Correlation and size dependence of the lattice strain, binding energy, elastic modulus, and thermal stability for Au and Ag nanostructures

Abstract

As a group of wonder materials, gold and silver at the nanoscale demonstrate many intriguing properties that cannot be seen from their bulk counterparts. However, consistent insight into the mechanism behind the fascinations and their interdependence given by one integrated model is highly desirable. Based on Goldschmidt-Pauling's rule of bond contraction and its extension to the local bond energy, binding energy density, and atomic cohesive energy, we have developed such a model that is able to reconcile the observed size dependence of the lattice strain, core level shift, elastic modulus, and thermal stability of Au and Ag nanostructures from the perspective of skin-depth bond order loss. Theoretical reproduction of the measured size trends confirms that the undercoordination-induced local bond contraction, bond strength gain, and the associated binding energy density gain, the cohesive energy loss and the tunable fraction of such undercoordinated atoms dictate the observed fascinations, which should shed light on the understanding of the unusual behavior of other nanostructured materials as well. V

Electronic Structure and Energy Band of IIIA Doped Group ZnO Nanosheets

“…For the structures that are doped, we considered two configurations: one IIIA ion replacing one Zn atom (M-Zn) and O atom (M-O). Goldschmidt-Pauling rule [26] of bond contraction induced by undercoordination, this results in the increase of band gap of M-Zn and M-O. The formation energies of M-doped ZnONSs were calculated to evaluate their stability.…”

Grain-size effects on the thermal conductivity of nanosolids

“…Nanoscale Au and Ag exhibit many interesting chemical and physical properties that cannot be observed with their bulk counterparts [1][2][3]. Liu et al [4] developed a model to reconcile the observed size dependence of lattice strain, core level shift and elastic modulus of Au and Ag nanostructures, which is based on Goldschmidt Pauling's rule of bond contraction and its extension to the local bond energy and binding energy density.…”

Detachment Limited Kinetics of Gold Diffusion through Ultrathin Oxide Layers

“…Similarly, the interaction of metals with surface defects on SiO 2 is weak and the binding of small gold clusters to the negatively charged defects on oxide surface would lead to much smaller or even opposite shifts (i.e., to lower binding energies) than it has been observed. , Since the measured dependence of the Au 4f 7/2 peak position on the nominal coverage follows the trend well documented in literature for similar systems, − the size effect could be identified as the primary contribution for the binding energy shift to higher energies. , However, the effect of the substrate oxide composition on the magnitude of the shift should be taken into account when different substrate oxides are employed due to a different substrate-cluster charge transfer character , and different ability of metal oxide supports to shield the final-state hole via extra-atomic relaxation . Using the results of recent experimental and theoretical works, , one can roughly correlate the measured binding energy with the average size of clusters which is marked by horizontal lines in Figure and characterized by the parameter K in Figure (b) together with the nominal coverage. The value of parameter K corresponds to the number of atoms in the cluster radius and can be calculated by the relation K = R / d b , where d b = 0.288 nm is the covalent bond length.…”

“…Since gold nanoparticles below a certain size are efficient catalysts, much effort has been invested in the determination of properties of small metal clusters as a function of their size. It has been found that the number of under-coordinated atoms in the near surface layers determine the size dependence of cohesive energy of these clusters , and, consequently, mechanical, thermal and electronic properties. For instance, elastic modulus, surface tension, melting point, and shift of binding energy within these clusters are inverse proportional to the characteristic feature size, e.g., cluster radius …”