Determination of the electrostriction tensor components in single-crystal CaF2 from the uniaxial stress dependence of the dielectric permittivity

Meng, Zhongyan

doi:10.1063/1.334779

Cited by 21 publications

(9 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In such materials, the electro-active response is dominated by a piezoelectric effect, which is linear with the applied electric field and the electrostriction is treated as the secondary contribution to total deformation. However, expressions (1) and (2) are often used to characterize materials in which the electrostriction response is the dominating electro-active effect [8,9,15]. Comparing equations (14) and (15) with equations (1) and (2) shows identical results for the electrostriction stresses and strains.…”

Section: Descriptions Of Electrostrictionmentioning

confidence: 58%

“…Conditions corresponding to figure 4a and b are identified as two limiting values of the loads: 'free-slip condition' in figure 4b was assumed for a nearly zero load and 'constrained condition' in figure 4a assumed for the load approaching infinity. A parallel-plate setup was also used by Meng and Cross [8] to measure stress-dielectric electrostriction parameters, but with no justifications for the stress components were provided. Yimnirun et al [15] also attempted to better define the boundary conditions in the parallel-plate setup by introducing ballbearings between the specimen and the loading cell.…”

Section: Methodsmentioning

confidence: 99%

“…The dielectric tensor of a linear dielectric material, " ik , is assumed to be independent of the applied electric field. For such materials, both equations (7) and (8) can be integrated over the electric field. The Helmholtz and Gibbs free energies of a polarized material in the electric field are expressed through the respective free energies without the field and field contribution: Either the Helmholtz or Gibbs free energies can be adopted for thermodynamic treatment of electro-active materials.…”

Section: Constitutive Equations: Hooke's Law In Polarized Materialsmentioning

confidence: 99%

“…strains, u({u ik }), or stresses, p({ ik }), the polarization is not convenient for describing the electrostriction. Hence, electrostriction relations are more frequently formulated through an electric field, E [8,9]:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Electrostriction: material parameters and stress/strain constitutive relations

Shkel

2007

Philosophical Magazine

View full text Add to dashboard Cite

The objective of this work is to formulate stress/strain constitutive relations in terms of material parameters. A secondary aim is to introduce a sequence of independent tests sufficient to evaluate these parameters. A stress constitutive equation in polarizable materials follows from the Helmholtz free energy related to a unit volume of deformed material. Similarly, a strain constitutive equation is obtained from the Gibbs free energy. These two relations explicitly account for the contribution of elastic deformation, electrostatic interactions of surface charges and the electrostriction effect. Both formulations of the constitutive relations are equivalent, yet yield different sets of electrostriction coefficients. For instance, a complete set of electrostriction parameters can be formulated based on either strain or stress dielectric rules. Strain-dielectric or stress-dielectric measurements necessitate monitoring variations in dielectric constants with the applied strains or stresses. Such measurements demand well-defined distribution of strains, stresses and the electric field across the sample. Meeting these requirements by traditional techniques used for dielectric measurements is quite challenging. This article introduces an experimental technique utilizing a rosette of planar dielectric sensors to overcome many of the experimental difficulties. Using both strain and stress definitions, electrostriction parameters are measured for a polycarbonate specimen. The obtained coefficients are in good agreement with the values provided by a microscopic model. The proposed description is valid for arbitrary anisotropic materials, while isotropic materials are considered as an illustrative example. In addition, all necessary relations for materials having cubic symmetry are provided in an appendix.

show abstract

Section: Descriptions Of Electrostrictionmentioning

confidence: 58%

Section: Methodsmentioning

confidence: 99%

Section: Constitutive Equations: Hooke's Law In Polarized Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Electrostriction: material parameters and stress/strain constitutive relations

Shkel

2007

Philosophical Magazine

View full text Add to dashboard Cite

show abstract

“…Determining these constants quasistatically or at sufficiently low frequencies would involve the measurement of permittivity under mechanical stress. Investigations of this type have been made by the group around Newnham and Cross (Uchino et al (1980), Rittenmyer et al (1983), Meng and Cross (1985)). …”

Section: Abcd and S +mentioning

confidence: 98%

Nonlinear Material Properties

Tichý

Erhart

Kittinger

et al. 2010

Fundamentals of Piezoelectric Sensorics

View full text Add to dashboard Cite

The formulation of Hooke's law rests on the assumption of infinitesimally small deformations. Its application to the simple model of a mass connected with a spring results in a linear force law and to the well known harmonic oscillation. Investigating even with very modest means the behavior of a real system of this sort shows that the limits of accuracy of this simple description are quite narrow indeed. A more general and accurate description will have to be a nonlinear one. This, in fact turns out to be true for all material properties, e.g. dielectric properties and the simple relation (4.2) is valid only for small fields and is an approximation in the same way as Hooke's law (3.51). If we are looking close enough we find that all phenomena actually are nonlinear, which means that the response of even simple systems to an external influence cannot be precisely described by a direct proportionality.The nonlinearity of the response, in general, is due to two different causes: The first one lies in the fact that the body under consideration changes its shape and size by the application of an external stimulus. Therefore, in the course of this process all quantities that are referred to unit volume (in fact obtained by dividing it by the volume of the body), or to unit area of a surface will be influenced by the continuous change of volume or of surface area, leading to a deviation from truly linear behavior. Effects of this sort are called geometrical nonlinearities.On the other hand we know that interatomic forces strongly depend on the separation of the particles and can be described by a linear force law only in the lowest approximation but are essentially nonlinear and this affects the response of the material itself such that we speak of material nonlinearity. A proper treatment of nonlinear effects has to take into account both of these nonlinearities.Let us consider Hooke's law as stated in (3.51'). The stiffness coefficients c λμ are clearly defined as constants. As a first step of approaching nonlinear behavior we could consider leaving the form of the law as it is, but interpreting the stiffness coefficients as functions of the strain S λμ . Such a procedure is frequently adopted in engineering practice. It has its place there and it has its merits for the sake of qualitative discussions and as a visualizing tool and we will use it in this sense later. The natural measure of nonlinearity then becomes the first derivative of this function. This approach clearly has its limits and a more general procedure (involving this 101

show abstract