Nuclear spin relaxation measurements were made of single crystals at temperatures of between 150 and 1500K, under an O partial pressure of 1atm. The nuclear magnetic resonance spectrum consisted of a doublet which resulted from 2 different orientations of the electric field gradient tensor at 2 different Ti sites in the unit cell of the rutile lattice. The electric field gradient tensor was due to the 6 surrounding O2- ions, which formed a stretched octahedron. From the temporal evolution of the nuclear spin relaxation rate after a step-wise change in the O partial pressure, 2 different types of motion of the intrinsic defects were deduced. It was found that the motion of interstitial Ti ions was described by the expression:
D (cm2/s) = 2.6 x 10-3exp[-0.42(eV)/kT]
while the motion of doubly-charged O vacancies was described by the expression:
D (cm2/s) = 9 x 10-6exp[-0.32(eV)/kT]
The use of site-selective nuclear spin relaxation methods revealed that some 1% of Ti diffusion occurred via jumps between the non-equivalent Ti lattice sites via a monovacancy process.
Nuclear Magnetic Resonance Study of Defect Motion and Cation Diffusion in Single Crystal Rutile (TiO2-x). Kolem, H., Kanert, O.: Zeitschrift für Metallkunde, 1989, 80[4], 227-34
Table 14
Diffusion of 44Ti in TiO2-δ
Temperature (C) | PO2(atm) | D (cm2/s) |
1000.0 | 9.61 x 10-19 | 8.00 x 10-9 |
1000.0 | 6.23 x 10-19 | 8.53 x 10-9 |
1000.0 | 1.10 x 10-16 | 2.80 x 10-9 |
1000.0 | 3.40 x 10-17 | 3.69 x 10-9 |
1000.0 | 1.01 x 10-17 | 4.96 x 10-9 |
1000.0 | 1.69 x 10-16 | 2.53 x 10-9 |
1025.0 | 1.69 x 10-16 | 5.19 x 10-9 |
1058.4 | 1.30 x 10-18 | 5.03 x 10-11 |
1058.4 | 8.51 x 10-18 | 1.62 x 10-10 |
1058.4 | 4.08 x 10-16 | 1.80 x 10-8 |
1058.4 | 1.28 x 10-16 | 2.21 x 10-8 |
1058.4 | 3.52 x 10-15 | 1.10 x 10-8 |
1058.4 | 7.65 x 10-15 | 9.34 x 10-9 |
1058.4 | 1.50 x 10-17 | 2.11 x 10-10 |
continued
Table 14 (continued)
Diffusion of 44Ti in TiO2-δ
Temperature (C) | PO2(atm) | D (cm2/s) |
1058.4 | 2.43 x 10-17 | 3.69 x 10-10 |
1058.4 | 2.96 x 10-17 | 8.58 x 10-10 |
1058.4 | 4.64 x 10-17 | 4.70 x 10-9 |
1058.4 | 5.44 x 10-17 | 5.90 x 10-9 |
1058.4 | 3.86 x 10-17 | 2.87 x 10-9 |
1058.4 | 1.46 x 10-16 | 2.31 x 10-8 |
1058.4 | 9.91 x 10-17 | 2.31 x 10-8 |
1058.4 | 2.94 x 10-16 | 2.09 x 10-8 |
1058.4 | 2.53 x 10-14 | 7.64 x 10-9 |
1058.4 | 7.23 x 10-17 | 2.15 x 10-8 |
1058.4 | 2.42 x 10-16 | 2.19 x 10-8 |
1058.4 | 9.13 x 10-16 | 1.81 x 10-8 |
1058.4 | 6.28 x 10-17 | 8.82 x 10-9 |
1058.4 | 6.53 x 10-16 | 1.62 x 10-8 |
1058.4 | 7.76 x 10-17 | 2.58 x 10-8 |
1058.4 | 4.21 x 10-16 | 2.03 x 10-8 |
1058.4 | 1.12 x 10-15 | 1.61 x 10-8 |
1058.4 | 6.99 x 10-17 | 9.33 x 10-9 |
1058.4 | 6.05 x 10-16 | 1.84 x 10-8 |
1058.4 | 1.57 x 10-16 | 2.89 x 10-8 |
1058.4 | 6.68 x 10-17 | 7.05 x 10-9 |
1058.4 | 2.14 x 10-15 | 1.53 x 10-8 |
1058.4 | 1.15 x 10-16 | 3.17 x 10-8 |
1058.4 | 3.75 x 10-15 | 1.54 x 10-8 |
1058.4 | 4.96 x 10-15 | 1.32 x 10-8 |
1058.4 | 1.82 x 10-14 | 8.39 x 10-9 |
continued
Table 14 (continued)
Diffusion of 44Ti in TiO2-δ
Temperature (C) | PO2(atm) | D (cm2/s) |
1058.4 | 1.57 x 10-13 | 5.45 x 10-9 |
1058.4 | 1.69 x 10-16 | 2.29 x 10-8 |
1079.6 | 1.69 x 10-16 | 3.22 x 10-8 |
1100.0 | 1.69 x 10-16 | 5.65 x 10-8 |
1100.0 | 9.09 x 10-16 | 1.74 x 10-8 |
1100.0 | 1.04 x 10-14 | 1.36 x 10-8 |
1100.0 | 6.32 x 10-14 | 8.51 x 10-9 |
1100.0 | 8.86 x 10-14 | 6.62 x 10-9 |