Table 1 Space group, cation radius and radius difference of RE4Al2O9 for design of high-entropy rare-earth aluminates (The data are obtained from the database of Materials Studio program, ©Accelrys Inc., San Diego, USA, 2014).
|
Space group
|
Rare-earth elements
|
Cation radius (Å)
|
Radius difference (%)
|
RE4Al2O9
|
P21/c
|
Nd
|
0.98
|
12.64
|
Sm
|
0.96
|
10.34
|
Eu
|
0.95
|
9.20
|
Y
|
0.90
|
3.45
|
Yb
|
0.87
|
0
|
Table 2 Refined lattice parameters, relative change of lattice parameters and theoretical density of high-entropy (Nd0.2Sm0.2Eu0.2Y0.2Yb0.2)4Al2O9 together with those of the single-component RE4Al2O9 (RE= Nd, Sm, Eu, Y and Yb) obtained from ICDD/JCPDS cards.
Phase
|
a (Å)
|
b (Å)
|
c (Å)
|
Δa/aYb (%)
|
Δb/bYb (%)
|
Δc/cYb (%)
|
b (º)
|
d (g/cm3)
|
HE RE4Al2O9
|
7.511
|
10.573
|
11.172
|
3.20
|
2.55
|
1.20
|
109.1
|
6.06
|
Nd4Al2O9
|
7.725
|
10.846
|
11.306
|
6.14
|
5.20
|
2.41
|
109.3
|
6.63
|
Sm4Al2O9
|
7.520
|
10.700
|
11.190
|
3.33
|
3.78
|
1.36
|
108.9
|
6.99
|
Eu4Al2O9
|
7.533
|
10.696
|
11.180
|
3.50
|
3.74
|
1.27
|
108.8
|
6.76
|
Y4Al2O9
|
7.379
|
10.469
|
11.116
|
1.39
|
1.54
|
0.69
|
108.6
|
5.28
|
Yb4Al2O9
|
7.278
|
10.310
|
11.040
|
0
|
0
|
0
|
108.3
|
8.30
|
Table 3 Anisotropic thermal expansion coefficients (αa, αb, and αc) and volumetric thermal expansion coefficient (αV) of (Nd0.2Sm0.2Eu0.2Y0.2Yb0.2)4Al2O9 together with those of Y4Al2O9.
Compounds
|
αa (10-6 /K)
|
αb (10-6 /K)
|
αc (10-6 /K)
|
αV (10-6 /K)
|
HE RE4Al2O9
|
10.59
|
8.93
|
5.66
|
24.40
|
Y4Al2O9
|
7.34
|
7.54
|
7.61
|
23.37
|
Table 4 Chemical parameters of each bond for (Nd0.2Sm0.2Eu0.2Y0.2Yb0.2)4Al2O9 and Y4Al2O9 by chemical bond theory.
|
Y4Al2O9
|
(Nd0.2Sm0.2Eu0.2Y0.2Yb0.2)4Al2O9
|
Bond
|
lm (Å)
|
fcm
|
Um (kJ∙mol-1)
|
lm (Å)
|
fcm
|
Um (kJ∙mol-1)
|
RE1-O3
|
2.0622
|
0.12
|
930
|
2.0931
|
0.13
|
919
|
RE1-O8
|
2.0917
|
0.12
|
999
|
2.0967
|
0.13
|
997
|
RE1-O7
|
2.2460
|
0.22
|
950
|
2.2778
|
0.22
|
940
|
RE1-O2
|
2.3991
|
0.12
|
897
|
2.4330
|
0.12
|
887
|
RE1-O6
|
2.5124
|
0.12
|
865
|
2.5247
|
0.12
|
862
|
RE1-O1
|
2.6015
|
0.12
|
841
|
2.6395
|
0.12
|
831
|
RE1-O5
|
2.8560
|
0.11
|
779
|
2.8723
|
0.12
|
775
|
RE2-O2
|
1.9238
|
0.18
|
1306
|
1.9509
|
0.18
|
1292
|
RE2-O3
|
2.1103
|
0.16
|
1116
|
2.1377
|
0.16
|
1105
|
RE2-O9
|
2.2430
|
0.17
|
1162
|
2.2482
|
0.17
|
1160
|
RE2-O1
|
2.3228
|
0.29
|
1130
|
2.3519
|
0.29
|
1119
|
RE2-O4
|
2.4799
|
0.16
|
1074
|
2.4936
|
0.16
|
1069
|
RE2-O7
|
2.5044
|
0.16
|
1065
|
2.5410
|
0.16
|
1053
|
RE3-O8
|
2.1966
|
0.12
|
962
|
2.2225
|
0.12
|
953
|
RE3-O2
|
2.2160
|
0.12
|
955
|
2.2279
|
0.12
|
951
|
RE3-O4
|
2.2762
|
0.12
|
935
|
2.3098
|
0.12
|
925
|
RE3-O8
|
2.4375
|
0.12
|
886
|
2.4467
|
0.12
|
884
|
RE3-O5
|
2.5367
|
0.12
|
858
|
2.5473
|
0.12
|
855
|
RE3-O6
|
2.5893
|
0.12
|
844
|
2.6255
|
0.12
|
835
|
RE3-O9
|
2.7703
|
0.11
|
799
|
2.8103
|
0.12
|
789
|
RE4-O3
|
2.1601
|
0.12
|
974
|
2.1866
|
0.12
|
965
|
RE4-O6
|
2.2073
|
0.12
|
958
|
2.2223
|
0.12
|
948
|
RE4-O9
|
2.2141
|
0.12
|
956
|
2.2381
|
0.12
|
953
|
RE4-O9
|
2.2888
|
0.12
|
931
|
2.3177
|
0.12
|
922
|
RE4-O8
|
2.4787
|
0.12
|
874
|
2.5148
|
0.12
|
864
|
RE4-O1
|
2.5418
|
0.12
|
857
|
2.5544
|
0.12
|
853
|
RE4-O7
|
2.7460
|
0.11
|
804
|
2.7523
|
0.12
|
803
|
Al1-O4
|
1.7267
|
0.57
|
2297
|
1.7314
|
0.58
|
2290
|
Al1-O3
|
1.8286
|
0.35
|
2097
|
1.8457
|
0.35
|
2082
|
Al1-O5
|
1.8338
|
0.39
|
2275
|
1.8644
|
0.39
|
2246
|
Al1-O2
|
1.9883
|
0.38
|
2146
|
1.9975
|
0.38
|
2136
|
Al2-O6
|
1.5632
|
0.41
|
2539
|
1.5703
|
0.41
|
2529
|
Al2-O5
|
1.6917
|
0.40
|
2407
|
1.7201
|
0.40
|
2377
|
Al2-O7
|
1.7978
|
0.39
|
2307
|
1.8114
|
0.39
|
2292
|
Al2-O1
|
1.8279
|
0.39
|
2280
|
1.8348
|
0.39
|
2272
|
Table 5 Thermal diffusivity (Dth), heat capacity (Cp), bulk density (d) and thermal conductivity (κ) of (Nd0.2Sm0.2Eu0.2Y0.2Yb0.2)4Al2O9 measured at room temperature.
Dth (mm2/s)
|
Cp (J·mol-1·K-1)
|
d (g/cm3)
|
κ (W·m-1·K-1)
|
0.62
|
306.92
|
6.02
|
1.50
|