Table I
The scattering tensors (ai) of Raman-active transitions in Th symmetry in the system of the cubic axes (first row) and the scattering matrices related to the experimental coordinate system (Fig. 1). R(γ,β,α): matrices describing the rotation around α, β, γ.
(ai) |
|
---|
|
|
|
|
|
|
|
|
Table II
Wavenumber, relative integrated intensities of the elements of the scattering matrix, and assignment of some Raman transitions in Y2O3(Eu3+). The intensities of the electronic transitions (see Table V) at 830, 948, and 1184 cm−1 cannot be compared directly with the other lines because they were observed with a higher gain. Precision of the intensities stated: ±10%, values in brackets: ±25%.
cm−1 | Components |
| Assignment |
---|
|
---|
αxx | αyx | αyz | αxz |
---|
162 | 20 | (6) | (5) | (5) | 2.6 | Tg+Ag |
319 | 21 | 9 | (15) | (6) | 1.43 | Tg+Eg |
331 | 10 | 16 | (18) | 28 | 0.56 | Eg |
380 | 114 | 66 | 68 | 37 | 1.71 | Tg+Ag |
431 | 6 | 3 | (0) | (5) | 1.80 | Tg |
469 | 45 | 25 | 22 | 22 | 1.59 | Tg |
595 | 24 | 13 | 9 | 11 | 1.85 | Tg |
830 | 52 | 64 | (25) | (35) | (1.94) | Eg |
948 | 62 | 60 | (107) | (94) | (0.61) | Eg |
1184 | 80 | 32 | (20) | (15) | 3.20 | Ag |
Table III
Raman-active (Ag, Eg, and Tg) and infrared-active (Tu) phonon transitions [values of McDevitt et al., Ref. (3)] of R.E. oxides, in cm−1. The infrared-active transitions have been observed at room temperature in powdered samples, the Raman-active ones at ~10 K. The temperature shift of the wavenumbers is negligible between 10 and 80 K; it is 3–4 cm−1 to lower values for a temperature rise from 80 to 300 K. Lines without assignment are Raman transitions too weak for identification, (el) means a possible electronic transition. The Tu values in the Y2O3(Er) and Y2O3(Eu) columns are values of pure yttria.
Type | Y2O3(Er) | | Y2O3(Eu) | Er2O3 | Yb2O3 |
---|
(el) | | | | 41.0 | |
| 81.8 | | | 83.2 | 83.2 |
Tu | | 120 | | | |
(Tg) | 132.8 | | 130.5 | 99.7 | 99.2 |
Ag+Tg | 164 | | 163.4 | 123.2 | 121.0 |
Tu | | 171 | | 126 | |
Tu | | 182 | | 133 | 132 |
| 195.7 | | 194.6 | | |
Tu | | 242 | | | |
| | 312 | | 298 | 304 |
Tg+Eg | 320.5 | | 319.0 | 316.4 | 279 |
Eg | 333.5 | | 332.0 | 337.9 | 305 |
Tu | | | | 323 | |
Tu | | 343 | | 335 | 341 |
(el) | | | | | 334 |
Tg+Ag | 380.9 | | 379.0 | 384.1 | 358 |
| | | | 391 | |
Tu | | 390 | | 375 | 388 |
Tu | | 405 | | 395 | 405 |
Tg | 433.8 | | 432.2 | 433.6 | 420 |
Tu | | 468 | | 475 | 490 |
Tg | 472.8 | | 471.2 | 484.0 | 443 |
| | | 480 | | |
Tu | | 561 | | 565 | 573 |
| | | 571.9 | 576.1 | 595 |
Tg | 597 | | 596.0 | 598.3 | 621 |
Table IV
Reducible representations of the unit cell of the cubic R.E. oxides. (a) 80 isolated ions in the unit cell, (b) the unit cell contains 8 rigid (R.E. O6) units on C3i sites and 24 isolated R.E. ions in C2 sites.
Th | E | 4C3 | 4C32 | 3C2 | i | 4S6 | 4S65 | 3σh |
---|
a | 240 | 0 | 0 | −24 | −24 | 0 | 0 | 0 |
b | 120 | 0 | 0 | −24 | 0 | 0 | 0 | 0 |
Table V
Symmetry types occurring in the decomposition of representations (a) and (b) of Table IV.
Repres. | Ag | Eg | Tg | Au | Eu | Tu |
---|
(a) | 6 | 6 | 30 | 8 | 8 | 36 |
(b) | 2 | 2 | 18 | 2 | 2 | 18 |
Activity | R. | R. | R. | ⋯ | ⋯ | ir |
Table VI
Correlation of symmetry types of the (R.E. O6) octahedron.
Oh | S6 | Th |
---|
A1g | Ag | Ag+Fg |
Eg | Eg | Eg+2Fg |
2F1u | 2(Au+Eu) | 2(Au+Fu+Eu+2Fu) |
F2g | Ag+Eg | Ag+Fg+Eg+2Fg |
F2u | Au+Eu | Au+Fu+Eu+2Fu |