J. Mater. Sci. Technol. ›› 2019, Vol. 35 ›› Issue (5): 833-851.DOI: 10.1016/j.jmst.2018.11.016
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Bin Liua, Yuchen Liua, Changhua Zhua, Huimin Xiangb, Hongfei Chena, Luchao Sunc, Yanfeng Gaoa, Yanchun Zhoub?()
Received:
2018-07-06
Accepted:
2018-10-09
Online:
2019-05-10
Published:
2019-02-20
Contact:
Zhou Yanchun
About author:
1 These authors contribute equally to this paper.
Bin Liu, Yuchen Liu, Changhua Zhu, Huimin Xiang, Hongfei Chen, Luchao Sun, Yanfeng Gao, Yanchun Zhou. Advances on strategies for searching for next generation thermal barrier coating materials[J]. J. Mater. Sci. Technol., 2019, 35(5): 833-851.
Compound | κcal | κexp | Compound | κcal | κexp |
---|---|---|---|---|---|
La2Zr2O7 | κmin?=?1.3 | κmin?=?1.5 | Gd2Zr2O7 | κmin?=?1.2 | κmin?=?1.3 |
Al5BO9 | κmin?=?1.59 | Yb2SiO5 | κ1200K?=?0.74 | κ1200K?=?1.5 | |
ZrSiO4 | κ1773K?=?1.75 κmin?=?1.54 | κ1773K?=?4 | HfSiO4 | κmin?=?1.24 | |
SrZrO3 | κmin?=?1.37 | κ1273K?=?2.08 | BaZrO3 | κmin?=?1.24 | κ1150K?=?3.42 |
Y4Al2O9 | κ1150K?=?1.13 | κ1150K?=?1.95 | YbAlO3 | κmin?=?1.15 | |
YAlO3 | κmin?=?1.61 | Y2SiO5 | κmin?=?1.13 | κ1200K?=?1.22 | |
γ-Y2Si2O7 | κmin?=?1.35 | κ1400K?=?1.9 | Yb3Al5O12 | κ1200K?=?1.22 | κ1200K?=?2.16 |
TiP2O7 | κmin?=?1.52 | HfP2O7 | κmin?=?0.99 | ||
ZrP2O7 | κmin?=?1.15 | κ?=?0.5~2 | β-Yb2Si2O7 | κmin?=?1.18 | κ1273K?=?2.1 |
AlPO4 | κmin?=?1.2 | GaPO4 | κmin?=?0.88 | ||
GdPO4 | κ1000K?=?0.98 | κ1000K?=?1.68 | LaPO4 | κ1273K?=?1.31 | κ1273K?=?1.09 |
La2SrAl2O7 | κ1273K?=?2.79 | κ1273K?=?2.49 | Gd2SrAl2O7 | κmin?=?2.22 | κ1273K?=?2.14 |
La2Sn2O7 | κ1273K?=?1.61 | κ1273K?=?1.96 | Gd2Sn2O7 | κ1273K?=?1.76 | κ1273K?=?2.07 |
Table 1 Calculated and experimentally determined thermal conductivities (in W/m·K) of some promising TBC materials [3,7,9,12,23,[32], [33], [34],[39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57]].
Compound | κcal | κexp | Compound | κcal | κexp |
---|---|---|---|---|---|
La2Zr2O7 | κmin?=?1.3 | κmin?=?1.5 | Gd2Zr2O7 | κmin?=?1.2 | κmin?=?1.3 |
Al5BO9 | κmin?=?1.59 | Yb2SiO5 | κ1200K?=?0.74 | κ1200K?=?1.5 | |
ZrSiO4 | κ1773K?=?1.75 κmin?=?1.54 | κ1773K?=?4 | HfSiO4 | κmin?=?1.24 | |
SrZrO3 | κmin?=?1.37 | κ1273K?=?2.08 | BaZrO3 | κmin?=?1.24 | κ1150K?=?3.42 |
Y4Al2O9 | κ1150K?=?1.13 | κ1150K?=?1.95 | YbAlO3 | κmin?=?1.15 | |
YAlO3 | κmin?=?1.61 | Y2SiO5 | κmin?=?1.13 | κ1200K?=?1.22 | |
γ-Y2Si2O7 | κmin?=?1.35 | κ1400K?=?1.9 | Yb3Al5O12 | κ1200K?=?1.22 | κ1200K?=?2.16 |
TiP2O7 | κmin?=?1.52 | HfP2O7 | κmin?=?0.99 | ||
ZrP2O7 | κmin?=?1.15 | κ?=?0.5~2 | β-Yb2Si2O7 | κmin?=?1.18 | κ1273K?=?2.1 |
AlPO4 | κmin?=?1.2 | GaPO4 | κmin?=?0.88 | ||
GdPO4 | κ1000K?=?0.98 | κ1000K?=?1.68 | LaPO4 | κ1273K?=?1.31 | κ1273K?=?1.09 |
La2SrAl2O7 | κ1273K?=?2.79 | κ1273K?=?2.49 | Gd2SrAl2O7 | κmin?=?2.22 | κ1273K?=?2.14 |
La2Sn2O7 | κ1273K?=?1.61 | κ1273K?=?1.96 | Gd2Sn2O7 | κ1273K?=?1.76 | κ1273K?=?2.07 |
c11 | c12 | c44 | B | G | E | Z | c12-c44 | G/B | |
---|---|---|---|---|---|---|---|---|---|
La2Ge2O7 | 315 | 143 | 111 | 200 | 100 | 258 | 1.29 | 32 | 0.5 |
La2Ti2O7 | 314 | 141 | 107 | 199 | 99 | 253 | 1.24 | 34 | 0.497 |
La2Sn2O7 | 299 | 136 | 106 | 190 | 95 | 245 | 1.29 | 30 | 0.5 |
La2Zr2O7 | 289 | 124 | 100 | 179 | 93 | 237 | 1.21 | 24 | 0.520 |
La2Hf2O7 | 286 | 126 | 94 | 180 | 88 | 228 | 1.18 | 32 | 0.489 |
Table 2 Elastic constants and mechanical properties (GPa) of La2T2O7 (T=Ge, Ti, Sn, Zr and Hf) [9,10].
c11 | c12 | c44 | B | G | E | Z | c12-c44 | G/B | |
---|---|---|---|---|---|---|---|---|---|
La2Ge2O7 | 315 | 143 | 111 | 200 | 100 | 258 | 1.29 | 32 | 0.5 |
La2Ti2O7 | 314 | 141 | 107 | 199 | 99 | 253 | 1.24 | 34 | 0.497 |
La2Sn2O7 | 299 | 136 | 106 | 190 | 95 | 245 | 1.29 | 30 | 0.5 |
La2Zr2O7 | 289 | 124 | 100 | 179 | 93 | 237 | 1.21 | 24 | 0.520 |
La2Hf2O7 | 286 | 126 | 94 | 180 | 88 | 228 | 1.18 | 32 | 0.489 |
Fig. 5 (a) Calculated temperature dependent thermal conductivities of La2T2O7 pyrochlore, where κmin are from ref [10]; and (b) comparison of calculated and experimental values [6,55] of La2Zr2O7 and La2Sn2O7.
Fig. 6 Minimum thermal conductivities of polycrystalline La2T2O7 pyrochlore together with their minimum thermal conductivities along specific crystalline directions.
c11 | c12 | c44 | B | G | E | Z | c12-c44 | G/B | |
---|---|---|---|---|---|---|---|---|---|
Rare earth stannates | |||||||||
La2Sn2O7 | 297 | 125 | 97 | 182 | 93 | 238 | 1.13 | 28 | 0.508 |
Nd2Sn2O7 | 314 | 124 | 94 | 187 | 94 | 242 | 0.99 | 30 | 0.504 |
Sm2Sn2O7 | 317 | 123 | 95 | 188 | 96 | 246 | 0.98 | 28 | 0.51 |
Gd2Sn2O7 | 301 | 115 | 99 | 177 | 97 | 245 | 1.06 | 16 | 0.546 |
Er2Sn2O7 | 323 | 122 | 98 | 189 | 99 | 253 | 0.97 | 24 | 0.524 |
Yb2Sn2O7 | 306 | 106 | 94 | 173 | 96 | 244 | 0.94 | 12 | 0.558 |
Rare earth zirconates | |||||||||
La2Zr2O7 | 282 | 122 | 92 | 176 | 87 | 224 | 1.15 | 30 | 0.494 |
Pr2Zr2O7 | 273 | 96 | 114 | 155 | 103 | 253 | 1.29 | -18 | 0.665 |
Nd2Zr2O7 | 243 | 69 | 47 | 127 | 60 | 156 | 0.54 | 22 | 0.472 |
Sm2Zr2O7 | 328 | 132 | 101 | 197 | 100 | 257 | 1.03 | 31 | 0.508 |
Eu2Zr2O7 | 281 | 83 | 51 | 149 | 67 | 175 | 0.52 | 32 | 0.45 |
Gd2Zr2O7 | 277 | 110 | 52 | 165 | 63 | 168 | 0.62 | 58 | 0.382 |
Table 3 Elastic constants and mechanical properties (GPa) of rare earth stannates and rare earth zirconates [26,55,63,64].
c11 | c12 | c44 | B | G | E | Z | c12-c44 | G/B | |
---|---|---|---|---|---|---|---|---|---|
Rare earth stannates | |||||||||
La2Sn2O7 | 297 | 125 | 97 | 182 | 93 | 238 | 1.13 | 28 | 0.508 |
Nd2Sn2O7 | 314 | 124 | 94 | 187 | 94 | 242 | 0.99 | 30 | 0.504 |
Sm2Sn2O7 | 317 | 123 | 95 | 188 | 96 | 246 | 0.98 | 28 | 0.51 |
Gd2Sn2O7 | 301 | 115 | 99 | 177 | 97 | 245 | 1.06 | 16 | 0.546 |
Er2Sn2O7 | 323 | 122 | 98 | 189 | 99 | 253 | 0.97 | 24 | 0.524 |
Yb2Sn2O7 | 306 | 106 | 94 | 173 | 96 | 244 | 0.94 | 12 | 0.558 |
Rare earth zirconates | |||||||||
La2Zr2O7 | 282 | 122 | 92 | 176 | 87 | 224 | 1.15 | 30 | 0.494 |
Pr2Zr2O7 | 273 | 96 | 114 | 155 | 103 | 253 | 1.29 | -18 | 0.665 |
Nd2Zr2O7 | 243 | 69 | 47 | 127 | 60 | 156 | 0.54 | 22 | 0.472 |
Sm2Zr2O7 | 328 | 132 | 101 | 197 | 100 | 257 | 1.03 | 31 | 0.508 |
Eu2Zr2O7 | 281 | 83 | 51 | 149 | 67 | 175 | 0.52 | 32 | 0.45 |
Gd2Zr2O7 | 277 | 110 | 52 | 165 | 63 | 168 | 0.62 | 58 | 0.382 |
Y4Al2O9 [ | YAlO3 [ | Y3Al5O12 [ | Yb4Al2O9 [ | YbAlO3 [ | Yb3Al5O12 [ | |
---|---|---|---|---|---|---|
c11 | 251 | 396 | 348 | 199 | 265 | 294 |
c22 | 225 | 310 | 348 | 195 | 330 | 294 |
c33 | 222 | 367 | 348 | 192 | 352 | 294 |
c44 | 74 | 174 | 116 | 55 | 122 | 97 |
c55 | 71 | 152 | 116 | 56 | 84 | 97 |
c66 | 89 | 110 | 116 | 67 | 141 | 97 |
c12 | 79 | 133 | 116 | 74 | 145 | 108 |
c13 | 82 | 153 | 116 | 78 | 133 | 108 |
c23 | 88 | 139 | 116 | 80 | 162 | 108 |
c15 | 11 | 8 | ||||
c25 | 10 | 3 | ||||
c35 | 4 | 8 | ||||
c46 | -0.5 | -0.9 | ||||
B | 132 | 213 | 193 | 116 | 201 | 163 |
G | 76 | 127 | 116 | 59 | 100 | 104 |
E | 191 | 318 | 290 | 151 | 257 | 257 |
ν | 0.26 | 0.25 | 0.25 | 0.28 | 0.287 | 0.24 |
G/B | 0.576 | 0.596 | 0.601 | 0.508 | 0.496 | 0.64 |
Table 4 Elastic constants and mechanical properties (GPa) of rare earth aluminum oxides.
Y4Al2O9 [ | YAlO3 [ | Y3Al5O12 [ | Yb4Al2O9 [ | YbAlO3 [ | Yb3Al5O12 [ | |
---|---|---|---|---|---|---|
c11 | 251 | 396 | 348 | 199 | 265 | 294 |
c22 | 225 | 310 | 348 | 195 | 330 | 294 |
c33 | 222 | 367 | 348 | 192 | 352 | 294 |
c44 | 74 | 174 | 116 | 55 | 122 | 97 |
c55 | 71 | 152 | 116 | 56 | 84 | 97 |
c66 | 89 | 110 | 116 | 67 | 141 | 97 |
c12 | 79 | 133 | 116 | 74 | 145 | 108 |
c13 | 82 | 153 | 116 | 78 | 133 | 108 |
c23 | 88 | 139 | 116 | 80 | 162 | 108 |
c15 | 11 | 8 | ||||
c25 | 10 | 3 | ||||
c35 | 4 | 8 | ||||
c46 | -0.5 | -0.9 | ||||
B | 132 | 213 | 193 | 116 | 201 | 163 |
G | 76 | 127 | 116 | 59 | 100 | 104 |
E | 191 | 318 | 290 | 151 | 257 | 257 |
ν | 0.26 | 0.25 | 0.25 | 0.28 | 0.287 | 0.24 |
G/B | 0.576 | 0.596 | 0.601 | 0.508 | 0.496 | 0.64 |
Fig. 11 Temperature dependent thermal conductivities of (a) Y4Al2O9, YAlO3 and Y3Al5O12 and (b) Yb4Al2O9, YbAlO3 and Yb3Al5O12, together with available experimental values [[46], [47], [48],50,79,80,85,86].
Fig. 12 Minimum thermal conductivities of polycrystalline and those along specific crystalline directions of (a) yttrium aluminum oxides and (b) ytterbium aluminum oxides.
Constants | SrTiO3 | SrZrO3 | SrHfO3 | BaTiO3 | BaZrO3 | BaHfO3 |
---|---|---|---|---|---|---|
c11 | 346.1 | 340.2 | 399.6 | 315.8 | 299.7 | 379.6 |
c12 | 101.3 | 75.5 | 59.9 | 109.5 | 61.1 | 69.7 |
c44 | 114.4 | 74.3 | 61.3 | 127.0 | 86.9 | 72.4 |
B | 183.0 | 163.7 | 173.6 | 178.1 | 140.6 | 173.0 |
G | 117.5 | 93.8 | 92.7 | 116.9 | 98.7 | 98.8 |
E | 290.4 | 236.2 | 236.2 | 287.8 | 239.9 | 248.9 |
ν | 0.24 | 0.26 | 0.27 | 0.23 | 0.22 | 0.26 |
Z | 0.93 | 0.56 | 0.36 | 1.23 | 0.72 | 0.46 |
HV | 16.35. | 11.85 | 10.59 | 16.81 | 16.40 | 12.24 |
G/B | 0.642 | 0.573 | 0.534 | 0.656 | 0.702 | 0.571 |
κmin | 1.74 | 1.37 | 1.15 | 1.52 | 1.24 | 1.09 |
Table 5 Elastic constants, mechanical properties (GPa) and thermal conductivity (W/m·K) of cubic perovskite oxides [57].
Constants | SrTiO3 | SrZrO3 | SrHfO3 | BaTiO3 | BaZrO3 | BaHfO3 |
---|---|---|---|---|---|---|
c11 | 346.1 | 340.2 | 399.6 | 315.8 | 299.7 | 379.6 |
c12 | 101.3 | 75.5 | 59.9 | 109.5 | 61.1 | 69.7 |
c44 | 114.4 | 74.3 | 61.3 | 127.0 | 86.9 | 72.4 |
B | 183.0 | 163.7 | 173.6 | 178.1 | 140.6 | 173.0 |
G | 117.5 | 93.8 | 92.7 | 116.9 | 98.7 | 98.8 |
E | 290.4 | 236.2 | 236.2 | 287.8 | 239.9 | 248.9 |
ν | 0.24 | 0.26 | 0.27 | 0.23 | 0.22 | 0.26 |
Z | 0.93 | 0.56 | 0.36 | 1.23 | 0.72 | 0.46 |
HV | 16.35. | 11.85 | 10.59 | 16.81 | 16.40 | 12.24 |
G/B | 0.642 | 0.573 | 0.534 | 0.656 | 0.702 | 0.571 |
κmin | 1.74 | 1.37 | 1.15 | 1.52 | 1.24 | 1.09 |
Fig. 14 Theoretical Young’s modulus and thermal conductivity of perovskites as the function of the electronegativity discrepancy between ‘A’ and ‘B’ site atoms in perovskites [57].
α-AlPO4 | α-GaPO4 | β-AlPO4 | β-GaPO4 | |
---|---|---|---|---|
c11 | 70.9 | 79.8 | 170.9 | 149.3 |
c33 | 81.2 | 106.3 | 179.6 | 165.9 |
c44 | 45.7 | 39.9 | 33.8 | 49.9 |
c66 | 31.6 | 31.6 | 44.7 | 32.7 |
c12 | 7.7 | 16.6 | 81.4 | 83.8 |
c13 | 9.9 | 30.6 | 110.4 | 109.9 |
c14 | 11.3 | -3.2 | ||
B | 30.8 | 45.8 | 126.2 | 117.5 |
G | 36.8 | 34.3 | 48.2 | 35.2 |
E | 77.4 | 82.4 | 128.2 | 96 |
ν | 0.08 | 0.20 | 0.33 | 0.36 |
G/B | 1.16 | 0.75 | 0.38 | 0.30 |
Table 6 Elastic constants and mechanical properties (in GPa) of α-?and β-MPO4 (M=Al, Ga) [23].
α-AlPO4 | α-GaPO4 | β-AlPO4 | β-GaPO4 | |
---|---|---|---|---|
c11 | 70.9 | 79.8 | 170.9 | 149.3 |
c33 | 81.2 | 106.3 | 179.6 | 165.9 |
c44 | 45.7 | 39.9 | 33.8 | 49.9 |
c66 | 31.6 | 31.6 | 44.7 | 32.7 |
c12 | 7.7 | 16.6 | 81.4 | 83.8 |
c13 | 9.9 | 30.6 | 110.4 | 109.9 |
c14 | 11.3 | -3.2 | ||
B | 30.8 | 45.8 | 126.2 | 117.5 |
G | 36.8 | 34.3 | 48.2 | 35.2 |
E | 77.4 | 82.4 | 128.2 | 96 |
ν | 0.08 | 0.20 | 0.33 | 0.36 |
G/B | 1.16 | 0.75 | 0.38 | 0.30 |
Fig. 17 (a) Temperature dependent thermal conductivities of α-?and β-MPO4 (M = Al, Ga); (b) their minimum thermal conductivities of polycrystalline together with minimum thermal conductivities along specific crystalline directions.
TiP2O7 | ZrP2O7 | HfP2O7 | α-Mg2Al4Si5O18 | β-Mg2Al4Si5O18 | |
---|---|---|---|---|---|
c11 | 301 | 250 | 255 | 232 | 220 |
c22 | 301 | 250 | 255 | 232 | 214 |
c33 | 301 | 250 | 255 | 200 | 190 |
c44 | 77 | 48 | 45 | 54 | 54 |
c55 | 77 | 48 | 45 | 54 | 48 |
c66 | 77 | 48 | 45 | 65 | 64 |
c12 | 100 | 95 | 89 | 103 | 102 |
c13 | 100 | 95 | 89 | 103 | 97 |
c23 | 100 | 95 | 89 | 103 | 100 |
B | 167 | 146 | 144 | 142 | 136 |
G | 85 | 58 | 58 | 58 | 55 |
E | 219 | 154 | 153 | 154 | 144 |
ν | 0.32 | 0.27 | 0.28 | 0.32 | 0.32 |
G/B | 0.51 | 0.40 | 0.40 | 0.409 | 0.402 |
κmin | 1.52 | 1.15 | 0.99 | 1.33 | 1.29 |
Table 7 Elastic constants, mechanical properties (GPa) and thermal conductivity (W/m·K) of MP2O7 (M=Ti, Zr and Hf) and Mg2Al4Si5O18 [49,51,98].
TiP2O7 | ZrP2O7 | HfP2O7 | α-Mg2Al4Si5O18 | β-Mg2Al4Si5O18 | |
---|---|---|---|---|---|
c11 | 301 | 250 | 255 | 232 | 220 |
c22 | 301 | 250 | 255 | 232 | 214 |
c33 | 301 | 250 | 255 | 200 | 190 |
c44 | 77 | 48 | 45 | 54 | 54 |
c55 | 77 | 48 | 45 | 54 | 48 |
c66 | 77 | 48 | 45 | 65 | 64 |
c12 | 100 | 95 | 89 | 103 | 102 |
c13 | 100 | 95 | 89 | 103 | 97 |
c23 | 100 | 95 | 89 | 103 | 100 |
B | 167 | 146 | 144 | 142 | 136 |
G | 85 | 58 | 58 | 58 | 55 |
E | 219 | 154 | 153 | 154 | 144 |
ν | 0.32 | 0.27 | 0.28 | 0.32 | 0.32 |
G/B | 0.51 | 0.40 | 0.40 | 0.409 | 0.402 |
κmin | 1.52 | 1.15 | 0.99 | 1.33 | 1.29 |
Tb2SiO5 | Dy2SiO5 | Ho2SiO5 | Er2SiO5 | Tm2SiO5 | Yb2SiO5 | Lu2SiO5 | Y2SiO5 | γ-Y2Si2O7 | β-Y2Si2O7 | β-Yb2Si2O7 | β-Lu2Si2O7 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
c11 | 211 | 215 | 220 | 225 | 225 | 223 | 240 | 224 | 196 | 303 | 263 | 298 |
c22 | 169 | 179 | 190 | 201 | 214 | 185 | 221 | 208 | 287 | 203 | 197 | 215 |
c33 | 181 | 184 | 185 | 188 | 179 | 202 | 194 | 154 | 225 | 203 | 198 | 210 |
c44 | 43 | 45 | 47 | 49 | 52 | 46 | 52 | 47 | 63 | 70 | 71 | 77 |
c55 | 75 | 76 | 76 | 77 | 72 | 83 | 81 | 64 | 98 | 103 | 97 | 107 |
c66 | 57 | 62 | 63 | 65 | 67 | 62 | 71 | 65 | 90 | 71 | 67 | 74 |
c12 | 51 | 54 | 58 | 61 | 66 | 55 | 67 | 92 | 126 | 116 | 109 | 119 |
c13 | 80 | 81 | 83 | 84 | 78 | 102 | 86 | 55 | 110 | 129 | 122 | 135 |
c15 | 17 | 16 | 15 | 14 | 8 | 16 | 9 | 5 | -7 | -24 | -12 | -24 |
c23 | 37 | 40 | 44 | 47 | 49 | 49 | 49 | 29 | 99 | 108 | 108 | 118 |
c25 | -16 | -16 | -30 | -17 | -20 | -18 | -20 | 0 | -16 | 45 | 46 | 42 |
c35 | -18 | -20 | -24 | -26 | -20 | -21 | -35 | 0 | 38 | -8 | -2 | -9 |
c46 | 10 | 10 | 11 | 11 | 10 | 15 | 11 | 10 | -33 | 31 | 27 | 28 |
B | 98 | 101 | 104 | 109 | 110 | 111.5 | 114.5 | 100.5 | 151 | 153 | 145 | 160 |
G | 58 | 60.5 | 61.5 | 63 | 64.5 | 62 | 67.5 | 60.5 | 68 | 65 | 62 | 68 |
E | 146 | 152 | 153 | 159 | 161 | 158 | 169 | 152 | 177 | 170 | 162 | 178 |
ν | 0.251 | 0.205 | 0.254 | 0.256 | 0.255 | 0.264 | 0.253 | 0.248 | 0.304 | 0.314 | 0.313 | 0.314 |
G/B | 0.592 | 0.599 | 0.591 | 0.578 | 0.586 | 0.556 | 0.590 | 0.602 | 0.450 | 0.425 | 0.428 | 0.425 |
Table 8 Elastic constants and mechanical properties (in GPa) of RE2SiO5 (RE=Tb, Dy, Ho, Er, Tm, Yb, Lu, and Y) [107], γ-Y2Si2O7 and β-RE2Si2O7 (RE=Yb, Lu and Y) [108].
Tb2SiO5 | Dy2SiO5 | Ho2SiO5 | Er2SiO5 | Tm2SiO5 | Yb2SiO5 | Lu2SiO5 | Y2SiO5 | γ-Y2Si2O7 | β-Y2Si2O7 | β-Yb2Si2O7 | β-Lu2Si2O7 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
c11 | 211 | 215 | 220 | 225 | 225 | 223 | 240 | 224 | 196 | 303 | 263 | 298 |
c22 | 169 | 179 | 190 | 201 | 214 | 185 | 221 | 208 | 287 | 203 | 197 | 215 |
c33 | 181 | 184 | 185 | 188 | 179 | 202 | 194 | 154 | 225 | 203 | 198 | 210 |
c44 | 43 | 45 | 47 | 49 | 52 | 46 | 52 | 47 | 63 | 70 | 71 | 77 |
c55 | 75 | 76 | 76 | 77 | 72 | 83 | 81 | 64 | 98 | 103 | 97 | 107 |
c66 | 57 | 62 | 63 | 65 | 67 | 62 | 71 | 65 | 90 | 71 | 67 | 74 |
c12 | 51 | 54 | 58 | 61 | 66 | 55 | 67 | 92 | 126 | 116 | 109 | 119 |
c13 | 80 | 81 | 83 | 84 | 78 | 102 | 86 | 55 | 110 | 129 | 122 | 135 |
c15 | 17 | 16 | 15 | 14 | 8 | 16 | 9 | 5 | -7 | -24 | -12 | -24 |
c23 | 37 | 40 | 44 | 47 | 49 | 49 | 49 | 29 | 99 | 108 | 108 | 118 |
c25 | -16 | -16 | -30 | -17 | -20 | -18 | -20 | 0 | -16 | 45 | 46 | 42 |
c35 | -18 | -20 | -24 | -26 | -20 | -21 | -35 | 0 | 38 | -8 | -2 | -9 |
c46 | 10 | 10 | 11 | 11 | 10 | 15 | 11 | 10 | -33 | 31 | 27 | 28 |
B | 98 | 101 | 104 | 109 | 110 | 111.5 | 114.5 | 100.5 | 151 | 153 | 145 | 160 |
G | 58 | 60.5 | 61.5 | 63 | 64.5 | 62 | 67.5 | 60.5 | 68 | 65 | 62 | 68 |
E | 146 | 152 | 153 | 159 | 161 | 158 | 169 | 152 | 177 | 170 | 162 | 178 |
ν | 0.251 | 0.205 | 0.254 | 0.256 | 0.255 | 0.264 | 0.253 | 0.248 | 0.304 | 0.314 | 0.313 | 0.314 |
G/B | 0.592 | 0.599 | 0.591 | 0.578 | 0.586 | 0.556 | 0.590 | 0.602 | 0.450 | 0.425 | 0.428 | 0.425 |
Fig. 19 Calculated temperature dependent thermal conductivities of (a) RE2SiO5 (RE=Tb, Dy, Ho, and Er), (b) RE2Si2O5 (RE=Tm, Yb, Lu, and Y), (c) γ-Y2Si2O7, β-Y2Si2O7, β-Yb2Si2O7, and β-Lu2Si2O7; together with (d) the minimum thermal conductivities of polycrystalline and those along specific crystalline directions for RE2Si2O7 [107,108].
Y5Si3O12N | Y4Si2O7N2 | YSiO2N | Y2Si3O3N4 | Y3Si5N9O | |
---|---|---|---|---|---|
c11 | 240 | 267 | 199 | 314 | 319 |
c22 | 329 | 266 | 199 | 327 | 363 |
c33 | 256 | 194 | 293 | 276 | 344 |
c44 | 75 | 81 | 114 | 75 | 111 |
c55 | 84 | 71 | 114 | 92 | 118 |
c66 | 72 | 79 | 65 | 125 | 107 |
c12 | 120 | 106 | 69 | 131 | 90 |
c13 | 93 | 86 | 133 | 102 | 116 |
c23 | 114 | 95 | 133 | 94 | 119 |
B | 142 | 162 | 142 | 173 | 186 |
G | 75 | 79 | 77 | 96 | 114 |
E | 191 | 204 | 196 | 244 | 284 |
ν | 0.275 | 0.290 | 0.271 | 0.265 | 0.245 |
G/B | 0.528 | 0.488 | 0.542 | 0.555 | 0.613 |
Table 9 Elastic constants and mechanical properties (in GPa) of Y5Si3O12N, Y4Si2O7N2, YSiO2N,Y2Si3O3N4 and Y3Si5N9O [112].
Y5Si3O12N | Y4Si2O7N2 | YSiO2N | Y2Si3O3N4 | Y3Si5N9O | |
---|---|---|---|---|---|
c11 | 240 | 267 | 199 | 314 | 319 |
c22 | 329 | 266 | 199 | 327 | 363 |
c33 | 256 | 194 | 293 | 276 | 344 |
c44 | 75 | 81 | 114 | 75 | 111 |
c55 | 84 | 71 | 114 | 92 | 118 |
c66 | 72 | 79 | 65 | 125 | 107 |
c12 | 120 | 106 | 69 | 131 | 90 |
c13 | 93 | 86 | 133 | 102 | 116 |
c23 | 114 | 95 | 133 | 94 | 119 |
B | 142 | 162 | 142 | 173 | 186 |
G | 75 | 79 | 77 | 96 | 114 |
E | 191 | 204 | 196 | 244 | 284 |
ν | 0.275 | 0.290 | 0.271 | 0.265 | 0.245 |
G/B | 0.528 | 0.488 | 0.542 | 0.555 | 0.613 |
Fig. 21 (a) Calculated temperature dependent thermal conductivities of five quaternary oxynitrides [112] and experimental values of Y4Si2O7N2 [111]; (b) Minimum thermal conductivities of polycrystalline quaternary oxynitrides together with their minimum thermal conductivities along specific crystalline directions.
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