Saswati Ganguly

Nonaffine displacements in crystalline solids in the harmonic limit

A systematic coarse graining of microscopic atomic displacements generates a local elastic deformation tensor D as well as a positive definite scalar χ measuring nonaffinity, 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 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,D) and the two-point spatial correlation functions for χ and D. We show that nonaffine 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 and the correlation length of χ diverge. Our work should be useful as a template for understanding nonaffine displacements in realistic systems with or without disorder and as a means for developing computational tools for studying the effects of nonaffine displacements in melting, plastic flow, and the glass transition.

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 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.Graphical AbstractWe show that it is possible to enhance non-affine displacement fluctuations in a crystal using an external field. Although transient, these fluctuations can shift the phonon density of states to low frequencies and cause “Boson peak” like phenomenon in an otherwise perfect crystal without quenched disorder.

On the Fluorescence Spectra of Naphthacene in Solid Solution of Anthracene for Different Exciting Wave‐Lengths

The fluorescence of green anthracene crystal (naphthacene in solid solution of anthracene) has been studied with exciting light of different wave‐lengths and the long wave‐length limit for excitation has been found. From the study of the fluorescence and absorption spectra an attempt has been made to interpret the mechanism of the fluorescence phenomenon in this crystal.

Pre-Yield Non-Affine Fluctuations and A Hidden Critical Point in Strained Crystals

A crystalline solid exhibits thermally induced localised 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 below the value at which the solid begins to yield. This critical point does not manifest in most thermodynamic or mechanical properties, but is 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.

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.

On the existence of thermodynamically stable rigid solids

Parswa Nath, Saswati Ganguly, Jürgen Horbach, Peter Sollich, Smarajit Karmakar, and Surajit Sengupta TIFR Centre for Interdisciplinary Sciences, 36/P Gopanpally, Hyderabad 500107, India Institut für Theoretische Physik II: Weiche Materie, Heinrich Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany King’s College London, Department of Mathematics, Strand, London WC2R 2LS, U.K. (Dated: November 9, 2018)Significance While common sense says that solids are rigid, careful arguments show that all solids under infinitesimal strain must eventually flow. Resolution of this paradoxical result lies at the core of our understanding of the behavior of solids under deformation. We provide a framework within which the paradox is reconciled and extract conditions wherein stable, rigid, crystalline solids are possible. Failure of ideal crystals is determined by a kinetic process similar to the decay of supercooled phases following quenches across a first-order phase boundary. This fresh conceptual viewpoint curiously allows us to study failure of perfect crystalline solids in quantitative detail without invoking specifics of many-body, defect–defect interactions, raising hope of a more unified description of materials in the future. Customarily, crystalline solids are defined to be 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 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 used to obtain the equilibrium free energy as a function of this variable. Our results lead to a unique 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 when an external field, which penalizes particle rearrangements, is switched on. 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.

Erratum: Statistics of non-affine defect precursors: Tailoring defect densities in colloidal crystals using external fields (Soft Matter (2015) 11(4517-4526))

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