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Universality classes for unstable crystal growth.

Sofia Biagi1, Chaouqi Misbah1, Paolo Politi2

  • 1Université Grenoble 1/CNRS, LIPhy UMR 5588, Grenoble, F-38401, France and Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary
This summary is machine-generated.

This study explores universality in unstable crystal growth, identifying two distinct classes based on pattern formation. Key exponents reveal that pattern symmetry and specific current functions are irrelevant to universality classes.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Universality is crucial for classifying equilibrium critical phenomena.
  • Nonequilibrium universality classes are less understood, with few established examples like phase separation and kinetic roughening.
  • Unstable crystal growth presents an out-of-equilibrium case between phase ordering and pattern formation.

Purpose of the Study:

  • To investigate universality in unstable crystal growth.
  • To identify critical exponents and relevant parameters for defining universality classes.
  • To analyze a 2+1 dimensional family of nonlinear equations for crystal surface height.

Main Methods:

  • Perturbative, multiscale analysis of nonlinear equations for crystal surface height.
  • Derivation of phase diffusion equations to capture dynamics.
  • Calculation of critical exponents governing pattern size and slope evolution.

Main Results:

  • Identified two critical exponents: coarsening exponent (n) and slope exponent (β).
  • Established two universality classes: one with faceting (n=1/3, β=0) and one without (n=1/4, β>0).
  • Determined that pattern symmetry and the specific form of the surface mass current are irrelevant to universality.

Conclusions:

  • Unstable crystal growth exhibits distinct universality classes determined by faceting.
  • The identified exponents and irrelevant parameters simplify the classification of these nonequilibrium phenomena.
  • Space dimensionality appears to be irrelevant for this system's universality.