I_h obtained from Fig. 2 allowed us to estimate the values of x for samples solidified under various $P_{\text{O}_{2}}$ conditions. Table 3 shows the calculated results of ε, x, ε_h, $\bar{r}_{\text{Mn}}$ and TF for DyMnO₃ samples solidified under various $P_{\text{O}_{2}}$ conditions, along with their constituent phases. This confirms that a decrease in oxygen potential during solidification increases ε_h as well as $\bar{r}_{\text{Mn}}$. The TF consequently becomes smaller.

Fig. 4

XRD patterns for artificially mixed samples of high purity powders of h-DyMnO₃, c-MnO, and c-Dy₂O₃ with various mole fractions (x values).

Fig. 5

Intensity ratio of diffraction peaks of c-MnO $(01\bar{1})$ and h-DyMnO₃ $(2\bar{1}2)$ with respect to the mole fraction of c-MnO in the sample.

Table 3 Total oxygen deficiency rate in the sample (ε), mole fraction of c-MnO formed (x), and the corresponding values of oxygen deficiency rate in h-DyMnO₃ (ε_h), mean radius of manganese ions in h-DyMnO₃ ($\bar{r}_{\text{Mn}}$), and the tolerance factor (TF), for the DyMnO₃ sample solidified under various $P_{\text{O}_{2}}$ conditions.

It is worth mentioning that o-DyMnO₃ is no longer detected when the calculated value of TF decreases to 0.837 at $P_{\text{O}_{2}} = 3 \times 10^{3}$ Pa. This is consistent with the conventional results of the relationship between the constituent phases and TF, calculated as a function of radii for Ln³⁺ in the LnMnO₃ system. The solidified HoMnO₃ sample with a TF = 0.837 consists solely of the h-LnMnO₃ phase, as explained in Table 1. This confirms that phase selection in the LnMnO₃ system is characterized by the TF when $\bar{r}_{\text{Mn}}$ is varied, as well as when the radii for Ln³⁺ ions are varied.

Szabo et al.¹⁴⁾ reported that the stable phase of the DyMnO₃ sample above 1900 K is h-DyMnO₃. Hayasaka et al.¹⁵⁾ reported that rapid solidification of the DyMnO₃ melt above 1900 K results in a decrease in the formation of o-DyMnO₃ and an increase in the formation of h-DyMnO₃. These are explicit examples of the effect of a decrease in TF corresponding to an increase in $\bar{r}_{\text{Mn}}$ resulting from oxygen deficiency.

For the DyMnO₃ sample solidified at $P_{\text{O}_{2}} \approx 1 \times 10^{5}$ Pa, where both h-DyMnO₃ and o-DyMnO₃ phases are formed, the calculated TF was slightly larger at 0.840. This may be due to the assumption that Mn²⁺, induced by the reduction of Mn³⁺, is included equally in both h-DyMnO₃ and o-DyMnO₃ phases. Since the formation of h-DyMnO₃ and the oxygen deficiency associated with Mn³⁺ → Mn²⁺ reduction are inseparable, Mn²⁺ is expected to be more abundant in h-DyMnO₃. As a result, it is possible that the TF of h-LnMnO₃ itself is smaller than 0.840.

5. Conclusion

In this study, we experimentally investigated the incorporation of Mn²⁺ into LnMnO₃, which solidified under conditions of low oxygen potential due to oxygen deficiency. We also validated whether the TF, calculated from the inclusion rate of Mn²⁺, characterizes the phase selection of LnMnO₃ as effectively as the TF calculated by altering the ionic radius of Ln³⁺. As a result, the following findings were elucidated:

1. (1)    The lower the oxygen potential during the solidification process, the higher the occurrence of oxygen deficiency in the DyMnO₃ sample.
2. (2)    The fraction of Mn²⁺ in h-DyMnO₃ increases with oxygen deficiency.
3. (3)    TF calculated from the Mn²⁺ content characterizes the phase selection in the LnMnO₃ system as well as TF calculated when the radius of the Ln³⁺ ion is varied.
4. (4)    The criterion for h-LnMnO₃ formation is TF ≤ 0.837.

REFERENCES

• 1)   H.L.J.  Yakel,  W.C.  Koehler,  E.F.  Bertaut and  E.F.  Forrat: Acta Crystallogr. 16 (1963) 957–962. doi:10.1107/S0365110X63002589
• 2)   M.S.V.  Kumar,  N.  Higaki,  K.  Kuribayasi,  T.  Hibiya and  S.  Yoda: J. Am. Ceram. Soc. 94 (2011) 281–288. doi:10.1111/j.1551-2916.2010.04042.x
• 3)   H.S.  Nair and  S.  Elizabeth: J. Crys. Growth 362 (2013) 24–28. doi:10.1016/j.jcrysgro.2012.05.043
• 4)   V.M.  Goldschmidt: Naturwissenschaften 14 (1926) 477–485. doi:10.1007/BF01507527
• 5)   A.S.  Gibbs,  K.S.  Knight and  P.  Lightfoot: Phys. Rev. B 83 (2011) 094111. doi:10.1103/PhysRevB.83.094111
• 6)   K.  Kuribayashi and  M.S.V.  Kumar: J. Phys. Conf. Ser. 327 (2011) 012019. doi:10.1088/1742-6596/327/1/012019
• 7)   R.D.  Shannon: Acta Crystallogr. Sec. A 32 (1976) 751–767. doi:10.1107/S0567739476001551
• 8)   N.  Kamegashira and  Y.  Hiyoshi: Mater. Lett. 2 (1984) 337–338. doi:10.1016/0167-577X(84)90048-X
• 9)   J.E.  Saal,  S.  Kirklin,  M.  Aykol,  B.  Meredig and  C.  Wolverton: J. Met. Mater. Miner. 65 (2013) 1501–1509. doi:10.1007/s11837-013-0755-4
• 10)   S.  Kirklin,  J.E.  Saal,  B.  Meredig,  A.  Thompson,  J.W.  Doak,  M.  Aykol,  S.  Rühl and  C.  Wolverton: NPJ Comput. Mater. 1 (2015) 15010. doi:10.1038/npjcompumats.2015.10
• 11)   A.  Bartos,  K.P.  Lieb,  M.  Uhrmacher and  D.  Wiarda: Acta Crystallogr. Sec. B 49 (1993) 165–169. doi:10.1107/S0108768192007742
• 12)   S.  Geller: Acta Crystallogr. Sec. B 27 (1971) 821–828. doi:10.1107/S0567740871002966
• 13)   J.  Takasaki,  K.  Kuribayashi and  S.  Ozawa: Mater. Trans. 59 (2018) 469–474. doi:10.2320/matertrans.M2017359
• 14)   G.  Szabo and  R.A.  Paris: C. R. Acad. Sci. Ser. C 268 (1969) 513–516 (in French).
• 15)   Y.  Hayasaka,  K.  Kuribayashi,  S.  Shiratori and  S.  Ozawa: Mater. Trans. 62 (2021) 982–987. doi:10.2320/matertrans.MT-M2021047