Home /
Expert Answers /
Advanced Physics /
the-primitive-translation-vectors-of-the-hexagonal-space-lattice-may-be-taken-as-a-1-3-1-2-pa142
(Solved): The primitive translation vectors of the hexagonal space lattice may be taken as: a_(1)=(3^((1)/(2) ...
The primitive translation vectors of the hexagonal space lattice may be taken as:
a_(1)=(3^((1)/(2))(a)/(2))hat(x)+((a)/(2))hat(y)
a_(2)=-(3^((1)/(2))(a)/(2))hat(x)+((a)/(2))widehat(y)
a_(3)=chat(z)(a) Show that the volume of the primitive cell is
((\sqrt(3))/(2))a^(2)c(b) Show that the primitive translations of the reciprocal lattice are:
b_(1)=(2(\pi )/(3^((1)/(2)))a)widehat(x)+(2(\pi )/(a))widehat(y)
b_(2)=-(2(\pi )/(3^((1)/(2)))a)widehat(x)+(2(\pi )/(a))widehat(y)
b_(3)=-(2(\pi )/(c))hat(z)so that the lattice is its own reciprocal, but with a rotation of axes. (c) Sketch and describe the first Brillouin zone of the hexagonal space lattice.
