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 nano-PbS 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.