Supporting Information

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1 Supporting Information Enhanced Electron Transport in Nb-doped TiO 2 Nanoparticles via Pressure-Induced Phase Transitions Xujie Lü,,, * Wenge Yang,,, * Zewei Quan, Tianquan Lin, # Ligang Bai, Lin Wang,, Fuqiang Huang, # Yusheng Zhao, * High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, United States High Pressure Synergetic Consortium, Geophysical Laboratory, Carnegie Institution of Washington, Argonne, Illinois 60439, United States Center for High Pressure Science and Technology Advanced Research, Pudong, Shanghai , China Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States # CAS Key Laboratory of Materials for Energy Conversion, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai , China Packing Factor Model: Crystal packing factor (PF) is a widely used crystal-structural parameter, which is computed by dividing the sum of spherical ion or atom volumes by the unit-cell volume, PF = Z (xv A + yv B + zv C ) / V unit-cell where Z is the number of the formula unit in one unit cell of a compound (A x B y C z ); V A, V B and V C are ion volumes calculated by assuming spherical ions with a Shannon radius that depends on the coordination number, 1 and V unit-cell is the unit-cell volume. S1

2 The PF model was proposed to evaluate the charge separation/transport abilities and photocatalytic activities of the materials with similar composition or structure. 2-6 The concept came from Prof. John B. Goodenough's idea that lower elastic stiffness can promote distortion, which increases internal field, and it can be easily implemented using the packing factor. 7,8 Lower PF structure with lower elastic stiffness possesses higher internal electric field, resulting in more efficient charge separation/transport and thus better photocatalytic activity. 2 In terms of the carrier lifetime and mobility, PF model can provide good explanations on the better properties for looser structure. An open structure (lower PF value) provides wider space for atom vibrations, leading to a higher momentary polarizing field. The more polarizable structure results in larger exciton Bohr radius, hence longer carrier lifetime. 5 In addition, a lower PF structure is usually more deformable, which lowers the hopping barrier for polarons, thus increasing their mobility. 2,9,10 The combination of increased carrier lifetime and mobility causes the higher electrical conductivity and better photocatalytic activity. Taking TiO 2 as an example, the electron transport of anatase phase is better than that of rutile, so does the photocatalytic activities. 11 This can be explained by the PF model that the anatase (PF = 64.6%) has a lower PF value than the rutile (PF = 70.5%). As another example, MSb 2 O 6 (M = Ca, Sr and Ba), the photocatalytic activity sequence is BaSb 2 O 6 > SrSb 2 O 6 > CaSb 2 O 6, with the PF values of 53.7%, 55.6% and 57.9%, respectively. More examples are listed in Table S1, confirming that a lower PF structure is correlated with higer charge separation and transport abilities, and better photocatalytic activity. Resistance Measurement: Electrical resistances of 5.0 mol% Nb-doped TiO 2 were measured by a four probe resistance test system in a diamond anvil cell (DAC) at pressures up to 42 GPa without pressure- S2

3 transmitting medium. The experimental arrangement for the resistance measurements was similar to that described in reference, 12 with an insulating gasket made from the mixture of cubic boron nitride (BN) powder and epoxy. The hole of BN gasket was filled by the sample and four platinum leads made from platinum foil were touched to the sample (see Figure S8a). A Keithley 6221 current source, 2182A nanovoltmeter and 7001 switch system were used as the current supply, voltmeter and voltage/current switcher respectively. The resistance was determined by the Van de Pauw method using the equation of exp (-πr 1 /R S ) + exp (-πr 2 /R S ) = 1, where R S is the sheet resistance of the sample, R 1 is the resistance determined by dividing the potential difference V D V C by the current going from A to B (Figure S8b), and R 2 is the resistance after switch, similarly determined by dividing the potential difference V B V C by the current going from A to D (Figure S8c). The pressure-induced resistance evolution of undoped TiO 2 was also measured following the same procedure. Figures: Scheme S1. Crystal structures of various TiO 2 : anatase, baddeleyite and columbite. S3

4 Figure S1. TEM images of the anatase TiO 2 nanoparticles with different Nb concentrations: (a) 0, (b) 2.5, (c) 5.0 and (d) 10.0 mol %. Figure S2. Synchrotron XRD patterns of Nb-doped TiO 2 nanoparticles with different Nb concentrations during compression and decompression: (a) 2.5 and (b) 10.0 mol%. The marked peaks belong to solid Ne crystals under pressures higher than 8 GPa. S4

5 Figure S3. (a) Raman spectra of Nb-doped TiO 2 nanoparticles with different doping concentrations at ambient pressure; (b) Raman peak positions versus Nb concentrations. Figure S4. Raman spectra of Nb-doped TiO 2 nanoparticles collected during compression (left) and decompression (right) cycle: (a) 2.5 and (b) 10.0 mol % Nb. S5

6 Figure S5. The resistances of undoped TiO 2 nanoparticles during first compression and decompression cycle, which displays similar changing behavior with the Nb-doped sample. Figure S6. Raman spectra of Nb-doped TiO 2 nanoparticles during first decompression (black lines), second compression (red lines) and decompression (blue lines) cycle. The results confirm that the phase transition between baddeleyite (B) and columbite (C) is reversible during recompression decompression cycles. S6

7 Figure S7. The microphotographs of the Nb-doped TiO 2 samples and ruby balls in DACs: (a) 0 and 5 mol%, and (b) 2.5 and 10.0 mol%. Figure S8. Four-probe electrical resistance measurement. (a) Microphotograph of the sample and electrodes in the DAC, and the schematic diagrams (b) before and (c) after switch. S7

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