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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
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