Simulating dislocation loop internal dynamics and collective diffusion using stochastic differential equations

Journal Article · Sat Oct 01 00:00:00 EDT 2011 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.84.134109· OSTI ID:21596889

Derlet, P M; Gilbert, M R; Dudarev, S L ^[1]

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1. Condensed Matter Theory Group, Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland)

Nanoscale prismatic loops are modeled via a partial stochastic differential equation that describes an overdamped continuum elastic string, with a view to describing both the internal and collective dynamics of the loop as a function of temperature. Within the framework of the Langevin equation, expressions are derived that relate the empirical parameters of the model, the friction per unit length, and the elastic stiffness per unit length, to observables that can be obtained directly via molecular-dynamics simulations of interstitial or vacancy prismatic loop mobility. The resulting expressions naturally exhibit the properties that the collective diffusion coefficient of the loop (i) scales inversely with the square root of the number of interstitials, a feature that has been observed in both atomistic simulation and in situ TEM investigations of loop mobility, and (ii) the collective diffusion coefficient is not at all dependent on the internal interactions within the loop, thus qualitatively rationalizing past simulation results showing that the characteristic migration energy barrier is comparable to that of a single interstitial, and cluster migration is a result of individual (but correlated) interstitial activity.

• OSTI ID: 21596889
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 84, Issue 13; Other Information: DOI: 10.1103/PhysRevB.84.134109; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
DIFFERENTIAL EQUATIONS
DIFFUSION
DISLOCATIONS
FLEXIBILITY
INTERACTIONS
INTERSTITIALS
LANGEVIN EQUATION
MIGRATION
MOBILITY
MOLECULAR DYNAMICS METHOD
NANOSTRUCTURES
SIMULATION
STOCHASTIC PROCESSES
TEMPERATURE DEPENDENCE
TRANSMISSION ELECTRON MICROSCOPY
VACANCIES
CALCULATION METHODS
CRYSTAL DEFECTS
CRYSTAL STRUCTURE
ELECTRON MICROSCOPY
EQUATIONS
LINE DEFECTS
MECHANICAL PROPERTIES
MICROSCOPY
POINT DEFECTS
TENSILE PROPERTIES