无机材料学报 ›› 2026, Vol. 41 ›› Issue (4): 445-454.DOI: 10.15541/jim20250272 CSTR: 32189.14.jim20250272
王禹贺1,2(
), 罗颐秀1(
), 郭会明3, 张广珩4, 张思岩4, 孙鲁超1, 王杰民1, 王京阳1(
)
收稿日期:2025-06-27
修回日期:2025-08-22
出版日期:2026-04-20
网络出版日期:2025-08-26
通讯作者:
罗颐秀, 项目研究员. E-mail: yxluo13s@imr.ac.cn;作者简介:王禹贺(2001-), 男, 硕士研究生. E-mail: yhwang23s@imr.ac.cn
基金资助:
WANG Yuhe1,2(
), LUO Yixiu1(
), GUO Huiming3, ZHANG Guangheng4, ZHANG Siyan4, SUN Luchao1, WANG Jiemin1, WANG Jingyang1(
)
Received:2025-06-27
Revised:2025-08-22
Published:2026-04-20
Online:2025-08-26
Contact:
LUO Yixiu, professor. E-mail: yxluo13s@imr.ac.cn;About author:WANG Yuhe (2001-), male, Master candidate. E-mail: yhwang23s@imr.ac.cn
Supported by:摘要:
应用于高推重比航空发动机热端部件的连续纤维增强碳化硅陶瓷基复合材料需采用热/环境障复合涂层(T/EBCs)进行防护。为了得到兼具低热导率、适配的热膨胀系数及良好的高温相稳定性的新型稀土氧化物热障涂层材料, 高熵化设计概念为其成分设计和性能调控提供了新思路和新契机。本研究针对复杂高熵陶瓷体系的结构建模和性能预测难题, 提出了一种基于特殊准随机结构(SQS)的新型高熵建模策略。该方法在保证计算精度的同时, 实现了对复杂结构陶瓷性能的快速预测。随后, 结合第一性原理计算方法, 预测并比较了四种高熵稀土氧化物材料的晶体结构、弹性性质及热物理性质, 重点揭示了不同稀土成分及Hf掺杂对材料低热导率性能的调控作用及原子尺度根源。本研究为航空发动机热端部件用T/EBCs材料的理论模拟和选材设计提供了科学思路与基础数据。
中图分类号:
王禹贺, 罗颐秀, 郭会明, 张广珩, 张思岩, 孙鲁超, 王杰民, 王京阳. 高熵稀土氧化物热障涂层材料弹性及热物性的第一性原理研究[J]. 无机材料学报, 2026, 41(4): 445-454.
WANG Yuhe, LUO Yixiu, GUO Huiming, ZHANG Guangheng, ZHANG Siyan, SUN Luchao, WANG Jiemin, WANG Jingyang. First-principles Investigation of Elastic and Thermophysical Properties of High-entropy Rare-earth Oxide Thermal Barrier Coating Materials[J]. Journal of Inorganic Materials, 2026, 41(4): 445-454.
图1 高熵稀土氧化物材料的晶体结构
Fig. 1 Crystal structures of high-entropy rare-earth oxide materials (a) C-RE2O3; (b) C-(REI1/4REII1/4REIII1/4REIV1/4)2O3; (c) C-(REI3/16REII3/16REIII3/16REIV3/16Hf1/4)2O3
| Compound | Method | a/Å | b/Å | c/Å | α/(°) | β/(°) | γ/(°) | ρ/(g•cm-3) |
|---|---|---|---|---|---|---|---|---|
| (Y1/4Ho1/4Er1/4Yb1/4)2O3 | Calc | 9.13 | 9.14 | 9.15 | 109.49 | 109.52 | 109.46 | 7.81 |
| (Er1/4Tm1/4Yb1/4Lu1/4)2O3 | Calc | 9.05 | 9.04 | 9.04 | 109.43 | 109.51 | 109.46 | 9.10 |
| (Y3/16Ho3/16Er3/16Yb3/16Hf1/4)2O3 | Calc | 9.01 | 9.06 | 9.01 | 109.34 | 109.37 | 109.55 | 8.43 |
| (Er3/16Tm3/16Yb3/16Lu3/16Hf1/4)2O3 | Calc | 8.92 | 9.00 | 8.98 | 109.53 | 109.74 | 109.47 | 9.46 |
表1 四种高熵稀土氧化物材料的计算晶格参数
Table 1 Calculated lattice parameters of four high-entropy rare-earth oxide materials
| Compound | Method | a/Å | b/Å | c/Å | α/(°) | β/(°) | γ/(°) | ρ/(g•cm-3) |
|---|---|---|---|---|---|---|---|---|
| (Y1/4Ho1/4Er1/4Yb1/4)2O3 | Calc | 9.13 | 9.14 | 9.15 | 109.49 | 109.52 | 109.46 | 7.81 |
| (Er1/4Tm1/4Yb1/4Lu1/4)2O3 | Calc | 9.05 | 9.04 | 9.04 | 109.43 | 109.51 | 109.46 | 9.10 |
| (Y3/16Ho3/16Er3/16Yb3/16Hf1/4)2O3 | Calc | 9.01 | 9.06 | 9.01 | 109.34 | 109.37 | 109.55 | 8.43 |
| (Er3/16Tm3/16Yb3/16Lu3/16Hf1/4)2O3 | Calc | 8.92 | 9.00 | 8.98 | 109.53 | 109.74 | 109.47 | 9.46 |
| Compound | c11 | c12 | c13 | c22 | c23 | c33 | c44 | c55 | c66 |
|---|---|---|---|---|---|---|---|---|---|
| (Y1/4Ho1/4Er1/4Yb1/4)2O3 | 244.79 | 95.97 | 95.90 | 240.43 | 101.79 | 239.03 | 69.14 | 62.94 | 63.10 |
| (Er1/4Tm1/4Yb1/4Lu1/4)2O3 | 257.22 | 100.81 | 99.30 | 251.14 | 107.11 | 250.74 | 72.87 | 66.14 | 66.16 |
| (Y3/16Ho3/16Er3/16Yb3/16Hf1/4)2O3 | 250.73 | 98.29 | 98.37 | 248.15 | 97.99 | 241.45 | 70.74 | 69.71 | 69.93 |
| (Er3/16Tm3/16Yb3/16Lu3/16Hf1/4)2O3 | 259.08 | 102.63 | 100.97 | 250.68 | 97.74 | 251.63 | 77.04 | 71.63 | 75.61 |
表2 四种高熵稀土氧化物材料的二阶弹性常数(GPa)
Table 2 Calculated second-order elastic coefficients of four high-entropy rare-earth oxide materials (GPa)
| Compound | c11 | c12 | c13 | c22 | c23 | c33 | c44 | c55 | c66 |
|---|---|---|---|---|---|---|---|---|---|
| (Y1/4Ho1/4Er1/4Yb1/4)2O3 | 244.79 | 95.97 | 95.90 | 240.43 | 101.79 | 239.03 | 69.14 | 62.94 | 63.10 |
| (Er1/4Tm1/4Yb1/4Lu1/4)2O3 | 257.22 | 100.81 | 99.30 | 251.14 | 107.11 | 250.74 | 72.87 | 66.14 | 66.16 |
| (Y3/16Ho3/16Er3/16Yb3/16Hf1/4)2O3 | 250.73 | 98.29 | 98.37 | 248.15 | 97.99 | 241.45 | 70.74 | 69.71 | 69.93 |
| (Er3/16Tm3/16Yb3/16Lu3/16Hf1/4)2O3 | 259.08 | 102.63 | 100.97 | 250.68 | 97.74 | 251.63 | 77.04 | 71.63 | 75.61 |
| Compound | B/GPa | G/GPa | E/GPa | Emax/GPa | Emin/GPa | Emax/Emin | G/B | ν/GPa |
|---|---|---|---|---|---|---|---|---|
| (Y1/4Ho1/4Er1/4Yb1/4)2O3 | 146 | 67 | 175 | 192 | 151 | 1.2753 | 0.4606 | 0.3004 |
| (Er1/4Tm1/4Yb1/4Lu1/4)2O3 | 153 | 71 | 183 | 201 | 159 | 1.2639 | 0.4624 | 0.2997 |
| (Y3/16Ho3/16Er3/16Yb3/16Hf1/4)2O3 | 148 | 72 | 185 | 197 | 174 | 1.1323 | 0.4852 | 0.2912 |
| (Er3/16Tm3/16Yb3/16Lu3/16Hf1/4)2O3 | 151 | 75 | 194 | 209 | 180 | 1.1605 | 0.4975 | 0.2866 |
表3 四种高熵稀土氧化物材料的弹性模量
Table 3 Calculated elastic modulus of four high-entropy rare-earth oxide materials
| Compound | B/GPa | G/GPa | E/GPa | Emax/GPa | Emin/GPa | Emax/Emin | G/B | ν/GPa |
|---|---|---|---|---|---|---|---|---|
| (Y1/4Ho1/4Er1/4Yb1/4)2O3 | 146 | 67 | 175 | 192 | 151 | 1.2753 | 0.4606 | 0.3004 |
| (Er1/4Tm1/4Yb1/4Lu1/4)2O3 | 153 | 71 | 183 | 201 | 159 | 1.2639 | 0.4624 | 0.2997 |
| (Y3/16Ho3/16Er3/16Yb3/16Hf1/4)2O3 | 148 | 72 | 185 | 197 | 174 | 1.1323 | 0.4852 | 0.2912 |
| (Er3/16Tm3/16Yb3/16Lu3/16Hf1/4)2O3 | 151 | 75 | 194 | 209 | 180 | 1.1605 | 0.4975 | 0.2866 |
图3 四种高熵稀土氧化物杨氏模量的3D形貌图和(001)、(010)、(100)投影图
Fig. 3 3D topography, (001), (010) and (100) projective pictures of Young's modulus of four high-entropy rare-earth oxides
| Compound | vs/(m·s-1) | vl/(m·s-1) | vm/(m·s-1) | ΘD/K | γ | αL/(×10-6, K-1) | kmin/(W·m-1·K-1) |
|---|---|---|---|---|---|---|---|
| (Y1/4Ho1/4Er1/4Yb1/4)2O3 | 2932 | 5489 | 3276 | 398 | 1.7749 | 11.4574 | 0.7567 |
| (Er1/4Tm1/4Yb1/4Lu1/4)2O3 | 2785 | 5207 | 3111 | 382 | 1.7707 | 11.2533 | 0.7334 |
| (Y3/16Ho3/16Er3/16Yb3/16Hf1/4)2O3 | 2915 | 5371 | 3253 | 400 | 1.7194 | 11.3375 | 0.7690 |
| (Er3/16Tm3/16Yb3/16Lu3/16Hf1/4)2O3 | 2823 | 5162 | 3148 | 390 | 1.6928 | 11.1577 | 0.7566 |
表4 四种高熵稀土氧化物材料的热物性参数
Table 4 Thermophysical parameters of four high-entropy rare-earth oxide materials
| Compound | vs/(m·s-1) | vl/(m·s-1) | vm/(m·s-1) | ΘD/K | γ | αL/(×10-6, K-1) | kmin/(W·m-1·K-1) |
|---|---|---|---|---|---|---|---|
| (Y1/4Ho1/4Er1/4Yb1/4)2O3 | 2932 | 5489 | 3276 | 398 | 1.7749 | 11.4574 | 0.7567 |
| (Er1/4Tm1/4Yb1/4Lu1/4)2O3 | 2785 | 5207 | 3111 | 382 | 1.7707 | 11.2533 | 0.7334 |
| (Y3/16Ho3/16Er3/16Yb3/16Hf1/4)2O3 | 2915 | 5371 | 3253 | 400 | 1.7194 | 11.3375 | 0.7690 |
| (Er3/16Tm3/16Yb3/16Lu3/16Hf1/4)2O3 | 2823 | 5162 | 3148 | 390 | 1.6928 | 11.1577 | 0.7566 |
| Parameter | 1-YHoErYb | 2-ErTmYbLu | 3-YHoErYbHf | 4-ErTmYbLuHf | Diff(1-3)/% | Diff(2-4)/% | Diff(1-2)/% | Diff(3-4)/% |
|---|---|---|---|---|---|---|---|---|
| kT | 898.98 | 892.94 | 1006.36 | 1050.75 | 12.07 | 17.70 | -0.68 | 4.32 |
| 1.44×10-12 | 1.62×10-12 | 1.49×10-12 | 1.62×10-12 | 3.15 | -0.01 | 11.90 | 8.48 | |
| ΘD3 | 6.31×107 | 5.58×107 | 6.40×107 | 5.95×107 | 1.36 | 6.69 | -11.69 | -7.05 |
| A(γ)/γ2 | 9.85×106 | 9.90×106 | 1.06×107 | 1.09×107 | 7.19 | 10.33 | 0.52 | 3.47 |
表5 四种高熵稀土氧化物材料的k~αT-1定量化关系及差异根源
Table 5 Quantitative relationship of k~αT-1 and origin of differences in four high-entropy rare-earth oxide materials
| Parameter | 1-YHoErYb | 2-ErTmYbLu | 3-YHoErYbHf | 4-ErTmYbLuHf | Diff(1-3)/% | Diff(2-4)/% | Diff(1-2)/% | Diff(3-4)/% |
|---|---|---|---|---|---|---|---|---|
| kT | 898.98 | 892.94 | 1006.36 | 1050.75 | 12.07 | 17.70 | -0.68 | 4.32 |
| 1.44×10-12 | 1.62×10-12 | 1.49×10-12 | 1.62×10-12 | 3.15 | -0.01 | 11.90 | 8.48 | |
| ΘD3 | 6.31×107 | 5.58×107 | 6.40×107 | 5.95×107 | 1.36 | 6.69 | -11.69 | -7.05 |
| A(γ)/γ2 | 9.85×106 | 9.90×106 | 1.06×107 | 1.09×107 | 7.19 | 10.33 | 0.52 | 3.47 |
| Site | RE1 | RE2 | |
|---|---|---|---|
| No.1 | NS | 4 | 12 |
| XS | XREⅠ=XREⅡ=XREⅢ= XREⅣ=1/4 | XREⅠ=XREⅡ=XREⅢ= XREIV=1/4 |
表S1 C-(REⅠ1/4REⅡ1/4REⅢ1/4REⅣ1/4)2O3的亚晶格位点数和成分组成
Table S1 Number of sites on sublattice and composition for C-(REⅠ1/4REⅡ1/4REⅢ1/4REⅣ1/4)2O3
| Site | RE1 | RE2 | |
|---|---|---|---|
| No.1 | NS | 4 | 12 |
| XS | XREⅠ=XREⅡ=XREⅢ= XREⅣ=1/4 | XREⅠ=XREⅡ=XREⅢ= XREIV=1/4 |
| Site | RE1 | RE2 | |
|---|---|---|---|
| No.1 | NS | 4 | 12 |
| XS | XREⅠ=0 XREⅡ=XREⅢ=XREⅣ= XHf =1/4 | XREⅠ=XHf=1/4 XREⅡ=XREⅢ=XREⅣ= 1/6 | |
| No.2 | NS | 4 | 12 |
| XS | XREⅡ=0 XREⅠ=XREⅢ=XREⅣ= XHf=1/4 | XREⅡ=XHf=1/4 XREⅠ=XREⅢ=XREⅣ= 1/6 | |
| No.3 | NS | 4 | 12 |
| XS | XREⅢ=0 XREⅠ=XREⅡ=XREⅣ= XHf=1/4 | XREⅢ=XHf=1/4 XREⅠ=XREⅡ=XREⅣ= 1/6 | |
| No.4 | NS | 4 | 12 |
| XS | XREⅣ=0 XREⅠ=XREⅡ=XREⅢ= XHf=1/4 | XREⅣ=XHf=1/4 XREⅠ=XREⅡ=XREⅢ= 1/6 | |
| No.5 | NS | 4 | 12 |
| XS | XHf=0 XREⅠ=XREⅡ=XREⅢ= XREⅣ=1/4 | XHf=1/3 XREⅠ=XREⅡ=XREⅢ= XREⅣ=1/6 |
表S2 C-(REⅠ3/16REⅡ3/16REⅢ3/16REⅣ3/16Hf1/4)2O3的亚晶格位点数和成分组成
Table S2 Number of sites on sublattice and composition for C-(REⅠ3/16REⅡ3/16REⅢ3/16REⅣ3/16Hf1/4)2O3
| Site | RE1 | RE2 | |
|---|---|---|---|
| No.1 | NS | 4 | 12 |
| XS | XREⅠ=0 XREⅡ=XREⅢ=XREⅣ= XHf =1/4 | XREⅠ=XHf=1/4 XREⅡ=XREⅢ=XREⅣ= 1/6 | |
| No.2 | NS | 4 | 12 |
| XS | XREⅡ=0 XREⅠ=XREⅢ=XREⅣ= XHf=1/4 | XREⅡ=XHf=1/4 XREⅠ=XREⅢ=XREⅣ= 1/6 | |
| No.3 | NS | 4 | 12 |
| XS | XREⅢ=0 XREⅠ=XREⅡ=XREⅣ= XHf=1/4 | XREⅢ=XHf=1/4 XREⅠ=XREⅡ=XREⅣ= 1/6 | |
| No.4 | NS | 4 | 12 |
| XS | XREⅣ=0 XREⅠ=XREⅡ=XREⅢ= XHf=1/4 | XREⅣ=XHf=1/4 XREⅠ=XREⅡ=XREⅢ= 1/6 | |
| No.5 | NS | 4 | 12 |
| XS | XHf=0 XREⅠ=XREⅡ=XREⅢ= XREⅣ=1/4 | XHf=1/3 XREⅠ=XREⅡ=XREⅢ= XREⅣ=1/6 |
| Compound | Unit | Average bond length/Å | |
|---|---|---|---|
| (Y1/4Ho1/4Er1/4Yb1/4)2O3 | YO6 | 2.2868 | |
| HoO6 | 2.2794 | ||
| ErO6 | 2.2700 | ||
| YbO6 | 2.2518 | ||
| REO6 | 2.2720 | ||
| (Er1/4Tm1/4Yb1/4Lu1/4)2O3 | ErO6 | 2.2631 | |
| TmO6 | 2.2535 | ||
| YbO6 | 2.2446 | ||
| LuO6 | 2.2356 | ||
| REO6 | 2.2492 | ||
| (Y3/16Ho3/16Er3/16Yb3/16Hf1/4)2O3 | YO6 | 2.2991 | |
| HoO6 | 2.2880 | ||
| ErO6 | 2.2794 | ||
| YbO6 | 2.2451 | ||
| REO6 | 2.2779 | ||
| HfO6 | 2.1893 | ||
| XO6* | 2.2558 | ||
| (Er3/16Tm3/16Yb3/16Lu3/16Hf1/4)2O3 | ErO6 | 2.2684 | |
| TmO6 | 2.2541 | ||
| YbO6 | 2.2437 | ||
| LuO6 | 2.2399 | ||
| REO6 | 2.2515 | ||
| HfO6 | 2.1936 | ||
| XO6* | 2.2370 | ||
表S3 四种高熵稀土氧化物材料多面体结构单元的平均键长
Table S3 Average bond length of polyhedral of four high-entropy rare-earth oxide materials
| Compound | Unit | Average bond length/Å | |
|---|---|---|---|
| (Y1/4Ho1/4Er1/4Yb1/4)2O3 | YO6 | 2.2868 | |
| HoO6 | 2.2794 | ||
| ErO6 | 2.2700 | ||
| YbO6 | 2.2518 | ||
| REO6 | 2.2720 | ||
| (Er1/4Tm1/4Yb1/4Lu1/4)2O3 | ErO6 | 2.2631 | |
| TmO6 | 2.2535 | ||
| YbO6 | 2.2446 | ||
| LuO6 | 2.2356 | ||
| REO6 | 2.2492 | ||
| (Y3/16Ho3/16Er3/16Yb3/16Hf1/4)2O3 | YO6 | 2.2991 | |
| HoO6 | 2.2880 | ||
| ErO6 | 2.2794 | ||
| YbO6 | 2.2451 | ||
| REO6 | 2.2779 | ||
| HfO6 | 2.1893 | ||
| XO6* | 2.2558 | ||
| (Er3/16Tm3/16Yb3/16Lu3/16Hf1/4)2O3 | ErO6 | 2.2684 | |
| TmO6 | 2.2541 | ||
| YbO6 | 2.2437 | ||
| LuO6 | 2.2399 | ||
| REO6 | 2.2515 | ||
| HfO6 | 2.1936 | ||
| XO6* | 2.2370 | ||
| Material | 1-YHoErYb | 2-ErTmYbLu | 3-YHoErYbHf | 4-ErTmYbLuHf |
|---|---|---|---|---|
| s11 | 0.005239 | 0.004968 | 0.005147 | 0.005011 |
| s12 | -0.001469 | -0.001396 | -0.001445 | -0.001504 |
| s13 | -0.001491 | -0.001365 | -0.001516 | -0.001426 |
| s14 | -0.000049 | -0.000006 | -0.000043 | -0.000120 |
| s15 | -0.000082 | -0.000019 | 0.000079 | 0.000086 |
| s16 | 0.000013 | 0.000002 | 0.000050 | -0.000122 |
| s22 | 0.005544 | 0.005321 | 0.005213 | 0.005182 |
| s23 | -0.001794 | -0.001739 | -0.001541 | -0.001420 |
| s24 | -0.000058 | 0.000003 | 0.000073 | -0.000020 |
| s25 | 0.000077 | -0.000031 | -0.000081 | -0.000353 |
| s26 | 0.000974 | 0.000913 | 0.000381 | 0.000603 |
| s33 | 0.005584 | 0.005303 | 0.005388 | 0.005103 |
| s34 | 0.000051 | -0.000014 | 0.000040 | 0.000062 |
| s35 | 0.000000 | 0.000049 | 0.000058 | 0.000069 |
| s36 | -0.000990 | -0.000888 | -0.000400 | -0.000397 |
| s44 | 0.014726 | 0.013938 | 0.014169 | 0.012992 |
| s45 | -0.002028 | -0.001789 | -0.000457 | -0.000304 |
| s46 | 0.000017 | -0.000002 | -0.000460 | 0.000002 |
| s55 | 0.016174 | 0.015356 | 0.014366 | 0.014004 |
| s56 | -0.000060 | 0.000077 | -0.000237 | -0.000343 |
| s66 | 0.016120 | 0.015338 | 0.014369 | 0.013311 |
表S4 四种高熵稀土氧化物材料的柔度系数
Table S4 Elastic compliance constants of four high-entropy rare-earth oxide materials
| Material | 1-YHoErYb | 2-ErTmYbLu | 3-YHoErYbHf | 4-ErTmYbLuHf |
|---|---|---|---|---|
| s11 | 0.005239 | 0.004968 | 0.005147 | 0.005011 |
| s12 | -0.001469 | -0.001396 | -0.001445 | -0.001504 |
| s13 | -0.001491 | -0.001365 | -0.001516 | -0.001426 |
| s14 | -0.000049 | -0.000006 | -0.000043 | -0.000120 |
| s15 | -0.000082 | -0.000019 | 0.000079 | 0.000086 |
| s16 | 0.000013 | 0.000002 | 0.000050 | -0.000122 |
| s22 | 0.005544 | 0.005321 | 0.005213 | 0.005182 |
| s23 | -0.001794 | -0.001739 | -0.001541 | -0.001420 |
| s24 | -0.000058 | 0.000003 | 0.000073 | -0.000020 |
| s25 | 0.000077 | -0.000031 | -0.000081 | -0.000353 |
| s26 | 0.000974 | 0.000913 | 0.000381 | 0.000603 |
| s33 | 0.005584 | 0.005303 | 0.005388 | 0.005103 |
| s34 | 0.000051 | -0.000014 | 0.000040 | 0.000062 |
| s35 | 0.000000 | 0.000049 | 0.000058 | 0.000069 |
| s36 | -0.000990 | -0.000888 | -0.000400 | -0.000397 |
| s44 | 0.014726 | 0.013938 | 0.014169 | 0.012992 |
| s45 | -0.002028 | -0.001789 | -0.000457 | -0.000304 |
| s46 | 0.000017 | -0.000002 | -0.000460 | 0.000002 |
| s55 | 0.016174 | 0.015356 | 0.014366 | 0.014004 |
| s56 | -0.000060 | 0.000077 | -0.000237 | -0.000343 |
| s66 | 0.016120 | 0.015338 | 0.014369 | 0.013311 |
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