Examples of phase stability in nanoparticle systems

Zhang and Banfield (1998) have made a detailed thermodynamic analysis of the nanocrystalline anatase and rutile system. Results suggested that at standard pressure, anatase is more stable than rutile when their particle sizes are below -14.5 nm (curve 1 in Fig. 16). In their calculation, the surface free energies for rutile and anatase were obtained through published data of surface energy calculated by molecule dynamics simulations and experimental data of heat capacity of ultrafme rutile samples  

The density data are pr = 4.249 g/cm and Pa = 3.893 g/cm. Both the density data and their structure analysis of the unsatisfied surface charges associated with several exposed faces of anatase and rutile support the fact that rutile has higher surface energy than anatase. Unfortunately, direct measurements of surface energies were not available. Based on the available data, the nanocrystalline anatase-rutile system is classified as Case 3 discussed above (a-phase = anatase and P-phase = rutile in Figs. 14 and 15). 

If external pressure is applied to this system, the phase boundary should move according to calculations with Equation (2). Calculated results by the present authors (Fig. 16) show that with increased external pressure, anatase becomes less stable (i.e., the 

Stability region of anatase becomes smaller). At 2 GPa and 5 GPa, respectively, anatase is predicted to be more stable only when the particles sizes are below 9 nm and 6 nm, respectively. 

Ti02(II) synthesized at higher pressure starts to transform to rutile at 450-600° Cover laboratory time scales (Aarik et al. 1996). With respect to Ti02(II), at standard pressure (1 bar), rutile is considered the stable phase at all temperatures (Jamieson and Olinger 

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