Direct Energy, 2018a

64 3.5 Problems
3.5 Problems
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 2.2, determine whether or not the material is piezoelectric.
• Using Table 2.2, determine whether or not the material is pyroelectric.
• Using Table 2.2, 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
C 12 H 22 O 11 and belongs to the crystal point group given by 2 in
Hermann-Maguin notation [38]. Reference [38] lists values specied
in cgse units for its piezoelectric constant as 10.2 · 10 −8
dyne esu and its
pyroelectric coecient as 0.53 esu
. Convert these values to the
cm2·0C SI units of m V and C
respectively.
m2·K Hint: The electrostatic unit or statcoulomb is a measure of charge [7]
where
1 esu =1statC =3.335641 · 10 −10 C
and the dyne is a measure of force where 1 dyne =10 −5 N.
3.3. A material has relative permittivity ɛ r x when no external electric
eld is applied. The coecient χ (2) is measured in the presence of
an external electric eld of strength | −→ E |. Assume that χ (3) and all
higher order coecients are zero. Find the Pockels coecient γ as a
function of the known quantities ɛ r x ,χ (2) , and | −→ E |.