- Email: [email protected]
Interstitial clustering in cascades in fast-neutron irradiated aluminium by diffuse X-ray scattering
169
Journal of Nuclear Materials 108 & 109 (1982) 169-173 North-Holland Publishing Company
INTERSTITIAL CLUSTERING IN CASCADES IN FAST-NEUTRON IRRADIATED ALUMINIUM BY DIFFUSE X-RAY SCATTERING D. GRASSE, B. von GUlkARD
and J. PEISL
Sekfion Physik der Universitiit Miinchen, 8 Miinchen 22, Federal Republic of Germany Received 8 January 1982; accepted
1 February 1982
We measure diffuse X-ray scattering close to Bragg reflections in aluminium single crystals after irradiation with fast-neutrons at 4.6 K. Comparing the intensity of the Huang scattering with that measured after e-irradiation for the same radiation-induced resistivity leads to tbe result that in Al during n-irradiation interstitial clusters containing an average of three defects are formed. The cluster size is independent of dose up to 2.4X lOI n/cm* which indicate8 the clusters to be formed in a single cascade. Very close to the Bragg peak is a modulation of the Huang intensity which shows that the interstitial clusters are not randomly distributed but are correlated in cascades. Fitting a theoretical curve to the modulation, a cascade radius R K = 50 A is obtained. During annealing the clusters grow and finally form interstitial loops. Long-range migration of the interstitials away from their nascent cascade is observed.
1. Introduftion
displacements written as
Irradiation of solids with fast neutrons produces vacancies and interstitials in displacement cascades. The actual defect concentration and correlation within a cascade is a fundamental problem and is of great technological relevance. Diffuse X-ray scattering has been successfully used to study point defects and small agglomerates. After n-irradiation at 4.6 K in copper [1] agglomerates containing an average of 25 interstitials were observed. In order to get more information about the mechanism of interstitial agglomeration, aluminium, where low defect density cascades were expected, was studied for several doses.
2. Theory Point defects or clusters which create a displacement field n decreasing as r-’ in a crystal, cause a shifting of the Bragg reflections, a decrease of the Bragg reflections due to a static Debye-Waller factor and a diffuse intensity distribution (2,3]. The long-range displacement field determines the scattering for small 9 (9 = K - G, the deviation of the scattering vector K from the corresponding reciprocal lattice point G), Huang diffuse scattering (HDS). If the
0022-3115/82/0000-0000/$02.75
0 1982 North-Holland
of the defects add linearly, HDS can be
F is the structure factor of a unit cell. The scattering intensity is determined by two Fourier transforms [2]. 1, the Fourier transform of the displacement field from one defect, can be described by the dipole tensor Pij using elastic continuum theory [3,4]. E, the Fourier transform of the concentration fluctuations, must be averaged over all equivalent defect distributions. (]c’]2) is a sum
(]E(9)]2)=c(l
-c)+Q(r>exp(iqr),
where the first term is due to a random distribution (c concentration) and e(r) is the additional probability to find a defect at a distance r from another defect above the random distribution probability. If all defects form agglomerates containing always I defects within a radius R,,(]F(q)]2)=zcforqal/R,isobtained.Thismeans all z defects in the agglomerate scatter coherently and act like one big defect. For q Z+ 1/R, one gets (I E(q)) ’ = c, the value for an uncorrelated random distribution. The behaviour in between can be calculated analytically for special defect distributions [5]. If the defects form dense clusters the lattice distortions close to the clusters can be large (Ku ) I]. In this case a different type of scattering is observed for larger
D. Grasse et al. / Interstitial clustering in fast-neutron irradiated AI
170 q. The
asymptotic or Stokes-Wilson
scattering [6] (SWS)
is
lo!
ZSW-c]TrP(ZC/q4. The change from l/q2 dependence to l/q4 dependence occurs at a certain value qC,. From rC,= l/q,, an estimate of the radius of the heavily strained region around the cluster can be made [6]. x
0
3. Experimental loL The rectangular samples were spark cut from one high-purity Al single crystal (resistivity ratio > 30000) from VAW. Next to the crystal, an Al wire (resistivity ratio 1200) was mounted to measure the resistivity change. The irradiations were performed in the low temperature irradiation facility of the FRM at Garching. The irradiated samples were transferred to the measuring cryostat without warming up. The set-up for the X-ray measurements consisted of a 6 kW rotating anode X-ray tube, a bent quartz-monochromator, and an X-ray cryostat, in which the sample temperature could be varied from 4 to 300 K. The measurements were performed at 8 K and the annealing program consisted of IO-mm annealing pulses. Scattering intensities were determined relative to a monitor counter in the primary beam and put on an absolute scale by scattering from polystyrene [7].
4. Results after irradiation Fig. 1 shows a typical result for measurements after irradiation. The scattered intensity close to a (400) Bragg peak measured in [lOO] direction is given for an Al crystal after irradiation at 4.6 K with 1.1 X lOI n/cm2 and after complete thermal annealing at 500 K. The great difference in [lOO] direction shows a pronounced asymmetry indicating that the distortion field is dominated by defects which expand the lattice i.e. interstitials [3]. To obtain the distortion-induced intensity, the scattered intensity after complete annealing at 500 K was subtracted in each case. Then the averaged difference from both sides in respect to the Bragg reflection was plotted on a double logarithmic scale versus q. This is shown in fig. 2 for the experimental results of fig. 1. The error bars in fig. 2 are determined by statistics. The typical l/q2 dependence of HDS and the l/q4 dependence of SWS is clearly demonstrated. For comparison HDS expected for the same defect concentra-
ro3
-6”
_/,O
-2’
00
2'
Lo
6'
-A20 Fig. 1. Diffuse scattered X-ray intensity from Al single crystal near (400) reflection in [NO] direction. X after irradiation at 4.6 K with 1.1 X lo’* n/cm’; 0 after thermal annealing at 500 K.
tion after electron irradiation [8] for the radial directions (q ]IG) is also shown (dashed-dotted line). The concentration is determined in both cases from the resistivity change. The increase of the scattered intensity after neutron irradiation is due to clustering of the interstitials *. z, the average number of interstitials per cluster, obtained from our measurements [S] are listed in table 1. We find that during neutron-irradiation at 4.6 K small clusters are created which contain in the average 3 interstitials. Since there is also a distortion-induced intensity in the [OlO]direction in fig. 2 and also in the [ 110) direction close to a (220) reflection [5], the distortion field has to have orthorhombic or lower symmetry. This is consistent with the symmetry of the * ) C I* differs for interstitials and vacancies in Al by a factor of about 100 due to the difference in the relative volume change [8]. Therefore the scattering is completely due to interstitials.
L). Grasse et ai. / ~nterstitiai clustering in fast-neutron
irradiated A f
171
05 x
1
\
103
.Ol
.02 -
-
.OL o ‘YG
Fig. 2. Defect-induced scattering intensity from Al near (400) after irradiation at 4.6 K with 1.1 X 10’s n/cm’. X in [ 1001 direction, 0 in [OlO] direction; dashed-dotted line, expected intensity for the same defect concentration caused by electron irradiation.
stable clusters of 3 interstitials calculated by Schober [9].There is no significant dose dependence of the average duster size since there is an experimental error of 10% for the absolute intensity. The slight inckse of t may be due to radiation-induced annealing. A constant
‘/G
Fig. 3. Defect-induced scattering intensity from MO near (440) after irradiation at 4.6 K with 3.1 X lo’* n/cm’ in [ 1lo] direr tion X. Dashed-dotted line, expected intensity for the same defect concentration caused by electron irradiation.
z is consistent with measurements of the Hall-effect [IO] and the thermo-power [ 1I]. Since the clustering is independent on dose it has to take place inside a cascade. From computer simulations 112-141 there was no evidence for formation of interstitial clusters. It has been proposed flS] that int~titi~~l~t~ can occur subsequent to the dynamic production of a cascade until
Table I Dosedependence of the single defect concentration and the size of the small clusters Dose ( lot8 n/cm2)
Reflection
Single defect concentration (10-J)
Average number of interstitials per small cluster
0.6 0.6 I.1 1.1 2.4 2.4
222 220 400 220 222 220
0.32 0.32 0.65 0.63 1.13 1.06
2.6 2.8 4.0 3.3 3.3 3.4
172
D. Grasse et al. / Intersiitial
clustering in fast-neutron
the energy is completely dissipated. This kind of mobility was observed during irradiation with heavy ions subsequent to p-irradiation [ 161. After low-temperature neutron irradiation similar agglomerates have been observed in Pt [17] and MO [18]. For example, in fig. 3 the distortion-induced intensity in MO after irradiation with 3.1 X 10” n/cm2 close to the (440) reflection in [ 1 lo] direction is shown. Again the increase in intensity compared to the’expected intensity after electron irradiation [19] with the same resistivity change is clearly seen. In MO an average number of of z = 2.3 interstitials per cluster is obtained. The average number of 3 interstitials per cluster can be obtained from generalized Waite equations assuming free migrating defects [20]. This number was observed also in e-irradiated Al subsequent to annealing to substage 1, [8]. A correlation of the small clusters in cascades should lead to an increased intensity very close to the Bragg peaks. Inspection of fig. 2 shows such an increased intensity which is even higher because due to resolution effects the intensity distribution is smeared out and the observed q-dependence of the scattering intensity very close to the Bragg peak is weaker than theoretically expected. Taking this into account and assuming a spherical volume for the cascade, a radius R, = 50 A for the cascade is obtained from the measured scattering distributions [5,21].
.
\. \ 0
-A-A-b Y
5. Results after annealing The overall results after irradiation with 2.4 X 10” n/cm2 are su mmarized in fig.4, where HDS can be compared with the recovery of the electrical resistivity. HDS for both the radial and perpendicular directions have been normalized to the radial value after irradiation for each reflection. The radial intensities clearly show the growth of the clusters above 30 K. During annealing the change from HDS (q-‘) to SWS ( qp4) is smeared out to a q-range which becomes larger with increasing temperature [5]. This indicates the formation of a wide range of sizes with the growth of the clusters. The relative stronger increase of the intensities in perpendicular directions indicates changes of the symmetry of the displacement field during the growth. The clusters tend to form dislocation loops [22]. After annealing at 70 K the radial intensities indicate an average z = 11 % 2 [5]. This z is a lower limit obtained with a volume change of Au = 1.9 51 (0 atomic volume) per interstitial [8]. This value may gradually change in a cluster to Au = 1 Q expected for a large
irradiated AI
it
\
‘\ \ 20
SO
Km
-
TIKl
200
Fig. 4 Huang diffuse scattering intensity normaliied to the intensity in direction qllG after irradiation with 2.4X lo’* n/cm’ versus annealing temperature. Near (220) 0 in [I 10) direction, A in [ Ii01 direction; near (222) 0 in [ 1I l] direction, A in [ 1701direction. X annealing of the resistivity change.
dislocation loop. z = 21 is obtained for Au = 1 s2. In fig. 5 the relative radial intensities of HDS for various doses are plotted versus the annealing temperatures. For the two highest doses the values are normalized to 70 K [5]. There is a clear dose dependence of the increase of HDS. This and the disappearing of the intensity increase close the Bragg reflections, which was explained by correlation of the small clusters in cascades, during annealing shows that the growth of the small clusters is not correlated inside the cascade. The great number of interstitials in a cluster after annealing at 70 K and the fact that there is a correlated annealing [23] of single interstitials but an uncorrelated cluster growth, indicate that below 70 K clusters also migrate. This can also explain the great variety in cluster sizes indicated by the smooth change from HDS to
173
D. Grasse et al. / Interstitial clustering in fast-neutron irradiated AI
A
Fig. 5. Huang diffuse the resistivity change. Dose
(X
10” n/cm*)
Reflection Symbols
scattering
intensity
normalized
to the intensity
after irradiation
versus annealing
temperature.
+ annealing
0.6
0.6
1.1
1.1
2.4
2.4
3.8
3.8
4.6
220
222
220
400
220
222
220
400
220
X
0
0
n
A
A
V
0
v
SWS. Not all clusters may have their most stable configuration after irradiation. During annealing in stage 1 they may partly dissolve and cause the observed wrrelated recombination. This work was supported by the Bundesministerium fur Forschung und Technologie. The authors acknowledge the support of Dr. K. Boning, Dr. W. Manse1 and their groups with the low-temperature reactor irradiation.
References [l] B. von Guerard and H. Peisl, in: Fundamental Aspects of Radiation Damage in Metals, Eds. M.T. Robinson and F.W. Young, Jr., Conf.-751006, Vol. 1 (Oak Ridge National Lab., Oak Ridge, Term., 1975). [2] M.A. Krivoglaz, Theory of X-Ray and Thermal Neutron Scattering by Real Crystals (Plenum, New York, 1969). (31 P.-H. Dederichs, J. Phys. F3 (1973) 471. [4] H. Trinkaus, Phys. Status Solidi B 51 (1972) 307. (51 D. Grasse, B. von Guerard and J. Peisl, Radiation Effects,submitted for publication. [6] H. Trinkaus, 2. Angew. Phys. 31 (1971) 229. [7] C.J. Sparks and B. Borie, in: Local Atomic Arrangements Studied by X-RAY Diffraction, Metallurgy Society Conf.
of
No. 36 (Gordon and Breach, New York, 1966). [8] P. Ehrhart and W. Schilling, Phys. Rev. B8 (1973) 2604; J.R. Roberto, B. Schoenfeld and P. Ehrhart, Phys. Rev. B18 (1978) 2591. [9] H.R. Schober, J. Phys. F 7 (1977) 1127. [lo] K. Boning, W. Mauer. K. Pfander and P. Rosner, Radiation Effects 29 (1976) 177. [ 1 l] G. Sieber, G. Wehr and K. Boning, J. Phys. F 7 (1977) 2503. [ 121 J.B. Gibson, A.N. Goland, M. Milgram and G.H. Vineyard, Phys. Rev. 120 (1960) 1229. [13] M.T. Robinson and I.M. Torrens, Phys. Rev. B 9 (1974) 5008. [ 141 J.R. Beeler, Jr., Phvs. Rev. 150 (1966) 470. 1151V. Marty&r&o, Radiation Effects 29 (1976) 129. 1161R.S. Averback and K.L. Merkle, Phys. Rev. B 16 (1977) 3860. 1171W. Hertz, D. Grasse, B. von Guerard and J. Peisl, to be published. [I81 D. Grasse, B. von Guerard and J. Peisl, to be published. 1191P. Ehrhart, J. Nucl. Mater. 69 (1978) 200. (201 R. Schroeder, Radiation Effects 17 (1973) 103. 1211B. van Guerard, D. Grasse and J. Peisl, Phys. Rev. Letters 44 (1980) 262. 1221H. Trinkaus, Phys. Status Solidi’B 54.(1972) 209. f231 M. Nakagawa, K. Boning, P. Rosner.and G. Vogl, Phys. Rev. B 16 (1977) 5285.
Journal of Nuclear Materials 108 & 109 (1982) 169-173 North-Holland Publishing Company
INTERSTITIAL CLUSTERING IN CASCADES IN FAST-NEUTRON IRRADIATED ALUMINIUM BY DIFFUSE X-RAY SCATTERING D. GRASSE, B. von GUlkARD
and J. PEISL
Sekfion Physik der Universitiit Miinchen, 8 Miinchen 22, Federal Republic of Germany Received 8 January 1982; accepted
1 February 1982
We measure diffuse X-ray scattering close to Bragg reflections in aluminium single crystals after irradiation with fast-neutrons at 4.6 K. Comparing the intensity of the Huang scattering with that measured after e-irradiation for the same radiation-induced resistivity leads to tbe result that in Al during n-irradiation interstitial clusters containing an average of three defects are formed. The cluster size is independent of dose up to 2.4X lOI n/cm* which indicate8 the clusters to be formed in a single cascade. Very close to the Bragg peak is a modulation of the Huang intensity which shows that the interstitial clusters are not randomly distributed but are correlated in cascades. Fitting a theoretical curve to the modulation, a cascade radius R K = 50 A is obtained. During annealing the clusters grow and finally form interstitial loops. Long-range migration of the interstitials away from their nascent cascade is observed.
1. Introduftion
displacements written as
Irradiation of solids with fast neutrons produces vacancies and interstitials in displacement cascades. The actual defect concentration and correlation within a cascade is a fundamental problem and is of great technological relevance. Diffuse X-ray scattering has been successfully used to study point defects and small agglomerates. After n-irradiation at 4.6 K in copper [1] agglomerates containing an average of 25 interstitials were observed. In order to get more information about the mechanism of interstitial agglomeration, aluminium, where low defect density cascades were expected, was studied for several doses.
2. Theory Point defects or clusters which create a displacement field n decreasing as r-’ in a crystal, cause a shifting of the Bragg reflections, a decrease of the Bragg reflections due to a static Debye-Waller factor and a diffuse intensity distribution (2,3]. The long-range displacement field determines the scattering for small 9 (9 = K - G, the deviation of the scattering vector K from the corresponding reciprocal lattice point G), Huang diffuse scattering (HDS). If the
0022-3115/82/0000-0000/$02.75
0 1982 North-Holland
of the defects add linearly, HDS can be
F is the structure factor of a unit cell. The scattering intensity is determined by two Fourier transforms [2]. 1, the Fourier transform of the displacement field from one defect, can be described by the dipole tensor Pij using elastic continuum theory [3,4]. E, the Fourier transform of the concentration fluctuations, must be averaged over all equivalent defect distributions. (]c’]2) is a sum
(]E(9)]2)=c(l
-c)+Q(r>exp(iqr),
where the first term is due to a random distribution (c concentration) and e(r) is the additional probability to find a defect at a distance r from another defect above the random distribution probability. If all defects form agglomerates containing always I defects within a radius R,,(]F(q)]2)=zcforqal/R,isobtained.Thismeans all z defects in the agglomerate scatter coherently and act like one big defect. For q Z+ 1/R, one gets (I E(q)) ’ = c, the value for an uncorrelated random distribution. The behaviour in between can be calculated analytically for special defect distributions [5]. If the defects form dense clusters the lattice distortions close to the clusters can be large (Ku ) I]. In this case a different type of scattering is observed for larger
D. Grasse et al. / Interstitial clustering in fast-neutron irradiated AI
170 q. The
asymptotic or Stokes-Wilson
scattering [6] (SWS)
is
lo!
ZSW-c]TrP(ZC/q4. The change from l/q2 dependence to l/q4 dependence occurs at a certain value qC,. From rC,= l/q,, an estimate of the radius of the heavily strained region around the cluster can be made [6]. x
0
3. Experimental loL The rectangular samples were spark cut from one high-purity Al single crystal (resistivity ratio > 30000) from VAW. Next to the crystal, an Al wire (resistivity ratio 1200) was mounted to measure the resistivity change. The irradiations were performed in the low temperature irradiation facility of the FRM at Garching. The irradiated samples were transferred to the measuring cryostat without warming up. The set-up for the X-ray measurements consisted of a 6 kW rotating anode X-ray tube, a bent quartz-monochromator, and an X-ray cryostat, in which the sample temperature could be varied from 4 to 300 K. The measurements were performed at 8 K and the annealing program consisted of IO-mm annealing pulses. Scattering intensities were determined relative to a monitor counter in the primary beam and put on an absolute scale by scattering from polystyrene [7].
4. Results after irradiation Fig. 1 shows a typical result for measurements after irradiation. The scattered intensity close to a (400) Bragg peak measured in [lOO] direction is given for an Al crystal after irradiation at 4.6 K with 1.1 X lOI n/cm2 and after complete thermal annealing at 500 K. The great difference in [lOO] direction shows a pronounced asymmetry indicating that the distortion field is dominated by defects which expand the lattice i.e. interstitials [3]. To obtain the distortion-induced intensity, the scattered intensity after complete annealing at 500 K was subtracted in each case. Then the averaged difference from both sides in respect to the Bragg reflection was plotted on a double logarithmic scale versus q. This is shown in fig. 2 for the experimental results of fig. 1. The error bars in fig. 2 are determined by statistics. The typical l/q2 dependence of HDS and the l/q4 dependence of SWS is clearly demonstrated. For comparison HDS expected for the same defect concentra-
ro3
-6”
_/,O
-2’
00
2'
Lo
6'
-A20 Fig. 1. Diffuse scattered X-ray intensity from Al single crystal near (400) reflection in [NO] direction. X after irradiation at 4.6 K with 1.1 X lo’* n/cm’; 0 after thermal annealing at 500 K.
tion after electron irradiation [8] for the radial directions (q ]IG) is also shown (dashed-dotted line). The concentration is determined in both cases from the resistivity change. The increase of the scattered intensity after neutron irradiation is due to clustering of the interstitials *. z, the average number of interstitials per cluster, obtained from our measurements [S] are listed in table 1. We find that during neutron-irradiation at 4.6 K small clusters are created which contain in the average 3 interstitials. Since there is also a distortion-induced intensity in the [OlO]direction in fig. 2 and also in the [ 110) direction close to a (220) reflection [5], the distortion field has to have orthorhombic or lower symmetry. This is consistent with the symmetry of the * ) C I* differs for interstitials and vacancies in Al by a factor of about 100 due to the difference in the relative volume change [8]. Therefore the scattering is completely due to interstitials.
L). Grasse et ai. / ~nterstitiai clustering in fast-neutron
irradiated A f
171
05 x
1
\
103
.Ol
.02 -
-
.OL o ‘YG
Fig. 2. Defect-induced scattering intensity from Al near (400) after irradiation at 4.6 K with 1.1 X 10’s n/cm’. X in [ 1001 direction, 0 in [OlO] direction; dashed-dotted line, expected intensity for the same defect concentration caused by electron irradiation.
stable clusters of 3 interstitials calculated by Schober [9].There is no significant dose dependence of the average duster size since there is an experimental error of 10% for the absolute intensity. The slight inckse of t may be due to radiation-induced annealing. A constant
‘/G
Fig. 3. Defect-induced scattering intensity from MO near (440) after irradiation at 4.6 K with 3.1 X lo’* n/cm’ in [ 1lo] direr tion X. Dashed-dotted line, expected intensity for the same defect concentration caused by electron irradiation.
z is consistent with measurements of the Hall-effect [IO] and the thermo-power [ 1I]. Since the clustering is independent on dose it has to take place inside a cascade. From computer simulations 112-141 there was no evidence for formation of interstitial clusters. It has been proposed flS] that int~titi~~l~t~ can occur subsequent to the dynamic production of a cascade until
Table I Dosedependence of the single defect concentration and the size of the small clusters Dose ( lot8 n/cm2)
Reflection
Single defect concentration (10-J)
Average number of interstitials per small cluster
0.6 0.6 I.1 1.1 2.4 2.4
222 220 400 220 222 220
0.32 0.32 0.65 0.63 1.13 1.06
2.6 2.8 4.0 3.3 3.3 3.4
172
D. Grasse et al. / Intersiitial
clustering in fast-neutron
the energy is completely dissipated. This kind of mobility was observed during irradiation with heavy ions subsequent to p-irradiation [ 161. After low-temperature neutron irradiation similar agglomerates have been observed in Pt [17] and MO [18]. For example, in fig. 3 the distortion-induced intensity in MO after irradiation with 3.1 X 10” n/cm2 close to the (440) reflection in [ 1 lo] direction is shown. Again the increase in intensity compared to the’expected intensity after electron irradiation [19] with the same resistivity change is clearly seen. In MO an average number of of z = 2.3 interstitials per cluster is obtained. The average number of 3 interstitials per cluster can be obtained from generalized Waite equations assuming free migrating defects [20]. This number was observed also in e-irradiated Al subsequent to annealing to substage 1, [8]. A correlation of the small clusters in cascades should lead to an increased intensity very close to the Bragg peaks. Inspection of fig. 2 shows such an increased intensity which is even higher because due to resolution effects the intensity distribution is smeared out and the observed q-dependence of the scattering intensity very close to the Bragg peak is weaker than theoretically expected. Taking this into account and assuming a spherical volume for the cascade, a radius R, = 50 A for the cascade is obtained from the measured scattering distributions [5,21].
.
\. \ 0
-A-A-b Y
5. Results after annealing The overall results after irradiation with 2.4 X 10” n/cm2 are su mmarized in fig.4, where HDS can be compared with the recovery of the electrical resistivity. HDS for both the radial and perpendicular directions have been normalized to the radial value after irradiation for each reflection. The radial intensities clearly show the growth of the clusters above 30 K. During annealing the change from HDS (q-‘) to SWS ( qp4) is smeared out to a q-range which becomes larger with increasing temperature [5]. This indicates the formation of a wide range of sizes with the growth of the clusters. The relative stronger increase of the intensities in perpendicular directions indicates changes of the symmetry of the displacement field during the growth. The clusters tend to form dislocation loops [22]. After annealing at 70 K the radial intensities indicate an average z = 11 % 2 [5]. This z is a lower limit obtained with a volume change of Au = 1.9 51 (0 atomic volume) per interstitial [8]. This value may gradually change in a cluster to Au = 1 Q expected for a large
irradiated AI
it
\
‘\ \ 20
SO
Km
-
TIKl
200
Fig. 4 Huang diffuse scattering intensity normaliied to the intensity in direction qllG after irradiation with 2.4X lo’* n/cm’ versus annealing temperature. Near (220) 0 in [I 10) direction, A in [ Ii01 direction; near (222) 0 in [ 1I l] direction, A in [ 1701direction. X annealing of the resistivity change.
dislocation loop. z = 21 is obtained for Au = 1 s2. In fig. 5 the relative radial intensities of HDS for various doses are plotted versus the annealing temperatures. For the two highest doses the values are normalized to 70 K [5]. There is a clear dose dependence of the increase of HDS. This and the disappearing of the intensity increase close the Bragg reflections, which was explained by correlation of the small clusters in cascades, during annealing shows that the growth of the small clusters is not correlated inside the cascade. The great number of interstitials in a cluster after annealing at 70 K and the fact that there is a correlated annealing [23] of single interstitials but an uncorrelated cluster growth, indicate that below 70 K clusters also migrate. This can also explain the great variety in cluster sizes indicated by the smooth change from HDS to
173
D. Grasse et al. / Interstitial clustering in fast-neutron irradiated AI
A
Fig. 5. Huang diffuse the resistivity change. Dose
(X
10” n/cm*)
Reflection Symbols
scattering
intensity
normalized
to the intensity
after irradiation
versus annealing
temperature.
+ annealing
0.6
0.6
1.1
1.1
2.4
2.4
3.8
3.8
4.6
220
222
220
400
220
222
220
400
220
X
0
0
n
A
A
V
0
v
SWS. Not all clusters may have their most stable configuration after irradiation. During annealing in stage 1 they may partly dissolve and cause the observed wrrelated recombination. This work was supported by the Bundesministerium fur Forschung und Technologie. The authors acknowledge the support of Dr. K. Boning, Dr. W. Manse1 and their groups with the low-temperature reactor irradiation.
References [l] B. von Guerard and H. Peisl, in: Fundamental Aspects of Radiation Damage in Metals, Eds. M.T. Robinson and F.W. Young, Jr., Conf.-751006, Vol. 1 (Oak Ridge National Lab., Oak Ridge, Term., 1975). [2] M.A. Krivoglaz, Theory of X-Ray and Thermal Neutron Scattering by Real Crystals (Plenum, New York, 1969). (31 P.-H. Dederichs, J. Phys. F3 (1973) 471. [4] H. Trinkaus, Phys. Status Solidi B 51 (1972) 307. (51 D. Grasse, B. von Guerard and J. Peisl, Radiation Effects,submitted for publication. [6] H. Trinkaus, 2. Angew. Phys. 31 (1971) 229. [7] C.J. Sparks and B. Borie, in: Local Atomic Arrangements Studied by X-RAY Diffraction, Metallurgy Society Conf.
of
No. 36 (Gordon and Breach, New York, 1966). [8] P. Ehrhart and W. Schilling, Phys. Rev. B8 (1973) 2604; J.R. Roberto, B. Schoenfeld and P. Ehrhart, Phys. Rev. B18 (1978) 2591. [9] H.R. Schober, J. Phys. F 7 (1977) 1127. [lo] K. Boning, W. Mauer. K. Pfander and P. Rosner, Radiation Effects 29 (1976) 177. [ 1 l] G. Sieber, G. Wehr and K. Boning, J. Phys. F 7 (1977) 2503. [ 121 J.B. Gibson, A.N. Goland, M. Milgram and G.H. Vineyard, Phys. Rev. 120 (1960) 1229. [13] M.T. Robinson and I.M. Torrens, Phys. Rev. B 9 (1974) 5008. [ 141 J.R. Beeler, Jr., Phvs. Rev. 150 (1966) 470. 1151V. Marty&r&o, Radiation Effects 29 (1976) 129. 1161R.S. Averback and K.L. Merkle, Phys. Rev. B 16 (1977) 3860. 1171W. Hertz, D. Grasse, B. von Guerard and J. Peisl, to be published. [I81 D. Grasse, B. von Guerard and J. Peisl, to be published. 1191P. Ehrhart, J. Nucl. Mater. 69 (1978) 200. (201 R. Schroeder, Radiation Effects 17 (1973) 103. 1211B. van Guerard, D. Grasse and J. Peisl, Phys. Rev. Letters 44 (1980) 262. 1221H. Trinkaus, Phys. Status Solidi’B 54.(1972) 209. f231 M. Nakagawa, K. Boning, P. Rosner.and G. Vogl, Phys. Rev. B 16 (1977) 5285.