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Register a new userMass transfer in Frenkel-Kontorova chain initiated by molecule impact
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Added by
Aliakbar Moradi Marjaneh
Publication date
2018
fields
Physics
and research's language is
English
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The Frenkel-Kontorova chain with a free end is used to study initiation and propagation of crowdions (anti-kinks) caused by impact of a molecule consisting of K atoms. It is found that molecules with 1 < K < 10 are more efficient in initiation of crowdions as compared to single atom (K = 1) because total energy needed to initiate the crowdions by molecules is smaller. This happens because single atom can initiate in the chain only sharp, fast-moving crowdions that requires a relatively large energy. Molecule has finite length, that is why it is able to excite a wider crowdion with a smaller velocity and smaller energy. Our results can shed light on the atomistic mechanisms of mass transfer in crystals subject to atom and molecule bombardment.
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By means of atomistic simulations, we demonstrate that a dislocation core exhibits intermittent quasistatic restructuring during incremental shear within the same Peierls valley. This can be regarded as a stick-slip transition, which is also reproduced for a one-dimensional Frenkel-Kontorova chain under rigid boundary conditions. This occurs due to a discontinuous jump in an order parameter of the system, which signifies the extent of region forbidden for the presence of particles in the chain. The stick-slip phenomenon observed in the dislocation core is also shown to be reflected after dimensionality reduction of the multidimensional atomic coordinates, which provides a basis for comparison with the simple one-dimensional chain.
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Simple models for friction are typically one-dimensional, but real interfaces are two-dimensional. We investigate the effects of the second dimension on static and dynamic friction by using the Frenkel-Kontorova (FK) model. We study the two most straightforward extensions of the FK model to two dimensions and simulate both the static and dynamic properties. We show that the behavior of the static friction is robust and remains similar in two dimensions for physically reasonable parameter values. The dynamic friction, however, is strongly influenced by the second dimension and the accompanying additional dynamics and parameters introduced into the models. We discuss our results in terms of the thermal equilibration and phonon dispersion relations of the lattices, establishing a physically realistic and suitable two-dimensional extension of the FK model. We find that the presence of additional dissipation channels can increase the friction and produces significantly different temperature-dependence when compared to the one-dimensional case. We also briefly study the anisotropy of the dynamic friction and show highly nontrivial effects, including that the friction anisotropy can lead to motion in different directions depending on the value of the initial velocity.
We solved the Frenkel-Kontorova model with the potential $V(u)= -frac{1}{2} |lambda|(u-{rm Int}[u]-frac{1}{2})^2$ exactly. For given $|lambda|$, there exists a positive integer $q_c$ such that for almost all values of the tensile force $sigma$, the winding number $omega$ of the ground state configuration is a rational number in the $q_c$-th level Farey tree. For fixed $omega=p/q$, there is a critical $lambda_c$ when a first order phase transition occurs. This phase transition can be understood as the dissociation of a large molecule into two smaller ones in a manner dictated by the Farey tree. A kind of ``commensurate-incommensurate transition occurs at critical values of $sigma$ when two sizes of molecules co-exist. ``Soliton in the usual sense does not exist but induces a transformation of one size of molecules into the other.
We study numerically phonon modes of the classical one-dimensional Frenkel-Kontorova chain, in the regime of pinned phase characterized by the phonon gap and devils staircase, as well as by a large number of states (configurational excitations), which energy splitting from the ground state is exponentially small. We demonstrate, these states behave like disorder media: their phonon modes are {it exponentially} localized, in contrast to the phonon modes in the ground state, where phonons are {it prelocalized} only. We demonstrate also, the phonon frequency spectrum of the ground state has an hierarchical structure, a direct manifestation of hierarchical spatial structure, found for the ground state of the FK chain in our recent work.
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