plantation depth of ϳ0.13 m.10 The positron lifetime spec-
tra were analyzed by Laplace inversion ͑CONTIN͒11 which
deconvolutes the time spectra into the probability density
function ͑pdf͒ as a function of positron lifetime, as shown in
the insert. Total counts of the spectra are limited to be
5
around 5ϫ10 , which may affect the width in the pdf
1
2
peaks. However, the peak positions are reasonably accurate
since they are generally not altered by statistics. For the
␣
-Al O scales on Fe AlϩY O and -NiAlϩHf, the major-
2 3 3 2 3
ity of positrons annihilate around 206 and 194 ps, respec-
tively, with satellite peaks ͑4%͒ of about 1400–1500 ps.
Positron lifetimes in defect-free alumina lattices are
about 140 ps and positrons trapped in aluminum-site vacan-
cies in alumina have lifetimes of about 165 ps.13 Thus, the
lifetimes ͑194–220 ps͒ measured for the scales are estimated
due to mainly di-vacancy sites by a linear extension of the
above two lifetimes, as indicated in Ref. 14 for semiconduc-
tors. Laplace inversion also reveals that the positron lifetimes
are significantly different for the Al O scales on
2
3
Fe AlϩY O ͑206 ps͒ and -NiAlϩHf ͑194 ps͒ even though
3
2
3
they were formed by the same oxidation process. This life-
time difference may be due to the chemical composition of
the scales, particularly the iron and nickel cation impurities.
For the PVD film, the main component of the lifetimes is
around 388 ps, much longer than the lifetimes for the ther-
mally grown scales. The PVD-film lifetime may be due to
the larger interatomic spaces in the amorphous structure,
which are approximately equivalent to the size of a cluster of
about 8 atomic vacancies in the crystalline mode.
FIG. 2. ͑a͒ Positron lifetimes and ͑b͒ related intensities for thermally grown
alumina scale on iron aluminide substrate as a function of positron energy.
For lower energies ͑Ͻ2 keV͒, I , I , I , and were determined by fitting
͑POSFIT͒ with 1 fixed at the average bulk lifetime ͑202.5 ps͒. For other
energies, all parameters were obtained by fitting.
2
2
3
2
3
Voids are also indicated by appearance of the long life-
time components around 600–1400 ps. TEM images indicate
that the thermally grown Al O scales contain a few percent
voids, generally 20–100 nm in size. This would yield a long
positron lifetime ͑Ͼ5 ns͒ if positronium is formed in these
voids. The observed shorter lifetimes may indicate that pos-
itrons are attached to the inner wall of the voids or that the
voids that trap positrons are much smaller.
scale thickness. Possible causes of increase are as follows:
͑1͒ interfacial dislocations, ͑2͒ larger vacancy clusters, and
͑3͒ the chemical difference around the interface. The differ-
ence between the positron lifetimes for 15 and 20 keV pos-
itrons injected into alumina scales on -NiAlϩHf is not as
large as that observed for Fe3AlϩY2O3. This suggests that
the size of the interfacial vacancy clusters for nickel alu-
2
3
2
Positron lifetime spectra measured as a function of pos-
itron energy in the range 0.25–23 keV, provided depth pro-
files of defects in the scales on Fe AlϩY O . Figures 2͑a͒
3
2
3
and 2͑b͒ show the positron lifetimes and their intensities,
respectively, as functions of positron energy. represents
2
the surface lifetime. and are the short and long com-
1
3
ponents of the bulk lifetime, respectively. The intensity of
the surface component (I ͒ decreases as the energy in-
2
creases, while the intensity of the bulk component (I ) varies
1
inversely. This variation is interpreted with the positron dif-
fusion process in which the low-energy positrons diffuse
back to the surface, while the high-energy positrons are
trapped in the bulk. The diffusion length was estimated to be
about 20 nm, which is much shorter than that of perfect
alumina lattices ͑100 nm͒. The truncated length confirms the
high concentration of microdefects in the scales.
A clear difference was observed between the lifetime
spectra of 15 and 20 keV positrons injected into the alumina
scale on Fe AlϩY O , as shown in Fig. 3. Laplace inversion
3
2
3
reveals that the lifetime for 15 keV peaks around 205 ps,
while 20 keV positrons annihilate around 219 ps. This dif-
ference is believed to be due to the interface since the mean
depth of positron penetration for 20 keV is close to the 1 m
FIG. 3. Probability density functions as a function of positron lifetime for
1
5 and 20 keV positrons ejected into the thermally grown Al O scale on the
2 3
iron–aluminide substrate.
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166 Appl. Phys. Lett., Vol. 71, No. 21, 24 November 1997 Xu et al.
34.153.41.27 On: Wed, 26 Nov 2014 15:14:05
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