Chemistry Reference
In-Depth Information
Fig. 6.19
Diffusional broadening of the Mössbauer resonance in Fe self-diffusion [
30
]
different lattice sites with a typical frequency of 10
7
s
-1
, which is roughly equal to
the inverse of the half-life time. In the crystal lattice, the atom is staying on the
lattice positions, and is vibrating with a phonon frequency of 10
12
s
-1
. When the
atom occasionally obtains thermal energy enough to overcome the potential barrier
between the different lattice sites, the atom is able to jump from a lattice site to
another, leading to diffusion. The duration of one jump is about 10
-12
s, which is
orders magnitude shorter than that of the atom staying on a lattice site. It turns out
that the
57
Fe atom performs a few jumps during emitting or absorbing c-ray, while
the coherency of the wave is broken due to the jump process. Consequently, the
lifetime of the 14.4 keV c-ray is practically observed to be shorter than the natural
lifetime. Taking into account of the Heisenberg time-energy uncertainty principle,
DE
s
M
& h, a shorter lifetime provides a broader linewidth of the Mössbauer
resonance.
A typical example, that of a Mössbauer study of Fe self-diffusion [
30
], is shown
in Fig.
6.19
.
Iron has three different solid phases: the a-phase (bcc) up to 1,184 K, the
c-phase (fcc) up to 1,665 K, and the d-phase (bcc) up to the melting point of
1809 K. The spectra of the c- and d-phases are shown in Fig.
6.19
. The linewidths
of all the spectra above 1656 K are much broader than that of the c-phase spectrum
at 1,623 K. The line broadenings observed in the d-phase can be interpreted to be
due to the atomic jumps of
57
Fe atoms within the lifetime, i.e. self-diffusion in the
d-phase. Since the line broadening, DC, is related to the jump frequency, 1/s,we
can deduce the diffusion coefficient, D, using the following formula [
30
]:
D
¼
R
2
12h
f
ð
h
Þ
DC