Table 2. Energetics of the biphase crystals at different phase ratios together with the optimized lattice parameters (a and b) and the Ti–O bond (d, Å) lengths.
| P1/P2 a | ΔE b (eV) | γ int b (J m–2) | a (Å) | b (Å) | P1 c | Inter | P2 |
| Rutile/TiO 2 -II (OR V) | |||||||
| 3R/4II | 0.01 | 0.02 | 4.61 | 5.57 | 1.92(1.95) | 2.00 | 2.00 |
| 3R/2II | 0.01 | 0.03 | 4.60 | 5.56 | 1.93(1.97) | 1.98 | 2.00 |
| 4R/1II | 0.00 | 0.01 | 4.61 | 5.57 | 1.95(1.97) | 2.00 | — |
| 6R/1II | 0.01 | 0.03 | 4.61 | 5.57 | 1.96(1.96) | 1.99 | — |
| Anatase/TiO 2 -II (OR VI) | |||||||
| 4A/4II | 0.04 | 0.19 | 5.54 | 5.13 | 1.91(1.97) | 1.99 | 2.00 |
| 8A/4II | 0.04 | 0.28 | 5.50 | 5.25 | 1.92(1.99) | 1.99 | 2.01 |
| 8A/2II | 0.03 | 0.14 | 5.45 | 5.40 | 1.94(2.00) | 2.00 | 2.02 |
| 12A/2II | 0.02 | 0.11 | 5.43 | 5.47 | 1.89(1.96) | 2.00 | 2.03 |
| Rutile/anatase (OR I) | |||||||
| 8A/15R | 0.11 | 1.49 | 4.86 | 5.52 | 1.91(2.00) | 1.99 | 1.89(1.98) |
| 16A/15R | 0.12 | 2.19 | 5.06 | 5.51 | 1.94(1.98) | 1.97 | 1.90(1.91) |
| 8A/3R | 0.11 | 0.65 | 5.23 | 5.60 | 1.91(2.02) | 1.93 | 1.84(2.08) |
| 12A/3R | 0.07 | 0.58 | 5.29 | 5.62 | 1.93(2.01) | 1.93 | 1.85(2.05) |
aThe name and ratio of two phases, e.g. 3R/4II stands for 3-layer rutile and 4-layer TiO2-II to form a biphase crystal.
bΔE, see eqn (7) and γint, see eqn (8).
cFor anatase and rutile, there are two types of Ti–O bonds in bulk TiO4 octahedron: equatorial and apical Ti–O bonds.