572
E. I. Get’man and S. V. Radio
Table 1 Data for the calculation of mixing energies and critical (maximum) decomposition
temperatures of solid solutions (Sc 1–x Ln x ) [(SiO 4 ) 0.5 O 0.5 ], Ln = Tb–Lu and Y (space group C2/c)
Ln
V, Å 3
δ a
Q δ , kJ/mol
χ Ln
ε
ε
T cr , K
Tb
876.80 [21]
0.0535
34.5
1.410
0.708
0.001
2060
Dy
856.57 [15]
0.0453
24.8
1.426
0.706
0.003
1480
Ho
843.04 [15]
0.0398
19.1
1.433
0.704
0.005
1150
Er
836.70 [15]
0.0372
16.7
1.438
0.703
0.006
1010
Tm
828.59 [15]
0.0338
13.8
1.455
0.699
0.010
860
Yb
824.07 [15]
0.0319
12.3
1.479
0.694
0.015
810
Lu
819.31 [15]
0.0299
10.8
1.431
0.705
0.004
650
Sc
749.97 [22]
–
–
1.415
0.709
–
–
Y
852.25 [21]
0.0435
22.8
1.340
0.722
0.013
1400
a Note According to the recommendations in [17, 18] and considering the dependence of the
interaction parameter on the difference in volumes of the unit cells of components [29], the
calculation of the dimensional parameter δ was carried out according to the volumes of the unit
cells
Table 2 Decomposition temperatures (stability) of (Sc 1–x Ln x ) [(SiO 4 ) 0.5 O 0.5 ] solid solutions for
x = 0.01, 0.03, 0.05, 0.10, and 0.20
x
Tb
Dy
Ho
Er
Tm
Yb
Lu
0.01
880
630
490
430
370
350
280
0.03
1110
800
620
550
469
440
350
0.05
1260
910
700
620
520
490
400
0.10
1500
1080
840
730
620
590
470
0.20
1780
1280
990
870
740
700
560
Fig. 1 The diagram of
thermodynamic stability of
solid solutions in the systems
(Sc 1–x Ln x ) [(SiO 4 ) 0.5 O 0.5 ],
where x = 0.01 (a), 0.03 (b),
0.05 (c), 0.10 (d), 0.20 (e),
and 0.50 (f)