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Engineering LibreTexts

3.4: Problems

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3.1. For each of the three crystalline materials below

  • Find the crystal point group to which it belongs. (Hint: use http://www.mindat.org )
  • Using Table 2.3.1, determine whether or not the material is piezoelectric.
  • Using Table 2.3.1, determine whether or not the material is pyroelectric.
  • Using Table 2.3.1, determine whether or not the material is Pockels electro-optic.

(a) ZnS (sphalerite)

(b) HgS (cinnabar)

(c) Diamond

3.2. Cane sugar, also called saccharose, has chemical composition C12H22O11 and belongs to the crystal point group given by 2 in Hermann-Maguin notation [38]. Reference [38] lists values specified in cgse units for its piezoelectric constant as 10.2108esudyne and its pyroelectric coefficient as 0.53esucm2C. Convert these values to the SI units of mV and Cm2K respectively.

Hint: The electrostatic unit or statcoulomb is a measure of charge [7] where 1 esu=1 statC=3.3356411010C

and the dyne is a measure of force where 1 dyne=105N.

3.3. A material has relative permittivity ϵrx when no external electric field is applied. The coefficient χ(2) is measured in the presence of an external electric field of strength |E|. Assume that χ(3) and all higher order coefficients are zero. Find the Pockels coefficient γ as a function of the known quantities ϵrx, χ(2), and |E|.

3.4. The first figure below shows the displacement flux density |D| as a function of the strength of an applied electric field intensity |E| in a non-electro-optic material. The second figure below shows the displacement flux density |D| as a function of the strength of an applied electric field intensity |E| in a ferroelectric electro-optic material. The solid line corresponds to an unpoled material. The dotted line corresponds to the material after it has been poled in the ˆaz direction, and the dashed line corresponds to the material after it has been poled in the ˆaz direction.

(a) For the non-electro-optic material, find the relative permittivity, ϵr. Also find the magnitude of the material polarization, P.

(b) Assume the ferroelectric electro-optic material is poled by a strong external electric field, and then the field is removed. Find the magnitude of the material polarization |P| after the external field is removed.

(c) Assume the ferroelectric material is poled in the ˆaz direction by a strong external field, and then the field is removed. A different external electric field given by E=100ˆazVm is applied. Find the approximate relative permittivity of the material.

3.4.1.png

3.4.2.png

3.5. A crystalline material is both piezoelectric and pyroelectric. When an external electric field of |E|=100Vm is applied, the material polarization is determined to be |P|=1500ϵ0Cm2. When both a stress of |ς|=30Nm2 and an external electric field of |E|=100Vm are applied, the material polarization is determined to be |P|=6.0123106Cm2. When a temperature gradient of ΔT=50C, a stress of |ς|=30Nm2, and an external electric field of |E|=100Vm are applied, the material polarization is determined to be |P|=6.3106Cm2. Find:

  • The relative permittivity of the material
  • The piezoelectric strain constant
  • The magnitude of the pyroelectric coefficient

This page titled 3.4: Problems is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Andrea M. Mitofsky via source content that was edited to the style and standards of the LibreTexts platform.

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