The equilibrium crystal structure of LnMnO₃ (Ln: lanthanide) has been reported to be orthorhombic when La³⁺ to Dy³⁺ are used as Ln³⁺, and hexagonal when Ho³⁺ to Lu³⁺ are used. Whereas Kumar et al. reported a two-phase structure of orthorhombic and hexagonal phases is formed in DyMnO₃ when it was solidified from the undercooled melt under containerless state. The reason for the formation of the two-phase structure was not thoroughly addressed and discussed. We investigated the formation mechanism for the two-phase structure from the undercooled melt of DyMnO₃ in detail. As a result, the surface morphology, microstructure, and crystal structure of the samples, in which the nucleation was forced at a predetermined temperature with a Mo needle, indicated that the hexagonal and orthorhombic phases are dominant at high and low temperatures, respectively. When the sample was quenched from below 1670 K in a water bath, as-solidified sample consisted of h-DyMnO₃ and o-DyMnO₃. Whereas a single phase of h-DyMnO₃ was obtained in the sample quenched from above 1670 K. This phenomenon can be quantified in terms of nucleation-rate determined phase selection. That is, the activation energy for forming a critical nucleus calculated based on the model of the crystal-melt interface proposed by Turnbull and Speapen suggests that the o-DyMnO₃ phase can be heterogeneously nucleated on the interface of the initially formed h-DyMnO₃ phase.

This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 85 (2021) 155–161. The abstract and captions of Figs. 1–10 are modified.

Fig. 5 Typical LSM images for the surface of DyMnO₃ samples nucleated from different ΔT by triggering the system with a Mo needle.

Hexagonal LnMnO₃ (h-LnMnO₃, Ln: Lanthanide, space group: P6₃cm) is attracting attention as a candidate material for a new concept of storage medium because of its multiferroic properties,^1–3) which include both ferroelectric and (anti) ferromagnetic properties. Stable phase of LnMnO₃ system is reported to be orthorhombic LnMnO₃ (o-LnMnO₃, space group: Pbnm) when the ionic radius of elemental Ln is comparatively large as La to Dy, and to be h-LnMnO₃ when it is comparatively small as Ho to Lu.⁴⁾ Whereas, Kumar et al. has reported that a two-phase structure of o-DyMnO₃ and h-DyMnO₃ is formed⁵⁾ in the DyMnO₃ sample solidified from the undercooled melt by using an aero-dynamic levitation furnace (ADL). Since the two-phase structure of o-DyMnO₃ and h-DyMnO₃ changes into the single phase of o-DyMnO₃ after annealing the sample at 1673 K, they attributed the formation of this two-phase structure to the freezing of the h-DyMnO₃ phase formed as a metastable phase.

Figure 1 shows the schematic presentation of Gibbs energy, G, as a function of temperature for o-DyMnO₃, h-DyMnO₃, and the liquid phase, under constant pressure.

Fig. 1

Schematic presentation of Gibbs energy for liquid, h-DyMnO₃, and o-DyMnO₃ as a function of temperature at constant pressure. (a) The case that G of o-DyMnO₃ is lower than that of h-DyMnO₃ and therefore they do not intersect. (b) The case that G of o-DyMnO₃ is lower than that of h-DyMnO₃ at low temperatures but higher at high temperatures. Therefore, the hypothetical melting point of o-DyMnO₃ is lower than that of h-DyMnO₃.

The stable phase is o-DyMnO₃ if the Gibbs energy of o-DyMnO₃ is lower than that of h-DyMnO₃ as shown in Fig. 1(a). However, if the activation energy for forming a critical nucleus of h-DyMnO₃, $\Delta G_{\text{n}}^{*}$, is lower than that of o-DyMnO₃, h-DyMnO₃ may be formed as a metastable phase. The classical nucleation theory indicates that the $\Delta G_{\text{n}}^{*}$ depends more strongly on the solid-liquid interfacial energy γ_sl than on the Gibbs energy difference, ΔG_V, between o-DyMnO₃ and h-DyMnO₃. Turnbull⁶⁾ and Spaepen⁷⁾ suggested that γ_sl depends on the entropy of fusion, ΔS_f. That is, the smaller ΔS_f, the smaller $\Delta G_{\text{n}}^{*}$.

According to the definition of the Gibbs energy, the slope of G(T) corresponds to the negative entropy of this phase. If we express the entropies of liquid, o-DyMnO₃, and h-DyMnO₃ phases as S_L, S_o and S_h, respectively, the relationship S_L > S_h > S_o commonly exists in these states. Hence, it can be easily understood that the entropy of fusion, ΔS_f of S_h, is smaller than that of S_o. In the case shown in Fig. 1(a), h-DyMnO₃ is nucleated easier than o-DyMnO₃ because ΔS_f of h-DyMnO₃ is smaller than that of o-DyMnO₃. In fact, in LnFeO₃ with the same crystal structure as that of LnMnO₃, h-LnFeO₃ nucleate more readily than o-LnFeO₃.⁸⁾

Szabo et al.⁹⁾ reported that o-DyMnO₃ transformed into h-DyMnO₃ after heating the DyMnO₃ sample to 1873 K. DyMnO₃ is located at the boundary where the stable phase changes from h-LnMnO₃ to o-LnMnO₃ regarding the increase in ionic radius of Ln. Based on their reports, the relationship between G and temperature in each phase should be as Fig. 1(b), and therefore the two-phase structure of o-DyMnO₃ and h-DyMnO₃ reported by Kumar et al. should be discussed from a view point of the kinetics in the phase transformation.

In the present investigation, we aimed to clarify whether the two-phase structure of o-DyMnO₃ and h-DyMnO₃ is controlled by the difference in nucleation frequency, or the kinetics of phase transformation between o-DyMnO₃ and h-DyMnO₃.

Powders of Dy₂O₃ and Mn₂O₃ with a purity of 99.9 mass% or more were weighed and mixed thoroughly in an agate mortar. The mixed powder was melted on a copper hearth by irradiation with a semiconductor laser to form an ingot with a composition of DyMnO₃. After crushing the resultant ingot, it was re-melted on the copper hearth to homogenize the sample composition and to form a spherical sample 2 mm in diameter (approximately 20 mg).

The spherical sample was placed on a nozzle of an aerodynamic levitation furnace (ADL) and then levitated on an oxygen gas jet from the bottom at a rate of ∼600 mL/min controlled by a mass flow controller (MC-3102L-NC, LINTEC), as shown in Fig. 2(a). The levitated sample was heated and melted by irradiation with the semiconductor laser from above, and then cooled by shutting off the laser and allowed to solidify from the undercooled melt in a containerless state. A Mo needle 0.2 mm in diameter was contacted on the surface of the levitated droplet to make the sample nucleate forcibly at a variable undercooling temperature, ΔT. Furthermore, forced nucleation and rapid solidification of the levitated droplet was carried out by quenching it in a water bath at various temperatures including the undercooling state by splitting the nozzle into two parts (Fig. 2(b)). The solidification behavior and surface morphology of the sample were monitored at 2000 frames/sec by using a high-speed camera (FASTCAM MC-MP, Photron). The temperature history of the sample was recorded at a sampling rate of 2000 Hz using a monochromatic pyrometer (FTK9-P600A, Japan Sensor) with a spot diameter of 1.0 mm, with the emissivity set at 0.9 for DyMnO₃ under the assumption that they are the same as that of LnFeO₃.¹⁰⁾ Furthermore, the emissivity of the liquid phase is assumed to be equal to that of the solid phase.

Fig. 2

Schematic drawing of aerodynamic levitator. The levitated melt can be nucleated at a given undercooling by (a) contact with a Mo needle or by (b) dropping it into a water bath by splitting the gas jet nozzle.

The surface morphology of the as-solidified sample was observed by using a confocal laser scanning microscope (LSM, OPTELICS H1200, Lasertec). The crystal structure was identified by powder X-ray diffraction (XRD, Miniflex 600, Rigaku) using CuK_α.

The undercooled DyMnO₃ melt was forcibly nucleated using the Mo needle at a variable undercooling level to clarify whether the phase selection in the undercooled melt of DyMnO₃ is controlled by the phase transformation between o-DyMnO₃ and h-DyMnO₃ or by the nucleation frequency of those phases. Figure 3 shows the typical cooling curves of the sample together with the sample images recorded by HSV at recalescence. When the levitated droplet was cooled by shutting off the laser, nucleation occurred spontaneously at 1545 K, and the post-recalescence temperature (T_pr) rose to ∼1910 K (ΔT = 365 K), as shown in Fig. 3(a). Even when nucleation of the undercooled melt was immediately triggered by the Mo needle, the T_pr increased to 1910 ± 3 K regardless of the undercooling temperature (Fig. 3(b)). Thus, the melting temperature T_E of DyMnO₃ was evaluated to be 1910 K.

Fig. 3

Typical cooling curves of DyMnO₃ samples nucleated from the undercooled melt (a) spontaneously and (b) forcibly triggered with a Mo needle.

Figures 4 and 5 depict the representative XRD profiles and the corresponding surface morphologies of the samples nucleated at different ΔT under levitated state. When the undercooled melt nucleated spontaneously at ΔT = 364 K, the XRD profile of the resultant sample detected the diffraction peaks of both o-DyMnO₃ (▲) and h-DyMnO₃ (□) phases. The surface morphology of the sample exhibits faceted dendrites as observed in Si and Ge solidified from an undercooled melt.¹¹⁾

Fig. 4

Typical XRD patterns of the DyMnO₃ samples nucleated from different ΔT by triggering the system with a Mo needle.

Fig. 5

Typical LSM images for the surface of DyMnO₃ samples nucleated from different ΔT by triggering the system with a Mo needle.

Although the intensity of the diffraction peak of o-DyMnO₃ decreases and that of h-DyMnO₃ increases as ΔT is decreased, no significant change is observed in the surface morphology depending on ΔT. However, a typical facet surface morphology appears in the microregion when ΔT reached 14 K. Kumar et al.⁵⁾ reported that faceted surface morphology is peculiar to h-DyMnO₃ and dendritic surface morphology corresponds to o-DyMnO₃. The relationship between the constituent phases and the surface morphology obtained in the present study corresponds well to the report by Kumar et al.⁵⁾

As described in the previous section, the amount of h-DyMnO₃ was increased as ΔT became small in the sample solidified from the undercooled melt under containerless state, while that of o-DyMnO₃ was increased as ΔT became large. However, the single-phase sample of h-DyMnO₃ or o-DyMnO₃ was not obtained at any ΔT. In order to quantify the relationship between ΔT and the constituent phases in the sample solidified from the undercooled melt under containerless state, the intensity ratio was investigated between diffraction peaks of (002)_h for h-DyMnO₃ and (111)_o for o-DyMnO₃, I_h/I_o, which are isolated and do not interfere with each other. The result is shown in Fig. 6. Although I_h/I_o continuously decreases with increasing ΔT at ΔT < 150 K and ΔT > 250 K, it plateaus at 150 K < ΔT < 250 K. This means that the formation of h-DyMnO₃ and o-DyMnO₃ is prominent at ΔT < 150 K and ΔT > 250 K, respectively, and that the intermediate 150 K < ΔT < 250 K is the transition region. Thus, it is reasonable that h-DyMnO₃ is not a metastable phase but a high-temperature phase. Furthermore, it can be interpreted that the transformation temperature of the primary phase from o-DyMnO₃ to h-DyMnO₃ and vice versa, T_tr, is in the range of 1640 K and 1760 K corresponding to 150 K < ΔT < 250 K.

Fig. 6

Intensity ratio of XRD peaks for (002)_h of h-DyMnO₃ and (111)_o of o-DyMnO₃ (I_h/I_o) as a function of undercooling.

However, there is still room for discussion regarding the detection of h-DyMnO₃ even in the sample nucleated from the undercooled melt at 1545 K (ΔT = 364 K) which is far below the above-mentioned temperature range as shown in Figs. 4 and 5. These results strongly suggest that the phase selection in the DyMnO₃ sample solidified from the undercooled melt is controlled, not by the phase transformation, but by the nucleation rate of o-DyMnO₃ and h-DyMnO₃. In order to clarify the competition of the nucleation rate between o-DyMnO₃ and h-DyMnO₃, the levitated droplet was rapidly solidified by dropping it into a water bath from various temperatures, including the undercooled state. Figure 7 exhibits the XRD patterns of the samples quenched from 1666 K and 1650 K, as typical examples showing a single phase of h-DyMnO₃ and two phases of h-DyMnO₃ and o-DyMnO₃, respectively. Table 1 shows the relationship between the quenched temperature and the constituent phases of the resultant samples. These results reveal that h-DyMnO₃ phase is formed even at low ΔT, while o-DyMnO₃ becomes nucleated only at ΔT > 260 K (below 1650 K).

Fig. 7

Typical XRD patterns of DyMnO₃ samples quenched by dropping from the undercooling state into a water bath.

Table 1 Relation between quenched temperature and phase constitution.

Not only h-DyMnO₃ but also o-DyMnO₃ nucleated from the undercooled melt when the levitated droplet was quenched at ΔT > 260 K (T < 1650 K) though only h-DyMnO₃ nucleated at ΔT < 244 K (T > 1666 K) as shown in Fig. 7 and Table 1. When considering this result from the point of view of nucleation, h-DyMnO₃ would have a higher melting point and a lower solid-liquid interfacial energy than those of o-DyMnO₃. The rate-determining process in the phase selection of h-DyMnO₃ and o-DyMnO₃ is discussed in terms of the nucleation rates of these phases.

According to the classical nucleation theory, the activation energy for forming a critical nucleus, $\Delta G_{\text{n}}^{*}$, is given by:   

Fig. 8

Schematic presentation for the method to estimate ΔT_hyp under the assumption that heat removal rate is constant during solidification.

However, ΔT_hyp of h-DyMnO₃ and o-DyMnO₃ cannot be evaluated directly from the temperature-time relationship adopted by Kuribayashi et al.¹⁷⁾ since single phases of h-DyMnO₃ and o-DyMnO₃ were not obtained at any ΔT (see Fig. 4). Therefore, we estimated ΔT_hyp of h-DyMnO₃ and o-DyMnO₃ by extrapolating the values of other LnMnO₃ systems as a function of ionic radius from the Lu side and La side, respectively, as shown in Fig. 9.

Fig. 9

ΔT_hyp and ΔS_f vs. ionic radius of Ln³⁺: Dashed and dotted lines are curves fitted by power series for the data from Lu³⁺ to Ho³⁺ and from Pr³⁺ to Tb³⁺, respectively. Since determining the melting point of h-DyMnO₃ and the hypothetical melting point of o-DyMnO₃ is difficult from the temperature-time relationship or HSV image, ΔT_hyp was calculated by extrapolating the fitted curves from the Lu side for h-DyMnO₃ and from the La side for o-DyMnO₃.

As already mentioned, h-DyMnO₃ is a high-temperature phase, and almost the same T_pr ≈ 1910 K was detected in the sample nucleated at any ΔT, representing that T_E of h-DyMnO₃ is 1910 K. Since T_E of h-DyMnO₃ and o-DyMnO₃ are so close that it was difficult to distinguish the nucleation behavior of these phases in HSV images, T_E of o-DyMnO₃ is assumed to be 1890 K in this study. As a result, ΔS_f and T_E of h-DyMnO₃ and o-DyMnO₃ are evaluated as shown in Table 2. ΔS_f of h-DyMnO₃ at T_E is smaller than that of o-DyMnO₃, and V_m of h-DyMnO₃ is larger than that of o-DyMnO₃. Therefore, $\Delta G_{\text{n}}^{\text{*}}$ of h-DyMnO₃ is smaller than that of o-DyMnO₃ as can be seen from eq. (4).

Table 2 Entropy of fusion ΔS_f, molar volume V_m and equilibrium melting temperature T_E of h-DyMnO₃ and o-DyMnO₃.

Based on these evaluations, $\Delta G_{\text{n}}^{\text{*}}$ is calculated as a function of temperature for h-DyMnO₃ and o-DyMnO₃ using eq. (4). The results are shown in Fig. 10. When there are no nucleation sites for both h-DyMnO₃ and o-DyMnO₃, i.e. f(θ) of these phases are 1.0 (f(θ)_h = f(θ)_o = 1.0), $\Delta G_{\text{n}}^{\text{*}}$ of h-DyMnO₃ is smaller than that of o-DyMnO₃ irrespective of temperature. This indicates that h-DyMnO₃ always nucleates ahead of o-DyMnO₃.

Fig. 10

Activation energy for forming critical nuclei of h-DyMnO₃ and o-DyMnO₃ expressed as a function of the undercooling. Here, f(θ), the catalytic capacity for heterogeneous nucleation, was assumed to be 1.0 for h-DyMnO₃, and was varied from 0.02 to 1.0 as an auxiliary variable for o-DyMnO₃.

Nucleation of o-DyMnO₃ occurs only when f(θ)_o is much smaller than f(θ)_h.

Assuming f(θ)_h = 1.0, the condition for nucleation of o-DyMnO₃ will be satisfied when the temperature drops down to around 1700 K if f(θ)_o is 0.4 to 0.5, since $\Delta G_{\text{n}}^{\text{*}}$ of o-DyMnO₃ will be lower than that of h-DyMnO₃. This situation is true when h-DyMnO₃ is nucleated first, followed by heterogeneous nucleation of o-DyMnO₃ using the interface between h-DyMnO₃ and the melt as the preferential site.

The difference between DyMnO₃ and the LnFeO₃ systems is that the first nucleated h-DyMnO₃ undergoes a (diffusion) phase transformation to o-DyMnO₃ depending on the cooling rate without remelting after nucleation of o-DyMnO₃. In other words, h-DyMnO₃ does not remain at room temperature under equilibrium condition, nevertheless the two-phase structure of h-DyMnO₃ and o-DyMnO₃ forms under a rapid cooling as in this investigation since the transformation cannot catch up with the solidification.

In order to elucidate the reason for the coexistence of o-DyMnO₃ and h-DyMnO₃ in the DyMnO₃ sample solidified from the undercooled melt, the nucleation of the sample was controlled by stimulation with a Mo needle and by quenching in a water bath. Furthermore, the activation energy for forming critical nuclei for o-DyMnO₃ and h-DyMnO₃ were calculated from the experimental results using Turnbull and Spaepen’s models. As a result, it was found that only h-DyMnO₃ formed when nucleated at ΔT < 244 K (T > 1666 K), while o-DyMnO₃ formed together with h-DyMnO₃ when nucleated at ΔT > 244 K (T < 1666 K). The nucleation of h-DyMnO₃ was indicated to always precede that of o-DyMnO₃ from the undercooled melt and o-DyMnO₃ can be heterogeneously formed only by using the interface between h-DyMnO₃ and liquid phase as the preferential nucleation site.

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Gibbs energy as a function of temperature at constant pressure [J]

Gibbs energy of formation for o-DyMnO₃ [J]

Gibbs energy of formation for h-DyMnO₃ [J]

Transformation temperature [K]

Undercooling [K]

Maximum temperature after recalescence [K]

Intensity of XRD peak for (002)_h of h-DyMnO₃

Intensity of XRD peak for (111)_o of o-DyMnO₃

Activation energy for forming critical nuclei [J]

Solid-liquid interfacial energy [J m⁻²]

Gibbs energy difference between the liquid and solid phases [J]

Contact angle [°]

Catalytic potency for heterogeneous nucleation

Avogadro’s number: 6.02 × 10²³ [mol⁻¹]

Molar volume [m³mol⁻¹]

Entropy of fusion [J K⁻¹mol⁻¹]

Turnbull coefficient⁶⁾

Nucleation temperature [K]

Hyper cooling limit [K]

Molar heat capacity [J mol⁻¹]

Specific heat at constant pressure [J K⁻¹mol⁻¹]

Equilibrium melting temperature [K]