Chapter 7
Diffraction of Waves and Particles
by Crystal
7.1 Production of X-Rays
(a) X-rays are produced when a beam of highly accelerated charged particles such
as electrons is allowed to strike a metal target. In the process, electrons suffer
rapid deceleration and the energy lost by them is emitted in the form of
“continuous X-rays,” that is,
DE max = eV max ¼
1
2
mv
2 = hm max ¼
hc
k min
or k min ¼
hc
eV max
¼
6.626 Â 10
À34 Js  3  10
8 ms
À1
1.6 Â 10
À19 C Â V
¼
1.24 Â 10
À6
V
V - m
ð7:1Þ
where m is the mass of electron, e the charge and V the electrode potential. The
continuous X-ray spectra of Tungsten at various accelerating potentials are
shown in Fig. 7.1.
The above equation also gives the maximum frequency of X-ray corresponding
to k min as
m max ¼
c
k min
(b) The characteristic X-rays (K a ; K b ; etc.) are produced when the bombarded
electrons eject some of the orbital electrons of the target atom and the corresponding vacancies are filled by the less energetic outer shell electrons
(Fig. 7.2). The energy level diagram and allowed transitions are shown in
Fig. 7.3. The allowed transitions are:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
M. A. Wahab, Numerical Problems in Crystallography,
https://doi.org/10.1007/978-981-15-9754-1_7
263
Diffraction of Waves and Particles
by Crystal
7.1 Production of X-Rays
(a) X-rays are produced when a beam of highly accelerated charged particles such
as electrons is allowed to strike a metal target. In the process, electrons suffer
rapid deceleration and the energy lost by them is emitted in the form of
“continuous X-rays,” that is,
DE max = eV max ¼
1
2
mv
2 = hm max ¼
hc
k min
or k min ¼
hc
eV max
¼
6.626 Â 10
À34 Js  3  10
8 ms
À1
1.6 Â 10
À19 C Â V
¼
1.24 Â 10
À6
V
V - m
ð7:1Þ
where m is the mass of electron, e the charge and V the electrode potential. The
continuous X-ray spectra of Tungsten at various accelerating potentials are
shown in Fig. 7.1.
The above equation also gives the maximum frequency of X-ray corresponding
to k min as
m max ¼
c
k min
(b) The characteristic X-rays (K a ; K b ; etc.) are produced when the bombarded
electrons eject some of the orbital electrons of the target atom and the corresponding vacancies are filled by the less energetic outer shell electrons
(Fig. 7.2). The energy level diagram and allowed transitions are shown in
Fig. 7.3. The allowed transitions are:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
M. A. Wahab, Numerical Problems in Crystallography,
https://doi.org/10.1007/978-981-15-9754-1_7
263