Kinetics driven commensurate -
incommensurate transitions in 2-d
Ising interfaces:
The steady state structure of an interface in an Ising system on a
square lattice placed in a non-uniform
external field, shows a commensurate -incommensurate transition driven
by the velocity of the interface. The non-uniform field has a profile
with a fixed shape which is designed to stabilize a flat interface, and
is translated
with velocity v. For small
velocities the interface is stuck to the profile and is rippled with a
periodicity which may be either commensurate or in-commensurate with
the lattice parameter of the square lattice. For a general orientat
ion of the
profile, the local slope of the interface locks in to one of infinitely
many rational directions producing a
devil's staircase structure. These
``lock-in'' or commensurate structures dissappear as v increases
through
a kinetics driven commensurate - incommensurate transition. For large v the
interface
becomes detached from the field profile and coarsens with
Kardar-Parisi-Zang exponents. We have obtained the complete
phase-diagram and the
multifractal spectrum
corresponding
to these structures numerically
together with several
exact analytic results
concerning the dynamics of the rippled phases. Our
work may have technological implications in crystal growth and the
production of surfaces with various desired surface morphologies.
Statics
and Dynamics of Solid liquid interfaces:
Publications:
- Abhishek Chaudhuri, P. A. Sreeram and Surajit Sengupta, A kinetics driven
commensurate - incommensurate transition, submitted to Phas. Trans.
(2004) pdf
- Abhishek Chaudhuri, P. A. Sreeram, Surajit Sengupta, Growing smooth
interfaces with inhomogeneous, moving external fields: dynamical
transitions, devil's staircases and self-assembled ripples
Phys. Rev. Lett. 89,
176101 (2002).
- Abhishek Chaudhuri and Surajit Sengupta, Profile-driven
interfaces in 1+1 dimensions: periodic steady states, dynamical melting
and detachment,
Physica A, 318, 30
(2003).
- S. Sengupta, H. R. Krishnamurthy and T. V. Ramakrishnan, A microscopic theory of
the b.c.c. - f.c.c. interface, Europhys. Lett. 27, 587, (1994).