In bulk titania crystals, each titanium atom bonds with six oxygen atoms. Then add a fifth oxygen directly above the titanium, forming a pyramid with a floor and sides that slope up to the apex. Finally, add a sixth oxygen beneath the central titanium. A normal crystal of bulk-titania consists of this unit structure repeated millions of times. So in a sense, the surface is a defect.
Defects are important because they are the keys to imbuing materials with new properties.
That's true of new metals and alloys, and especially semiconductors, such as titania. Carefully controlled chemical defects are key to the specific properties of computer chips, transistors and many other commercially important electronic products based on semiconductors. As titania crystals become smaller, the surface defects and distortions become dominant. In the extreme, the broad, flat portion of the typical bulk crystal is minimized, and the surface curvature is maximized. Argonne's research found that in titania particles that measure 4.3 nanometers across, the typical surface titanium atom is bound to only five oxygen atoms.