Anomalous grain dynamics and grain locomotion of odd crystals

Abstract

Crystalline or polycrystalline systems governed by odd elastic responses are known to exhibit complex dynamical behaviors involving self-propelled dynamics of topological defects with spontaneous self-rotation of chiral crystallites. Unveiling and controlling the underlying mechanisms require studies across multiple scales. We develop such a type of approach that bridges between microscopic and mesoscopic scales, in the form of a phase field crystal model incorporating transverse interactions. This continuum density field theory features two-dimensional parity symmetry breaking and odd elasticity, and generates a variety of interesting phenomena that agree well with recent experiments and particle-based simulations of active and living chiral crystals, including self-rotating crystallites, dislocation self-propulsion and proliferation, and fragmentation in polycrystals. We identify a distinct type of surface cusp instability induced by self-generated surface odd stress that results in self-fission of single-crystalline grains. This mechanism is pivotal for the occurrence of various anomalous grain dynamics for odd crystals, particularly the predictions of a transition from normal to reverse Ostwald ripening for self-rotating odd grains, and a transition from grain coarsening to grain self-fragmentation in the dynamical polycrystalline state with an increase of transverse interaction strength. We also demonstrate that the single-grain dynamics can be maneuvered through the variation of interparticle transverse interactions. This allows to steer the desired pathway of grain locomotion and to control the transition between grain self-rotation, self-rolling, and self-translation. Our results provide insights for the design and control of structural and dynamical properties of active odd elastic materials.

Figures (5)

• Figure 1: T-PFC simulation results for self-rotating odd crystals and motile defects. (A) A snapshot of a self-rotating single-crystalline grain at $\alpha_1=2$, with a schematic illustrating nonzero net transverse force on the surface. (B) The scaling of grain rotation frequency $\omega$ vs particle number $N$, showing a data collapse for different transverse interaction strength $\alpha_1$. The inset shows the experimental data of starfish-embryos living crystals in Ref. TanNature22 for the same $N$ range. The simulation results are fitted into a power law scaling which is also indicated in the inset for comparison. (C) Schematic of a penta-hepta dislocation with local nonzero net transverse force, which leads to dislocation self-glide and the unbinding of a dislocation dipole as shown in the snapshots of the simulated $\psi$ profile. The Burgers vector $\mathbf{b}$ is labeled for each dislocation. (D) A self-expanding circular grain boundary within a self-rotating crystallite, with $8^\circ$ misorientation at $\alpha_1=1$. (E) The climb and self-glide of two dislocations of opposite Burgers vectors at $\alpha_1=1$. Small arrows indicate the climb direction, and large arrows give the direction of self-glide along the Burgers vectors.
• Figure 2: (A) Critical grain radius $R_c$ for the onset of surface cusp instability as a function of transverse interaction strength $\alpha_1$, as identified from T-PFC simulations (up to $t=10^6$). Snapshots of the $\psi$ profile are shown in the inset of (A) for the instability onset and in (B) for the surface-emitted motile dislocations at $\alpha_1=2$, and in (C) for grain self-fission at $\alpha_1=3$.
• Figure 3: (A) Time evolution of grain sizes during the ripening process of two crystalline grains, showing a transition from normal to reverse Ostwald ripening with the increase of $\alpha_1$. (B and C) Simulation snapshots at $t=1000$ and $99400$ during the process of reverse Ostwald ripening with $\alpha_1=3$.
• Figure 4: Multigrain dynamics of the odd polycrystalline state. (A-C) Simulation snapshots at $t=10^5$, each showing the central quarter of the $2048 \times 2048$ simulated system, for initial conditions of multiple crystalline nuclei with $\bar{\psi}_0=-0.09$ at (A) $\alpha_1=1$ governed by grain coarsening dynamics and (B) $\alpha_1=3$ governed by grain self-fragmentation, and (C) from homogeneous initial state with $\bar{\psi}_0=0$ at $\alpha_1=3$. (D) Circularly averaged correlation function $C(r)$, with inset showing the exponential decay of its peak values, and (E) circularly averaged structure factor $S(q)$, with the corresponding log-log plots given in the inset, both at $t=10^5$ and for initial conditions of multiple nuclei. (F) Time variation of the correlation length $\xi$, showing a transition from grain coarsening to self-fragmentation dynamics with the increase of transverse interaction strength $\alpha_1$. (G and H) $\langle \xi \rangle$ and $\langle L_1 \rangle$, averaged over the late time stage ($t=8 \times 10^4$--$10^5$), as a function of $\alpha_1$, for two types of initial conditions. Power-law scalings are identified in the regime of grain self-fragmentation. Results in (D-H) have been averaged over 20 simulation runs for $2048 \times 2048$ system size.
• Figure 5: Odd grain locomotion simulated via the T-PFC model. (A) A transition from self-rotation, self-rolling, to self-translation of grain locomotion as controlled via spatially-varying transverse interaction strength $\alpha_0=\alpha_1$. The rotational and translational directions of the grain are indicated as arrows in the top panel which shows the simulation snapshot. The arrows in the middle panel illustrate the net surface transverse forces for each grain, and the spatial dependence of self-translation velocity $\langle v_c \rangle$ and self-rotation frequency $\langle \omega \rangle$ (averaged over $t=3000$--$5000$) is given in the bottom panel, with dashed curves being the fitting to the data calculated from simulations. (B and C) The controlled transport of odd elastic grains along (B) a circular trajectory and (C) S-shaped tracks, through the pre-designed 2D spatial distribution of $\alpha_{j=0,1}$.