Investigation on the Thermal–Mechanical Properties of YbRESiO₅ (RE = Yb, Eu, Gd, Ho, Tm, Lu, Y, Sc): First-Principles Calculations and Thermal Performance Experiments

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article is devoted to the Investigation on the thermal-mechanical properties of monosilicates doped with different rare-earth elements: first-principles calculations and thermal performance experiments. The article is written in good language and sounds scientifically. The authors utilize the equipment and methods described in the article at a high level of experiment and theory. This article may be of interest to researchers and scientists working in the field of material science.

Reviewer comments

Line 16, “YbReSiO₅ (Re = Yb, Eu,” Re symbol is confusing because it belongs to element Rhenium. Authors can change it to something different like “REth” or “RE”. When “Re = Yb” is it equal Yb₂SiO₅? In this case the composition isn’t clear.

Table 4. Units are missed in the header.” / Å” means Å^-1? Correction needed.

Line 319 Weird commas.

Line 381 “Yb2SiO” Typos.

For the reviewer, there is an incorrect term “doping” used in the article. Doping means less than a few percent dopant additive to the bulk mass. Please consider doping in semiconductors or in metal alloy production. One to one rare earth metals composition isn’t doping but metals composition in compound.

The elastic constants decipher for Table 5, line 319 is very far from it and located at the beginning of the text, line 140.

The title of the article does not quite accurately reflect its content. Perhaps the word “doping” can be replaced with “Yb with different rare earth metal composition”.

Conclusion

Accept after minor revision.

Author Response

Thank you for your kindly suggestions.

Investigation on the thermal-mechanical properties of monosilicates doped with different rare-earth elements: first-principles calculations and thermal performance experiments

Coatings

1.“YbReSiO₅ (Re = Yb, Eu,” Re symbol is confusing because it belongs to element Rhenium. Authors can change it to something different like “REth” or “RE”. When “Re = Yb” is it equal Yb₂SiO₅? In this case the composition isn’t clear.

Thank you for pointing this out. We agree with this comment. We have replaced Re in this article with RE. And we have added an explanation in the text, “When RE is Yb, the material is Yb₂SiO₅.” Thank you very much for your suggestion!

2. Units are missed in the header.” / Å” means Å^-1? Correction needed.

Thank you for pointing this out. Already revised. / Å has been replaced with Å^-1.

3.Weird commas.

Thank you for pointing this out. Already revised.

4“Yb2SiO” Typos

Thank you for pointing this out. Revised as follow “Yb₂SiO₅”

5 For the reviewer, there is an incorrect term “doping” used in the article. Doping means less than a few percent dopant additive to the bulk mass. Please consider doping in semiconductors or in metal alloy production. One to one rare earth metals composition isn’t doping but metals composition in compound.

Thank you for pointing this out. We agree with you and choose to replace “dope” with “add”

6 The elastic constants decipher for Table 5, line 319 is very far from it and located at the beginning of the text, line 140

Thank you for pointing this out. Already revised.

7 The title of the article does not quite accurately reflect its content. Perhaps the word “doping” can be replaced with “Yb with different rare earth metal composition”.

Thank you for pointing this out. Based on the comments you have made, we have chosen, after careful consideration, to change the title to “Investigation on the thermal-mechanical properties of YbRESiO₅ (RE = Yb, Eu, Gd, Ho, Tm, Lu, Y, Sc): first-principles calculations and thermal performance experiments

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

To improve the clarity and the quality of presentation, the following concerns should be addressed:

1.     The Introduction should provide information of the following:

1.1. In which part of the aircraft are the focused materials used? What is the common range of operating conditions (temperature and pressure) of such parts? What is the usual lifespan of the material.

1.2. It would be good if the manuscript reported the range of the gas flow rate and the shear force applied to the material.

1.3. What are the characteristics of Re₂SiO₅ that make it interesting for focused applications? (line 62)

1.4. Lines 78-79, “The mechanical and thermal properties of the material are greatly impacted by these features [18-20].” How? Please elaborate on the mentioned impacts.

1.5.  Line 82, giving examples of quantitative data of the increased resistance to water corrosion will be helpful.

1.6.  Line 84, please give examples of “…the rare earth cations”.

1.7.  Lines 80-88, it is unclear why the information in the paragraph is presented and how it is related to this work.

1.8.  Lines 89, it is unclear why “the lattice structures and elastic properties” are focused on in this work.

1.9. Lines 91-92: “…, simulations of Si-O bond lengths”: What computation method/technique/theory is used in the investigation?

1.10. Lines 95-96, it is unclear what exactly the studied mechanical and thermodynamic properties are. Please describe them specifically.

2.     The following terms need clarification and/or elaboration:

2.1. Aircraft engines' pressure ratios (line 31)

2.2. endurance thresholds (lines 32-33)

2.3. conventional high-temperature alloys (line 33)

2.4. two chemical degradation mechanisms (line 39)

2.5. alkaline salts (line 43)

2.6. low thermal expansion coefficient (line 53)

2.7. low elastic modulus (line 54)

2.8. high melting temperature (line 58)

2.9. low temperature (line 58)

2.10. thermal expansion coefficients (line 58): low or high?

2.11. What are the X1 and X2 phases (line 62)?

2.12. Range of the atomic numbers of rare-earth elements (Re) (lines 64-65)

2.13.  …low temperatures (line 68)

2.14.  …high temperatures (line 69)

2.15. …high temperatures (line 71)

2.16. The lowest thermal conductivity (line 86)

2.17. Please briefly elaborate on “the first irreducible Brillouin zone” (line 120).

2.18. Please briefly elaborate on the “four sets of uniform strain configurations” (lines 133-135).

2.19. Please briefly elaborate on “the Hellmann-Feynman force” (lines 138-139).

2.20. Please briefly elaborate on “the Mulliken population cutoff distance” (line 130).

3.     Please provide references for the following:

3.1. Bloch waves (line 118)

3.2. Monkhorst-Pack technique (line 121)

3.3. local density approximation (LDA) (line 122)

3.4. Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization approach (lines 124-125)

3.5. Milman and Warren (lines 132-133)

3.6. Archimedes' method (line 178). Please also provide a brief elaboration.

3.7. Neumann-Kopp law (line 179). Please also provide a brief elaboration.

4.     In section 2.3, please clarify the known parameters and calculated variables in the equations for each system (rare-each compound).

5.     The value of properties should be reported, in parentheses, along with each compound mentioned.

5.1. Lines 254-255, the smallest unit cell volume, for example, “YbScSiO5 (750.4240 ų) ＜YbHoSiO5 (794.8210 ų) ＜ …”

5.2. Lines 266-267: the average Re-O bond lengths in [ReO6] polyhedra

5.3. Lines 268-269: Re-O bond lengths

5.4.  Lines 269-270: The lattice distortion in [ReO7]

5.5. Lines 271-272: The lattice distortion in [ReO6] polyhedral

5.6. Line 311: YbEuSiO5 has the longest Si-O bond length

5.7. Line 312: it also has a lower Milliken population and bond density than Yb2SiO5

5.8.  Lines 316-317: water vapor corrosion resistance of the eight different rare earth monociliates

5.9. Lines 325-327: magnitude for average sound velocity and Debye temperature.

5.10. Lines 327-328: Young’s modulus

5.11. Lines 363-364: unit cell volumes

6.     Other comments

6.1. Lines 41-42: I suggest showing (i) recession … and (ii) thermal corrosion in the long sentence to make the two properties noticeable to the reader.

6.2. Line 120, “2×3×4k” is unclear. Do you mean 2000x3000x4000?

6.3. What is the unit of 1×10^-3 (line 129)?

6.4. In Table 1, please use the full word for the “Theo” (second column) and “Cal” (third column). Also, The Deviation (the fourth column) is unclear; please provide its definition to show which of the two is the reference value?

6.5.  Equation (4) and line 251, please replace the term “M-O” with a simple term (e.g., MO) to avoid confusion.

6.6. Some tables and figures (e.g., Table 4, Table 5, Figure 3, …) are not mentioned in the content. Please make sure that all the figures and tables are introduced.

6.7. In Table 3, the list of “bond lengths” (the fourth column) is unclear. Please show the line to separate each row to avoid confusion.

6.8. In Table 7, what is the meaning of the dot before “Compound” (first column)?

6.9. In Figures 1-2: Please indicate the elements presented in different colors.

6.10. I suggest presenting Figure 3 in bar charts

6.11. In Figures 7-8, the color and order of each item should be consistent.

6.12. In Figures 7 and 9, Please adjust the size of subfigures.

7.     Please indicate the authors' contribution.

Author Response

Thank you for your kindly suggestions.

Investigation on the thermal-mechanical properties of monosilicates doped with different rare-earth elements: first-principles calculations and thermal performance experiments

Coatings

Reviewer #2

1. In which part of the aircraft are the focused materials used? What is the common range of

operating conditions (temperature and pressure) of such parts? What is the usual lifespan of the material?

Thank you for pointing this out. We agree with this comment. Therefore we therefore chose to add “According to the needs of the current development, the surface temperature of the hot end components of the new generation of aero-engine can reach 1400 ℃, while the maximum working temperature of single-crystal nickel-based alloys is 1100 ℃, Ni3Al single-crystal high-temperature limit of 1200 ℃, so there is an urgent need to develop a new type of material matrix” after line 32 of the original text. After line 47 of the original text, insert “Experimental results from NASA et al. show that the loss rate of the ceramic surface is about 270 um/kh in a combustion environment (1200°C; pressure 1013.25KPa; airflow velocity: 90 m/s)”. After line 64 of the original text, insert “BASA's volatilization loss for 1000h at 1400°C, 6atm total pressure and 24m/s gas flow rate is as high as 70μm. The third-generation rare earth silicate system has a high melting point, low thermal conductivity, and a coefficient of thermal expansion similar to that of silicon-based ceramic materials, as well as excellent thermal insulation properties. And according to research, it can serve thousands of hours in water vapor environment at 1482℃, with excellent water vapor corrosion resistance. Therefore, rare earth silicate materials are drawing more and more attention”

• It would be good if the manuscript reported the range of the gas flow rate and the shear force applied to the material.

Thank you very much for your suggestion. With your suggestion, we introduced the airflow velocity in the water vapor corrosion experiments in the introductory part of the article, and for the shear force acting on the material, after we thought about it, we chose not to carry out this aspect of the study for the time being since it is not covered in this article

• What are the characteristics of Re₂SiO₅that make it interesting for focused applications? (line 62)

Thank you for pointing this out. The main reason is that the Re2SiO5 has a high melting point, low thermal conductivity, a coefficient of thermal expansion similar to that of silicon-based ceramic materials, and excellent thermal insulation and corrosion resistance, which are also mentioned in the original article, line 65.

• Lines 78-79, “The mechanical and thermal properties of the material are greatly impacted by these features [18-20].” How? Please elaborate on the mentioned impacts.

Thank you for pointing this out. Explanation has been added after lines 78 and 79.“The rigidity of the [SiO₄] tetrahedra endows the material with a higher modulus of elasticity and lower coefficient of thermal expansion, and thus the material typically exhibits better structural stability. In contrast, the weaker bonding of the [REO₇] and [REO₆] units allows for increased flexibility of the material, but may result in higher coefficients of thermal expansion and lower modulus of elasticity.”

• Line 82, giving examples of quantitative data of the increased resistance to water corrosion will be helpful

Already added. “For example, K. NLEE experimentally showed that the water vapor corrosion resistance of Yb₂SiO₅ is greater than that of Lu₂SiO₅. And han et al. calculated the Si-O bond length of Yb₂SiO₅ to be 1.6137 Å by the first nature principle, which is smaller than the Si-O bond length of Lu₂SiO₅ of 1.6246 Å”

• Line 84, please give examples of “…the rare earth cations”.

Thank you for pointing this out. You can refer to the following literature, “Z. Tian, L. Zheng, J. Wang, P. Wan, J. Li, J. Wang, Theoretical and experimental determination of the major thermo-mechanical properties of RE₂SiO₅ (RE = Tb, Dy, Ho, Er, Tm, Yb, Lu, and Y) for environmental and thermal barrier coating applications, Journal of the European Ceramic Society 36(1) (2016) 189-202.”which has specific experiments as well as validation of the results. “For example, according to the experiments, RE₂SiO₅ increases the elastic modulus from Tb₂SiO₅ (143.72 Gpa) to Lu₂SiO₅ (171.3 Gpa) and the shear modulus from Tb₂SiO₅ (61 Gpa) to Lu₂SiO₅ (71 Gpa) as the radius of the rare earth elements decreases.”

• Lines 80-88, it is unclear why the information in the paragraph is presented and how it is related to this work.

“Han et al. [21]showed that the strength of Si-O bonds may be used to define the water corrosion vapor resistance of rare earth monosilicates, higher Si-O bond strength corresponds to increased resistance to water corrosion. The flexural strength, elastic modulus, and thermal shock resistance of monoclinic Re2SiO5 for orthosilicates are dependent on the mass and radius of the rare earth cations, as demonstrated by both experimental and Density Functional Theory (DFT) calculations [6]. Moreover, it is shown that the lowest thermal conductivity among doped elements is obtained by mixing rare earth disilicates in equimolar proportions; this prediction also holds true for monosilicate materials [22].”

Revised as follows: “For multi-component rare earth monosilicates the introduction of rare earth elements needs to be carefully selected, and different rare earth elements will have an impact on the Si-O bond strength and mechanical properties. It has been shown that the strength of Si-O bond is proportional to the water vapor corrosion resistance of multi-component rare earth monosilicates, and the higher the strength of Si-O bond, the stronger the water vapor corrosion resistance. For example, K. NLEE experimentally showed that the water vapor corrosion resistance of Yb₂SiO₅ is greater than that of Lu₂SiO₅. And han et al. calculated the Si-O bond length of Yb₂SiO₅ to be 1.6137 Å by the first nature principle, which is smaller than the Si-O bond length of Lu₂SiO₅ of 1.6246 Å[21]. The flexural strength, elastic modulus, and thermal shock resistance of monoclinic Re₂SiO₅ for orthosilicates are dependent on the mass and radius of the rare earth cations, as demonstrated by both experimental and Density Functional Theory (DFT) calculations. For example, according to the experiments, RE₂SiO₅ increases the elastic modulus from Tb₂SiO₅ (143.72 Gpa) to Lu₂SiO₅ (171.3 Gpa) and the shear modulus from Tb₂SiO₅ (61 Gpa) to Lu₂SiO₅ (71 Gpa) as the radius of the rare earth elements decreases”

• Lines 89, it is unclear why “the lattice structures and elastic properties” are focused on in this work.

“Using first-principles computations, the lattice structures and elastic properties of Yb₂SiO₅ and YbRESiO₅ (where RE = Sc, Y, Eu, Gd, Ho, Tm, Lu) were examined in this work.”

Thank you for pointing this out. Revised as follows: “In order to study the lattice distortions as well as the mechanical properties of Yb₂SiO₅ and YbRESiO₅ (where RE = Sc, Y, Eu, Gd, Ho, Tm, Lu), we calculated the crystal structures of the materials as well as the elasticity parameters using first principles.”

• Lines 91-92: “…, simulations of Si-O bond lengths”: What computation method/technique/theory is used in the investigation?

Thank you for pointing this out. For this problem, the computational principles, parameters, technique and theory have been introduced in Section 2.1 Computational models of this paper.

• Lines 95-96, it is unclear what exactly the studied mechanical and thermodynamic properties are. Please describe them specifically.

“Last but not least, this study can provide the theoretical framework for the creation of new EBCs materials by examining the effects of the combination of various rare earth elements on the crystalline structure, thermal characteristics, and mechanical properties of Yb₂SiO₅.”

Revised as follows: “Last but not least, by investigating the effects of crystal structure, coefficient of thermal expansion, thermal conductivity, and elastic constants of different rare-earth monosilicates, this study may provide a theoretical framework for the creation of novel EBC materials.”

2. The following terms need clarification and/or elaboration:
   • Aircraft engines' pressure ratios (line 31)
   • endurance thresholds (lines 32-33)
   • conventional high-temperature alloys (line 33)

“As the aviation sector develops, aircraft engines' pressure ratios rise in an effort to maximize efficiency, and internal gas temperatures have risen above the endurance thresholds of conventional high-temperature alloys”

Revised as follows: “As the aviation sector develops, thrust-weight ratio increases in new generation, internal gas temperatures exceed the bearing limits if nickel-based superalloys”

• two chemical degradation mechanisms (line 39)

“Due to two chemical degradation mechanisms, poor environmental durability still prevents them from being used in combustion environments: recession, which is the loss of silicon-based ceramics from repeated oxidation and volatilization when exposed to high-speed water vapor in turbines, and thermal corrosion, which is caused by alkaline salts in combustion atmospheres that can form liquid silicates and cause pits in silicon-based ceramics”

Revised as follows: “Poor environmental durability still prevents them from being used in combustion environments due to the presence of two chemical degradation mechanisms, recession and thermal corrosion. (i) Recession is the loss of silicon-based ceramics due to repeated oxidation and volatilization when exposed to high-velocity water vapor in a turbine. (ii) Thermal corrosion is caused by alkaline salts in the combustion environment, which form liquid silicates and cause craters in silicon-based ceramics.”

• alkaline salts (line 43)

An explanation of alkaline salts has been added after line 43. “Alkaline salts are salts formed by the reaction of an alkaline metal (e.g., sodium, potassium) or an alkaline earth metal (e.g., calcium, magnesium) with an acid.” And it is explained in detail in the “N. Rohbeck, P. Morrell, P. Xiao, Degradation of ytterbium disilicate environmental barrier coatings in high temperature steam atmosphere, Journal of the European Ceramic Society 39(10) (2019) 3153-3163.”

• low thermal expansion coefficient (line 53)
• low elastic modulus (line 54)

“Later, BSAS (1-xBaO-xSrO-Al₂O₃-2SiO₂, 0 ≤ x ≤ 1) materials with low thermal expansion coefficients and low elastic modulus were used to develop the second generation of EBCs.”

Revised as follows: “Later, BSAS (1-xBaO-xSrO-Al₂O₃-2SiO₂, 0 ≤ x ≤ 1) materials with low thermal expansion coefficients (4×10^-6·K^-1-5.15×10^-6·K^-1, and thus a close match with SiC,4.02×10^-6·K^-1) and low elastic modulus(60-70Gpa) were used to develop the second generation of EBCs.”

• high melting temperature (line 58)
• low temperature (line 58)

“With its high melting temperatures, low thermal conductivity, thermal expansion coefficients akin to those of silicon-based ceramics, superior thermal insulation, and corrosion resistance, the third-generation rare earth silicate system is drawing more and more attention”

Revised as follows: “The third-generation rare earth silicate system has a high melting point(1950℃), low thermal conductivity（2.3 W·m^-1·K^-1 -1.5 W·m^-1·K^-1）, and a coefficient of thermal expansion(6-8×10^-6·K^-1) similar to that of silicon-based ceramic materials(5×10^-6·K^-1).”

• thermal expansion coefficients (line 58): low or high?

Thank you for pointing this out. In this section it means matching the coefficient of thermal expansion of the rare earth monosilicates and the matrix.

• What are the X1 and X2 phases (line 62)?

Thank you for pointing this out. Explanation has been added after line 62. “All RE₂SiO₅ are monoclinic and stable as either space group P2₁/c or C2/c, which are generally termed the X1 and X2 structure.”

• Range of the atomic numbers of rare-earth elements (Re) (lines 64-65)

Already added after line 64-65

• low temperatures 
• high temperatures
• high temperatures

“the X1 phase is stable at low temperatures and the X2 phase emerges and is stable at high temperatures. Volume differences brought forth by changes in crystal shape affect stress fields and raise the possibility of cracking. Consequently, X2-phase monosilicates at high temperatures are frequently utilized in Environmental Barrier Coatings (EBCs)”

Revised as follows: “the X1 phase is stable at low temperatures(800℃-1200℃) and the X2 phase emerges and is stable at high temperatures（1550℃-1950℃）. Volume differences brought forth by changes in crystal shape affect stress fields and raise the possibility of cracking. Consequently, X2-phase monosilicates at high temperatures（1450℃-1550℃） are frequently utilized in Environmental Barrier Coatings (EBCs)” And it is explained in detail in the “Y. Wang, Y. Niu, X. Zhong, M. Shi, F. Mao, L. Zhang, Q. Li, X. Zheng, Water vapor corrosion behaviors of plasma sprayed RE_sSiO₅ (RE = Gd, Y, Er) coatings, Corrosion Science 167 (2020) 108529”

• The lowest thermal conductivity (line 86)

“Moreover, it is shown that the lowest thermal conductivity among doped elements is obtained by mixing rare earth disilicates in equimolar proportions; this prediction also holds true for monosilicate materials”

Thank you for pointing this out. After our careful consideration, we chose to delete this section since the effect of different ratios of rare-earth doping on the minimum thermal conductivity of the material is not discussed in this paper.

• Please briefly elaborate on “the first irreducible Brillouin zone” (line 120).

Already added after line120. “The first irreducible Brillouin zone is the smallest, uniquely defined region in reciprocal space that contains all the distinct momentum states of a crystal, crucial for simplifying electronic band structure calculations.”

• Please briefly elaborate on the “four sets of uniform strain configurations” (lines 133-135).

Already added after line135. “Four sets of uniform strain configurations (which refer to four different strain states applied in various directions and magnitudes to study changes in a material's structure and properties) were used to calculate the 13 independent elastic constants (c₁₁, c₂₂, c₃₃, c₄₄, c₅₅, c₆₆, c₁₂, c₁₃, c₂₃, c₁₅, c₂₅, c₃₅, and c₄₆) of Yb₂SiO₅”

• Please briefly elaborate on “the Hellmann-Feynman force” (lines 138-139).

Already added in lines 138-139. “Hellmann-Feynman force (which is the force on an atom or particle derived directly from the gradient of the potential energy with respect to atomic positions)”

• Please briefly elaborate on “the Mulliken population cutoff distance” (line 130).

Already added. “Mulliken population cutoff distance(which is the threshold distance used to determine which atomic contributions to electronic charge density are considered significant in the Mulliken population analysis)”

3. Please provide references for the following
   • Bloch waves (line 118)

Already added.

• Monkhorst-Pack technique (line 121)

Already added.

• local density approximation (LDA) (line 122)

Already added.

• Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization approach (lines 124-125)

Already added.

• Milman and Warren (lines 132-133)

Already added.

• Archimedes' method (line 178). Please also provide a brief elaboration.

Already added. “was determined using the Archimedes' method(which is using the principle of buoyancy to determine the volume of an irregularly shaped object)”

• Neumann-Kopp law (line 179). Please also provide a brief elaboration.

Already added. “Neumann-Kopp law(which states that the heat capacity of a substance is proportional to the number of atoms or molecules in a compound).”

4. In section 2.3, please clarify the known parameters and calculated variables in the equations for each system (rare-each compound).

Thank you for pointing this out. The parameters in the equations in section 2.3, such as ， ，， ，  ，  ， and  will be discussed in detail in the discussion section later in the paper, so after our careful consideration, we think that we can just list the calculation equations in this section without discussing the values of the experimental parameters and the trend, thank you again for your comments.

5. The value of properties should be reported, in parentheses, along with each compound mentioned.
   • Lines 254-255, the smallest unit cell volume, for example, “YbScSiO5 (750.4240 Å³) ＜YbHoSiO5 (794.8210 Å³) ＜…”

Already added. Revise as follow: “YbScSiO₅(750.4240 Å³)＜YbHoSiO₅(794.8210 Å³)＜Yb₂SiO₅(794.7620 Å³)＜YbTmSiO₅(800.1510 Å³)＜YbGdSiO₅(806.6770 Å³)＜YbYSiO₅(809.2980 Å³)＜YbLuSiO₅(812.4510 Å³)＜YbEuSiO₅(813.6240 Å³)”

• Lines 266-267: the average Re-O bond lengths in [ReO6] polyhedra

Already added. Revise as follow: “YbScSiO₅(2.10674 Å)＜YbHoSiO₅(2.21699Å)＜YbTmSiO₅(2.21344Å)＜Yb₂SiO₅(2.21750Å)＜YbLuSiO₅(2.24643Å)＜YbGdSiO₅(2.23314Å)＜YbEuSiO₅(2.23771Å).”

• Lines 268-269: Re-O bond lengths

Already added. Revise as follow: “YbScSiO₅(2.29198Å)＜Yb₂SiO₅(2.30098Å)＜YbTmSiO₅(2.30253Å)＜YbYSiO₅(2.31480Å)＜YbLuSiO₅(2.31456Å)＜YbHoSiO₅(2.32545Å)＜YbGdSiO₅(2.32157Å)＜YbEuSiO₅(2.33001Å).

• Lines 269-270: The lattice distortion in [ReO7]

Already added. Revise as follow:

• Lines 271-272: The lattice distortion in [ReO6] polyhedral

Already added. Revise as follow: “YbEuSiO₅(1.26024‰)＜YbGdSiO₅(1.27335‰)＜Yb₂SiO₅(1.63300‰)＜YbTmSiO₅(1.68259‰)＜YbLuSiO₅(1.82196‰) ＜YbYSiO₅(2.07000‰)＜YbHoSiO₅(2.37837‰)＜YbScSiO₅(3.31675‰).”

• Line 311: YbEuSiO5 has the longest Si-O bond length

Already added. Revise as follow: “YbEuSiO₅ has the longest Si-O bond length(0.61000 Å); 

• Line 312: it also has a lower Milliken population and bond density than Yb2SiO5

Already added. Revise as follow: “nevertheless, it also has a lower Milliken population (0.61000), and bond density(0.3794Å^-1) than Yb₂SiO₅”

• Lines 316-317: water vapor corrosion resistance of the eight different rare earth monociliates

Already added. Revise as follow: “YbLuSiO₅(0.3764Å^-1)＜YbEuSiO₅(0.3794Å^-1)＜YbGdSiO₅(0.3810Å^-1)＜YbYSiO₅(0.3811Å^-1)＜Yb₂SiO₅(0.3844Å^-1)＜YbTmSiO₅(0.3851Å^-1)＜YbHoSiO₅(0.3860 Å^-1)＜YbScSiO₅(0.3963Å^-1).”

• Lines 325-327: magnitude for average sound velocity and Debye temperature.

Already added. Revise as follow: “YbGdSiO₅(2875.6370m/s)＜YbEuSiO₅(3027.7198m/s)＜YbHoSiO₅(3047.4524m/s)＜YbTmSiO₅(3115.4777m/s)＜Yb₂SiO₅(3116.0476m/s)＜YbLuSiO₅(3136.1570m/s)＜YbYSiO₅(3282.3078 m/s)＜YbScSiO₅(3669.7119m/s); The ranking of Debye temperature is: YbGdSiO₅(367.7621K)＜YbEuSiO₅(392.4537K)＜YbHoSiO₅(394.2189K)＜YbTmSiO₅(395.7621K)＜Yb₂SiO₅(400.2373K)＜YbLuSiO₅(403.6193K)＜YbYSiO₅(419.4569K)＜YbScSiO₅(481.4030K )”

• Lines 327-328: Young’s modulus

Already added. Revise as follow: “YbGdSiO₅(125.8217Gpa)＜YbEuSiO₅(134.4732Gpa)＜YbHoSiO₅(139.7532Gpa)＜YbYSiO₅(145.4985Gpa)＜YbTmSiO₅(145.6084Gpa)＜YbLuSiO₅(151.7248Gpa)＜Yb₂SiO₅(153.4019Gpa)＜YbScSiO₅(162.0600Gpa)”

• Lines 363-364: unit cell volumes

Already added. Revise as follow: “YbScSiO₅(750.4240)＜Yb₂SiO₅(794.7620)＜YbEuSiO₅(813.6240)”

6. Other comments
   • Lines 41-42: I suggest showing (i) recession … and (ii) thermal corrosion in the long sentence to make the two properties noticeable to the reader.

Thank you for pointing out this. We agree with this comment. Revise as follow: “Poor environmental durability still prevents them from being used in combustion environments due to the presence of two chemical degradation mechanisms, recession and thermal corrosion. (i)Recession is the loss of silicon-based ceramics due to repeated oxidation and volatilization when exposed to high-velocity water vapor in a turbine. (ii)Thermal corrosion is caused by alkaline salts in the combustion environment, which form liquid silicates and cause craters in silicon-based ceramics.”

• Line 120, “2×3×4k” is unclear. Do you mean 2000x3000x4000?

Thank you for pointing out this. The k in this place is a computational parameter needed for first principles calculations, not a unit. Revise as follow “2×3×4”

• What is the unit of 1×10-3 (line 129)?

Thank you for pointing out this problem. Revise as follow: “1×10^-3 Å”

• In Table 1, please use the full word for the “Theo” (second column) and “Cal” (third column). Also, The Deviation (the fourth column) is unclear; please provide its definition to show which of the two is the reference value?

Thank you for pointing out problem. Already added. Revise as follow: “Deviation in this section is defined as the gap between the geometrically optimized lattice parameters of the material and the theoretical lattice parameters.”

• Equation (4) and line 251, please replace the term “M-O” with a simple term (e.g., MO) to avoid confusion

Thank you for pointing out problem. Already replaced.

• Some tables and figures (e.g., Table 4, Table 5, Figure 3, …) are not mentioned in the content. Please make sure that all the figures and tables are introduced.

Thank you for pointing out problem. Already replaced

• In Table 3, the list of “bond lengths” (the fourth column) is unclear. Please show the line to separate each row to avoid confusion.

Thank you for pointing out problem. Already replaced.

• In Table 7, what is the meaning of the dot before “Compound” (first column)?

Thank you for pointing out problem. The dot has been deleted. Revise as follow “Compound”

• In Figures 1-2: Please indicate the elements presented in different colors.

Thank you for pointing out problem. The symbols for each element have been added to the EDS element distribution map.

• I suggest presenting Figure 3 in bar charts

Thank you for pointing out problem. After our careful consideration, we think that the line graph is more responsive to the effect of different rare earth elements on the water vapor corrosion resistance of rare earth monosilicates, and it can better reflect the trend of the water vapor corrosion resistance of different materials. Thank you again for your suggestion.

• In Figures 7-8, the color and order of each item should be consistent.

Thank you for pointing out problem. Already replaced.

• In Figures 7 and 9, Please adjust the size of subfigures.

Thank you for pointing out problem. Already revised.

7. Please indicate the authors' contribution.

Thank you for pointing out this problem. Already added

Author Response File: Author Response.pdf