The figure below shows a slice of reciprocal space defined by the unit vectors b_(1),b_(2) for an
arbitrary material. The Ewald sphere is used as a visual representation of the phenomenon of
diffraction in reciprocal space. K_(1) is the incident wave vector.
Circle the correct answer in the sentences below regaraing the Ewald sphere:
a) In order to construct the Ewald sphere in reciprocal space, the (start / end) of the incident K_(I)
vector coincides with the origin.
b) As the wavelength of the incident wave increases, the radius of the Ewald sphere (increases
(decreases).
c) The incident wave vector K_(I) and the diffracted wave vector K_(D) start at the same position and
have the same magnitude. The angle between the two vectors is (( heta )/(2)( heta )/(4) heta ).
d) The start of K_(1) and K_(D) vectors (does / does not need) to coincide with a reciprocal lattice
point.
Answer the following questions.
e) How many sets of lattice planes will fulfill the condition for constructive interference and give
rise to diffraction peaks in the sketch above.
f) Draw the possible diffracted wave vector(s) on the figure above.
g) Draw the Ghk vector(s) for which the condition for diffraction is fulfilled.
h) What are the Miller indices (hk) of the corresponding plane(s) in real space that are responsible
for diffraction?
i) If the angle between b_(1) and b_(2) is 60deg , draw the unit cell of the corresponding real space lattice.
diffraction in reciprocal space. Kr is the incident wave vector.
vector coincides with the origin.
/decreases). have the same magnitude. The angle between the two vectors is (0 / 20 / 40). d) The start of K and Ko vectors (does / does not need) to coincide with a reciprocal lattice point. e) How many sets of lattice planes will fulfill the condition for constructive interference and give Answer the following questions. rise to diffraction peaks in the sketch above f) Draw the possible diffracted wave vector(s) on the figure above. g)Draw the Ghk vector(s) for which the condition for diffraction is fulfilled. h)What are the Miller indices(hk) of the corresponding plane(s) in real space that are responsible for diffraction? iif the angle between b and bz is 609,draw the unit cell of the corresponding real space lattice
