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Statistical mechanics of dislocation pileups in two dimensions. | LitMetric

Statistical mechanics of dislocation pileups in two dimensions.

Phys Rev E

Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

Published: February 2021

AI Article Synopsis

  • Dislocation pileups affect the properties of crystalline solids, and this research examines their statistical mechanics in two-dimensional crystals where dislocations form one-dimensional lattices.* -
  • The study identifies two types of phase transitions in dislocation pileups, including a thermal depinning transition from a pinned-defect phase to a floating-defect state and a melting transition to a defect liquid.* -
  • Key findings include the analysis of transition temperatures observable through the one-dimensional structure factor, revealing changes in Bragg peaks as the system transitions from pinned to melting states, with critical exponents calculated using random matrix theory.*

Article Abstract

Dislocation pileups directly impact the material properties of crystalline solids through the arrangement and collective motion of interacting dislocations. We study the statistical mechanics of these ordered defect structures embedded in two-dimensional crystals, where the dislocations themselves form one-dimensional lattices. In particular, pileups exemplify a new class of inhomogeneous crystals characterized by spatially varying lattice spacings. By analytically formulating key statistical quantities and comparing our theory to numerical experiments using an intriguing mapping of dislocation positions onto the eigenvalues of recently studied random matrix ensembles, we uncover two types of one-dimensional phase transitions in dislocation pileups: A thermal depinning transition out of long-range translational order from the pinned-defect phase, due to a periodic Peierls potential, to a floating-defect state, and finally the melting out of a quasi-long-range ordered floating-defect solid phase to a defect liquid. We also find the set of transition temperatures at which these transitions can be directly observed through the one-dimensional structure factor, where the delta function Bragg peaks, at the pinned-defect to floating-defect transition, broaden into algebraically diverging Bragg peaks, which then sequentially disappear as one approaches the two-dimensional melting transition of the host crystal. We calculate a set of temperature-dependent critical exponents for the structure factor and radial distribution function, and obtain their exact forms for both uniform and inhomogeneous pileups using random matrix theory.

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Source
http://dx.doi.org/10.1103/PhysRevE.103.022139DOI Listing

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