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Twinning in Strained Ferroelastics: Microstructure and Statistics
X. Ding1,2, T. Lookman2, A. Saxena2, J. Sun1, E.K.H. Salje1,2,3
[email protected]
1 State
Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049,
China
2 Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3 Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK
The dynamic evolution in ferroelastic crystals under external shear is explored by computer simulation
of a two-dimensional model. The characteristic geometrical patterns obtained during shear
deformation include dynamic tweed in the elastic regime as well as interpenetrating needle domains in
the plastic regime. As a result, the statistics of ‘jerk energy’ differ in the elastic and plastic regimes. In
the elastic regime the distributions of jerk energy are sensitive to temperature and initial
configurations. However, in the plastic regime the jerk distributions are rather robust and do not
depend much on the details of the configurations, although the geometrical pattern formed after yield
is strongly influenced by the elastic constants of the materials and the configurations we used.
Specifically, for all geometrical configurations we studied, the energy distribution of jerks shows a
power law noise pattern P(E) ~ E-(γ-1) (γ-1= 1.3-2) at low temperatures and a Vogel-Fulcher distribution
P(E) ~ exp-(E/E0) at high temperatures. More complex behavior occurs at the crossover between
these two regimes where our simulated jerk distributions are very well described by a generalized
Poisson distributions P(E) ~ E-(γ-1) exp-(E/E0)n with n=0.4-0.5 and γ-1 ≈ 0 (Kohlrausch law). The
geometrical mechanisms for the evolution of the ferroelastic microstructure under strain deformation
remain similar in all thermal regimes whereas their thermodynamic behavior differs dramatically: on
heating, from power law statistics via the Kohlrausch law to a Vogel-Fulcher law. There is hence no
simple way to predict the local evolution of the twin microstructure from just the observed statistical
behavior of a ferroelastic crystal. It is shown that the Poisson distribution is a convenient way to
describe the crossover behavior contained in all the experimental data. In addition, We find that shear
on materials with soft bulk moduli have much higher junction densities than those with hard bulk
moduli. Soft materials also show an increase in the junction density with diminishing sample size. The
change of the complexity and the number density of twin boundaries represents an important step
forward in the development of ‘domain boundary engineering’, where the functionality of the materials
is directly linked to the domain pattern.
References
[1] X. Ding, Z. Zhao, T. Looman, A.Saxena, E.Salje, Advanced Materials, 2012, 24, pp.5385-5389.
[2] X. Ding, T. Looman, Z. Zhao, A.Saxena, J. Sun, E.Salje, Physical Review B, 2013, in proof
[3] E. Salje, X. Ding, Z.Zhao, T.Lookman, A.Saxena, Physical Review B, 2011, 83, pp104109
[4] X. Ding, T. Lookman, E. K. H. Salje, and A. Saxena,, JOM, 2013, 65:pp 401-407
Keywords: twin boundary density; junctions; driven dynamical system; soft and hard materials.
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