  The atomic structure and mechanical properties of the carbyne (monatomic
linear chains), containing from 2 to 21 carbon atoms, are theoretically
investigated by ab-initio methods. We demonstrate the existence of a stable
cumulene-structure in the inner part of chains with the number of atoms N>=10.
We present a general stress-strain diagram of chains until the moment when they
break, which enables to determine their strength, elasticity and fragility. For
chains with N>=4, the relationship between the strength of the chain and the
binding energy of the edge atom in the chain is established. The existence of
scale-effect and "even-odd" effect for such properties as strength, elasticity
and fragility is observed. We demonstrate that the 5-atom carbon chains show
the maximum strength value.
