Problem 2
Cane sugar, also called saccharose, has chemical composition \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) 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 \(10.2 \cdot 10^{-8} \frac{\mathrm{esu}}{\mathrm{dyne}}\) and its pyroelectric coefficient as \(0.53 \frac{\mathrm{esu}}{\mathrm{cm}^{2,0} \mathrm{C}}\). Convert these values to the SI units of \(\frac{\mathrm{m}}{\mathrm{V}}\) and \(\frac{\mathrm{C}}{\mathrm{m}^{2} \cdot \mathrm{K}}\) respectively. Hint: The electrostatic unit or statcoulomb is a measure of charge [7] where $$ 1 \mathrm{esu}=1 \text { stat } \mathrm{C}=3.335641 \cdot 10^{-10} \mathrm{C} $$ and the dyne is a measure of force where 1 dyne \(=10^{-5} \mathrm{~N}\).
Problem 3
A material has relative permittivity \(\epsilon_{r} x\) when no external electric field is applied. The coefficient \(\chi^{(2)}\) is measured in the presence of an external electric field of strength \(|\vec{E}| .\) Assume that \(\chi^{(3)}\) and all higher order coefficients are zero. Find the Pockels coefficient \(\gamma\) as a function of the known quantities \(\epsilon_{r} x, \chi^{(2)},\) and \(|\vec{E}|\)
Problem 5
A crystalline material is both piezoelectric and pyroelectric. When an external electric field of \(|\vec{E}|=100 \frac{\mathrm{V}}{\mathrm{m}}\) is applied, the material polarization is determined to be \(|\vec{P}|=1500 \epsilon_{0} \frac{\mathrm{C}}{\mathrm{m}^{2}}\). When both a stress of \(|\vec{\varsigma}|=30 \frac{\mathrm{N}}{\mathrm{m}^{2}}\) and an external electric field of \(|\vec{E}|=100 \frac{\mathrm{V}}{\mathrm{m}}\) are applied, the material polarization is determined to be \(|\vec{P}|=\) \(6.0123 \cdot 10^{-6} \frac{\mathrm{C}}{\mathrm{m}^{2}}\). When a temperature gradient of \(\Delta T=50{ }^{0} \mathrm{C}, \mathrm{a}\) stress of \(|\vec{\varsigma}|=30 \frac{\mathrm{N}}{\mathrm{m}^{2}},\) and an external electric field of \(|\vec{E}|=100 \frac{\mathrm{V}}{\mathrm{m}}\) are applied, the material polarization is determined to be \(|\vec{P}|=\) \(6.3 \cdot 10^{-6} \frac{\mathrm{C}}{\mathrm{m}^{2}} .\) Find: \- The relative permittivity of the material \- The piezoelectric strain constant \- The magnitude of the pyroelectric coefficient
