  This report deals with the correlation between the mechanical strength and
thermal stability of systems extending from monatomic chains to surface skins
and solids over the whole range of sizes with emphasis on the significance of
atomic coordination imperfection. Derived solutions show that a competition
between the bond order loss and the associated bond strength gain of the lower
coordinated atoms dictate the thermo-mechanics of the low dimensional systems.
Bond order loss lowers the atomic cohesive energy that determines the
temperature of melting (Tm), or the activation energy for atomic dislocation,
whereas bond strength gain enhances the energy density, or mechanical strength,
in the surface skin. Therefore, the surface is harder at T << Tm whereas the
surface becomes softer when the T approaches the surface Tm that is lower than
the bulk due to bond order loss. Hence, the strained nanostructures are usually
stiffer at low T whereas the harder skins melt easier. Quantitative information
has been obtained about the bonding identities in metallic monatomic chains and
carbon nanotubes. Solutions also enable us to reproduce the inverse Hall-Petch
relationship with clarification of factors dominating the transition from
hardening to softening in the nanometer regime.
