Phase Relations in the Ln2O3–Cr2O3–B2O3 (Ln = Gd–Lu) Ternary Oxide Systems

In this work, isothermal sections of the Ln2O3–Cr2O3–B2O3 (Ln = Gd–Lu) ternary oxide systems at 900, 1000, and 1100 °C were constructed by determining the phase relations by using a powder X-ray diffraction technique. As a result, these systems were divided into subsidiary subsystems. Two types of double borates, LnCr3(BO3)4 (Ln = Gd–Er) and LnCr(BO3)2 (Ln = Ho–Lu), were observed in the investigated systems. Regions of phase stability for LnCr3(BO3)4 and LnCr(BO3)2 were determined. It was shown that the LnCr3(BO3)4 compounds crystallized in rhombohedral and monoclinic polytype modifications up to 1100 °C; above this temperature and up to the melting points, the monoclinic modification was predominantly formed. The LnCr3(BO3)4 (Ln = Gd–Er) and LnCr(BO3)2 (Ln = Ho–Lu) compounds were characterized by using a powder X-ray diffraction method and thermal analysis.


Introduction
The Ln 2 O 3 -Cr 2 O 3 -B 2 O 3 (Ln = Gd-Lu) ternary oxide systems have not been studied so far in terms of their phase relations in an air atmosphere. However, compounds synthesized in binary systems corresponding to the sides of these ternary diagrams are of great interest in terms of both their crystal structures and their physicochemical properties.
PXRD was carried out by using an ARL X'tra diffractometer (Thermo Fisher Scientific, Basel, Switzerland) equipped with a MYTHEN2 R 1D detector (Dectris, Baden-Daettwil, Switzerland). The diffraction patterns of the SSR products were recorded in continuous mode at room temperature by using CuK α1,2 radiation (λ = 1.540562 Å) in the range of 10 • ≤ 2θ ≤ 70 • with a scan speed of 8 • per minute, U = 40 kV, and I = 40 mA. Long PXRD scans were collected in the range of 10 • ≤ 2θ ≤ 90 • for LnCr 3 (BO 3 ) 4 and LnCr(BO 3 ) 2 to carry out a quantitative analysis.
Compounds were identified by matching the experimental PXRD patterns to those of the ICDD PDF-2 powder diffraction database release 2020 [52].

The Dy2O3-Cr2O3-B2O3 Ternary System
The phase relations in the Dy2O3-Cr2O3-B2O3 ternary system at 900, 1000, and 1100 °С ( Figure 3, Table 2) were determined based on 21 experimental compositions (seven specimens for each isothermal section). The system exhibited six subsidiary subsystems. The dysprosium chromium borate, DyCr3(BO3)4, was observed. DyBO3 [PDF-2 #01-074-1933] demonstrated the vaterite modification. The powder data from the PDF-2 #01-083-9837 card were used to determine the Dy2O3 phase. Dy(BO2)3 was determined from the similarity with the PXRD patterns of known metaborates of Ln(BO2)3 (Ln = Gd, Tb). The oxyborate Dy3BO6 was isostructural with Y3BO6. All compounds established in the considered diagram were stable up to 1100 °C. Thus, in the investigated ternary systems, the reactions proceeded according to the following equations: Figure 2a shows that the borate GdBO 3 crystallized in the low-temperature (LT, PDF-2 #01-089-6545) modification at 800 • C, while the high-temperature (HT) vaterite modification of GdBO 3 formed above 900 • C. This was consistent with the data of Ren et al. [17].
Vicat et al. [40] reported the synthesis of the double borate DyCr(BO 3 ) 2 with a dolomitetype structure. However, the existence of this phase is doubtful. For example, Doi et al. [50] synthesized only LnCr(BO 3 ) 2 (Ln = Y, Ho-Lu) borates. Our results confirm these data.
The study of the stability of DyCr 3 (BO 3 ) 4 was carried out in the range of 800-1300 • C. It was found that above 1250 • C, DyBO 3    Vicat et al. [40] reported the synthesis of the double borate DyCr(BO3)2 with a dolomite-type structure. However, the existence of this phase is doubtful. For example, Doi et al. [50] synthesized only LnCr(BO3)2 (Ln = Y, Ho-Lu) borates. Our results confirm these data.
The study of the stability LnCr(BO 3 ) 2 borates in the range of 800-1200 • C showed that above 1150 • C, the LnBO 3 and Cr 2 O 3 phases formed (Figure 9). At temperatures from 900 to 1150 • C, LnCr(BO 3 ) 2 borates coexisted with LnBO 3 , CrBO 3 , and Cr 2 O 3 . The LnBO 3 and Cr 2 O 3 compounds were observed below 900 • C. Therefore, the following reactions occurred: Ln2O3 + B2O3 → 2LnBO3 (800-1200 °С) Cr2O3 + B2O3 → 2CrBO3 (900-1150 °С) Ln2O3 + Cr2O3 + 2B2O3 → 2LnCr(BO3)2 (900-1150 °С) In the Lu2O3-Cr2O3-B2O3 system, at 800 °C, the borate LuBO3 was obtained only in a vaterite-type structure (LT modification of LuBO3); in the temperature range of 900-1000 °C, there were vaterite-and calcite-type structures, and at higher temperatures, they crystallized only in a calcite-type structure (HT modification of LuBO3). The obtained materials were consistent with the data obtained by the authors of [15]. It should be noted that the borate LuBO3 with only the calcite structure in the isothermal section at 1000 °C was observed for regions with a high content of boron oxide (regions 1 and 5 in Figure 8). The coexistence of calcite and vaterite modifications of the borate LuBO3 was observed in Therefore, the following reactions occurred: In the Lu 2 O 3 -Cr 2 O 3 -B 2 O 3 system, at 800 • C, the borate LuBO 3 was obtained only in a vaterite-type structure (LT modification of LuBO 3 ); in the temperature range of 900-1000 • C, there were vaterite-and calcite-type structures, and at higher temperatures, they crystallized only in a calcite-type structure (HT modification of LuBO 3 ). The obtained materials were consistent with the data obtained by the authors of [15]. It should be noted that the borate LuBO 3 with only the calcite structure in the isothermal section at 1000 • C was observed for regions with a high content of boron oxide (regions 1 and 5 in Figure 8). The coexistence of calcite and vaterite modifications of the borate LuBO 3 was observed in other regions.

Powder X-ray Diffraction
The Le Bail fit was used to confirm the structural similarity of the borates within the families of LnCr 3 (BO 3 ) 4 and LnCr(BO 3 ) 2 . All huntite-type LnCr 3 (BO 3 ) 4 borates turned out to be polytypes and contained a significant number of rhombohedral (sp. gr. R32, α-LnCr 3 (BO 3 ) 4 ) and monoclinic (sp. gr. C2/c, β-LnCr 3 (BO 3 ) 4 ) modifications. The refined lattice parameters are presented in Tables 5 and 6 for α-, β-LnCr 3 (BO 3 ) 4 and LnCr(BO 3 ) 2 , respectively. As an example, the convergences of the Le Bail fittings for α-, β-GdCr 3 (BO 3 ) 4 and LuCr(BO 3 ) 2 are shown in Figure 10. After the refinement, there was a good agreement between the calculated and experimental diffraction patterns with low-reliability factors. Peaks of impurity phases of LnBO 3 , CrBO 3 , and Cr 2 O 3 existed in the diffraction patterns. The decrease in the values of a, b, and c for both groups of compounds was due to a decrease in the ionic radii from Gd 3+ to Er 3+ [55]. The small deviation of the lattice parameters of LnCr(BO 3 ) 2 (Table 6) from those presented by Doi at el. [50] can be attributed to the disorder of Ln 3+ and Cr 3+ ions in the crystal structure. Table 5. Lattice parameters of α-, β-LnCr 3 (BO 3 ) 4 (Ln = Gd-Er) borates (sp. gr. R32 and sp. gr. C2/c).  LuCr(BO3)2 are shown in Figure 10. After the refinement, there was a good agreement between the calculated and experimental diffraction patterns with low-reliability factors. Peaks of impurity phases of LnBO3, CrBO3, and Cr2O3 existed in the diffraction patterns. The decrease in the values of a, b, and c for both groups of compounds was due to a decrease in the ionic radii from Gd 3+ to Er 3+ [55]. The small deviation of the lattice parameters of LnCr(BO3)2 (Table 6) from those presented by Doi at el. [50] can be attributed to the disorder of Ln 3+ and Cr 3+ ions in the crystal structure.  It is noted that with an increase in the synthesis temperature, the amount of the monoclinic β-LnCr 3 (BO 3 ) 4 modification increased, with a simultaneous decrease in the rhombohedral α-LnCr 3 (BO 3 ) 4 one. This is shown in Figure 11 by using DyCr 3 (BO 3 ) 4 as an example. Thus, this confirms the high-temperature nature of the monoclinic modification.

Thermal Analysis
A thermal analysis was carried out to determine the melting points of rare-earth chromium borates. Figure 12 shows fragments of the DSC curves for the Ln2O3:3Cr2O3:4B2O3 (Ln = Gd-Er) and Ln2O3:Cr2O3:2B2O3 (Ln = Ho-Lu) compositions in the range of the melting points of the LnCr3(BO3)4 and LnCr(BO3)2 borates. The DSC curves had one or two endopeaks. One peak was observed for the Ln2O3:3Cr2O3:4B2O3 (Ln = Gd-Dy) and Ln2O3:Cr2O3:2B2O3 (Ln = Tm-Lu) compositions, and two were observed for the Ln2O3:3Cr2O3:4B2O3 (Ln = Ho, Er) and Ln2O3:Cr2O3:2B2O3 (Ln = Ho, Er) compositions. In the first case, one peak was explained by the melting of LnCr3(BO3)4 or LnCr(BO3)2 (the melting points are presented in Table 7). In the second case, the picture was more complicated. The coexistence of two borates, LnCr3(BO3)4 and LnCr(BO3)2, was found for the Ln2O3:3Cr2O3:4B2O3 (Ln = Ho, Er) and Ln2O3:Cr2O3:2B2O3 (Ln = Ho, Er) compositions (Section 3.1). Thus, the two peaks on the DSC curve were explained by the alternate melting of these two compounds. Table 7 shows that the melting point of the LnCr3(BO3)4 (Ln = Gd-Dy) borates gradually decreased as the atomic number of the rare-earth element in these compounds increased. At the same time, the melting point of the LnCr(BO3)2 (Ln = Tm-Lu) borates increased. Based on this, we attributed the low-temperature peak in the DSC curves to LnCr3(BO3)4 (Ln = Ho, Er), and we attributed the high-temperature peak to LnCr(BO3)2 (Ln = Ho, Er). In this case, we were guided by the peak value of the melting

Thermal Analysis
A thermal analysis was carried out to determine the melting points of rare-earth chromium borates. Figure 12 Table 7). In the second case, the picture was more complicated. The coexistence of two borates, LnCr 3 (BO 3 ) 4 and LnCr(BO 3 ) 2 , was found for the Ln 2 O 3 :3Cr 2 O 3 :4B 2 O 3 (Ln = Ho, Er) and Ln 2 O 3 :Cr 2 O 3 :2B 2 O 3 (Ln = Ho, Er) compositions (Section 3.1). Thus, the two peaks on the DSC curve were explained by the alternate melting of these two compounds. Table 7 shows that the melting point of the LnCr 3 (BO 3 ) 4 (Ln = Gd-Dy) borates gradually decreased as the atomic number of the rare-earth element in these compounds increased. At the same time, the melting point of the LnCr(BO 3 ) 2 (Ln = Tm-Lu) borates increased. Based on this, we attributed the low-temperature peak in the DSC curves to LnCr 3 (BO 3 ) 4 (Ln = Ho, Er), and we attributed the high-temperature peak to LnCr(BO 3 ) 2 (Ln = Ho, Er). In this case, we were guided by the peak value of the melting temperature, since, in our opinion, it reflected it better (there was a very wide peak for the ErCr 3 (BO 3 ) 4 borate, which was possibly due to the polycrystalline nature of the samples).

Conflicts of Interest:
The authors declare no conflict of interest.