arXiv subjects

Nikhil Chandra Admal

Publications and source records attributed to Nikhil Chandra Admal.

16 recordsLinked to original sources

arXiv2026

Grain Boundary Phase Transitions Enable Diffusionless Climb of Disconnections

Dislocation-grain boundary (GB) interactions govern the mechanical response of polycrystalline materials by controlling dislocation absorption, transmission, and interfacial plasticity. While disconnection climb is conventionally understood to require the absorption or emission of point defects supplied through long range bulk diffusion, GBs possess intrinsic configurational degrees of freedom associated with their atomic structure, or microstate, that may provide an alternative mechanism. Here, using bicrystallography and molecular dynamics simulations, we investigate the interaction of shear dislocation loops with the [1 1 0](-5 5 14) symmetric tilt grain boundary in Al. We show that dislocation absorption generates a mobile extrinsic disconnection with a nonzero climb component that propagates conservatively along the interface without long-range bulk point-defect transport. Its motion is accompanied by a localized GB phase transformation mediated by cooperative atomic rearrangements within the GB core, producing successive metastable GB microstates. These findings establish a direct coupling between lattice dislocations and GB phase evolution and reveal a conservative mechanism for disconnection climb fundamentally distinct from conventional vacancy-mediated climb.

cond-mat.mtrl-sci↗

arXiv2026

Inverse design of heterodeformations for strain soliton networks in bilayer 2D materials

Strain soliton networks strongly influence the structural and electronic properties of heterodeformed bilayer systems, yet their design remains challenging due to the high dimensionality of heterodeformation space and the absence of a direct map between deformation and network geometry. In this work, we introduce a geometric framework that establishes a one-to-one mapping between heterodeformations and the geometry of the strain soliton network expressed as line vector-Burgers vector pairs. The admissible networks are constrained by topology dictated by the generalized stacking fault energy landscape. We show that the moiré Bravais lattice, corresponding to a uniform heterodeformation, alone is insufficient to characterize the interface: distinct heterodeformations can share identical moiré Bravais lattices while producing different soliton networks, reflecting an inherent many-to-one mapping when only translational symmetry is considered. In contrast, the soliton network encodes the full multilattice geometry of the interface, including topology and connectivity, which are not captured by the moiré Bravais lattice alone. The proposed framework enables the direct construction of heterodeformations from target networks, providing a systematic route for inverse design of moiré interfaces beyond conventional twist-based approaches.

cond-mat.mtrl-sci↗

arXiv2026

Multiscale analysis of large twist ferroelectricity and swirling dislocations in bilayer hexagonal boron nitride

With its atomically thin structure and intrinsic ferroelectric properties, heterodeformed bilayer hexagonal boron nitride (hBN) has gained prominence in next-generation non-volatile memory applications. However, studies to date have focused almost exclusively on small$-$twist bilayer hBN, leaving the question of whether ferroelectricity can persist under small heterostrain and large heterodeformation entirely unexplored. In this work, we establish the crystallographic origin of ferroelectricity in bilayer hBN configurations heterodeformed relative to high-symmetry configurations such as the AA-stacking and the $21.786789^\circ$ twisted configuration ($Σ7$), using Smith normal form bicrystallography. We then demonstrate out-of-plane ferroelectricity in bilayer hBN across configurations vicinal to both the AA and $\Sigma7$ stackings. Atomistic simulations reveal that AA-vicinal systems support ferroelectricity under both small twist and small strain, with polarization switching in the latter governed by the deformation of swirling dislocations rather than the straight interface dislocations seen in the former. For $\Sigma7$-vicinal systems, where existing interatomic potentials underperform particularly under extreme out-of-plane compression, we develop a density-functional-theory-informed continuum framework-the bicrystallography-informed frame-invariant multiscale (BFIM) model, which captures out-of-plane ferroelectricity in heterodeformed configurations vicinal to the $Σ7$ stacking. Interface dislocations in these large heterodeformed bilayer configurations exhibit markedly smaller Burgers vectors compared to the interface dislocations in small-twist and small-strain bilayer hBN. The BFIM model reproduces experimental results and provides a powerful, computationally efficient framework for predicting ferroelectricity in large-unit-cell heterostructures.

cond-mat.mtrl-sci↗

arXiv2025

Energetics of the nucleation and glide of disconnection modes in symmetric tilt grain boundaries

GBs evolve by the nucleation and glide of disconnections, which are dislocations with a step character. In this work, motivated by recent success in predicting GB properties such as the shear coupling factor and mobility from the intrinsic properties of disconnections, we develop a systematic method to calculate the energy barriers for the nucleation and glide of individual disconnection modes under arbitrary driving forces. This method combines tools from bicrystallography to enumerate disconnection modes and the NEB method to calculate their energetics, yielding minimum energy paths and atomistic mechanisms for the nucleation and glide of each disconnection mode. We apply the method to accurately predict shear coupling factors of [001] symmetric tilt grain boundaries in Cu. Particular attention is paid to the boundaries where the classical disconnection nucleation model produces incorrect nucleation barriers. We demonstrate that the method can accurately compute the energy barriers and predict the shear coupling factors for low temperature regime.

cond-mat.mtrl-sci↗

arXiv2025

Quantifying superlubricity of bilayer graphene from the mobility of interface dislocations

Van der Waals (vdW) heterostructures subjected to interlayer twists or heterostrains demonstrate structural superlubricity, leading to their potential use as superlubricants in micro- and nano-electro-mechanical devices. However, quantifying superlubricity across the vast four-dimensional heterodeformation space using experiments or atomic-scale simulations is a challenging task. In this work, we develop an atomically informed dynamic Frenkel--Kontorova (DFK) model for predicting the interface friction drag coefficient of an arbitrarily heterodeformed bilayer graphene (BG) system. The model is motivated by MD simulations of friction in heterodeformed BG. In particular, we note that interface dislocations formed during structural relaxation translate in unison when a heterodeformed BG is subjected to shear traction, leading us to the hypothesis that the kinetic properties of interface dislocations determine the friction drag coefficient of the interface. The constitutive law of the DFK model comprises the generalized stacking fault energy of the AB stacking, a scalar displacement drag coefficient, and the elastic properties of graphene, which are all obtained from atomistic simulations. Simulations of the DFK model confirm our hypothesis since a single choice of the displacement drag coefficient, fit to the kinetic property of an individual dislocation in an atomistic simulation, predicts interface friction in any heterodeformed BG. By bridging the gap between dislocation kinetics at the microscale to interface friction at the macroscale, the DFK model enables a high-throughput investigation of strain-engineered vdW heterostructures.

cond-mat.mes-hall↗

arXiv2023

Statistics of grain microstructure evolution under anisotropic grain boundary energies and mobilities using threshold-dynamics

This paper investigates the statistical behavior of two-dimensional grain microstructures during grain growth under anisotropic grain boundary characters. We employ the threshold-dynamics method, which allows for unparalleled computational speed, to simulate the full-field curvature motion of grain boundaries in a large polycrystal ensemble. Two sets of numerical experiments are performed to explore the effect of grain boundary anisotropy on the evolution of microstructure features. In the first experiment, we focus on abnormal grain growth and find that grain boundary anisotropy introduces a statistical preference for certain grain orientations. This leads to changes in the overall grain size distribution from the isotropic case. In the second experiment, we examine the texture development and growth of twin grain boundaries at different initial microstructures. We find that both phenomena are more pronounced when the initial microstructure has a dominant fraction of high-angle grain boundaries. Our results suggest effective grain boundary engineering strategies for improving material properties.

cond-mat.mtrl-sci↗

arXiv2023

Bicrystallography-informed Frenkel-Kontorova model for interlayer dislocations in strained 2D heterostructures

In recent years, van der Waals (vdW) heterostructures and homostructures, which consist of stacks of two-dimensional (2D) materials, have risen to prominence due to their association with exotic quantum phenomena. Atomistic scale relaxation effects play an extremely important role in the electronic scale quantum physics of these systems. We investigate such structural relaxation effects in this work using atomistic and mesoscale models, within the context of twisted bilayer graphene -- a well-known heterostructure system that features moire patterns arising from the lattices of the two graphene layers. For small twist angles, atomic relaxation effects in this system are associated with the natural emergence of interface dislocations or strain solitons, which result from the cyclic nature of the generalized stacking fault energy (GSFE), that measures the interface energy based on the relative movement of the two layers. In this work, we first demonstrate using atomistic simulations that atomic reconstruction in bilayer graphene under a large twist also results from interface dislocations, although the Burgers vectors of such dislocations are considerably smaller than those observed in small-twist systems. To reveal the translational invariance of the heterointerface responsible for the formation of such dislocations, we derive the translational symmetry of the GSFE of a 2D heterostructure using the notions of coincident site lattices (CSLs) and displacement shift complete lattices (DSCLs). The workhorse for this exercise is a recently developed Smith normal form bicrystallography framework. Next, we construct a bicrystallography-informed and frame-invariant Frenkel-Kontorova model, which can predict the formation of strain solitons in arbitrary 2D heterostructures, and apply it to study a heterostrained, large-twist bilayer graphene system.

cond-mat.mes-hall↗

arXiv2021

A crystal symmetry-invariant Kobayashi--Warren--Carter grain boundary model and its implementation using a thresholding algorithm

One of the most important aims of grain boundary modeling is to predict the evolution of a large collection of grains in phenomena such as abnormal grain growth, coupled grain boundary motion, and recrystallization that occur under extreme thermomechanical loads. A unified framework to study the coevolution of grain boundaries with bulk plasticity has recently been developed by Admal et al. (2018), which is based on modeling grain boundaries as continuum dislocations governed by an energy based on the Kobayashi--Warren--Carter (KWC) model (Kobayashi et al., 1998, 2000). While the resulting unified model demonstrates coupled grain boundary motion and polygonization (seen in recrystallization), it is restricted to grain boundary energies of the Read--Shockley type, which applies only to small misorientation angles. In addition, the implementation of the unified model using finite elements inherits the computational challenges of the KWC model that originate from the singular diffusive nature of its governing equations. The main goal of this study is to generalize the KWC functional to grain boundary energies beyond the Read--Shockley-type that respect the bicrystallography of grain boundaries. The computational challenges of the KWC model are addressed by developing a thresholding method that relies on a primal dual algorithm and the fast marching method, resulting in an O(NlogN) algorithm, where N is the number of grid points. We validate the model by demonstrating the Herring angle relation, followed by a study of the grain microstructure evolution in a two-dimensional face-centered cubic copper polycrystal with crystal symmetry-invariant grain boundary energy data obtained from the lattice matching method of Runnels et al. (2016a,b).

cond-mat.mtrl-sci↗

arXiv2021

Polycrystal plasticity with grain boundary evolution: A numerically efficient dislocation-based diffuse-interface model

Grain structure plays a key role in the mechanical properties of alloy materials. Engineering the grain structure requires a comprehensive understanding of the evolution of grain boundaries (GBs) when a material is subjected to various manufacturing processes. To this end, we present a computationally efficient framework to describe the co-evolution of bulk plasticity and GBs. We represent GBs as diffused geometrically necessary dislocations, whose evolution describes GB plasticity. Under this representation, the evolution of GBs and bulk plasticity is described in unison using the evolution equation for the plastic deformation gradient, an equation central to classical crystal plasticity theories. To reduce the number of degrees of freedom, we present a procedure which combines the governing equations for each slip rates into a set of governing equations for the plastic deformation gradient. Finally, we outline a method to introduce a synthetic potential to drive migration of a flat GB. Three numerical examples are presented to demonstrate the model. First, a scaling test is used to demonstrate the computational efficiency of our framework. Second, we study the evolution of a tricrystal, formed by embedding a circular grain into a bicrystal, and demonstrate qualitative agreement between the predictions of our model and those of molecular dynamics simulations by Trautt and Mishin (2014). Finally, we demonstrate the effect of applied loading in texture evolution by simulating the evolution of a synthetic polycrystal under applied displacements.

cond-mat.mtrl-sci↗

arXiv2019

The Green tensor of Mindlin's anisotropic first strain gradient elasticity

We derive the Green tensor of Mindlin's anisotropic first strain gradient elasticity. The Green tensor is valid for arbitrary anisotropic materials, with up to 21 elastic constants and 171 gradient elastic constants in the general case of triclinic media. In contrast to its classical counterpart, the Green tensor is non-singular at the origin, and it converges to the classical tensor a few characteristic lengths away from the origin. Therefore, the Green tensor of Mindlin's first strain gradient elasticity can be regarded as a physical regularization of the classical anisotropic Green tensor. The isotropic Green tensor and other special cases are recovered as particular instances of the general anisotropic result. The Green tensor is implemented numerically and applied to the Kelvin problem with elastic constants determined from interatomic potentials. Results are compared to molecular statics calculations carried out with the same potentials.

cond-mat.mtrl-sci↗

arXiv2017

A non-singular theory of dislocations in anisotropic crystals

We develop a non-singular theory of three-dimensional dislocation loops in a particular version of Mindlin's anisotropic gradient elasticity with up to six length scale parameters. The theory is systematically developed as a generalization of the classical anisotropic theory in the framework of linearized incompatible elasticity. The non-singular version of all key equations of anisotropic dislocation theory are derived as line integrals, including the Burgers displacement equation with isolated solid angle, the Peach-Koehler stress equation, the Mura-Willis equation for the elastic distortion, and the Peach-Koehler force. The expression for the interaction energy between two dislocation loops as a double line integral is obtained directly, without the use of a stress function. It is shown that all the elastic fields are non-singular, and that they converge to their classical counterparts a few characteristic lengths away from the dislocation core. In practice, the non-singular fields can be obtained from the classical ones by replacing the classical (singular) anisotropic Green's tensor with the non-singular anisotropic Green's tensor derived by \cite{Lazar:2015ja}. The elastic solution is valid for arbitrary anisotropic media. In addition to the classical anisotropic elastic constants, the non-singular Green's tensor depends on a second order symmetric tensor of length scale parameters modeling a weak non-locality, whose structure depends on the specific class of crystal symmetry. The anisotropic Helmholtz operator defined by such tensor admits a Green's function which is used as the spreading function for the Burgers vector density. As a consequence, the Burgers vector density spreads differently in different crystal structures.

cond-mat.mtrl-sci↗

arXiv2017

A unified framework for polycrystal plasticity with grain boundary evolution

Plastic deformation in polycrystals is governed by the interplay between intra-granular slip and grain boundary-mediated plasticity. However, while the role played by bulk dislocations is relatively well-understood, the contribution of grain boundaries (GBs) has only recently begun to be studied. GB plasticity is known to play a key role along with bulk plasticity under a wide range of conditions, such as dynamic recovery, superplasticity, severe plastic deformation , etc., and developing models capable of simultaneously capturing GB and bulk plasticity has become a topic of high relevance. In this paper we develop a thermodynamically-consistent polycrystal plasticity model capable of simulating a variety of grain boundary-mediated plastic processes in conjunction with bulk dislocation slip. The model starts from the description of a single crystal and creates lattice strain-free polycrystalline configurations by using a specially-designed multiplicative decomposition developed by the authors. This leads to the introduction of a particular class of geometrically necessary dislocations (GND) that define fundamental GB features such as misorientation and inclination. The evolution of the system is based on an energy functional that uses a non-standard function of the GND tensor to account for the grain boundary energy, as well as for the standard elastic energy. Our implementation builds on smooth descriptions of GBs inspired on diffuse-interface models of grain evolution for numerical convenience. We demonstrate the generality and potential of the methodology by simulating a wide variety of phenomena such as shear-induced GB sliding, coupled GB motion, curvature-induced grain rotation and shrinkage, and polygonization via dislocation sub-grain formation.

cond-mat.mtrl-sci↗

arXiv2017

Diffuse-interface polycrystal plasticity: Expressing grain boundaries as geometrically necessary dislocations

The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F(X,t) = F^L(X,t) F^P(X,t), an initial stress-free polycrystal is constructed by imposing F^L to be a piecewise constant rotation field R^0(X), and F^P = R^0(X)^T, thereby having F(X,0) = I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.

physics.comp-ph↗

arXiv2016

The atomistic representation of first strain-gradient elastic tensors

We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical (2nd-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy-Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices and multi-lattices. We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.

cond-mat.mtrl-sci↗

arXiv2015

Stress and heat flux for arbitrary multi-body potentials: A unified framework

A two-step unified framework for the evaluation of continuum field expressions from molecular simulations for arbitrary interatomic potentials is presented. First, pointwise continuum fields are obtained using a generalization of the Irving-Kirkwood procedure to arbitrary multi-body potentials. Two ambiguities associated with the original Irving-Kirkwood procedure (which was limited to pair potential interactions) are addressed in its generalization. The first ambiguity is due to the non-uniqueness of the decomposition of the force on an atom as a sum of central forces, which is a result of the non-uniqueness of the potential energy representation in terms of distances between the particles. This is in turn related to the shape space of the system. The second ambiguity is due to the non-uniqueness of the energy decomposition between particles. The latter can be completely avoided through an alternate derivation for the energy balance. It is found that the expressions for the specific internal energy and the heat flux obtained through the alternate derivation are quite different from the original Irving-Kirkwood procedure and appear to be more physically reasonable. Next, in the second step of the unified framework, spatial averaging is applied to the pointwise field to obtain the corresponding macroscopic quantities. These lead to expressions suitable for computation in molecular dynamics simulations. It is shown that the important commonly-used microscopic definitions for the stress tensor and heat flux vector are recovered in this process as special cases (generalized to arbitrary multi-body potentials). Several numerical experiments are conducted to compare the new expression for the specific internal energy with the original one.

physics.chem-ph↗

arXiv2010

A Unified Interpretation of Stress in Molecular Systems

The microscopic definition for the Cauchy stress tensor has been examined in the past from many different perspectives. This has led to different expressions for the stress tensor and consequently the "correct" definition has been a subject of debate and controversy. In this work, a unified framework is set up in which all existing definitions can be derived, thus establishing the connections between them. The framework is based on the non-equilibrium statistical mechanics procedure introduced by Irving, Kirkwood and Noll, followed by spatial averaging. The Irving--Kirkwood--Noll procedure is extended to multi-body potentials with continuously differentiable extensions and generalized to non-straight bonds, which may be important for particles with internal structure. Connections between this approach and the direct spatial averaging approach of Murdoch and Hardy are discussed and the Murdoch--Hardy procedure is systematized. Possible sources of non-uniqueness of the stress tensor, resulting separately from both procedures, are identified and addressed. Numerical experiments using molecular dynamics and lattice statics are conducted to examine the behavior of the resulting stress definitions including their convergence with the spatial averaging domain size and their symmetry properties.

math-ph↗