Synchrotron-based high-pressure x-ray diffraction measurements indicate that compressibility, a fundamental materials property, can have a size-specific minimum value. The bulk modulus of nanocrystalline titania has a maximum at particle size of 15 nm. This can be explained by dislocation behavior because very high dislocation contents can be achieved when shear stress induced within nanoparticles counters the repulsion between dislocations. As particle size decreases, compression increasingly generates dislocation networks ͑hardened by overlap of strain fields͒ that shield intervening regions from external pressure. However, when particles become too small to sustain high dislocation concentrations, elastic stiffening declines. The compressibility has a minimum at intermediate sizes.

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