PSI - Issue 23

Sergiy Kotrechko et al. / Procedia Structural Integrity 23 (2019) 310–315 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

312

3

The specific feature of this model is that the magnitude of fluctuation C  depends on the force f F (Fig. 2). This is due to the fact that the fluctuation causes a short-term instability of the atomic interaction. To break an atomic bond, it is necessary for this fluctuation to be “picked up” by the applied force. Accordingly, the expression for the probability of the atomic bond break is the following:

u

br



 k T d ] B

  0

exp

[ ( ) /

  



     br C u C )

(

P

(2)



 k T d ] B

exp

[ ( ) /

  



where T is the temperature; B k is the Boltzmann constant; ( )   is the energy fluctuation; br u is the displacement of an atom when the bond is broken (Fig. 2): ) ( ) ( ) ( f f E u E u      (3) where E is the energy; f u is the displacement of an atom due to the force f F .

Fig. 2 . Strain diagram for contact bond (scheme):

f F is the value

of “applied” force; f u is the deviation of an atom from the equilibrium position due to mechanical load; un F and un u are the force and displacement of a contact bond instability, respectively; un δ is the instability fluctuation; c u and C  are the critical displacement and critical fluctuation, respectively; br u is the displacement of bond break

Fig. 3 . Dependence of force, F , acting in a contact bond, on its length, 01 a , as well as accompanied changes in the lengths of atomic bonds 12 a , 23 a , 34 a , 45 a and 56 a inside of the carbyne chain (adapted from Kotrechko et al. (2017))

Accordingly, the average waiting time for a break,  , at a constant value of force f F is:

   0

(4)

( P  

)

C

where 0  is the average period of atomic vibrations. For the object in question within the temperature range (600 К