Surface stress of nano-crystals

Surface stress is rarely discussed in chemistry but chemistry has much to do with surface stress. Size-dependent lattice contraction and expansion have been theoretically associated with tensile (+) and compressive (-) surface stress. Here, we review crystal-size-dependent lattice-changes in nanocrystals of two noble metals, five oxides and a semiconductor. For gold and platinum crystallites, their lattice increasingly contracts with decreasing crystallite-size (d), which yields tensile surface stress with a numerical value near that of the corresponding surface energy implying clean surfaces. Here, the smaller coordination of surface atoms shortens local bonds while the lattice-matching between the surface and interior induces surface tension. For the oxides and the semiconductor PbS, however, their increasing lattice expansion with decreasing d implies compressive surface stress. Standard methods yield surface stress ranging from -5.6 to -1.1 N/m for five nano-oxides. The size-dependent bulk-modulus (B(d)) shows a maximum at a crystal-size of 6.7 nm PbS (B = 66.4 GPa), 33 nm CeO2 (B = 340 GPa) and 14 nm MgO (B = 165 GPa) with surface stresses at -2.14, -4.8, & -3.5 N/m, respectively. The expanding lattice with decreasing crystal-size in nano-oxides originates from different sources. First and most importantly, adsorbents and surfactants increase the coordination of surface atoms and lengthen local bonds. Second, auto-reduction of cations results in larger cations and expands lattice. Third, a negative pressure from electrostatics lengthens ionic bonds. While these three factors all cause the lattice in nano-crystals to expand, only those that are directly surface related are contributing to compressive surface stress. As PbS crystallites morph to cube-like when larger than 7 nm, oleic acid weakly bonded to (100) seemingly decreases nano-PbS's stiffness and surface stress. In nano-oxides and nanoPbS the main factor of compressive surface stress is the increased coordination of the surface atoms which lengthens local bonds while registering with interior lattice creates surface compressive stress.

Automated summary

Surface stress is rarely discussed in chemistry, but it is closely related to size-dependent lattice changes in nanocrystals. Different materials exhibit different surface stress behaviors with changes in crystal size, with some materials showing tensile surface stress and others showing compressive surface stress. The coordination of surface atoms and lattice-matching between surface and interior play key roles in determining surface stress in nanostructures.