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Book ChapterDOI

A Comparison of the Relative Importance of Helium and Vacancy Accumulation in Void Nucleation

01 Jan 1987-ASTM special technical publications (ASTM International)-Iss: 955, pp 358-370

AbstractVoid nucleation in irradiated austenitic stainless steels generally requires the presence of either residual or transmutant gases. Classical nucleation rates are much too low to account for the number of voids observed attemperatures greater than about 450°C. An alternate path is generally believed to be responsible for void formation; namely, the growth of gas-stabilized bubbles until they reach a critical size beyond which further gas accumulation is not required to promote growth. Two limiting paths can be envisioned for void nucleation on a population of sub-critical helium/vacancy clusters; one is limited to growth by helium accumulation alone and the other to growth by stochastic fluctuations in the vacancy accumulation. As bubbles approach the critical size, stochastic processes could begin to contribute to the void nucleation rate. A comparison is made of nucleation rates along these two limiting paths as a function of the gas content of the clusters. The calculations indicate that the gas accumulation path is generally dominant, particularly at higher temperatures and for lower gas contents. The fraction of the critical size required for the vacancy path to contribute to the total nucleation rate increases with temperature. The results confirm the important role of transmutant helium in promoting void swelling.

Topics: Nucleation (64%), Population (51%), Vacancy defect (50%)

Summary (1 min read)

Nucleation by Stochastic Fluctuations

  • The method developed here is similar to that of Katz and Wiedersich (6) , Clement and Wood (26) and Mansur and Wolfer (27) .
  • It should be pointed out that the void nucleation rate is quite sensitive to the dislocation density (see Fig. 3b below).
  • The number of vacancies which correspond to this critical size will be designated n*.
  • The values of the cluster concentrations in the constrained equilibrium distribution are elevated relative to the steady state distribution for n < n* also, this is accounted for in the theory by the introduction of the so-called Zeldovich factor.
  • The term involving the products of the p. can safely be eliminated by noting two facts.

Nucleation by Helium Accumulation

  • The critical bubble size corresponding to n\u is in general not the same as the critical size associated with n discussed above.
  • For a fixed value of the vacancy supersaturation, the family of curves shov/n in Figure 1 represent three different levels of helium.
  • The curves labeled I and II contain a region in radius space for which the net growth rate is negative.
  • Since the procedure used here is similar to that which has been discussed previously (20) only a brief summary will be given.

He D He S? e

  • G^ is the helium generation rate and D^e is the heliur.i diffusivity.
  • Based on the foregoing helium partitioning model, the arrival rate of helium atoms at a bubble with a radius r(n,m) is EQUATION ) where N is the total number of bubbles among which the helium from the dislocations is partitioned.
  • This bubble density is taken from Ref. 20 and reflects experimentally observed values.

values of certain of these parameters listed in the table have been varied

  • In the analysis and they will be discussed further in the text.
  • These parameter values are similar to those which have been used previously in rate theory simulations of void swelling (18) (19) (20) .
  • 2c where the ratio of the nucleation times has been plotted.
  • For lower gas contents the nucleation time due to helium accumulation is always much less than that for the stochastic process.

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A COMPARISON
OF THE
RELATIVE IMPORTANCE
OF
HELIUM
AND
VACANCY
ACCUMULATION
IN
VOID NUCLEATION*
R. E.
Stoller
1
"
and G. R.
Odette*
^Metals
and
Ceramics Division,
Oak
Ridge National Laboratory,
P. 0. Box X, Oak
Ridge,
TN
37831
(USA)
^Department
of
Chemical
and
Nuclear Engineering, University
of
California,
Santa Barbara,
CA
93106
(USA)
CONF-860605--29
ABSTRACT
DE87 000230
Void nucleation
in
irradiated austenitic stainless steels generally
requires
the
presence
of
either residual
or
transmutant gases. Classical
nucleation rates
are
much
too low
to
account
for the
number
of
voids
observed
at
temperatures greater than about 450°C.
An
alternate path
is
generally believed
to be
responsible
for
void formation; viz.
the
growth
of
gas-stabilized bubbles until they reach
a
critical size beyond which
further gas accumulation
is
not
required
to
promote growth.
Two
limiting
paths
can
be
envisioned
for
void nucleation
on a
population
of
sub-critical
helium/vacancy clusters;
one
is
limited
to
growth
by
helium accumulation
alone
and the
other
to
growth
by
stochastic fluctuations
in
the
vacancy
accumulation.
As
bubbles approach
the
critical size, stochastic processes
could begin
to
contribute
to
the
void nucleation rate.
A
comparison
is
made
of
nucleation rates along these
two
limiting paths
as a
function
of
the gas
content
of
the
clusters.
The
calculations indicate that
the gas
*Research sponsored
by
the
Division
of
Materials Sciences, U.S.
Department
of
Energy, under contract DE-AC05-840R21400 with Martin Marietta
Energy Systems, Inc.
and the
Office
of
Fusion Energy, U.S. Department
of
Energy, under contract AM03-765F00034 with the University
of
California
at
Santa Barbara.
Bv acceptance
of
this article,
the
publisher
or
recipient acknowledges
the
U.S.
Government's right
ta
retain
a
nonexclusive, royalty-free
license
in and to anv
copyright
covering
the
article.
DISTRIDUHOK
Q?
i'HIii
DOCUMtKT
$
UfH.IMITEIi

accumulation path is generally dominant, particularly at higher tempera-
tures and for lower gas contents. The fraction of the critical size
required for the vacancy path to contribute to the total nucleation rate
increases with temperature. The results confirm the important role of
transmutant helium in promoting void swelling.
KEY WORDS: cavities, helium effects, radiation damage, void nucleation,
void swelling

INTRODUCTION
From the time that the phenomenon of void swelling in neutron irra-
diated structural materials was first discovered, transmutant and residual
gases have been suspected of playing an important role in void formation
(1,2).
Subsequently, a considerable amount of theoretical and experimental
research has confirmed those initial suspicions. Most of this work has
focused on the effects of the helium which is produced by transmutation
reactions between both fast and thermal neutrons and the various atomic
species that comprise the material. Because helium is chemically inert
and insoluble in most metals, it has been assumed that it would be a more
potent aid to void nucleation than either transmutant hydrogen or residual
gases such as nitrogen or oxygen. While recent work has suggested that
residual oxygen can have a significant influence on void nucleation in an
austenitic alloy during heavy ion irradiation in the absence of helium (3),
when the same alloy is co-implanted with helium during the ion bombardment
the effect of the helium appears to swamp that of the oxygen (4). Hence,
the following discussion explicitly considers only the influence of
transmutant helium on void nucleation. The method developed to demonstrate
the importance of this gas should also be applicable for other gases that
are chemically inert with respect to alloy constituents.
Classical homogeneous nucleation theory was applied to the problem of
void formation in austenitic stainless steels very early
(5-8).
Russell
and coworkers have continued to develop this theory over the past 10 years
to include the effects of helium and heterogeneous nucleation
(9—13).

4
Wolfer and coworkers have developed a Fokker-Planck formulation of the void
nucleation problem and have explored the effects of mobile di-vacancies and
solute segregation to void surfaces
(14—16).
Despite these refinements,
the classical theory fails to predict the experimentally observed void den-
sities in the intermediate to high temperature range (450 < T < 700°C)
where measurable void swelling occurs in these steels
(12,16,17).
An
alternate mechanism has has been proposed to cause void formation at these
temperatures and to promote void formation at low temperatures. This
mechanism involves the growth of small gas-stabilized bubbles until they
reach a critical size beyond which further gas accumulation is not required
to promote growth. Theoretical and recent experimental work has shown that
the time required for these small bubbles to reach the critical size corre-
lates well with observed void swelling nucleation times
(18-23).
Accordingly, one can envision two limiting paths for void formation on a
population of subcritical helium/vacancy clusters; one is limited to growth
by helium accumulation alone and the other to growth by stochastic fluc-
tuations in the vacancy cluster population. A recent discussion concerning
the relative magnitudes of these two processes provided some of the impetus
for this work (24). A mathematical description of the two paths is given
below and their magnitudes are compared for irradiation conditions typical
of fast reactors.
Models of Void Formation
The two methods discussed below attempt to compute a characteristic
time for nucleation or the nucleation rate per cluster for a helium/vacancy

cluster with a given number of helium atoms. The number of vacancies in
this cluster or bubble is computed assuming that the bubble radius is that
of a stable bubble in an irradiation environment characterized by a vacancy
supersaturation S at a temperature T where:
D
v
C
,
This stable bubble radius is slightly larger than the equilibrium bubble
radius as discussed elsewhere
(21,25).
In Eq. (1), the terms DC and
D.^.
are the vacancy and interstitial fluxes impinging on the bubble and
DC is the self-diffusion coefficient. The bubble radius and the gas
pressure in the bubble are computed using a hard sphere equation of state
as described in Ref. 25.
For both models, the point defect concentrations are computed using
the conventional rate theory and the temperature dependent sink strengths
for extended defects discussed in Ref. 20. The sink strength of the sub-
critical bubble population is insignificant when compared to the other
sinks in the system, therefore it is not included when computing the point
defect concentrations. The calculations assume that only the mono-defects
and heliun gas atoms are mobile and that the only defects which the bubbles
emit are vacancies. The use of the principle of detailed balance and
thermodynamic equilibrium (8,9) leads to the following form for the

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Abstract: The extensive literature on oxygen chemisorption and solubility in metals is briefly reviewed, with special emphasis on the reduction of surface tension associated with oxygen adsorption. A thermodynamic model based on the adsorption equations of Gibbs and Langmuir is developed to determine the relative stability in the presence of oxygen of the void compared to the dislocation loop and stacking fault tetrahedron. Representative calculations are performed for copper, nickel, and austenitic stainless steel. Atomistic and elastic continuum calculations predict that void formation should not occur in most pure face-centered cubic metals during quenching or irradiation. However, the thermodynamic model predicts that oxygen concentrations of 30 to 1000 appm will stabilize void formation in copper, nickel, and stainless steel. Foils of copper and several Fe-Cr-Ni stainless steels containing various amounts of oxygen have been examined with electron microscopy following ion bombardment. The presence of 30 to 1000 appm O resulted in significant amounts of void formation, whereas no voids were observed in low-oxygen specimens, in agreement with the model predictions. Oxygen introduced by ion implantation was more effective in promoting void formation than residual oxygen. Solutes such as phosphorus in stainless steel reduced the effectiveness of oxygen as a void-stabilizing agent.

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Cites background from "A Comparison of the Relative Import..."

  • ...There are two nucleation pathways for void formation under irradiation [18,20,21]....

    [...]