arXiv subjects

Saswati Ganguly

Publications and source records attributed to Saswati Ganguly.

15 recordsLinked to original sources

arXiv2025

Vibrational similarities in jamming-unjamming of polycrystalline and disordered granular packings

We investigate the vibrational properties of polycrystalline monodisperse and disordered bidisperse granular packings during jamming and unjamming using discrete element method simulations. Both systems deviate from Debye scaling at low frequencies $(ω)$, but only bidisperse packings exhibit a low-$ω$ plateau. The low $ω$ exponent ($α$) in bidisperse packings evolves smoothly from zero (plateau) to near one (Debye scaling) with increasing packing fraction, whereas in polycrystalline packings, it changes discontinuously near jamming/unjamming, due to the nature of the contact network rearrangements. Despite structural modifications during the compression-decompression cycle, the exponent remains unchanged at the same distance from jamming density, regardless of the history. Nonaffine displacements and contact orientational order further confirm that structural features that impact low-$ω$ vibrational states and, hence, mechanical properties are largely restored upon decompression, reinforcing vibrational similarities between jamming and unjamming states.

cond-mat.soft↗

arXiv2022

Continuum mechanics for the elastic properties of crystals: Microscopic approach based on projection-operator formalism

We present a microscopic derivation of the laws of continuum mechanics of nonideal ordered solids including dissipation, defect diffusion, and heat transport. Starting point is the classical many-body Hamiltonian. The approach relies on the Zwanzig-Mori projection operator formalism to connect microscopic fluctuations to thermodynamic derivatives and transport coefficients. Conservation laws and spontaneous symmetry breaking, implemented via Bogoliubov's inequality, determine the selection of the slow variables. Density fluctuations in reciprocal space encode the displacement field and the defect concentration. Isothermal and adiabatic elastic constants are obtained from equilibrium correlations, while transport coefficients are given as Green-Kubo formulae, providing the basis for their measurement in atomistic simulations or colloidal experiments. The approach and results are compared to others from the literature.

cond-mat.stat-mech↗

arXiv2021

Elasticity in crystals with high density of local defects : insights from ultra-soft colloids

In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a microscopic basis to include and account for the motion of point-defects in an otherwise ordered crystalline structure. We study the elastic properties of a point-defect rich crystal within a first-principles theoretical framework derived from microscopic equations of motion. This framework allows us to make specific predictions pertaining to the mechanical properties which we can validate through deformation experiments performed in Molecular Dynamics simulations.

cond-mat.soft↗

arXiv2018

Plastic deformation of a permanently bonded network: stress relaxation by pleats

We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing `pleats'; system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on itself. To understand the pleating process, we introduce an external field that couples to local {\em non-affine} displacements, i.e. those displacements of neighbouring vertices that cannot be represented as a local affine strain. We obtain both zero and finite temperature phase diagrams in the strain -- field plane. Pleats occur here as a result of an equilibrium first-order transition from the homogeneous network to a heterogeneous phase where stress is localised within pleats and eliminated elsewhere. We show that in the thermodynamic limit the un-pleated state is always metastable at vanishing field for infinitesimal strain. Plastic deformation of the initially homogeneous network is akin to the decay of a metastable phase via a dynamical transition. We make predictions concerning local stress distributions and thermal effects associated with pleats which may be observable in suitable experimental systems.

cond-mat.soft↗

arXiv2018

The free energy of grain boundaries from atomistic computer simulation

A novel thermodynamic integration (TI) scheme is presented that allows computing the free energy of grain boundaries (GBs) in crystals from atomistic computer simulation. Unlike previous approaches, the method can be applied at arbitrary temperatures and allows for a systematic extrapolation to the thermodynamic limit. It is applied to a $\Sigma11$ GB in a face centered cubic (FCC) Lennard-Jones crystal. At a constant density, the GB free energy shows a non-monotonic temperature dependence with a maximum at about half the melting temperature and the GB changes from a rigid to a rough interface with distinct finite size scaling above this temperature.

cond-mat.stat-mech↗

arXiv2018

Do thermodynamically stable rigid solids exist?

Customarily, crystalline solids are defined to be {\em rigid} since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the {\em metastable} state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then employed to obtain the equilibrium free energy as a function of this variable. Our results lead to a new view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable by switching on an external field, which penalises particle rearrangements. This produces a line of first-order phase transitions in the field - strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference.

cond-mat.mtrl-sci↗

arXiv2017

Translationally invariant colloidal crystal templates

We show that dynamic, feed-back controlled optical traps, whose positions depend on the instantaneous local configuration of particles in a pre-determined way, can stabilise colloidal particles in finite lattices of ${\it any}$ given symmetry. Unlike in a static template, the crystal so formed is translationally invariant and retains all possible zero energy modes. We demonstrate this ${\it in-silico}$ by stabilising the unstable two-dimensional ${\it square}$ lattice in a model soft solid with isotropic interactions.

cond-mat.soft↗

arXiv2017

Contrasting the dynamics of elastic and non-elastic deformations across an experimental colloidal Martensitic transition

We present a framework to segregate the roles of elastic and non-elastic deformations in the examination of real-space experiments of solid-solid Martensitic transitions. The Martensitic transformation of a body-centred-tetragonal(BCT) to a body-centred-orthorhombic(BCO) crystal structure has been studied in a model system of micron-scale ionic microgel colloids. Non-affine fluctuations, i.e., displacement fluctuations that do not arise from purely elastic(affine) deformations, are detected in particle configurations acquired from the experiment. Tracking these fluctuations serves as a highly sensitive tool in signaling the onset of the Martensitic transition and precisely locating particle rearrangements occurring at length scales of a few particle diameters. Particle rearrangements associated with non-affine displacement modes become increasingly favorable during the transformation process. The nature of the displacement fluctuation modes that govern the transformation are shown to be different from those predominant in an equilibrium crystal. We show that BCO crystallites formed through shear may, remarkably, co-exist with those resulting from local rearrangements within the same sample.

cond-mat.soft↗

arXiv2017

Statistics of non-affine defect precursors: tailoring defect densities in colloidal crystals using external fields

Coarse-graining atomic displacements in a solid produces both local affine strains and "non-affine" fluctuations. Here we study the equilibrium dynamics of these coarse grained quantities to obtain space-time dependent correlation functions. We show how a subset of these thermally excited, non-affine fluctuations act as precursors for the nucleation of lattice defects and suggest how defect probabilities may be altered by an {\it experimentally realisable} "external" field conjugate to the global non-affinity parameter. Our results are amenable to verification in experiments on colloidal crystals using commonly available holographic laser tweezer and video microscopy techniques, and may lead to simple ways of controlling the defect density of a colloidal solid.

cond-mat.soft↗

arXiv2016

Excess vibrational modes of a crystal in an external non-affine field

Thermal displacement fluctuations in a crystal may be classified as either "affine" or "non-affine". While the former couples to external stress with familiar consequences, the response of a crystal when {\em non-affine} displacements are enhanced using the thermodynamically conjugate field, is relatively less studied. We examine this using a simple model of a crystal in two dimensions for which analytical calculations are possible. Enhancing non-affine fluctuations destabilises the crystal. The population of small frequency phonon modes increases, with the phonon density of states shifting, as a whole, towards zero frequency. Even though the crystal is free of disorder, we observe growing length and time scales. Our results, which may have implications for the glass transition and structural phase transitions in solids, are compared to molecular dynamics simulations. Possibility of experimental verification of these results is also discussed.

cond-mat.soft↗

arXiv2016

Amorphization of a crystalline solid by plastic deformation

We demonstrate that plastic deformation in solids is associated with a dynamic transition that is reminiscent to the transition from a superconducting to a mixed phase in Type II superconductors. We report analytic calculations, extensive molecular dynamics and sequential umbrella sampling Monte Carlo simulations of a two dimensional triangular crystalline solid undergoing plastic deformation under strain. The solid consists of particles connected by harmonic springs. Non-affine displacement fluctuations of the solid are enhanced using an external field, causing a rich deformation behaviour. The external field leads to a mixed phase, where defect and stress-free crystallites are surrounded by a network of amorphous regions with large local internal stress --- a "stress Meissner" effect. The transition shows slow ageing dynamics caused by the presence of many competing, non-crystalline free-energy minima. Under uniform uniaxial strain, this amorphization transition gives rise to irreversible plastic deformation with the amorphous regions appearing as band-like structures. Our results may be checked by careful experiments on colloidal crystals using holographic optical tweezers.

cond-mat.soft↗

arXiv2016

Equilibrium and dynamic pleating of a crystalline bonded network

We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the homogeneous phase, a number of heterogeneous "pleated" phases, which can be stabilised by an external field. This field is conjugate to a global collective variable quantifying "non-affineness", i.e.~the deviation of local particle displacements from local affine deformation. In the pleated phase, stress is localised in ordered rows of pleats and eliminated from the rest of the lattice. The {\em kinetics} of the phase transition is unobservably slow in molecular dynamics simulation near coexistence, due to very large free energy barriers. When the external field is increased further to lower these barriers, the network exhibits rich dynamic behaviour: it transforms into a {\em metastable} phase with the stress now localised in a {\em disordered} arrangement of pleats. The pattern of pleats shows ageing dynamics and slow relaxation to equilibrium. Our predictions may be checked by experiments on tethered colloidal solids in dynamic laser traps.

cond-mat.soft↗

arXiv2015

Non-affine fluctuations and the Statistics of Defect Precursors in the Planar Honeycomb Lattice

Certain localised displacement fluctuations in the planar honeycomb lattice may be identified as precursors to topological defects. We show that these fluctuations are among the most pronounced {\em non-affine} distortions of an elemental coarse graining volume of the honeycomb structure at non zero temperatures. We obtain the statistics of these precursor modes in the canonical ensemble, evaluating exactly their single point and two-point spatio-temporal distributions, for a lattice with harmonic nearest neighbour and next near neighbour bonds. As the solid is destabilised by tuning interactions, the precursor fluctuations diverge and correlations become long-lived and long-ranged.

cond-mat.mtrl-sci↗

arXiv2015

Pre-yield non-affine fluctuations and a hidden critical point in strained crystals

A crystalline solid exhibits thermally induced localised {\em non-affine} droplets in the absence of external stress. Here we show that upon an imposed shear, the size of these droplets grow until they percolate at a critical strain, well {\em below} the value at which the solid begins to yield. This critical point does not manifest in bulk thermodynamic or mechanical properties, but is {\em hidden} and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets and a sudden enhancement in defect pair concentration. Slow relaxation of stress and an-elasticity appear as observable dynamical consequences of this hidden criticality. Our results may be directly verified in colloidal crystals with video microscopy techniques but are expected to have more general validity.

cond-mat.mtrl-sci↗

arXiv2012

Non-affine displacements in crystalline solids in the harmonic limit

A systematic coarse graining of microscopic atomic displacements generates a local elastic deformation tensor ${\mathsf D}$ as well as a positive definite scalar $χ$ measuring non-affinity, i.e. the extent to which the displacements are not representable as affine deformations of a reference crystal. We perform an exact calculation of the statistics of $χ$ and ${\mathsf D}$ and their spatial correlations for solids at low temperatures, within a harmonic approximation and in one and two dimensions. We obtain the joint distribution $P(χ, {\mathsf D})$ and the two point spatial correlation functions for $χ$ and ${\mathsf D}$. We show that non-affine and affine deformations are coupled even in a harmonic solid, with a strength that depends on the size of the coarse graining volume $Ω$ and dimensionality. As a corollary to our work, we identify the field, $h_χ$, conjugate to $χ$ and show that this field may be tuned to produce a transition to a state where the ensemble average, $<χ>$, and the correlation length of $χ$ diverge. Our work should be useful as a template for understanding non-affine displacements in realistic systems with or without disorder and as a means for developing computational tools for studying the effects of non-affine displacements in melting, plastic flow and the glass transition.

cond-mat.stat-mech↗