Journal of Nuclear Materials 419 (2011) 9–14

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Journal of Nuclear Materials
journal homepage: www.elsevier.com/locate/jnucmat

Vacancy defects in a stress-corrosion-cracked Type 304 stainless steel
investigated by positron annihilation spectroscopy
A. Yabuuchi ⇑, M. Maekawa, A. Kawasuso
Advanced Science Research Center, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japana r t i c l e

i n f oArticle history:
Received 26 May 2011
Accepted 3 August 2011
Available online 22 August 2011a b s t r a c t
To reveal vacancy formation during the stress corrosion cracking (SCC), three factors inﬂuencing SCC in
Type 304 stainless steels—sensitization heat treatment, corrosion treatment and tensile plastic deformation—were investigated by means of positron annihilation spectroscopy. Vacancy defects induced by thesensitization heat treatment and by tensile deformation were identiﬁed as monovacancies. These monovacancies were annealed within the same temperature range in which light water reactors are operated(280–320 °C). The above results allow us to conclude that such vacancy defects play an important role inhigh-temperature-water SCC crack propagation.
Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction
Stainless steels are generally highly resistant to corrosion,owing to the formation of a stable chromium oxide barrier. Upon
heating at 450–800 °C, however, the corrosion resistance of stainless steels deteriorates markedly. This is due to the formation ofchromium carbide (Cr23C6) at grain boundaries and an associatedreduction of available chromium atoms for oxide barrier formation.
This phenomenon is called sensitization. In 1970s, it was reported
that stress corrosion cracking (SCC) occurs when both stress andcorrosion conditions are jointly conducive to it. Therefore, fromthe 1980s, low-carbon stainless steels, in which sensitization rarely
occurs, have been used as nuclear reactor materials; indeed, SCCinduced failures have been substantially reduced. Even so, however, such failures have not been completely avoided, even in
low-carbon stainless steels. This suggests that there are still important factors behind SCC failures that are not sufﬁciently suppressedby simply improving corrosion resistance. Thus, the mechanism for
SCC within stainless steels is an important research topic, particularly with regards to such critical applications as long-term use inlight water nuclear reactors.
Recently, a hypothesis that SCC crack propagation is mediatedby atomic vacancies under a stress gradient at the crack tip has
been proposed [1–3].
Positron annihilation spectroscopy offers a unique approach to
studying vacancy defects. It is based on the tendency for positrons
implanted into a solid to become trapped by vacancy defects andannihilate with electrons to emit 511 keV gamma-rays. Such annihilation gamma-rays convey information about the vacancy
defects from which they originated. In the present study, Type⇑ Corresponding author. Tel.: +81 27 346 9330; fax: +81 27 346 9432.
E-mail address: yabuuchi.atsushi@jaea.go.jp (A. Yabuuchi).
0022-3115/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jnucmat.2011.08.012

304 stainless steels subjected to sensitization heat treatment, corrosion treatment, and tensile plastic deformation were examinedby means of positron annihilation spectroscopy to elucidate vacancy formation during SCC.
2. Experimental
The samples used in this study were commercially available
Type 304 stainless steel foils or sheets with a thickness of
0.05 mm or 1 mm. To suppress chromium carbide precipitation,
all the samples were annealed at 1150 °C for 2 h in vacuum silica
tube and subsequently quenched into ice water. The above heat
treatment is called solution annealing. With regards to the thicksamples, this state was deﬁned as the initial (reference) state. For
the thin samples, an additional annealing step was carried out at
400 °C for 30 min to remove quenched-in thermal equilibrium
vacancies. Both the thin and thick samples were then separately
subjected to the following: (i) sensitization heat treatment at
650 °C for 24 h in vacuum, (ii) plastic deformation up to a strainof 14% under a 150 MPa tensile stress at room temperature, (iii)a corrosion treatment in boiling water containing 35% MgCl2 at
approximately 130 °C for 72 h, and (iv) irradiation with 2 MeV
electrons to a dose of 3  1018 e/cm2 at a temperature below
60 °C. Finally, to investigate the thermal stability of defects
induced by these treatments, the samples were isochronallyannealed in vacuum with a temperature step of 100 °C and a duration of 30 min. After each annealing step, the samples werequenched into ice water.
Positron annihilation measurements were conducted using a
positron microbeam (energy: 20 keV; spot size: 20 lm) [4], an energy-variable positron beam (energy: 0.2–30 keV; spot size:
5 mm), and a conventional positron source (22NaCl, 700 kBq)
deposited onto a titanium foil (thickness: 5 lm). In the positron

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A. Yabuuchi et al. / Journal of Nuclear Materials 419 (2011) 9–14

(a)

680
250
220
190
160
130
4

Tensile stress (MPa)(b)

would be greater than 250 MPa and hence plastic deformation
would be expected to occur. Fig. 1c shows scanning DBAR measurements as taken with the positron microbeam over the same region as Fig. 1a. Although the S parameter does not increasesigniﬁcantly within the low stress regions beside the notch, it does
increase along with the stress gradient emanating from the notch
tip as shown in Fig. 1b. This fact implies that vacancy defects are
introduced by local plastic deformation caused by the stressconcentration.
Fig. 2a and b shows the optical microscope image and S parameter image, respectively, obtained after SCC propagation. Over a
200–400 lm range from the SCC crack, the S parameter clearly increases. Observing Fig. 1c, we note that plastic deformation successively occurs at the crack tip during crack propagation. Since thetemperature of boiling MgCl2 water (130 °C) is lower than theannealing temperature of vacancy defects induced by plastic deformation as discussed in Section 3.6, we also note that most vacancy
defects survive during SCC propagation.

(a)

1.03
1.02
1.01
1.00

Normalized S parameter(c)Fig. 1. (a) Optical microscope image, (b) tensile stress distribution calculated using
the ABAQUS code, and (c) S parameter mapping with a pixel size of 100  100 lm2,
obtained under a tensile stress of approximately 150 MPa in the horizontal
direction.

beam experiments, Doppler broadening of the annihilation radiation (DBAR) measurements were carried out using a high-purity
germanium detector. To monitor the presence of vacancy defects,
the DBAR spectra thus obtained were characterized in terms ofan S parameter, which is deﬁned as the peak intensity. All the S
parameters were normalized to those obtained for the initial state.
Positron annihilation lifetime measurements were performed
using the positron source and a fast–fast spectrometer with a time
resolution of 245 ps (full width at half-maximum, FWHM).

(b)

3. Results and discussion

1.04

Fig. 1a shows an optical microscope image of a notched andsolution-annealed sample (thickness: 0.05 mm). A tensile stressof approximately 150 MPa is applied horizontally relative to theﬁgure. This is less than the yield stress of Type 304 stainless steels(250 MPa). However, as shown in Fig. 1b, ﬁnite-element analysis(ABAQUS code) shows that tensile stress concentrates at the notch
tip. This concentration is such that in the red1 region, tensile stress1
For interpretation of color in Figs. 1 and 2, the reader is referred to the web
version of this article.

1.03
1.02
1.01

Normalized S parameter

1.05

3.1. SCC propagation

1.00
Fig. 2. (a) Optical microscope image and (b) S parameter mapping with a pixel sizeof 40  40 lm2 obtained for a sensitized sample after SCC treatment.

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A. Yabuuchi et al. / Journal of Nuclear Materials 419 (2011) 9–14

3.2. Effect of sensitization heat treatment

3.3. Plastic deformation under tensile stressFig. 3 shows the S parameter as a function of incident positronenergy before and after sensitization heat treatment. Mean positron implantation depth is also shown on the top horizontal axis.
The increase in S parameter in the low positron energy region(E < 5 keV) is related to surface effects [5,6] and not to the sensitization heat treatment. At E > 10 keV, the S parameter of the sensitized sample is sufﬁciently higher than that of the unsensitizedsample. This suggests that vacancy defects are introduced by thesensitization heat treatment. The solid lines shown in the ﬁgureshow the results of an analysis based on a one-dimensional positron diffusion model using a VEPFIT code [7,8]. The positron diffusion lengths before and after the sensitization heat treatment were
80 nm and 22 nm, respectively. This also indicates an introductionof vacancy defects.
Vacancy defects observed after the sensitization heat treatment are probably generated by the Kirkendall effect. It is
known that the inverse Kirkendall effect leads to chromium
depletion near the grain boundaries within the irradiation-assisted stress corrosion cracking (IASCC) [9–14]. This migrationof irradiation-induced vacancies to grain boundaries results ina corresponding migration of chromium atoms in the opposite
direction. Consequently, chromium depletion occurs near thegrain boundaries. In a sensitization heat treatment, chromium
depletion also occurs near the grain boundaries because of theformation of Cr23C6 precipitates. Such a chromium concentration
gradient causes a migration of the chromium atoms toward thegrain boundaries (by the Kirkendall effect) and a ﬂow of vacancies into the grains.
An alternative explanation for the increase in the S parameter
after sensitization heat treatment is an introduction of misﬁt dislocations at precipitate interfaces as reported for Ti-doped austenitic
stainless steels in which TiC precipitation occurs inside grains [15].
Note, however, that Cr23C6 precipitates are formed at grain boundaries in Type 304 stainless steels and that the grain diameter of thesamples is approximately 50 lm, which is far larger than the positron diffusion length. Therefore, nearly all positrons would be expected to annihilate inside the grains. That is, the increase in the S
parameter might not be attributable to misﬁt dislocations accompanying the Cr23C6 precipitates.

To estimate the concentration of vacancy defects induced by astress concentration as shown in Fig. 1b, a tensile deformation test
was performed. Fig. 4 shows the change in the S parameter for foil
tensile test pieces during tensile deformation. It is seen that the S
parameter monotonically increases with strain. This indicates anintroduction of vacancy defects by plastic deformation. From acomparison of the electron-irradiated sample and its annealing
process (see Sections 3.5 and 3.6), it is shown that monovacancies
are mainly responsible for positron trapping in a plastically deformed sample. Here, the S parameter may be given by S =(1  f)SB + f SV, where SB and SV are S parameters for the bulk(=1.000) and vacancy defects, f is the annihilation fraction of positrons at vacancy defects ð¼ lC V =ðs1
B þ lC V ÞÞ, and l and CV are thespeciﬁc trapping rate and the concentration, respectively, of vacancy defects. As shown in Section 3.5, sB = 102 ps and SV = 1.127
for monovacancies. The vacancy concentration introduced by plastic deformation is phenomenologically given by CV = gn, where gand n are constants and  is strain [16]. The solid line in Fig. 4 isthe calculated S parameter as given by the above equations withﬁtting parameters of lg(=1.4  1010 s1) and n(=0.6). Under anassumption that the speciﬁc trapping rate of a monovacancy inType 304 stainless steel is similar to that in pure Fe(1.1  1015 s1) [17], the vacancy concentration is estimated tobe 3  106 at  = 10%. Subsequently, we estimate the vacancy concentration at the notch tip shown in Fig. 1. CV can be described as
CV = (S  SB)/sBl(SV  S) by transforming the above-mentioned formulae. S = 1.03 is observed at the notch tip as shown in Fig. 1c.
Consequently, the vacancy concentration of that region is estimated to be 3  106. From the result of the tensile test, this corresponds to the tensile deformation at  = 10%. Incidentally,
recent EBSD studies have revealed that approximately 10% of localized tensile strain is distributed near grain boundaries around SCC
cracks [18,19]. The observed result of S parameter at the notch tip
is consistent with the results of recent EBSD studies. These results
imply that a high concentration of vacancy defects is introduced
around SCC cracks.

As shown in Fig. 5, the S parameter increases in the sub-surface
region (up to 50 nm) upon a corrosion treatment after sensitization
heat treatment. A detailed VEPFIT analysis indicated that this modulated layer thickness and its S parameter were 12 nm and 1.250,
respectively. These results imply that some porous structures, suchas an oxide layer (Fe3O4) [20], are induced by the corrosion treatment. At E > 15 keV, the S parameter slightly decreases upon a corrosion treatment. Considering the fact that the corrosion treatment

Mean implantation depth (nm)
500

100

1000

1.20
1.05

1.15
1.10

After sensitization

1.05
1.00
Before sensitization

0.95

0

5

10

15

20

25

30

Incident positron energy (keV)

Normalized S parameter

Normalized S parameter

1.25

0

3.4. Effect of corrosion treatment

1.04
1.03
1.02
1.01
1.00
0.00

0.05

0.10

0.15

Nominal strain
Fig. 3. S parameter as a function of incident positron energy obtained before (ﬁlled
circles) and after (ﬁlled squares) sensitization heat treatment. Solid lines are ﬁtting
curves calculated using VEPFIT code.

Fig. 4. S parameter as a function of tensile strain. Solid line is the ﬁtting curve
calculated using equations described in the text.

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A. Yabuuchi et al. / Journal of Nuclear Materials 419 (2011) 9–14

3.5. Comparison with electron irradiation

Mean implantation depth (nm)
1.25

0

100

500

1000

Normalized S parameter

After sensitization and corrosion

1.20
1.15
1.10
1.05
After sensitization

1.00
0.95

0

5

10

15

20

25

30

Incident positron energy (keV)
Fig. 5. S parameter as a function of incident positron energy obtained before (ﬁlled
circles) and after (ﬁlled squares) corrosion treatment. Solid lines are ﬁtting curves
calculated using the VEPFIT code.

was carried out at approximately 130 °C, the decrease of the S
parameter in the deeper region can be explained as a partial
annealing of the sensitization-induced vacancies as discussed in
Section 3.6.

Mean implantation depth (nm)Normalized S parameter

1.25

0

100

500

1000

(a)

1.20
1.15
1.10

After irradiation

1.05

Fig. 6a and b shows the S parameter as a function of incident
positron energy and positron annihilation lifetime spectra, respectively, before and after electron irradiation. A VEPFIT analysis suggested that the S parameter and the positron diffusion length of theirradiated layer are S = 1.076 and L = 39 nm, respectively. A single
positron lifetime of 102 ps was obtained for the unirradiated sample. Upon electron irradiation, two positron lifetime components(s1 = 57 ps and I1 = 22%, s2 = 177 ps and I2 = 78%) were obtained.
The second component is related to vacancy defects introducedby irradiation. Taking lCV = (I2/I1)(1/sB  1/sV) = 14.7 ns1, the S
parameter of the vacancy defects is determined to be SV = 1.127
in a way similar to that described in Section 3.3. Fig. 7 shows anexperimental DBAR spectrum obtained after electron irradiation.
To see the detailed spectrum shape, the original spectra are divided
point-by-point by the spectrum for the reference sample. The spectrum shape exhibits a typical feature for vacancy defects.
From previous studies on metals [21,22], the above positron
lifetime (s2 = 177 ps) seems to be attributable to monovacancies.
To conﬁrm this inference, theoretical calculations were conductedbased on the atomic superposition method developed by Puska etal. [23]. Also, DBAR spectra were calculated based on the two-component density functional theory. In the calculations, the crystal
structure, the lattice constant and the alloy composition are assumed to be face-centered cubic (fcc), 3.593 Å and Fe/Cr/
Ni = 0.73/0.19/0.08, respectively. The details of the calculations
are described elsewhere [24,25]. The calculated positron lifetimes
for the bulk, monovacancy and divacancy in a Type 304 stainlesssteel were 101 ps, 176 ps and 194 ps, respectively. The solid line
in Fig. 7 is the calculated DBAR spectrum for a monovacancy. The
observed positron lifetime before irradiation (102 ps) agrees wellwith the calculated bulk lifetime. Thus, before irradiation, the concentration of vacancy defects is under the detection limit (<107).
The observed second lifetime (s2 = 177 ps) and the DBAR spectrum
are in good agreement with those calculated for a monovacancy.
Thus, vacancy defects induced by the electron irradiation can be
identiﬁed as monovacancies and not as further vacancy clusters.
In pure iron, monovacancies are not stable at room temperature[26]. Monovacancies in stainless steels might be stable becauseof the crystal structure and/or composition of those alloys [27–30].
As seen in Fig. 7, the DBAR spectra after the sensitization heat
treatment and plastic deformation are in good agreement with thatafter the electron irradiation. This suggests that monovacancies are

1.00
Before irradiation

0.95

0

5

10

15

20

25

Electron momentum (10-3 m0c)300Incident positron energy (keV)

10

20

10

-1

10

-2

10

-3

(b)
After irradiation

1.0
0.8
0.6
0.4

Before irradiation

10

N(E)/N ref (E)Counting rate (arb. units)

1.2
10 0

511

-4

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Time (ns)Fig. 6. (a) S parameter as a function of incident positron energy and (b) positronannihilation lifetime spectra obtained before (ﬁlled circles) and after (ﬁlled squares)
electron irradiation to a dose of 3  1018 e/cm2. Solid lines are ﬁtting curves
calculated using VEPFIT code.

513

515

517

Gamma-ray energy (keV)
Fig. 7. DBAR spectra obtained after electron irradiation to a dose of 3  1018 e/cm2(ﬁlled circles), sensitization treatment at 650 °C for 24 h (open circles) and plastic
deformation at a strain of 14% (open squares). The spectrum amplitude of theplastic deformation is adjusted by a factor of 2.5. All these spectra are differentiatedby the spectrum for the reference sample. Solid line is the theoretical DBAR
spectrum for a monovacancy in Type 304 stainless steel.

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A. Yabuuchi et al. / Journal of Nuclear Materials 419 (2011) 9–14

3.6. Annealing properties
To reveal the thermal stabilities of vacancy defects within theabove samples, we also investigate annealing process. Fig. 8 shows
S parameters for samples after sensitization heat treatment, tensile
deformation, and electron irradiation as a function of annealing
temperature. It is found that these S parameters commonly decrease to the initial level in the temperature range of 200–400 °C,
again increase in the range of 600–900 °C and subsequently decrease toward 1000 °C. The ﬁrst recovery at 200–400 °C is explainable as a disappearance of monovacancies. The increase in S
parameters at 600–900 °C may be attributed to a re-introductionof vacancy defects due to sensitization as described in Section
3.2. This temperature range is corresponding to a temperature
where austenitic stainless steels are sensitized. The decrease of S
parameters toward 1000 °C for the sensitization heat-treated andthe electron-irradiated samples indicates re-solution. The S parameter of the tensile deformed sample does not decrease above
1000 °C. In this study, stainless steel foils with a thickness of
0.05 mm were used for the tensile-deformed sample while stainless steel sheets with a thickness of 1 mm were used for the sensitization heat-treated and the electron-irradiated samples. Thus,
the cooling rate of the tensile-deformed sample is more rapid thanthat of the other samples. We consider that the increase in S
parameter at 600–900 °C is caused by sensitization effect and the
keeping of high S parameter for the tensile deformed sample
quenched from 1000 °C is caused by freezing thermal equilibrium
vacancies which existed at 1000 °C. It is reported that positrons begin to detect thermal equilibrium vacancies of austenitic stainlesssteels from 900 °C [32]. Indeed, the S parameter of undeformed foil
sample which is quenched from 1000 °C is higher than that of thereference sample, and decreases when it is annealed at 400 °C. Thisshows that thermal equilibrium vacancies are frozen in thequenched foil sample. In a previous positron annihilation lifetime

spectroscopy study, it is reported that a large amount of monovacancy is detected from the electron-irradiated Fe–0.2 wt%C, Fe–
0.5 wt%Si, Fe–1.5 wt%Mn and Fe–0.3 wt%Cu dilute alloys while
only a small amount of vacancy cluster is detected from the electron-irradiated pure-Fe [33]. It indicates strong interactions between the vacancies and the solute atoms. Therefore, it isthought that thermal equilibrium vacancies which existed in thestainless steel foil at 1000 °C are trapped by impurity atoms likeC, Mn or Si atoms during quenching and stabilized without clustering at room temperature.
The ﬁrst recovery of S parameters (200–400 °C) corresponds to alight water reactor operating temperature. That is, monovacancies
in stainless steels are mobile at reactor operating temperature. This
indicates a possibility that monovacancies accumulate at crack tip
grain boundaries, resulting in the development of tight cracks.
Fig. 9a shows S parameters as a function of incident positron energy obtained after the corrosion treatment. Fig. 9b shows the result of VEPFIT analyses with two-layer model. It is found thatupon annealing, the S parameter gradually decreases at 0–3 keV
and that the layer thickness increases with increasing annealing
temperature. The corrosion-induced layer still remains at 600 °C.
This indicates that the increase in the S parameter in the corrosion-induced layer is not caused by the formation ofmonovacancies.

Mean implantation depth (nm)
1.25

0

100

500

1000

(a)

After corrosion

Normalized S parameter

responsible for positron trapping in these samples, too. However,the spectrum after the plastic deformation looks partially different
from the other spectra at high gamma-ray energy region. It is
known that dislocation acts as shallow positron trap in materials[31]. The plastic deformed sample differs from other samples inthat high density dislocations are included. Therefore, it is inferredthat implanted positrons in the plastic deformed sample weretrapped at vacancies and dislocations. We consider that the difference of the spectrum shape at high-energy region is attributed tothe positrons annihilated at dislocations.

1.20
1.15
1.10
1.05
Corrosion + 400 oC annealing

1.00

Corrosion + 600 oC annealing

0.95

0

5

10

15

20

25

1.25

(b)

Normalized S parameter

1.10
1.08
1.06
1.04

Normalized S parameter

After corrosion: Electron irradiation: Sensitization: Tensile deformation

30

Incident positron energy (keV)

1.20

o

Corrosion + 400 C annealing

1.15
Corrosion + 600 oC annealing

1.10
1.05
1.00

1.02
0.95
1.00

0

50

100

150

200

Depth (nm)
0

500

1000

Annealing temperature ( oC)
Fig. 8. S parameter for sensitization heat treated (ﬁlled squares), tensile deformed(ﬁlled diamonds) and electron irradiated (ﬁlled circles) samples as a function of
annealing temperature.

Fig. 9. (a) S parameter as a function of incident positron energy after corrosion
treatment (ﬁlled circles) and subsequent annealing at 400 °C (ﬁlled squares) or
600 °C (ﬁlled diamonds). Solid lines are ﬁtting curves calculated using VEPFIT code.
(b) Depth proﬁles of S parameters obtained through VEPFIT analyses for the above
samples.

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A. Yabuuchi et al. / Journal of Nuclear Materials 419 (2011) 9–14

4. Conclusions
We utilized positron annihilation spectroscopy to examine
three factors inﬂuencing SCC in Type 304 stainless steels—sensitization heat treatment, corrosion treatment and tensile plastic
deformation. A thin porous layer was found to be formed upon
the corrosion treatment. However, it is not clear if mobile vacancy
defects are involved there. Major sources of vacancy defects are theplastic deformation and, during the sensitization heat treatment,
the Kirkendall effect. These vacancy defects are monovacancies
and are annealed at 200–400 °C. This recovery temperature corresponds to the light water reactor operating temperatures (280–
320 °C). It has thus been suggested that monovacancies play animportant role in the high-temperature-water SCC crack propagation mechanism.
Acknowledgements
This study was carried out as part of the project ‘‘In situ analysis
of crack tips in stainless steels under tensile stress’’, entrusted to
the Japan Atomic Energy Agency (JAEA) by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT)
and was partially supported by a MEXT Grant-in-Aid for Young Scientists (B), No. 22760682, 2010. The electron irradiation experiments were performed using the Takasaki-JAEA facility.
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