- Email: [email protected]
Surface erosion of stressed materials under high energy helium ion irradiation
Vacuum/volume Printed in Great
35/number Britain
B/pages
0042-207X/85$3.00+ .OO Pergamon Press Ltd
149 to 153/q 985
Surface erosion of stressed materials energy helium ion irradiation A P Komissarov Leninsky received 9
and N A Machlin,
prosp 49, Moscow October
V-334,
Baikov Institute USSR
of Metallurgy,
Academy
under
of Sciences
high
of the USSR,
1984
Experiments on the influence of external mechanical loading on radiation blistering and flaking of stainless steel and aluminium were carried out. An increase in the critical dose for blistering or flaking of materials was observed when the level of stress increased from zero up to the yield point in a particular temperature range. This phemonenon is discussed in the frame of enhanced capture of helium atoms by bent dislocations in the presence of external mechanical loading. Some supplementary experiments supported the possibility of a dislocation-based mechanism.
Introduction Recent interest in investigations of the influence of the stressed state of materials on their erosion during irradiation by high energy gas ions has arisen because in real radiation situations, for example in controlled fusion reactors, the material will indeed be in a complicated stressed state due to swelling, temperature cycling and differences in thermal expansion coefficients of the construction material and its coating. Also the study of radiation blistering and exfoliation of metals under conditions of external mechanical loading with controlled levels of stresses has a large scientific interest for the development of our understanding of blistering phenomenon. He/
Experimental
methods
In order to investigate the influence of stress state on radiation erosion of materials several special methods have been developed which allow in situ application of various kinds of mechanical loading to the sample during irradiation. These methods include axial tension (a scheme is represented in Figure l), irradiation of strained and compressed surfaces of bent samples under constant (Figure 2) or sign-variable (Figure 3) loading. The unloaded samples were irradiated simultaneously under identical temperature and radiation conditions. Full experimental details are given in refs 1-3. In the present work the behaviour of chromium-manganese low nickel stainless-steel EP-838 and aluminium A7 was studied. Irradiations were carried out on an accelerator with magnetic separation. A scanned helium ion beam of 175 keV energy was used. The irradiation temperature used corresponded to the range where flaking and high temperature blistering of these materials occur. The methods of investigation were scanning electron microscopy, high voltage transmission electron microscopy, surface profilometry and gas re-emission.
Figure 1. Schematic diagram of apparatus used for irradiation of a sample under constant tensile load. 1. Sample; 2. heat shield; 3. electrical heater; 4. diaphragm; 5. Faraday cups; 6. unit for dose measurement.
./.* He’ /
/
’
i-,----6
Figure 2. Apparatus
for irradiation of a bent sample under constant load. 1. Immovable block; 2. stressed and unstressed samples; 3. heat shield and electrical heater; 4. thermocouple; 5. diaphragm; 6. load. 149
A P Komissarov
and N A Machlint
Surface
erosion
of stressed
materials
under
high
energy
helium
ion irradiation
Figure 4. Surfaces of EP-838 stainless steel samples after 175 keV helium ion irradiation at 700 K, dose, 1.5 x 10” cm-’ at the different levels of tensile stresses. (a) a=O; (b) a=6 kg mmm2; (c) a=8 kg mm-*; (d) o= 10 kg mm-‘.
Figure 3. Apparatus for irradiation of samples under the action of a signvariable load. 1. Stressed sample; 2. unstressed sample; 3. upper clamp; 4. lower clamp; 5. electric heater; 6. diaphragm; 7. thermocouple; 8. rocker; 9. electromagnetic coils.
Results and discussion
For the first time we have observed the influence of the stressed state of a material on its radiation erosion for EP-848 stainless steel under axial tension. Irradiation was with a 175 keV helium ion beam’. At an irradiation temperature of 470 K the critical dosefor flaking increased from 8 to 10 x 10” cm-2 when thelevel of stress was increased to a value near the yield point. At a temperature of 700 K, which is in the region where there is a transition from flaking to high temperature blistering for this steel, the critical dose increased from 5 to 6.25 x 10” cmm2. At this temperature a very interesting phenomenon was noted. If on the unstressed samples dome-shaped blistering occurred, then flaking resulted on the surfaces of stressed samples. Moreover, the area of destroyed surface increased when the level of stress was increased. Apictureillustrating this phenomenon is shown in Figure 4. Thus, external loading of the sample increased the temperature range for flaking. In this case the degree of surface erosion or the degree of exfoliated surface increased 1.4 times when the level of stress was increased from zero up to the yield point. Aluminium A-7 shows the same behaviour after irradiation at a temperature of 373 K (0.4 T,,) under stress. Moreover the experimental results show that the increase in critical dose for flaking occurs regardless of the sign of stress2 (that is, it occurs for irradiation of both strained and compressed surfaces of bent samples). The value of the critical dose depends only upon the level of stress and is independent of its sign. A typical eroded surface of aluminium A-7 is shown in Figure 5. The application of a sign-variable load also leads to an increase in the critical dose3. All our experimental results of the influence of constant and sign-variable loading on radiation erosion of aluminium A-7 after irradiation with high energy helium ions are given in Table 1. At a temperature of 473 K (0.5 T,) we did not observe any 150
Figure 5. Surface of aluminium A-7 samples after I75 keV helium ion irradiation at 373 K with the dose of 5.5 x IO” cm-‘. (a) Unloaded sample; (b) strained sample o = 1.3 kg mm-‘; (c) compressed sample CJ= - 1.3 kg mm-‘,
consistent change in blistering parameters with change in the stresses in aluminium A-7. Thus, at this temperature, the influence of loading on high temperature blistering of aluminium disappeared. To explain our results we have examined various possible mechanisms for the influence of stressed-state conditions of materials on their erosion. Firstly, this influence cannot be explained by simple superposition of internal integrated lateral stresses due to helium ion implantation and so-called external stresses due to loading. Using the model of integrated lateral stresses, we would expect to find an increase in the critical dose under application of a strain load, and a decrease when a compressive load acts; we observe the opposite. Secondly, our measurements of the thickness of the exfoliated flakes show that there is no correlation between the thickness and the magnitude and sign of load. Thus the profile of the helium distribution does not change its position in a stressed material compared to that for an unstressed one. Thirdly, the change in kinetics of helium bubble growth under external loading due to stress-induced intensification of vacancy
A P Komissarov
and N A Mach/in:
Table 1. The influence
Surface erosion of stressed materials under high energy helium ion irradiation
of stresses upon radiation
erosion of aluminium A-7 irradiated
Temperature Level of stress x 10’N mm2 (u)
Critical dose x 10” cm-’
0 f0.3 +0.5
5.5
373 K
Temperature Degree of the first exfoliation (?I)
95
6.5
-0.8 - 1.3
7.5
0
6.5
* 1.2 +2.4
7.5
390 K aluminium
10”
Average blister diameter x 10m6 m
3.8 3.8
15.2 15.1 -
3.8
16.5
3.8
17.2 -
3.8
16.4 -
A-7
46 56 58
flow to the bubblescan take place only at high temperature, about 0.5 T, and higher. This fact was shown by Wolfer4 in his works devoted to void growth in stressed materials. All these mechanisms are also unable to explain the absence of any influence of stresses on the erosion of materials at a temperature of about 0.5 T,. We have analysed the possibility of changing the efficiency of lattice defects as sinks for helium atoms in the presence of lattice stress. From published literature and our own data we can say that, after irradiation of metals with helium ions, when the fluence corresponds to a critical dose of blistering, about S-10 dpa, a high density dislocation network is formed. The density of dislocation lines is about 10” cm-‘, as can be seen in Figure 6a. In this case the dislocation sink population is
N,=47rr,C,-
Critical dose x 10” cm-’
7.5
Temperature cold-worked
and it is comparable
473 K
6.5
+0.8 + 1.3 -0.3 -0.5
N,=27rp/ln(r,/r,)-p-
with 175 keV helium ions
10”
1 l+v = ----p 27c l-v
w,,,
sink population.
to
AVa -0.3
to 0.4 eV.
When an external load is employed the energy of interaction between a helium atom and a bent dislocation would rise by the value of the deformation energy W&, = W,,, + Udef. The maximum
cmm2
with the helium bubbles
The similarity of the sink population of dislocations and helium bubbles also follows from energetic consideration. Martinenko’ has shown that the binding energy of a helium atom with a bubble decreases when the ratio m/n increases and the binding energy falls to zero when m/n -3 to 4 (m and n are the number of helium atoms and vacancies in a bubble, respectively). Estimating a binding energy of a helium atom to an edge dislocation one can obtain that
udef
=
value of deformation
energy
W2)2W2~
can be about 0.02-0.03 eV, when ~~~~-0.1
p.
Thus, when applying an external load to a sample, redistribution of implanted helium between bubbles and dislocations should take place. We now write the equations for helium concentration in a lattice for stressed and unstressed materials: jM”(x)
= D&C&(47Tr,C, + 2rrzp + l/AR;)
JM(x)
= D&H,
(471r&
+ 27rzp + l/AR;).
Fipe 6. Defect layer structures of afuminium A-7 after helium ion irradiation at various temperatures. (a) Irradiation temperature of 373 K. (b) Irradiation temperature of 473 K.
If we suppose that the number of helium atoms in a bubble in the region of an interbubble crack are equal for stressed and unstressed samples mcr=m~, and if
dm/dt = 4nr, D,,C,,
(5) 151
A P Komissarov and N A Mach/in:
Surface erosion of stressed materials under high energy helium ion irradiation
we will have
C,, and CL, will be defined by the presence and population of sinks for helium atoms in the samples. Supposing that in some volume V of a sample which contains a dislocation line, implanted helium atoms are distributed over this volume and captured by the dislocation line it is easy to show that C He_ CL,
(W-
he-I/
UdefMkT)
+
T/
d
where W is the energy of interaction of a helium atom with a dislocation, and V, is the volume in which a dislocation line can interact with an impurity. A diffusion coefficient for helium atoms in elastically deformed matter is determined as Dte = D,,
by dislocations when they explained the redistribution and liningup of helium bubbles during annealing of cold-worked irradiated aluminium alloys. So, together with the reduction of helium concentration in the interbubble fracture region, the expansion of the helium distribution profile should take place in an elasticallydeformed material AR; > AR, in comparison with an unstressed one. Now, using Evans’interbubble fracture model’, it is clear that for a wide helium profile and for a wide profile of pressure in helium bubbles, Evans’ conditions for the production of interbubble cracks occur for a larger number of bubble layers compared with a material with a narrow helium profile. Thus, an interbubble crack in a stressed material should be wider than in an unstressed one when the critical blistering dose is achieved. A schematic diagram of this phenomenon is shown in Figure 7. To
PM P;b t tHe'r t
D~~/D;;~ = e -
(n~rn)i(kT)
z
1.
vd e-
(pprzcHe -
(w-
vd e-
f,‘def)/(kT) w/(kT)
+
+ T/
t tHe+t
t
tttie’t
1 tHe?
t
t
b
I/ ’
Now, if we carry out calculations for real radiation conditions for aluminium irradiated with helium ions where C,- 10” cm- 3, V,=&d21-1.25x V=l/G-lo-” cm3, p- 10” cme2, lo-l9 cm3, WxfW,,,x0.17 eV, Udel-0.015 eV, kT=O.O32eV (T= 373 K), we shall obtain an increase in the critical dose of blistering of up to 1.5 times. This agrees well with the experimental value. Thus the analytical treatment shows that the application of elastic stresses to a material during its irradiation with high energy helium ions can lead to a decrease in helium concentration in bubbles in comparison with unstressed material. Therefore an increase in critical dose should take place. This dislocation-based mechanism also explains the independence of critical dose on the sign of the applied stress. At the temperature of 0.5 T, (473 K for aluminium) the dislocation density is not so high due to recovery and recrystallization processes. So the number of helium atoms captured by bent dislocations is not so high and the change of helium concentration in bubbles is very small. Estimates show that a decrease in dislocation density of about an order of magnitude p - 10” cme2 should lead to an increase in critical dose for the stressed material of only about loo/,. The increase in the degree of exfoliated surface when applying a load to materials can also be explained by the increase in capture of helium atoms by bent dislocation lines. We have observed this phenomenon on EP-838 stainless steel. Helium atoms captured by a dislocation can be removed by the moving dislocation line from the region of high helium concentration to an area with a low one. Tani et aL6 used this mechanism of removing helium atoms 152
pbl p,,
Figure 7. The interbubble crack formation in unloaded material with (a) helium distribution profile and (b) in stressed material with a wide helium distribution profile.
Thus
Ge
t tHe’t t
e(“wm’/(kT)
where D,,, is the diffusion coefficient in the unstressed material, 0 is the level of stress, w, is an activation volume for migration of an impurity, which approximately equals 0.3 R, R is the volume of a vacancy. If we estimate the change in diffusion coefficient of helium atoms in aluminium under application of stress we will have
CPU
t tHe-t t
(a)
9-8-
-.-.-
400
500
c=+2.4x107
600
700
800
(K) (b)
@I
Figure 8. (a) Differential curves of helium re-emission from aluminium A-7 samples irradiated with 175 keV helium ions at 393 K dose 6.25 x 10” cm-’ under the action of the sign-variable load and unloaded. (b)Corresponding pictures of surface topography at 500 K. (c) Pictures of surface topography at 680 K.
A P Komissarov and N A Mach/in:
Surface erosion of stressed materials under high energy helium ion irradiation
maintain the equilibrium growth of the interbubble crack the increase in its width should be accompanied by an increase in its length. So in a stressed material the area over which interbubble cracks spread should be greater than in an unstressed one. This is an explanation of the observed increase in surface erosion with increasing level of stress.
cooclosioos It has been shown that a dislocation-based model can qualitatively explain the main experimentally observed regularities of the influence of external loading upon radiation erosion. Further supplementary experiments have been performed and give results which support the possibility of this dislocation based mechanism. For instance transmission electron microscopy of helium-irradiated aluminium has shown that a dense dislocation network had been formed at a temperature of 373 K (p-5x 10” cm-‘) and at 473 K the dislocation density was about 10’ cm-‘. Typical dislocation structures of aluminium are shown in Figure 6. We also carried out a number of experiments on gas re-emission from He-irradiated aluminium in stressed and unstressed conditions. The results of these experiments are shown in Figure 8. As
can be seen from this figure, in the stressed material a larger quantity of implanted helium is released into the interbubble crack and into the blister cavity in comparison with unstressed material. There is less helium left in bubbles after the interbubble crack has been formed. In conclusion it is necessary to remark that this dislocationbased mechanism acts only in a definite temperature range where a sufficiently dense dislocation structure can be formed and then retained. We have not taken into account the influence of stresses on the vacancy flow to bubbles. This is acceptable however for the range of low and moderate temperature, i.e. less than 0.5 T,.
References
1L I Ivanov, A P Komissarov, N A Machlin et al, J Nucl Mater, 76-77, 211 (1978). ’ A P Komissarov and N A Machlin, Phys Rad Damage Issue, 3,47 (1979). (In Russian.) a L I Ivanov, A P Komissarov, N A Machlin et al, Rad Eficts, 60, 231 (1982). 4 W G Wolfer and J L Straalsund Scripta Metall, 7, 161 (1973). ’ Yu V Martinenko, Theory of Blistering, preprint, Institute of Atomic Energy-3145, Moscow (1979). (In Russian.). 6 S Tani, S Ishino and Y Mishima, J Nucl Sci Tech&, 13, 722 (1976). ’ J H Evans, An interbubble fracture mechanism of blister formation on helium-irradiated metals, J Nucl Mater, 68, 129 (1977).
153
35/number Britain
B/pages
0042-207X/85$3.00+ .OO Pergamon Press Ltd
149 to 153/q 985
Surface erosion of stressed materials energy helium ion irradiation A P Komissarov Leninsky received 9
and N A Machlin,
prosp 49, Moscow October
V-334,
Baikov Institute USSR
of Metallurgy,
Academy
under
of Sciences
high
of the USSR,
1984
Experiments on the influence of external mechanical loading on radiation blistering and flaking of stainless steel and aluminium were carried out. An increase in the critical dose for blistering or flaking of materials was observed when the level of stress increased from zero up to the yield point in a particular temperature range. This phemonenon is discussed in the frame of enhanced capture of helium atoms by bent dislocations in the presence of external mechanical loading. Some supplementary experiments supported the possibility of a dislocation-based mechanism.
Introduction Recent interest in investigations of the influence of the stressed state of materials on their erosion during irradiation by high energy gas ions has arisen because in real radiation situations, for example in controlled fusion reactors, the material will indeed be in a complicated stressed state due to swelling, temperature cycling and differences in thermal expansion coefficients of the construction material and its coating. Also the study of radiation blistering and exfoliation of metals under conditions of external mechanical loading with controlled levels of stresses has a large scientific interest for the development of our understanding of blistering phenomenon. He/
Experimental
methods
In order to investigate the influence of stress state on radiation erosion of materials several special methods have been developed which allow in situ application of various kinds of mechanical loading to the sample during irradiation. These methods include axial tension (a scheme is represented in Figure l), irradiation of strained and compressed surfaces of bent samples under constant (Figure 2) or sign-variable (Figure 3) loading. The unloaded samples were irradiated simultaneously under identical temperature and radiation conditions. Full experimental details are given in refs 1-3. In the present work the behaviour of chromium-manganese low nickel stainless-steel EP-838 and aluminium A7 was studied. Irradiations were carried out on an accelerator with magnetic separation. A scanned helium ion beam of 175 keV energy was used. The irradiation temperature used corresponded to the range where flaking and high temperature blistering of these materials occur. The methods of investigation were scanning electron microscopy, high voltage transmission electron microscopy, surface profilometry and gas re-emission.
Figure 1. Schematic diagram of apparatus used for irradiation of a sample under constant tensile load. 1. Sample; 2. heat shield; 3. electrical heater; 4. diaphragm; 5. Faraday cups; 6. unit for dose measurement.
./.* He’ /
/
’
i-,----6
Figure 2. Apparatus
for irradiation of a bent sample under constant load. 1. Immovable block; 2. stressed and unstressed samples; 3. heat shield and electrical heater; 4. thermocouple; 5. diaphragm; 6. load. 149
A P Komissarov
and N A Machlint
Surface
erosion
of stressed
materials
under
high
energy
helium
ion irradiation
Figure 4. Surfaces of EP-838 stainless steel samples after 175 keV helium ion irradiation at 700 K, dose, 1.5 x 10” cm-’ at the different levels of tensile stresses. (a) a=O; (b) a=6 kg mmm2; (c) a=8 kg mm-*; (d) o= 10 kg mm-‘.
Figure 3. Apparatus for irradiation of samples under the action of a signvariable load. 1. Stressed sample; 2. unstressed sample; 3. upper clamp; 4. lower clamp; 5. electric heater; 6. diaphragm; 7. thermocouple; 8. rocker; 9. electromagnetic coils.
Results and discussion
For the first time we have observed the influence of the stressed state of a material on its radiation erosion for EP-848 stainless steel under axial tension. Irradiation was with a 175 keV helium ion beam’. At an irradiation temperature of 470 K the critical dosefor flaking increased from 8 to 10 x 10” cm-2 when thelevel of stress was increased to a value near the yield point. At a temperature of 700 K, which is in the region where there is a transition from flaking to high temperature blistering for this steel, the critical dose increased from 5 to 6.25 x 10” cmm2. At this temperature a very interesting phenomenon was noted. If on the unstressed samples dome-shaped blistering occurred, then flaking resulted on the surfaces of stressed samples. Moreover, the area of destroyed surface increased when the level of stress was increased. Apictureillustrating this phenomenon is shown in Figure 4. Thus, external loading of the sample increased the temperature range for flaking. In this case the degree of surface erosion or the degree of exfoliated surface increased 1.4 times when the level of stress was increased from zero up to the yield point. Aluminium A-7 shows the same behaviour after irradiation at a temperature of 373 K (0.4 T,,) under stress. Moreover the experimental results show that the increase in critical dose for flaking occurs regardless of the sign of stress2 (that is, it occurs for irradiation of both strained and compressed surfaces of bent samples). The value of the critical dose depends only upon the level of stress and is independent of its sign. A typical eroded surface of aluminium A-7 is shown in Figure 5. The application of a sign-variable load also leads to an increase in the critical dose3. All our experimental results of the influence of constant and sign-variable loading on radiation erosion of aluminium A-7 after irradiation with high energy helium ions are given in Table 1. At a temperature of 473 K (0.5 T,) we did not observe any 150
Figure 5. Surface of aluminium A-7 samples after I75 keV helium ion irradiation at 373 K with the dose of 5.5 x IO” cm-‘. (a) Unloaded sample; (b) strained sample o = 1.3 kg mm-‘; (c) compressed sample CJ= - 1.3 kg mm-‘,
consistent change in blistering parameters with change in the stresses in aluminium A-7. Thus, at this temperature, the influence of loading on high temperature blistering of aluminium disappeared. To explain our results we have examined various possible mechanisms for the influence of stressed-state conditions of materials on their erosion. Firstly, this influence cannot be explained by simple superposition of internal integrated lateral stresses due to helium ion implantation and so-called external stresses due to loading. Using the model of integrated lateral stresses, we would expect to find an increase in the critical dose under application of a strain load, and a decrease when a compressive load acts; we observe the opposite. Secondly, our measurements of the thickness of the exfoliated flakes show that there is no correlation between the thickness and the magnitude and sign of load. Thus the profile of the helium distribution does not change its position in a stressed material compared to that for an unstressed one. Thirdly, the change in kinetics of helium bubble growth under external loading due to stress-induced intensification of vacancy
A P Komissarov
and N A Mach/in:
Table 1. The influence
Surface erosion of stressed materials under high energy helium ion irradiation
of stresses upon radiation
erosion of aluminium A-7 irradiated
Temperature Level of stress x 10’N mm2 (u)
Critical dose x 10” cm-’
0 f0.3 +0.5
5.5
373 K
Temperature Degree of the first exfoliation (?I)
95
6.5
-0.8 - 1.3
7.5
0
6.5
* 1.2 +2.4
7.5
390 K aluminium
10”
Average blister diameter x 10m6 m
3.8 3.8
15.2 15.1 -
3.8
16.5
3.8
17.2 -
3.8
16.4 -
A-7
46 56 58
flow to the bubblescan take place only at high temperature, about 0.5 T, and higher. This fact was shown by Wolfer4 in his works devoted to void growth in stressed materials. All these mechanisms are also unable to explain the absence of any influence of stresses on the erosion of materials at a temperature of about 0.5 T,. We have analysed the possibility of changing the efficiency of lattice defects as sinks for helium atoms in the presence of lattice stress. From published literature and our own data we can say that, after irradiation of metals with helium ions, when the fluence corresponds to a critical dose of blistering, about S-10 dpa, a high density dislocation network is formed. The density of dislocation lines is about 10” cm-‘, as can be seen in Figure 6a. In this case the dislocation sink population is
N,=47rr,C,-
Critical dose x 10” cm-’
7.5
Temperature cold-worked
and it is comparable
473 K
6.5
+0.8 + 1.3 -0.3 -0.5
N,=27rp/ln(r,/r,)-p-
with 175 keV helium ions
10”
1 l+v = ----p 27c l-v
w,,,
sink population.
to
AVa -0.3
to 0.4 eV.
When an external load is employed the energy of interaction between a helium atom and a bent dislocation would rise by the value of the deformation energy W&, = W,,, + Udef. The maximum
cmm2
with the helium bubbles
The similarity of the sink population of dislocations and helium bubbles also follows from energetic consideration. Martinenko’ has shown that the binding energy of a helium atom with a bubble decreases when the ratio m/n increases and the binding energy falls to zero when m/n -3 to 4 (m and n are the number of helium atoms and vacancies in a bubble, respectively). Estimating a binding energy of a helium atom to an edge dislocation one can obtain that
udef
=
value of deformation
energy
W2)2W2~
can be about 0.02-0.03 eV, when ~~~~-0.1
p.
Thus, when applying an external load to a sample, redistribution of implanted helium between bubbles and dislocations should take place. We now write the equations for helium concentration in a lattice for stressed and unstressed materials: jM”(x)
= D&C&(47Tr,C, + 2rrzp + l/AR;)
JM(x)
= D&H,
(471r&
+ 27rzp + l/AR;).
Fipe 6. Defect layer structures of afuminium A-7 after helium ion irradiation at various temperatures. (a) Irradiation temperature of 373 K. (b) Irradiation temperature of 473 K.
If we suppose that the number of helium atoms in a bubble in the region of an interbubble crack are equal for stressed and unstressed samples mcr=m~, and if
dm/dt = 4nr, D,,C,,
(5) 151
A P Komissarov and N A Mach/in:
Surface erosion of stressed materials under high energy helium ion irradiation
we will have
C,, and CL, will be defined by the presence and population of sinks for helium atoms in the samples. Supposing that in some volume V of a sample which contains a dislocation line, implanted helium atoms are distributed over this volume and captured by the dislocation line it is easy to show that C He_ CL,
(W-
he-I/
UdefMkT)
+
T/
d
where W is the energy of interaction of a helium atom with a dislocation, and V, is the volume in which a dislocation line can interact with an impurity. A diffusion coefficient for helium atoms in elastically deformed matter is determined as Dte = D,,
by dislocations when they explained the redistribution and liningup of helium bubbles during annealing of cold-worked irradiated aluminium alloys. So, together with the reduction of helium concentration in the interbubble fracture region, the expansion of the helium distribution profile should take place in an elasticallydeformed material AR; > AR, in comparison with an unstressed one. Now, using Evans’interbubble fracture model’, it is clear that for a wide helium profile and for a wide profile of pressure in helium bubbles, Evans’ conditions for the production of interbubble cracks occur for a larger number of bubble layers compared with a material with a narrow helium profile. Thus, an interbubble crack in a stressed material should be wider than in an unstressed one when the critical blistering dose is achieved. A schematic diagram of this phenomenon is shown in Figure 7. To
PM P;b t tHe'r t
D~~/D;;~ = e -
(n~rn)i(kT)
z
1.
vd e-
(pprzcHe -
(w-
vd e-
f,‘def)/(kT) w/(kT)
+
+ T/
t tHe+t
t
tttie’t
1 tHe?
t
t
b
I/ ’
Now, if we carry out calculations for real radiation conditions for aluminium irradiated with helium ions where C,- 10” cm- 3, V,=&d21-1.25x V=l/G-lo-” cm3, p- 10” cme2, lo-l9 cm3, WxfW,,,x0.17 eV, Udel-0.015 eV, kT=O.O32eV (T= 373 K), we shall obtain an increase in the critical dose of blistering of up to 1.5 times. This agrees well with the experimental value. Thus the analytical treatment shows that the application of elastic stresses to a material during its irradiation with high energy helium ions can lead to a decrease in helium concentration in bubbles in comparison with unstressed material. Therefore an increase in critical dose should take place. This dislocation-based mechanism also explains the independence of critical dose on the sign of the applied stress. At the temperature of 0.5 T, (473 K for aluminium) the dislocation density is not so high due to recovery and recrystallization processes. So the number of helium atoms captured by bent dislocations is not so high and the change of helium concentration in bubbles is very small. Estimates show that a decrease in dislocation density of about an order of magnitude p - 10” cme2 should lead to an increase in critical dose for the stressed material of only about loo/,. The increase in the degree of exfoliated surface when applying a load to materials can also be explained by the increase in capture of helium atoms by bent dislocation lines. We have observed this phenomenon on EP-838 stainless steel. Helium atoms captured by a dislocation can be removed by the moving dislocation line from the region of high helium concentration to an area with a low one. Tani et aL6 used this mechanism of removing helium atoms 152
pbl p,,
Figure 7. The interbubble crack formation in unloaded material with (a) helium distribution profile and (b) in stressed material with a wide helium distribution profile.
Thus
Ge
t tHe’t t
e(“wm’/(kT)
where D,,, is the diffusion coefficient in the unstressed material, 0 is the level of stress, w, is an activation volume for migration of an impurity, which approximately equals 0.3 R, R is the volume of a vacancy. If we estimate the change in diffusion coefficient of helium atoms in aluminium under application of stress we will have
CPU
t tHe-t t
(a)
9-8-
-.-.-
400
500
c=+2.4x107
600
700
800
(K) (b)
@I
Figure 8. (a) Differential curves of helium re-emission from aluminium A-7 samples irradiated with 175 keV helium ions at 393 K dose 6.25 x 10” cm-’ under the action of the sign-variable load and unloaded. (b)Corresponding pictures of surface topography at 500 K. (c) Pictures of surface topography at 680 K.
A P Komissarov and N A Mach/in:
Surface erosion of stressed materials under high energy helium ion irradiation
maintain the equilibrium growth of the interbubble crack the increase in its width should be accompanied by an increase in its length. So in a stressed material the area over which interbubble cracks spread should be greater than in an unstressed one. This is an explanation of the observed increase in surface erosion with increasing level of stress.
cooclosioos It has been shown that a dislocation-based model can qualitatively explain the main experimentally observed regularities of the influence of external loading upon radiation erosion. Further supplementary experiments have been performed and give results which support the possibility of this dislocation based mechanism. For instance transmission electron microscopy of helium-irradiated aluminium has shown that a dense dislocation network had been formed at a temperature of 373 K (p-5x 10” cm-‘) and at 473 K the dislocation density was about 10’ cm-‘. Typical dislocation structures of aluminium are shown in Figure 6. We also carried out a number of experiments on gas re-emission from He-irradiated aluminium in stressed and unstressed conditions. The results of these experiments are shown in Figure 8. As
can be seen from this figure, in the stressed material a larger quantity of implanted helium is released into the interbubble crack and into the blister cavity in comparison with unstressed material. There is less helium left in bubbles after the interbubble crack has been formed. In conclusion it is necessary to remark that this dislocationbased mechanism acts only in a definite temperature range where a sufficiently dense dislocation structure can be formed and then retained. We have not taken into account the influence of stresses on the vacancy flow to bubbles. This is acceptable however for the range of low and moderate temperature, i.e. less than 0.5 T,.
References
1L I Ivanov, A P Komissarov, N A Machlin et al, J Nucl Mater, 76-77, 211 (1978). ’ A P Komissarov and N A Machlin, Phys Rad Damage Issue, 3,47 (1979). (In Russian.) a L I Ivanov, A P Komissarov, N A Machlin et al, Rad Eficts, 60, 231 (1982). 4 W G Wolfer and J L Straalsund Scripta Metall, 7, 161 (1973). ’ Yu V Martinenko, Theory of Blistering, preprint, Institute of Atomic Energy-3145, Moscow (1979). (In Russian.). 6 S Tani, S Ishino and Y Mishima, J Nucl Sci Tech&, 13, 722 (1976). ’ J H Evans, An interbubble fracture mechanism of blister formation on helium-irradiated metals, J Nucl Mater, 68, 129 (1977).
153