Lattice-dynamics approach to the theory of diatomic elastic dielectrics

Aşkar, Attila; Lee, P. C. Y.

doi:10.1103/physrevb.9.5291

Cited by 16 publications

(9 citation statements)

References 11 publications

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“…The main feature of the original approach consists in accounting for the polarization gradient in the constitutive equations in order to describe electroelastic couplings, just at a linear level, also in polarizable crystals which do not allow for the piezoelectric effect. A lattice's dynamic derivation of electroelastic coupling in alkali halide has supported this point of view showing that, in the long-wave approximation, contributions due to polarization gradient arise in the linearized model as a consequence of shell-shell and core-core interactions between the lattice's constituents (Askar et al 1970, Askar andLee, 1974).…”

Section: Introductionmentioning

confidence: 82%

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Dynamic eigenvector problem in thermoelectroelasticity of dissipative ionic crystals

Romeo

2010

European Journal of Mechanics - A/Solids

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A two dimensional problem in the Stroh formalism is derived for the continuum theory of thermoelectroelasticity with polarization gradients. Dissipative effects are accounted for, according to a constitutive model outlined in previous works. The eigenvector problem is studied in the frequency domain to obtain a representation of the solution in terms of two classes of modes corresponding to opposite signs of imaginary part of the eigenvalues. Impedance and admittance tensors are exploited to express the energy flux of the thermoelectroelastic transformed field across an interface S. The compatibility conditions at S are also derived. The eigenvector equations are then rewritten in the time domain to obtain two convolution-type integral equations for the Hilbert transforms of the real fields corresponding to each mode.

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Section: Introductionmentioning

confidence: 82%

“…Romeo 2008). The last quantity is a constitutive parameter of the polarizable continuum, which depends on the microscopic structure of the crystal lattice (Askar and Lee 1974). According to the previous equations, the energy flux vector of the thermoelectroelastic field can be written as…”

Section: Thermoelectroelastic Continuum Model For Ionic Crystalsmentioning

confidence: 99%

Dynamic eigenvector problem in thermoelectroelasticity of dissipative ionic crystals

Romeo

2010

European Journal of Mechanics - A/Solids

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“…A theory the including polarization gradient and inertia effects in diatomic elastic dielectrics was derived in [43]. A lattice dynamics approach of diatomic dielectrics can be found in [44]. A systematic presentation of the polarization gradient theory was given in [45].…”

Section: Polarization Gradient Theorymentioning

confidence: 99%

“…where ∇ 2 is the two-dimensional Laplacian, c = c 44 , e = e 15 , ε = ε 11 , and α = α 11 . The nontrivial ones of Equation (8.57) take the form…”

Section: Antiplane Problems Of Polarized Ceramicsmentioning

confidence: 99%

Nonlocal and Gradient Effects

Yang

2009

Special Topics in the Theory of Piezoelectricity

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Classical continuum theories such as elasticity, electrostatics, and piezoelectricity are the long-wave and low-frequency limits of the equations of lattice dynamics. The partial differential equations of these continuum theories can be obtained from the finite difference equations of lattice dynamics by Taylor expansions and truncations. The equations of classical continuum theories are accurate for phenomena with a characteristic length much larger than microscopic characteristic lengths, for example, the distance between neighboring atoms in a lattice. When the characteristic length of a problem is not much larger than the microscopic characteristic length, classical continuum theories do not predict results consistent with lattice dynamics, and hence are no longer valid. For example, lattice waves are dispersive but the theory of elasticity only predicts nondispersive plane waves which are the long wave limit of lattice waves.There are different ways to modify the classical continuum theories so that their range of applicability can be extended to problems with smaller characteristic lengths, with results closer to lattice dynamics in a wider range of wave lengths.One is to generalize the constitutive relations in classical continuum theories from local to nonlocal [1][2][3][4][5]. In classical continuum theories, the constitutive relations are for stress and strain (or electric field and polarization) at the same material point, with a zero interaction distance (local theories). These constitutive relations neglect the microstructure of real materials and lead to macroscopic theories for large characteristic lengths. In nonlocal constitutive relations, a finite microscopic interaction distance is

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“…This is the case of the theory of ionic crystals (see Mindlin, 1968;Maugin, 1988) where the occurrence of polarization gradients in the constitutive assumptions has been justified by a simplified lattice-dynamics theory of alkali halide crystals (Askar et al, 1970;Askar and Lee, 1974). In particular, all the fundamental electromechanical couplings, polarization inertia and dissipative effects have been included in the non-linear theory by Maugin (1988) (see chapter 7) which reduces to the original theory by Mindlin (1968) in the linear case.…”

Section: Introductionmentioning

confidence: 97%

Surface and interfacial waves in ionic crystals

Romeo

2008

International Journal of Solids and Structures

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The continuum linear theory of ionic crystals is applied to develop a two-dimensional eigenvalue problem in the Stroh formalism. An integral approach is exploited to study the occurrence of surface waves along a free boundary of the crystal. Dispersion relations are obtained by separating real and imaginary parts of the governing system and various boundary conditions are examined. The problem of interfacial waves along the separation boundary between two different crystals is also outlined. Numerical computations are performed for a centrosymmetric crystal (KCl) in order to evaluate bulk wave speeds, limiting speed of surface waves and solutions to the dispersion equations for different boundary conditions.

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Lattice-dynamics approach to the theory of diatomic elastic dielectrics

Cited by 16 publications

References 11 publications

Dynamic eigenvector problem in thermoelectroelasticity of dissipative ionic crystals

Dynamic eigenvector problem in thermoelectroelasticity of dissipative ionic crystals

Nonlocal and Gradient Effects

Surface and interfacial waves in ionic crystals

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