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

Abstract

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.

1. Introduction

The Ln₂O₃–Cr₂O₃–B₂O₃ (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.

The reactivity of the binary oxide systems of Ln₂O₃–B₂O₃, Cr₂O₃–B₂O₃, and Ln₂O₃–Cr₂O₃ has been analyzed in a number of publications, although some of these systems have not yet been sufficiently investigated. Most studies refer to binary diagrams of Ln₂O₃–B₂O₃ (Ln = Y, La–Nd, Sm–Lu), where the compounds of Ln(BO₂)₃, LnBO₃, Ln₃BO₆, and LnB₅O₉ are described [1,2,3,4]. Lanthanide metaborates, Ln(BO₂)₃ (Ln = La–Nd, Sm–Dy), exhibit two structural modifications under normal pressure: α-Ln(BO₂)₃, where Ln = La–Nd, Sm–Tb (space group (sp. gr.) I2/a) [5,6,7,8,9,10,11], and β-Ln(BO₂)₃, where Ln = Tb–Dy with sp. gr. Pnma [12,13]. It was found that the metaborates of Ln(BO₂)₃ (Ln = La, Nd) melt congruently, while the metaborates of Ln(BO₂)₃ (Ln = Sm–Gd) melt incongruently at 1000–1150 °C [1,2]. In the latter case, melting occurs with the formation of LnBO₃ (Ln = Eu, Gd) and B₂O₃ [1]. Rare-earth orthoborates, LnBO₃ (Ln = Y, La–Nd, Sm–Lu), are isostructural to three CaCO₃ modifications at normal pressure depending on the Ln-cation: aragonite (λ-LnBO₃, with Ln = La–Nd), vaterite (π- and/or μ-LnBO₃, with Ln = Y, Sm–Lu), and calcite (β-LuBO₃) [1,14,15,16,17]. They melt congruently in the temperature range of 1600–1700 °C [1,2]. Rare-earth oxyborates with the general formula of Ln₃BO₆ (Ln = Y, La–Nd, Sm–Lu) are the most understudied compounds in this diagram. Initially, oxyborates were found in the La₂O₃–B₂O₃ system, and their formula was determined as Ln₃BO₆ based on phase identification [2]. However, the structural formulas of Ln₃BO₆ (Ln = La, Nd), Ln₃BO₆ (Ln = Y, Gd), and Yb₃BO₆ were further revised as Ln₂₆(BO₃)₈O₂₇ (Ln = La, Nd) [18,19], Ln_17.33(BO₃)₄(B₂O₅)₂O₁₆ (Ln = Y, Gd) [20,21], and Yb₂₆(BO₃)₄(B₂O₅)₂(B₄O₁₁)O₂₄ [22]. Thus, the oxyborate family is divided into three groups: Ln₃BO₆ (Ln = La–Nd) with sp. gr. P2₁/c, Ln₃BO₆ (Ln = Y, Sm–Tm) with sp. gr. Cm, and Ln₃BO₆ (Ln = Yb, Lu) with sp. gr. C2/m. Levin et al. [2] found that La₃BO₆ oxyborate melts incongruently at 1386 °C. Lanthanide pentaborates, LnB₅O₉ (Ln = La–Nd, Sm–Er), were obtained through the decomposition of Ln[B₈O₁₁(OH)₅] (Ln = La–Nd), Ln[B₉O₁₃(OH)₄] (Ln = Pr, Nd, Sm, Eu), and Ln[B₆O₉(OH)₃] (Ln = Sm–Er) [3,4]. These compounds have two structural modifications: β-LnB₅O₉ (Ln = La, Ce) (sp. gr. P2₁/c) and α-LnB₅O₉ (Ln = Pr, Nd, Sm–Er) (sp. gr. I4₁/acd). Pentaborates decompose at 800–900 °C into metaborates Ln(BO₂)₃ (Ln = Sm–Tb) and orthoborates LnBO₃ (Ln = Dy–Er). The representatives of the Ln₂O₃–B₂O₃ system are considered to be promising candidates for luminescent and nonlinear optical materials [23,24,25].

The binary system of Cr₂O₃–B₂O₃ has been investigated less. Two solid phases, CrBO₃ [26] and Cr₃BO₆ [27], were reported to exist in it. Chromium orthoborate, CrBO₃, has a calcite-type structure (sp. gr. $R\overline{3}c$) and decomposes at 1220 °C to form Cr₂O₃ and B₂O₃. Bither et al. [28] reported that CrBO₃ appeared to be a low-temperature antiferromagnetic material with the Néel temperature (T_N) of 15 K. Chromium oxyborate, Cr₃BO₆, crystallizes in the sp. gr. Pnma. This compound demonstrates low thermal stability in air and decomposes into Cr₂O₃ and CrBO₃ at 800 °C. The electrochemical properties of these materials were investigated, and it was shown that Cr₃BO₆ could be interesting as a negative electrode for lithium-ion batteries [27].

According to data from the literature, only LnCrO₃ phases were found in the binary systems of Ln₂O₃–Cr₂O₃ (Ln = Y, La–Nd, Sm–Lu) [29]. They exhibited perovskite-type structure with the sp. gr. Pbnm [30,31] and demonstrated high congruent melting points at 2300–2400 °C [32]. These compounds are antiferromagnetically ordered with T_N in the temperature range of 110–290 K [33,34]. Multiferroic properties were observed for some rare-earth orthochromites [35,36]. LnCrO₃ materials are p-type semiconductors, which are valuable for sensor applications [37].

In the Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Y, La–Nd, Sm–Lu) ternary systems, two double borates were found: LnCr₃(BO₃)₄ with a huntite-type structure (sp. gr. R32) [38,39] and LnCr(BO₃)₂ with a dolomite-type structure (sp. gr. $R\overline{3}$) [40,41]. Both borate families are still poorly studied. Rare-earth chromium borates of the huntite family were synthesized from multicomponent flux melts [42] and through solid-state reactions [43]. In addition to their rhombohedral structure, LnCr₃(BO₃)₄ compounds also have a monoclinic modification with sp. gr. C2/c [44,45,46]. These materials have been found to exhibit antiferromagnetic ordering with T_N in the temperature range of 6.5–10 K [43,47,48,49]. Several studies of LnCr(BO₃)₂ compounds have been performed, including the refinement of their crystal structure and measurements of antiferromagnetic ordering temperatures (6.1–8.1 K) [50,51].

The great variety of properties specific to borates appearing both in binary Ln₂O₃–B₂O₃ (Ln = Gd–Lu), Cr₂O₃–B₂O₃, and Ln₂O₃–Cr₂O₃ (Ln = Gd–Lu) and in ternary Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Gd–Lu) diagrams makes such systems interesting and challenging for further investigation. Therefore, the purpose of this work is to study the phase relations in Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Gd–Lu) ternary systems, the phase formation of promising magnetic materials in them, and the determination of the structural and thermal properties of the latter.

2. Materials and Methods

The ternary diagrams were studied through the solid-state reaction (SSR) in a high-temperature muffle furnace in air. The initial reagents were oxides (Ln₂O₃ (Ln = Gd, Dy–Lu) (99.9%), Tb₄O₇ (99.9%), Cr₂O₃ (99.9%)) and orthoboric acid (H₃BO₃ (99.9%)). The oxides were preliminarily calcined before mixing to remove water. After that, they were mixed with orthoboric acid in the required proportions in an agate mortar. A 5 mol.% excess of H₃BO₃ was added to compensate for the loss of B₂O₃ due to volatilization during heating. This mixture was pressed into tablets (12 mm in diameter) and held in alumina crucibles at 400 °C to decompose the orthoboric acid. Then, the mixture was ground again in acetone, heated at a rate of 4 °C/min, and held at 24 h in the temperature range of 800–1300 °C. After each heating stage, the samples were left in the furnace until they cooled to room temperature; then, the phase composition was determined with a powder X-ray diffraction (PXRD) method. The heating was repeated until the PXRD patterns remained absolutely stable. New tablets were used for each sintering temperature.

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 LnCr₃(BO₃)₄ and LnCr(BO₃)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 refinement of the lattice parameters of the rare-earth chromium borates and dysprosium metaborate was carried out through the Le Bail method by using the JANA2006 software package [53]. All parameters were refined with the least-square method. The pseudo-Voigt function was used as the peak profile function. The initial structural parameters were the structural data for DyCr₃(BO₃)₄ (monoclinic, sp. gr. C2/c, a = 7.394 Å, b = 9.450 Å, c = 11.357 Å, α = γ = 90°, β = 103.9°; rhombohedral, sp. gr. R32, a = 9.461 Å, c = 7.488 Å, α = β = 90°; γ = 120°) [49] and α-Tb(BO₂)₃ (monoclinic, sp. gr. C2/c, a = 6.21781(5) Å, b = 8.02564(6) Å, c = 7.80659(4) Å, α = γ = 90°, β = 93.6935(7)°) [11].

Differential scanning calorimetry (DSC) was performed by means of STA 449 F5 Jupiter equipment (Netzsch, Selb, Germany) in the temperature range of 50–1500 °C with a heating rate of 20 °C/min in Ar gas flow. PtRh crucibles were used in the DSC experiments.

3. Results and Discussion

3.1. Phase Formation in the Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Gd–Lu) Systems

3.1.1. Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Gd, Tb) Ternary Systems

The phase relations in the Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Gd, Tb) ternary systems at 900, 1000, and 1100 °C (Figure 1,

Table 1. Phase compositions of specimens in the Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Gd, Tb) systems as indicated by PXRD.

Samples	Ln2O3, mol.%	Cr2O3, mol.%	B2O3, mol.%	Phase Composition
1	10	30	60	LnCr3(BO3)4 + CrBO3 + Ln(BO2)3 a + LnBO3 b,c
2	30	10	60	LnCr3(BO3)4 + Ln(BO2)3 a,d + LnBO3
3	60	10	30	LnBO3 + LnCrO3 + Ln3BO6
4	80	10	10	Ln2O3 + LnCrO3 + Ln3BO6
5	35	50	15	LnBO3 + LnCrO3 + Cr2O3
6	20	45	35	LnCr3(BO3)4 + Cr2O3 + LnBO3
7	4	53	43	LnCr3(BO3)4 + CrBO3 + Cr2O3
8	12.5	37.5	50	LnCr3(BO3)4 + LnBO3 + Cr2O3 + Ln(BO2)3 d,e

^a At 900 and 1000 °C for Ln = Gd. ^b At 1100 °C for Ln = Gd. ^c At 900, 1000, 1100 °C for Ln = Tb. ^d At 900 °C for Ln = Tb. ^e At 900 °C for Ln = Tb.

) were determined based on an analysis of 24 samples (eight samples per isothermal section). Each diagram had seven different subsidiary subsystems. Double borates LnCr₃(BO₃)₄ (GdCr₃(BO₃)₄ [PDF-2 #01-085-4144]) were established in both systems. Metaborates (Gd(BO₂)₃ [PDF-2 #01-086-3642] and Tb(BO₂)₃ [PDF-2 #01-072-3639]) crystallized in the α-modification. There was no α-Gd(BO₂)₃ compound in the cross-section at 1100 °C (Figure 1b), which was due to its melting at 1085 °C [54]. The metaborate α-Tb(BO₂)₃ was not observed at temperatures above 900 °C due to its lower melting point than that of α-Gd(BO₂)₃. The results obtained correlated well with the decrease in the melting point in the Ln(BO₂)₃ series from La to Gd [1,2]. Orthoborates (GdBO₃ [PDF-2 #01-089-6546] and TbBO₃ [PDF-2 #01-080-3937]) crystallized in a vaterite modification. The data from the PDF-2 #01-074-3085 card were used to determine the Gd₂O₃ phase. Oxyborates Ln₃BO₆ (Ln = Gd, Tb) were identified based on the PXRD data of the isostructural compound Y₃BO₆ [PDF-2 #00-034-0291].

The stability of the LnCr₃(BO₃)₄ compounds in the range of 800–1250 °C was investigated (Figure 2). Double borates of LnCr₃(BO₃)₄ coexisted with LnBO₃, α-Ln(BO₂)₃, and Cr₂O₃ at 900 °C, and in the temperature range of 1000–1200 °C, they existed with LnBO₃ and Cr₂O₃. The compounds of LnBO₃ and Cr₂O₃ [PDF-2 #00-038-1479] were observed at temperatures of 1250 °C, while LnBO₃, α-Ln(BO₂)₃, and Cr₂O₃ were formed at 800 °C.

Thus, in the investigated ternary systems, the reactions proceeded according to the following equations:

Ln₂O₃ + B₂O₃ → 2LnBO₃ (800–1250 °C)

(1)

Ln₂O₃ + 3B₂O₃ → 2α-Ln(BO₂)₃ (800–1000 °C for Ln = Gd,
800–900 °C for Ln = Tb)

(2)

Ln₂O₃ + 3Cr₂O₃ + 4B₂O₃ → 2LnCr₃(BO₃)₄ (900–1200 °C)

(3)

Figure 2a shows that the borate GdBO₃ crystallized in the low-temperature (LT, PDF-2 #01-089-6545) modification at 800 °C, while the high-temperature (HT) vaterite modification of GdBO₃ formed above 900 °C. This was consistent with the data of Ren et al. [17].

3.1.2. The Dy₂O₃–Cr₂O₃–B₂O₃ Ternary System

The phase relations in the Dy₂O₃–Cr₂O₃–B₂O₃ ternary system at 900, 1000, and 1100 °C (Figure 3,

Table 2. Phase compositions of specimens in the Dy₂O₃–Cr₂O₃–B₂O₃ system as indicated by PXRD.

Samples	Dy2O3, mol.%	Cr2O3, mol.%	B2O3, mol.%	Phase Composition
1	10	30	60	DyCr3(BO3)4 + CrBO3 + DyBO3
2	60	10	30	DyBO3 + DyCrO3 + Dy3BO6
3	80	10	10	Dy2O3 + DyCrO3 + Dy3BO6
4	35	50	15	DyBO3 + DyCrO3 + Cr2O3
5	20	45	35	DyCr3(BO3)4 + Cr2O3 + DyBO3
6	4	53	43	DyCr3(BO3)4 + CrBO3 + Cr2O3
7	12.5	37.5	50	DyCr3(BO3)4 + DyBO3 + Cr2O3

) 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.

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 of DyCr₃(BO₃)₄ was carried out in the range of 800–1300 °C. It was found that above 1250 °C, DyBO₃ and Cr₂O₃ were formed (Figure 4). DyCr₃(BO₃)₄ coexisted with DyBO₃ and Cr₂O₃ in the range of 900–1250 °C. The compounds DyBO₃, α-Dy(BO₂)₃, and Cr₂O₃ were observed below 900 °C.

Consequently, the following reactions proceeded:

Dy₂O₃ + B₂O₃ → 2DyBO₃ (800–1300 °C)

(4)

Dy₂O₃ + 3B₂O₃ → 2α-Dy(BO₂)₃ (800 °C)

(5)

Dy₂O₃ + 3Cr₂O₃ + 4B₂O₃ → 2DyCr₃(BO₃)₄ (900–1250 °C)

(6)

3.1.3. The Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Ho, Er) Ternary Systems

The phase relations in the Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Ho, Er) ternary systems at 900, 1000, and 1100 °C (Figure 5,

Table 3. Phase compositions of specimens in the Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Ho, Er) systems as indicated by PXRD.

Samples	Ln2O3, mol.%	Cr2O3, mol.%	B2O3, mol.%	Phase Composition
1	15	25	60	LnCr3(BO3)4 + LnCr(BO3)2 + CrBO3 + LnBO3
2	60	10	30	LnBO3 + LnCrO3 + Ln3BO6
3	80	10	10	Ln2O3 + LnCrO3 + Ln3BO6
4	35	50	15	LnBO3 + LnCrO3 + Cr2O3
5	27	36	37	LnCr(BO3)2 + Cr2O3 + LnBO3
6	18	36	46	LnCr3(BO3)4 + LnCr(BO3)2 + Cr2O3
7	4	53	43	LnCr3(BO3)4 + CrBO3 + Cr2O3
8	12.5	37.5	50	LnCr3(BO3)4 + LnBO3+ Cr2O3
9	25	25	50	LnCr3(BO3)4 + LnCr(BO3)2 + Cr2O3 + LnBO3

) on the basis of 27 samples (nine specimens per isothermal section) were investigated. There were seven subsidiary subsystems in each of the systems considered. LnCr₃(BO₃)₄ and LnCr(BO₃)₂ (HoCr(BO₃)₂ [PDF-2 #01-082-9333] and ErCr(BO₃)₂ [PDF-2 #01-082-9334]) borates were found. The orthoborates (HoBO₃ [PDF-2 #01-074-1934] and ErBO₃ [PDF-2 #01-013-0486] were isostructural to the vaterite modification. The Ho₂O₃ and Er₂O₃ phases were determined by using the powder data from the PDF-2 #01-074-3085 and PDF-2 #00-013-0387 cards, respectively. The PXRD data of the isostructural compound Y₃BO₆ were used to determine the Ln₃BO₆ phases. All compounds of these systems were stable up to 1100 °C.

Our results confirm the existence of the ErCr₃(BO₃)₄ compound, which was reported only by Kurazhkovskaya et al. [45].

The study of the stability of the borates LnCr₃(BO₃)₄ and LnCr(BO₃)₂ in the range of 800–1250 °C showed that LnBO₃ and Cr₂O₃ were formed above 1200 °C (Figure 6 and Figure 7). The HoCr₃(BO₄)₃, HoBO₃, and Cr₂O₃ phases were stable at 1200 °C for the Ho₂O₃:3Cr₂O₃:4B₂O₃ and Ho₂O₃:Cr₂O₃:2B₂O₃ compositions. The ErCr(BO₃)₂, ErBO₃, and Cr₂O₃ phases were stable at 1200 °C for the Er₂O₃:3Cr₂O₃:4B₂O₃ and Er₂O₃:Cr₂O₃:2B₂O₃ compositions. The LnCr₃(BO₃)₄, LnCr(BO₃)₂, LnBO₃, and Cr₂O₃ phases coexisted from 900 to 1100 °C for the Ln₂O₃:3Cr₂O₃:4B₂O₃ (Ln = Ho, Er) and Ln₂O₃:Cr₂O₃:2B₂O₃ (Ln = Ho, Er) compositions. The LnBO₃ and Cr₂O₃ compounds were observed below 900 °C.

Thus, the following reactions occurred:

Ln₂O₃ + B₂O₃ → 2LnBO₃ (800–1250 °C)

(7)

Ln₂O₃ + Cr₂O₃ + 2B₂O₃ → 2LnCr(BO₃)₂ (900–1200 °C for Ln = Er and 900–1100 °C for Ln = Ho)

(8)

Ln₂O₃ + 3Cr₂O₃ + 4B₂O₃ → 2LnCr₃(BO₃)₄ (900–1200 °C for Ln = Ho and 900–1100 °C for Ln = Er)

(9)

3.1.4. The Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Tm–Lu) Ternary Systems

The phase relations in the Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Tm–Lu) ternary systems were defined at 1000 °C (

Table 4. Phase compositions of specimens in the Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Tm–Lu) systems as indicated by PXRD.

Samples	Ln2O3, mol.%	Cr2O3, mol.%	B2O3, mol.%	Phase Composition
1	20	20	60	LnCr(BO2)3 + CrBO3 + LnBO3 a
2	60	10	30	LnBO3 b + LnCrO3 + Ln3BO6
3	80	10	10	Ln2O3 + LnCrO3 + Ln3BO6
4	35	50	15	LnBO3 b + LnCrO3 + Cr2O3
5	27	36	37	LnCr(BO3)2 + Cr2O3 + LnBO3 a
6	10	50	40	LnCr(BO3)2 + CrBO3 + Cr2O3
7	25	25	50	LnCr(BO3)2 + LnBO3 a + CrBO3 + Cr2O3

^a Calcite modification for Ln = Lu. ^b Calcite modification for Ln = Lu.

, Figure 8) based on the phase compositions for 21 samples (seven samples per system). There were six subsidiary subsystems. The double borates (TmCr(BO₃)₂ [PDF-2 #01-082-9335], YbCr(BO₃)₂ [PDF-2 #01-082-9336], and LuCr(BO₃)₂ [PDF-2 #01-082-9337]) were found. The orthoborates TmBO₃ [PDF-2 #00-013-0482] and YbBO₃ [PDF-2 #01-076-7335] were isostructural to the vaterite modification, and LuBO₃ crystallized in the vaterite [PDF-2 #01-085-7631] and calcite [PDF-2 #01-085-7534] modifications. The Tm₂O₃, Yb₂O₃, and Lu₂O₃ phases were determined by using the powder data from the PDF-2 #00-041-1090, PDF-2 #00-041-1106, PDF-2 #00-012-0728 cards, respectively. The oxyborate Tm₃BO₆ was determined from the PXRD patterns of the isostructural compound Y₃BO₆, and Ln₃BO₆ (Ln = Yb, Lu) was established through similarity with the PXRD patterns from the literature [22].

Leonyuk et al. [39] reported the formation of YbCr₃(BO₃)₄. Nevertheless, the existence of this phase is in doubt. In studies on the synthesis and characterization of LnCr₃(BO₃)₄ compounds by using vibrational spectroscopy, the authors of [44,45,46] reported huntite-type borates with Ln = La, Pr, Nd, Sm–Er, which corresponded with our data.

The study of the stability LnCr(BO₃)₂ borates in the range of 800–1200 °C showed that above 1150 °C, the LnBO₃ and Cr₂O₃ phases formed (Figure 9). At temperatures from 900 to 1150 °C, LnCr(BO₃)₂ borates coexisted with LnBO₃, CrBO₃, and Cr₂O₃. The LnBO₃ and Cr₂O₃ compounds were observed below 900 °C.

Therefore, the following reactions occurred:

Ln₂O₃ + B₂O₃ → 2LnBO₃ (800–1200 °C)

(10)

Cr₂O₃ + B₂O₃ → 2CrBO₃ (900–1150 °C)

(11)

Ln₂O₃ + Cr₂O₃ + 2B₂O₃ → 2LnCr(BO₃)₂ (900–1150 °C)

(12)

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 other regions.

3.2. Powder X-ray Diffraction

The Le Bail fit was used to confirm the structural similarity of the borates within the families of LnCr₃(BO₃)₄ and LnCr(BO₃)₂. All huntite-type LnCr₃(BO₃)₄ borates turned out to be polytypes and contained a significant number of rhombohedral (sp. gr. R32, α-LnCr₃(BO₃)₄) and monoclinic (sp. gr. C2/c, β-LnCr₃(BO₃)₄) modifications. The refined lattice parameters are presented in

Table 5. Lattice parameters of α-, β-LnCr₃(BO₃)₄ (Ln = Gd–Er) borates (sp. gr. R32 and sp. gr. C2/c).

Refined Parameters	β-GdCr3(BO3)4	β-TbCr3(BO3)4	β-DyCr3(BO3)4	β-HoCr3(BO3)4	β-ErCr3(BO3)4
a (Å)	7.3939	7.3912	7.3828	7.3741	7.3712
b (Å)	9.4873	9.4846	9.4763	9.4728	9.4647
c (Å)	11.4031	11.3934	11.3782	11.3773	11.3731
β (°)	103.853	103.861	103.847	103.843	103.852
V (Å3)	776.63	775.45	772.90	771.66	770.38
	α-GdCr3(BO3)4	α-TbCr3(BO3)4	α-DyCr3(BO3)4	α-HoCr3(BO3)4	α-ErCr3(BO3)4
a (Å)	9.4700	9.4693	9.4657	9.4650	9.4637
c (Å)	7.4976	7.4959	7.4801	7.4747	7.4684
V (Å3)	582.31	582.09	580.42	579.92	579.26
Rwp (%)	1.01	1.13	1.13	1.33	1.51
Rp (%)	0.76	0.85	0.83	0.95	1.04
Tsynthesis (°C)	1200	1200	1200	1200	1100

and

Table 6. Lattice parameters of LnCr(BO₃)₂ (Ln = Ho–Lu) borates (sp. gr. $R\overline{3}$ ).

Refined Parameters	HoCr(BO3)2	ErCr(BO3)2	TmCr(BO3)2	YbCr(BO3)2	LuCr(BO3)2
a (Å)	4.7664	4.7591	4.7528	4.7471	4.7442
c (Å)	15.5415	15.490	15.4835	15.4061	15.3471
V (Å3)	305.77	303.84	302.90	300.66	299.14
Rwp (%)	1.75	3.19	3.15	2.83	2.36
Rp (%)	1.20	2.00	2.04	1.79	1.58
Tsynthesis (°C)	1000	1200	1100	1100	1100

for α-, β-LnCr₃(BO₃)₄ and LnCr(BO₃)₂, respectively. As an example, the convergences of the Le Bail fittings for α-, β-GdCr₃(BO₃)₄ and 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 Gd³⁺ to Er³⁺ [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 Ln³⁺ and Cr³⁺ ions in the crystal structure.

It is noted that with an increase in the synthesis temperature, the amount of the monoclinic β-LnCr₃(BO₃)₄ modification increased, with a simultaneous decrease in the rhombohedral α-LnCr₃(BO₃)₄ one. This is shown in Figure 11 by using DyCr₃(BO₃)₄ as an example. Thus, this confirms the high-temperature nature of the monoclinic modification.

Mukherjee et al. [11] reported that they obtained a mixture of α-Dy(BO₂)₃ and DyBO₃. However, they did not give structural parameters for the metaborate α-Dy(BO₂)₃. The metaborate α-Dy(BO₂)₃ was also refined with the Le Bail method. The lattice parameters were a = 6.1982 Å, b = 8.0213 Å, c = 7.8021 Å, β = 93.249°, and V = 386.27 ų. R_wp = 0.77 and R_p = 1.03 became the final values of the R-factors. The additional phases were DyBO₃ and Cr₂O₃. The obtained lattice parameters correlated with the trend towards a decrease in the lattice parameters of the α-Ln(BO₂)₃ (Ln = La–Nd, Sm–Tb) metaborates with the decrease in the ionic radius of the rare-earth ions [11].

3.3. 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. Melting points of the LnCr₃(BO₃)₄ (Ln = Gd–Er) and LnCr(BO₃)₂ (Ln = Ho–Lu) borates.

Compound	Peak (°C)	Onset (°C)
GdCr3(BO3)4	1327	1312
TbCr3(BO3)4	1321	1303
DyCr3(BO3)4	1311	1298
HoCr3(BO3)4	1331	1302
ErCr3(BO3)4	1343	1263
HoCr(BO3)2	1347	1333
ErCr(BO3)2	1379	1366
TmCr(BO3)2	1402	1391
YbCr(BO3)2	1424	1413
LuCr(BO3)2	>1500	1448

). 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 temperature, since, in our opinion, it reflected it better (there was a very wide peak for the ErCr₃(BO₃)₄ borate, which was possibly due to the polycrystalline nature of the samples).

According to DSC and PXRD data (Section 3.1), the thermally induced processes can be illustrated with the following reactions:

2LnCr₃(BO₃)₄ → 2LnBO₃ + 3Cr₂O₃ + 3B₂O₃ (Ln = Gd–Dy) (1310–1330 °C)

(13)

4LnCr₃(BO₃)₄ → 2LnCr(BO₃)₂ + 2LnBO₃ + 5Cr₂O₃ + 5B₂O₃ (Ln = Ho–Er) (1320–1330 °C)

(14)

2LnCr(BO₃)₂ → 2LnBO₃ + Cr₂O₃ + B₂O₃ (Ln = Ho–Lu) (1330–1450 °C)

(15)

4. Conclusions

The Ln₂O₃–Cr₂O₃–B₂O₃ (Ln = Gd–Lu) ternary oxide systems were studied with PXRD. In these systems, it was found that the LnCr₃(BO₃)₄ borates were stable up to Ln = Er, after which LnCr(BO₃)₂ borates crystallized. It was established that LnCr₃(BO₃)₄ borates crystallized in rhombohedral (α-LnCr₃(BO₃)₄) and monoclinic (β-LnCr₃(BO₃)₄) polytype modifications. The latter prevailed at temperatures above 1100 °C. The melting points of LnCr₃(BO₃)₄ (Ln = Gd–Er) were slightly higher than those for LnAl₃(BO₃)₄ (Ln = Gd–Er). They increased with a decrease in the ionic radius of rare-earth ions for LnCr(BO₃)₂ (Ln = Ho–Lu) borates, while for LnCr₃(BO₃)₄ (Ln = Gd–Er) borates, they decreased to Ln = Dy and then increased.