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