PSI - Issue 28

Kotrechko Sergiy et al. / Procedia Structural Integrity 28 (2020) 116–123 Kotrechko Sergiy et al / Structural Integrity Procedia 00 (2019) 000–000

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Keywords: carbyne; carbyne-graphene nanoelements; lifetime; nanomechanic; nanodevice; thermal fluctuations .

1. Introduction Rapid development of nanotechnology enables to create nanostructures with extraordinary properties. However, the key factor pre-determining the possibility of their practical use is their lifetime. Therefore, both to elucidate the mechanisms that govern the stability of these structures and to develop, on this basis, the lifetime prediction technique is a new challenge for micro (nano) - mechanics. Solving this problem requires the development of fundamentally new approaches that take into account the specific features of mechanisms of both instability and failure of nanostructures. A key feature of reaching the ultimate state of nanostructures and nanoelements is that it is directly related to the breaking of individual atomic bonds. In ordinary macro-sized solids, the effect of atomic interaction on strength is indirect; it is realized via the formation and evolution of defects (dislocations, crack nuclei, etc.). A characteristic feature of the atomism of breaking bonds is its fluctuation nature. Atoms are in constant vibrational motion, so, the breaking of interatomic bonds is initiated by random fluctuations of the displacements of atoms relatively to their equilibrium position. From an energy point of view, this means that failure can be considered as overcoming the energy barrier. This enables the employment of the Arrhenius–Kramers reaction theory [Smith (2008)] to predict the probability of this event. The need for experimental determination of fitting constants as a function of failure probability is a disadvantage of this approach due to the extremely small size of nanoelements. Trying to overcome this drawback has been made by Lin et al. (2011), Lin and Chen (2013). No fit constants are used in this approach. Information on atomic interaction is obtained based on the parameters of the static potential along a minimum energy path. Typically, these parameters are determined by the findings of ab initio (DFT) calculations. This approach was used by Lin et al. (2011) to predict the average migration time of a contact atom in a carbyne–graphene nanoelement at T≈1200–2000 K, and also to estimate the average waiting time for an interatomic bond break in the center of a carbyne chain at T = 600–800K. Later, this model was employed to analyze the regularities of the gaseous medium effect on the lifetime of nanochains of carbon and gold atoms [Lin and Chen (2013)]. A feature of these and other works is that lifetime is evaluated for mechanically unloaded systems. Accounting for the effect of mechanical load on the probability of atomic bonds break within the framework of above models is associated with considerable difficulties. The main assumption of the current approach to predict the lifetime of nanoelements under the conditions of mechanical stresses is the postulation of the linear law of lowering the energy barrier under the action of these stresses. The coefficient characterising the slope of this dependence is considered as a constant of the material (activation volume).This approach is usually employed to describe thermally activated processes in 3D-macroscopic solids. Now an attempt is being made to transfer it to nanoobjects. However, for nano objects this approach is ineffective, since for them the dependence of the barrier height on stress is essentially nonlinear [Zhu et al. (2008), Dumitrica et al. (2006), Slutsker (2004)]. This, in particular, leads to an increase in the number of fitting constants that need to be determined. A fundamentally different approach to predicting the lifetime of nanoelements was proposed by Kotrechko et al. (2017). In this approach, no assumptions are introduced about the law of changing the height of the energy barrier. The probability of an atomic bond breaking is directly calculated as the probability of reaching a critical atomic displacement c  . The value of this critical displacement, c  , is computed from both the stress-strain diagram of the interatomic bond and the level of acting stresses. For this purpose the results of DFT-calculations are used. The absence of fitting constants is one of the advantages of this approach. It was utilised to predict the lifetime of carbyne-graphene nanoelements consisting of graphene sheets connected by a carbyne chain. However, in the general case, it can be used for a wide class of nanomaterials comprising a combination of one-, two-, and three dimensional nanostructures. A common feature of such structures is presence of the contact bonds, which stability governs the lifetime of the entire nanoelement. This paper gives a brief summary of the main effects that govern the lifetime of nanoelements and also formulates an approach to predict it magnitude.