Work hardening in colloidal crystals

Abstract Colloidal crystals are fascinating materials1-4. They exhibit a rich behavior that is in many ways analogous to their atomic counterparts: they have the same crystal structures2,5-7; they undergo the same phase transitions8-10; and they possess the same crystallographic defects11-15. In contrast to these structural properties, the mechanical properties of colloidal crystals are quite distinct from those of atomic systems. For example, unlike in atomic systems, the elasticity of hard-sphere colloidal crystals is purely entropic16; as a result, they are so soft that they can be melted just by stirring17-19. In addition, crystalline materials deform plastically when subjected to increasing shear and actually become stronger due to the ubiquitous process of work hardening20, which has not been observed in colloidal crystals. Here we show that hard-sphere colloidal crystals do exhibit work hardening; moreover, despite their softness, the shear strength of colloidal crystals can increase and approach the theoretical limit for crystals, a value reached in very few other materials. We use confocal microscopy to show that the strength of colloidal crystals scales as the square root of dislocation density, in good agreement with the classic Taylor prediction21. We find that, surprisingly, Taylor hardening arises through the formation of dislocation junctions, in direct analogy to atomic systems, even though hard-sphere interactions lack the complexity of atomic interactions22,23. The Taylor hardening regime, however, is established only after a transient phase, and it ceases when the crystals become so hard that the strain is localized within a thin boundary layer where slip results from unconventional motion of dislocations. The striking resemblance between colloidal and atomic crystals, despite the many orders of magnitude difference in particle size and shear modulus, demonstrates the universality of work hardening.