Correction to: Phase Relations in the CaO-B₂O₃-Sc₂O₃ Ternary System

1 Correction to: J. Phase Equilib. Diffus. (2022) 43:98–108 https://doi.org/10.1007/s11669-021-00929-2

Note of changes: Abstract section

• “nonlinear optical” is modified to “nonlinear optical (NLO)”

• “systemically studied” is modified to “investigated comprehensively”

• “thermo dynamic” is modified to “thermodynamic”

• “electron probe microanalysis and x-ray diffraction” is modified to “electron probe microanalysis (EPMA) and X-ray diffraction (XRD)”

Note of changes: Introduction

“As the core devices of solid-state laser systems, nonlinear optical (NLO) materials can effectively expand the frequency range of commonly used laser sources and play an important role in the field of laser related science and technology, for example,” is modified to “NLO materials, as the core devices of solid state laser systems, can effectively broaden the frequency range of commonly used laser sources and play an important role in the field of laser related science and technology, including”.  “However, the availability of lasers with different wavelengths is limited which requires exploration of new laser materials with other wave-lengths.^[7] For an NLO material to be highly efficient it is important that it is phase matchable.” is modified to “the availability of lasers with various wavelengths is restricted, necessitating the exploration of new laser materials with additional wavelengths.^[7] It is critical for a NLO material to be phase matchable in order to be extremely efficient.^[8]” “Since the second order (SO) NLO materials have excellent second-harmonic generation (SHG) capability, they have attracted much attention.^[7] Up to now, a variety of NLO materials have been discovered, including borates, carbonates, and silicates.^[9–16]” is modifed to “Due to the outstanding second-harmonic generation (SHG) capacity of second-order (SO) NLO materials, they have garnered considerable attention.^[7] There have been several discoveries of NLO materials to date, including borates, carbonates and silicates.^[9–16]”

• “complex” is modified to “complicated”

• “nonlinear optical (NLO)” is modified to “NLO”

• “second-harmonic generation (SHG)” is modified to “SHG”

• “Second-order” is modified to “SO”

• “The compounds Ca₄LaO(BO₃)₃^[25], Ca₄YO(BO₃)₃^[28], and Ca₄GdO(BO₃)₃^[29], which are likely to be possible good candidates for NLO materials.” is modified to “Ca₄LaO(BO₃)₃^[25], Ca₄YO(BO₃)₃^[28], and Ca₄GdO(BO₃)₃^[29] are all compounds that are anticipated to be good candidates for NLO materials”

• “nonlinear optical” is modified to “NLO”

Note of changes: Experiment

• Experiment” is modified to “Experimental”

• “with 0.0001 g accuracy” is modified to “with a precision of 0.0001 g”

• “then the powder” is modified to “then filled with the powder”

• “after reaching the holding time it took 5 min to quench the samples.” is modified to “the samples were to be quenched after the holding period had expired.”

• “The samples were analyzed quantitatively by” is modified to “Quantitative analysis of the samples was done using”

Note of changes: Section 3.1.1

• “the Ca₃B₂O₆^[39] Ca₂B₂O₅,^[40] CaB_2-O₄,^[41] and CaB₄O₇^[42] phases are found in the binary system CaO-B₂O₃.^[43] Ca₃B₂O₆ (C₃B), CaB₂O₅ (C₂B) and CaB₂O₄ (CB) exist at 1373 K and C₃B and C₂B exist at 1473 K.” is modified to “the Ca₃B₂O₆ (C₃B),^[39] Ca₂B₂O₅ (C₂B),^[40]CaB₂O₄ (CB),^[41] and CaB₄O₇ (CB₂)^[42] phases are found in the binary CaO-B₂O₃.^[43] C₃B, C₂B and CB phases are existed at 1373 K and C₃B and C₂B phases are existed at 1473 K.”

Note of changes: Section 3.1.2

“there is only ScBO₃^[45] which exists at 1373 K and 1473 K.” is modified to “there is only ScBO₃^[45] existed at 1373 K and 1473 K.”

Note of changes: Section 3.2.1

“The different chemical compositions of all phases result in different brightness in the grayscale image of the micrographs and, therefore, these phases can be distinguished easily.” is modified to “Because of the various chemical compositions of each phase, the grayscale micrographs show a distinct difference in brightness, making it easy to identify between them.”

• “C_3-B” is modified to “C₃-B”

• “Ca_4-ScO(BO₃)₃” is modified to “Ca₄-ScO(BO₃)₃”

• “Ca_3-Sc₂(BO₃)₄” is modified to “Ca₃-Sc₂(BO₃)₄”

• “C_2-B” is modified to “C₂-B”

Note of changes: Section 3.2.2

• “Fig. 4 and 5” is modified to “ Figs. 4 and 5”

• “C₂B+ Ca₃Sc₂(-BO₃)₄+L” is modified to “C₂B+Ca₃-Sc₂(BO₃)₄+L”

• “According to the lever,^[47]” is modified to “According to the lever rule,^[47]”

• “strongly” is modified to “substantially”

Note to changes: Section 3.3

• “Ca_4-ScO(BO₃)₃” is modified to “Ca₄-ScO(BO₃)₃”

• “So” is modified to “Accordingly”

• “found” is modified to “discovered”

• “The electron exchange correlation functions are calculated using” is modified to “The electron exchange correlation functions are calculated using”

• “The calculated results are consistent with the experimental results. The experimental results are shown in Fig. 9 and 10. The calculated results are consistent with the experimental results.” is modified to “There is no discrepancy between the calculated and experimental results. Figs. 9 and 10 demonstrate the experimental results. There is agreement between the calculated and experimental results.”

• “Fig. 9 and 10” is modified to “Figs. 9 and 10”

Note of changes: Conclusions

“The data could also be used for theoretical calculations to understand and describe the ternary CaO-B₂O₃-Sc₂O₃ system.” is modified to “Also, theoretical calculations based on the data might be employed in an effort to better comprehend and explain the ternary CaO-B₂O₃-Sc₂O₃ system.”

Note of changes: The title of Fig. 1 is modified as follows:

Fig. 1 Phase diagram in the system CaO-B₂O₃.^[43] C=CaO, B=B₂O₃. ① CaO+Ca₃B₂O₆, ② Ca₂B₂O₅+Ca₃B₂O₆, ③ CaB₂O₄+Ca₂B₂O₅, ④ CaB₂O₄+CaB₄O₇, ⑤ CaB₄O₇+Liquid, ⑥ Liquid+Liquid1, ⑦ CaB₄O₇+Liquid, ⑧ CaB₂O₄+Liquid, ⑨ CaB₂O₄+Liquid, ⑩ Ca₂B₂O₅+Liquid, ⑪ Ca₂B₂O₅+Liquid, ⑫ Ca₃B₂O₆+Liquid, ⑬ Ca₃B₂O₆+Liquid, ⑭ CaO+Liquid, ⑮ Liquid” is modified to “Fig. 1 Phase diagram in the system CaO-B₂O₃,^[43] C=CaO, B=B₂O₃, L=Liquid. ① CaO+C₃B, ② C₂B+C₃B, ③ CB+C₂B, ④ CB+CB₂, ⑤ CB₂+L, ⑥ L+L1, ⑦ CB₂+L, ⑧ CB₂+L, ⑨ CB₂+L, ⑩ C₂B+L, ⑪ C₂B+L, ⑫ C₃B+L, ⑬ C₃B+L, ⑭ CaO+L, ⑮ L. In addition, “wt %” is modified to “wt.%” in the Fig. 1.

Fig. 1

Phase diagram in the system CaO-B₂O₃,^[43] C=CaO, B=B₂O₃, L=Liquid. ① CaO+C₃B, ② C₂B+C₃B, ③ CB+C₂B, ④ CB+CB₂, ⑤ CB₂+L, ⑥ L+L1, ⑦ CB₂+L, ⑧ CB₂+L, ⑨ CB₂+L, ⑩ C₂B+L, ⑪ C₂B+L, ⑫ C₃B+L, ⑬ C₃B+L, ⑭ CaO+L, ⑮ L

Note of changes: The title of Fig. 2 is modified as follows:

“Fig. 2 Phase diagram in the system Sc₂O₃-B₂O₃.^[44] ① Sc₂O₃+ScBO₃, ② ScBO₃+L, ③ ScBO₃+L, ④ ScBO₃+L, ⑤ Sc₂BO₃+L, ⑥ L”. In addition, “wt %” is modified to “wt. %” in the Fig. 2.

Fig. 2

Phase diagram in the system Sc₂O₃-B₂O₃.^[44] ① Sc₂O₃+ScBO₃, ② ScBO₃+L, ③ ScBO₃+L, ④ ScBO₃+L, ⑤ Sc₂BO₃+L, ⑥ L”

Note of changes: The temperature (1373 K or 1473 K) is added and the order (from small to large) is changed in Fig. 3. The modified result is as follows:

Fig. 3

Microstructures of the quenched slag samples. (a) ScBO₃ in equilibrium with L; (b) Ca₃Sc₂(BO₃)₄, ScBO₃ and Ca₄ScO(BO₃)₃ in equilibrium; (c) Ca₃Sc₂(BO₃)₄ and ScBO₃ in equilibrium with L; (d) C₂B (Sc₂O₃), ScBO₃ and Ca₄ScO(BO₃)₃ in equilibrium; “I” is modified to “(e)” CaScBO₄, Ca₃Sc₂(BO₃)₄ and ScBO₃ in equilibrium; (f) B₂O₃ and ScBO₃ in equilibrium with L; (g) C₂B (Sc₂O₃) and ScBO₃ in equilibrium; (h) CaScBO₄, Ca₃Sc₂(BO₃)₄ and Ca₄ScO(BO₃)₃ in equilibrium; (i) CaScBO₄, Ca₄ScO(BO₃)₃ and C₃B (Sc₂O₃) in equilibrium; (j) C₂B (Sc₂O₃), C₃B (Sc₂O₃) and ScBO₃ in equilibrium; (k) C₂B (Sc₂O₃), C₃B (Sc₂O₃) and Ca₄ScO(BO₃)₃ in equilibrium; (l) C₂B (Sc₂O₃), Ca₄ScO(BO₃)₃ and Ca₃Sc₂(BO₃)₄ in equilibrium; (m) C₂B (Sc₂O₃) and C₃B (Sc₂O₃) in equilibrium; (n) CB (Sc₂O₃) and Ca₃Sc₂(BO₃)₄ in equilibrium with L; (o) C₂B (Sc₂O₃) and Ca₃Sc₂(BO₃)₄ in equilibrium with L; (p) CB (Sc₂O₃), C₂B (Sc₂O₃) and Ca₃Sc₂(BO₃)₄ in equilibrium

Note of changes: “wt %” is modified to “wt. %” in the Figs. 4 and 5. The modified results are as follows:

Fig. 4

Isothermal phase diagram of B₂O₃-Sc₂O₃-CaO system at 1373 K

Fig. 5

Isothermal phase diagram of B₂O₃-Sc₂O₃-CaO system at 1473 K

Note of changes: “Calculative data” is modified to “Calculated data” in Figs. 6-8. The boxes on the “Calculated data” and “Experimental data” are removed in Figs. 6-8. The modified results are as follows:

Fig. 6

(a) Crystal structure of Ca₄ScO(BO₃)₃ (b) Experimental and calculated XRD patterns of Ca₄ScO(BO₃)₃

Fig. 7

(a) Crystal structure of CaScBO₄ (b) Experimental and calculated XRD patterns of CaScBO₄

Fig. 8

(a) Crystal structure of Ca₃Sc₂(BO₃)₄ (b) Experimental and calculated XRD patterns of Ca₃Sc₂(BO₃)₄

Note of changes: The boxes on the “Experimental data”, “JCPDS NO.17-0778 (ScBO₃)”, “CaScBO₄” and “Ca₃Sc₂(BO₃)₄” are removed in Fig. 9. The modified result is as follows:

Fig. 9

XRD patterns of the CaScBO₄, Ca₃Sc₂(BO₃)₄ and ScBO₃

Note of changes: The boxes on the “Experimental data”, “JCPDS NO.17-0778 (ScBO₃)”, “JCPDS NO. 03-0683 (Ca₂B₂O₅)”, “CaScBO₄” and “Ca₃Sc₂(BO₃)₄” are removed in Fig. 10. The modified result is as follows:

Fig. 10

XRD patterns of the Ca₄ScO(BO₃)₃, Ca₂B₂O₅ and ScBO₃

Note of changes: The modified results of Tables 1-5 (three-line tables) are as follows:

Table 1 Initial compositions (wt. %) for the system CaO-B₂O₃-Sc₂O₃ at 1373 K and 1473 K

Table 2 Phase relations and compositions in the systems CaO-B₂O₃-Sc₂O₃ at 1373 K and 1473 K

Table 3 Calculated structural parameters from powder X-ray analysis of Ca₄ScO(BO₃)₃ for space group Cm, a=9.0268 Å, b=9.0268 Å, and c=3.5647 Å

Table 4 Selected bond distances (Å) in Ca₄ScO(BO₃)₃

Table 5 Calculated structural parameters from powder X-ray analysis of CaScBO₄ for space group Pnma, a=10.3449 Å, b=3.386 Å, and c=9.57 Å

Note of changes: “Y” is modified to “Sc”, and the modified results of Table 6 (three-line tables) are as follows:

Table 6 Selected bond distances (Å) in CaScBO₄

Note of changes: The modified results of Tables 7-8 (three-line tables) are as follows:

Table 7 Calculated structural parameters from powder X-ray analysis of Ca₃Sc₂(BO₃)₄ for space group Pnma, a=7.123 Å, b=15.633 Å, and c=9.1764 Å

Table 8 Selected bond distances (Å) in Ca₃Sc₂(BO₃)₄

Note of changes: Reference Section

• Reference “19. M. Mutailipu, M. Zhang, X. Su, Z. Yang, Y. Chen, and S. Pan, Structural Insights into Borates with an Anion-Templated OpenFramework Configuration: Asymmetric K2BaB16O26 versus Centrosymmetric K3CsB20O32 and Na2M2NB18O30 (M=Rb, Cs;N= Ba, Pb), Chem. Eur. J., 2017, 23, p 13910–13918.” is modified to “19. M. Mutailipu, M. Zhang, X. Su, Z. Yang, Y. Chen, and S. Pan, Structural Insights into Borates with an Anion-Templated Open-Framework Configuration: Asymmetric K₂BaB₁₆O₂₆ versus Centrosymmetric K₃CsB₂₀O₃₂ and Na₂M₂NB₁₈O₃₀ (M=Rb, Cs; N=Ba, Pb), Chem. Eur. J., 2017, 23, p 13910–13918.”

• Reference “24. H.Y.-P. Hong, and K. Dwight, Crystal Structure and Fluorescence Lifetime of NdAl3 (BO3) 4, A Promising Laser Material, Mater. Res. Bull., 1974, 9, p 1661–1665. https://doi.org/10.1016/0025-5408(74)90158-5” is modified to “24. H.Y.-P. Hong, and K. Dwight, Crystal Structure and Fluorescence Lifetime of NdAl₃(BO₃)₄, A Promising Laser Material, Mater. Res. Bull., 1974, 9, p 1661–1665. https://doi.org/10.1016/0025-5408(74)90158-5.”