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

Ganguly, Saswati; Sengupta, Surajit

doi:10.1007/s12039-017-1305-3

Cited by 10 publications

(11 citation statements)

References 27 publications

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“…The deformation is measured from a set of fixed reference coordinates. In a series of papers [14][15][16][17][18][19] (see also Appendix A for details) some of us have worked out in detail the statistical thermodynamics of χ i , which quantifies the "non-affine" component of the particle displacements, analytically and numerically for a number of two dimensional (2d) crystals at finite temperature. At any T > 0, X behaves as a regular thermodynamic variable with a well-defined mean and variance ∼ N −1 .…”

Section: Introductionmentioning

confidence: 99%

On the existence of thermodynamically stable rigid solids

Nath

Ganguly

Horbach

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

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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.

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Section: Introductionmentioning

confidence: 99%

On the existence of thermodynamically stable rigid solids

Nath

Ganguly

Horbach

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

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“…excess with respect to Debye's ω 2 law in the vibrational density of states), which is typically observed in glasses but has recently also been measured in α-quartz [15]. Recent works have highlighted the close connection between nonaffine elasticity and the boson peak anomaly [16,17], and it has been suggested that the root cause of both boson peak and nonaffine elasticity could be traced back to the inherent lack of centrosymmetry of both glasses and non-centrosymmetric crystals such as α-quartz [16].…”

Section: Introductionmentioning

confidence: 80%

Nonaffine lattice dynamics with the Ewald method reveals strongly nonaffine elasticity of α-quartz

Cui

Zaccone

Rodney

2019

The Journal of Chemical Physics

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A lattice dynamical formalism based on nonaffine response theory is derived for noncentrosymmetric crystals, accounting for long-range interatomic interactions using the Ewald method. The framework takes equilibrated static configurations as input to compute the elastic constants in excellent agreement with both experimental data and calculations under strain. Besides this methodological improvement, which enables faster evaluation of elastic constants without the need of explicitly simulating the deformation process, the framework provides insights into the nonaffine contribution to the elastic constants of α-quartz. It turns out that, due to the noncentrosymmetric lattice structure, the nonaffine (softening) correction to the elastic constants is very large, such that the overall elastic constants are at least 3-4 times smaller than the affine Born-Huang estimate. * az302@cam.ac.uk

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“…The analytical and numerical results 20 show that if the non-affine displacements are enhanced via an external field there is an accumulation of low-frequency modes in the density of states, also linking non-affine fluctuations to the boson peak.…”

Section: Correlation Of the Boson Peak With Isb Fluctuationsmentioning

confidence: 96%

Non-affine lattice dynamics of defective fcc crystals

2017

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The mechanical, thermal and vibrational properties of defective crystals are important in many different contexts, from metallurgy and solid-state physics to, more recently, soft matter and colloidal physics. Here we study two different models of disordered fcc crystal lattices, with randomly-removed bonds and with vacancies, respectively, within the framework of non-affine lattice dynamics. We find that both systems feature the same scaling of the shear modulus with the newly defined inversion-symmetry breaking (ISB) parameter, which shows that local inversion-symmetry breaking around defects is the universal root source of the non-affine softening of the shear modulus. This finding allows us to derive analytical relations for the non-affine (zero-frequency) shear modulus as a function of vacancy concentration in excellent agreement with numerical simulations. Nevertheless, due to the different microstructural disorder, the spatial fluctuations of the local ISB parameter are different in the vacancy and bonddepleted case. The vacancy fcc exhibits comparatively a more heterogenous microstructural disorder (due to the broader distribution of coordination number Z), which is reflected in a different scaling relation between boson peak frequency in the DOS and the averageZ. These differences are less important at low vacancy concentrations, where the numerical DOS of the vacancy fcc can be well described theoretically by coherent-potential approximation, presented here for the bond-depleted fcc lattice in 3d.

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

Cited by 10 publications

References 27 publications

On the existence of thermodynamically stable rigid solids

On the existence of thermodynamically stable rigid solids

Nonaffine lattice dynamics with the Ewald method reveals strongly nonaffine elasticity of α-quartz

Non-affine lattice dynamics of defective fcc crystals

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