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A measurement of the local density of 3He-implanted metal foils by the doppler shift attenuation method
Journal of Nuclear Materials 96 (1981) 51-56 0 North-Holland Publishing Company
A MEASUREMENT OF THE LOCAL DENSITY OF 3He-IMPLANTED DOPPLER SHIFT ATTENUATION METHOD T.K. ALEXANDER,
METAL FOILS BY THE
G.C. BALL, W.G. DAVIES and I.V. MITCHELL
Atomic Energy of Canada Limited, Chalk River Nuclear Laboratories,
Chalk River, Ontario, Canada KOJ lJ0
Received 27 May 1980
A new experimental method has been devised to measure density changes in the helium implanted region of metal foils. The principle is demonstrated for the case of 35 keV 3He ions implanted into Zr, Nb and Au foils, and it is shown that large swelling occurs for fluences from 2 to 7 X 1O*r ‘He/m*.
information about the rate of change of the recoil ion velocity. The technique essentially measures the deviations from the full unattenuated Doppler shifted energy for y-rays emitted by recoiling heavy ions produced within the implanted helium region. The magnitude of these deviations is dependent upon two factors: (1) the mean nuclear lifetime, 7, of the decaying ions, and (2) the rate of change of velocity, du/dt, of the recoiling ions in the stopping medium. The rate of change of velocity depends on the ion stopping power and the density of the material in which the ion is slowing down. The method is particularly sensitive to changes in the density of the implanted layer if a significant number of ions decay while traversing this region, i.e., when the “radiation length”, ur, is comparable to the width of the helium implant range profile. Here we show that the density of the target is lowered by helium implantation and that the experimental method gives quantitative information on the swelling responsible for the reduced density.
1. Introduction The phenomenon of material swelling caused by the bombardment of metals by electrons, neutrons or energetic ions is well-known [l]. The behaviour of metals subjected to high fluences (lO*l to lo** ions/ m”) of energetic helium ions is of particular interest. This interest has gained momentum through the research into surface blistering and erosion, both possible problems in fusion reactor technology. Some of the techniques for determining the swelling of helium implanted foils are electron microscopy of the metal [2,3], optical interferometry to determine the surface expansion [4,5] and the observation of foil bending induced by stress build-up [6]. In this paper, we describe a new experimental method that provides quantitative information on changes in the density of the layer where the helium resides in the metal. Our interest in the subject of metal swelling arose from a project to develop a reliable technique of measuring nuclear mean lifetimes in the few femto second (10-l ’ s) region. The Doppler-shift attenuation method [7] has been used in conjunction with helium implanted targets, to deduce the lifetime of recoiling, yemitting nuclei formed by nuclear reactions between the implanted helium target atoms and a beam of high velocity heavy ions [8,9]. Through the Doppler effect, the energy spectrum of the emitted y-rays gives direct
2. Experimental The principle is demonstrated for the case of “C ions excited to the 2.000 MeV level by the 3He(12C, a)’ ‘C reaction. The “C ions have a radiation length UT (the recoil velocity u being about 4.7% the velocity of light and the lifetime T about 10 fs) comparable 51
T.K. Alexander
52
et al. /A measurement
of the local density of 3He-implanted
metal foils
APERTURES PARTICLE TELESCOPE VACUUM CHAMBER
SHRQUD COOLED LN TEMPERATURE To
\
TO
l5E 1
Pb
ABSORBER Ge
:
/
(LI 1 DETECTOR II
(COUNTER
APERTURES (3mlpl
\
/COOLED TARGET FOIL IMPLANTED WITH 35 keV 3He
Ge ii-i)
DETECTOR
(COUNTER
2
1
Fig. 1. A schematic diagram of the apparatus used. The inset shows a typical range dis~bution of 35 keV 3He in a metal foil and compares its width with a vector representation of the “radiation length” VTfor ’ 'C (2.000 MeV). The vector starts at the centre of the distribution where most of the *‘C ions originate and the vector length equals UT.
with the profde width of 35 keV 3He ions implanted in Au, Zr (625 @g/cm’ on Au) or Nb. The inset in fig. 1 shows schematically the relationship between UT and the range distribution of 35 keV 3He in Au. The vector length equals ur and starts at the centre of the distribution where most of the “C ions originate from the reaction, It is seen that ur is appro~mately equal to the fwhm of the 3He concentration profile, a condition that results in good sensitivity. The characteristics of the 3He implanted targets are summarized in table 1. The targets were prepared under high vacuum conditions using the CRNL 70 kV isotope separator. The 3He was implanted unifo~y into an
area of 1 cm2 in each foil. A ba~kscatter~g analysis using the 3He(d, p) o reaction confirmed that the retained 3He and the fluence of 3He were linearly related for all the targets listed in table 1. Fig. 1 shows a schematic diagram of the apparatus used to bombard the various targets of 3He with 39 MeV “C ions. Alpha particles from the 3He(‘2C, ar)“C reaction were detected in the AE-E surface barrier counter telescope at OO.Coincident Dopplershifted 2.000 MeV Frays were detected in a Ge(Li) detector also positioned at 0’ as shown in fig. 1. A second Ge(Li) detector (counter 2 in fig. 1) was shielded from reaction y-rays and was used to detect
53
TX. Alexander et al. /A measurement of the local density of 3He-implanted metal foils Table 1 Characteristics of targets implanted with 35 keV 3He+ ions Material
Thickness (pm)
Dose a) (10Z1/m2)
R b, (urn)
0 b) (pm)
co c, (at%)
$-p:
Au Au Nb Zr
25 25 25 630 ccg/cm* on 25 pm Au
2 6 I
0.120 0.120 0.093
0.062 0.062 0.071
22 65 69
1.944 1.944 1.417
1.02 1.06 1.074
4
0.128
0.074
51
1.074
1.055
(1 + 6) e,
a) The retained 3He and the fluence of 3He are linearly related for all targets (see text). b, The projected range R and variance o are adopted values based on those given in ref. [ 111, [ 121 and [ 131. The values correspond to normal density. c, co is the peak atomic concentration of 3He in the material assuming a Gaussian range distribution and 100% retention. d, The slowing down parameter for 1 ‘C at u = 0.047 c in the unimplanted material calculated from the stopping powers of ref. [ 141 modified as outlined in ref. [ 151. e, The correction to ’ 'C stopping power for the 3He in the material at concentration co.
88Y source -y-ray s in coincidence with counter 1 for stabilization of the energy measuring electronics. Considerable care was taken to ensure that the targets were kept cool and free of condensable conA cooled taminants during the ‘*C bombardment. shroud surrounded the target ladder and the beam path in front of it. Differential pumping was employed to decouple the vacuum system from the beam transport vacuum system preceding the target chamber. The targets were also cooled by conduction to the liquid nitrogen reservoir (see fig. 1). It is estimated that in ah cases the target foil temperature was 5250 K and no loss of 3He was observed during the ‘*C bombardment at a beam power of ~0.5 watt. Fig. 2 shows parts of the coincident y-ray spectra in the region of the Doppler-shifted 2.000 MeV fullenergy peak for three different targets. The top panel shows the spectrum obtained from an Au foil implanted with 6 X lO*l/m * 3He, the middle from a Nb foil implanted with 7 X lO*l/m* 3He and the bottom spectrum from a Zr foil, 4 X 1021/m2. In addition, spectra were also obtained for the 6 X 1021/m2 3He Au foil rotated through 45” (to increase the range profile depth) and for a 2 X lo* l/m* 3He Au foil (to reduce the density effect). The centroids of these y-ray peaks were taken from the data and used to determine the lifetime of the 2.000 MeV level in ’ 'C and the density change within the target foils following an analysis procedure based on that described by Warburton et al. [lo]. For
short lifetimes, the average gamma-ray energy observed at 0” for the case of a homogeneous medium is given by [lo]: (E,) =E,(r
= 0) -A&o&
(1)
where E,(t = 0) is the fully shifted y-ray energy, A& is the full Doppler shift and 0;;’ = (l/u)(du/dt) is the characteristic slowing down time of the material. If it is assumed that the fluence of 3He swells the material according to [S] : AV
y=Ac
where c is the local atomic concentration and A is a material dependent proportionality constant then the characteristic slowing down time becomes a-1
=
1+6 oil 1 +Ac
(3)
where 1 t 6 is the correction factor to the stopping power for the added ‘He. The factor 1 t 6 is the ratio of the stopping power of the compound material (host atom t c 3He) to that of the host metal alone. Furthermore, if the target is approximated by a two-layer medium, in which the Gaussian implant profile with peak concentration co and variance CJis .assumed to be a rectangular profile with a constant atomic concentration co and a width of fi u, then (E,) = E,(r
= 0) - AE+Y&
(4)
T.K. Alexander
54
et al. /A measurement
of the local density of 3He-implanted
metal foils
1 +Aco + 1+6 exp(-@‘td~)Q ..,
I i Au
( 3He,
6x
IO”/
m2
i i
I --I 3. t . -I
’t
Nbf
‘lie,
-I- =10.6
7x102’/m2
and To = fi a/2u is the average time for the ions to traverse the layer containing the 3He in the absence
of swelling. Here C& is an effective slowing down parameter that depends on the swelling parameter, A, and on the ratio of 7’e to the nuclear lifetime 7. The centroid data were analyzed by calculating CY.&for each implanted target for an assumed value of T close to the actual value and for various values of A assumed to be material independent. The procedure was iterated once r was known. For each value of A the measured CEy>values were fitted to -eq. (4) and x2 evaiulated. The best fit (x2 = 0.75) was obtained with A = 0.75 + 0.25 as shown in fig. 3b (curve 1). The fit to the data points is shown in fig. 3a and the slope of the line gives T = 10.9 + 1.5 fs. The sensitivity of the value of A to the assumed
f “C’
rr
f 1.5 fs
1 INTERCEPT
*
(5)
:
’ ’ keV) ’ (2000
2095
26
+ 0
14
’
i
i
‘I
(0)
keV
t 1 Zr
‘OO! i
Zrf
3He,
T = IO.2
Nb
4 xlO”/m’) + 2.4
fs
L-L-.-L-
O
10
20
(b) Ii
A(Zr) A(Au)
21
A(Zr) A(Au)
CHANNEL Fig. 2. Doppler broadened gamma-ray lineshapes in various targets for the 2.000 --t 0 MeV transition in r ‘C. The dispersion is 1 keV/channel. The solid lines are best fits to the lineshapes for the lifetime values shown.
where 1+6
( )(
f& =aI;’
-
1
+Aco
1 - exp(-(T&)(1
+-Ace))
= AfNb)
= A
= A = A(Nb)
=
II
= A
Fig. 3. (a) A plot of the average gamma-ray energy Er as a function of & for the targets listed in tables 1 and 2. The best fit to the data is for A = 0.75 * 0.25 and is shown as the straight line. tb) The value of x2 is plotted as a function of A, the swelling parameter. For curve 1 it is assumed that A is the same for all metals. For curve 2, it was assumed that A = 1.1 for Zr and Nb and A for Au was varied.
T.K. Alexander et al. /A measurement of the locai density of 3He-im~~a~tedmetal folk Table 2 Summary of lifetime lineshape analysis of the “C, MeV level Target
Dose (lO*l/m*)
7 (fs)
Au Au Au at 45” Average of Au targets Nb Zr Average from lineshape analysis
2 6 6
8.9 11.9 9.8 10.2 10.6 10.2
7 4
Centroid shift analysis Average
2.000
* l.l(l.0) a) t 1.2(1.0) f 1.2(1.1) 2 0.8(0.6) f. l.S(l.4) + 2.4c2.3)
10.3 r 0.7 10.9 t: 1.5 10.4 + 0.6
a) Values in brackets are combined uncertainties including statistical uncertainties, uncertainties in A, in the recoil distribution, and in the counter response function. The full uncertainties in&de an additional 5% uncertainty in 02.
widths, u, of the implanted 3He distributions (see table 1) was investigated by varying the widths while keeping a c0 constant, A change of +20% in u changed the best value of A by only +7%, and indicates the value of A is not too sensitive to the detailed assumed shape of the implant distribution but to the total amount of 3He. The experimental Doppler broadened lineshapes presented in fig. 2 were also analyzed with the computer program described in ref. [8] and [9]. The calculated lineshapes took into account the measured velocity distribution of the 1‘C ions, the gamma-ray detector response function and the swelling of the target layer (where the same two layer target approximation with A = 0.75 was used). Representative best fits are shown as solid lines in fig. 2 and a summary of the results is given in table 2. The lifetimes obtained are consistent with each other and the weighted average T = 10.3 ?r 0.7 fs is in good agreement with the value +f= 10.9 + 1.5 fs obtained from the centroid shift analysis.
3. Results and discussion In the present experiment, the density change in the material has been assumed to arise from expan-
55
sion in the direction normal to the foil surface. It has also been assumed that A is the same for the three metals used: however, the present experimental value is weighted in favour of that for Au because of its large I$ and the three data points (see fig. 3). The value obtained, A = 0.75 f 0.25, is in reasonable accord with the values from other techniques and from theoretical estimates [lo]. Saint-Jacques et al. [5] have measured a value of A = 1.l for 5-25 keV 4He in Nb by surface step-height measurements. A similar value has been measured for 160 keV 4He in Er by Blewer and Beezhold [4] using the same technique, If we assume A = I .l for Nb and Zr, then A for gold is 0.95 +_0.25, T = 10.4 fs, but x2 = 1.25 (curve 2 of Ag. 3b) compared to x2 = 0.75 when A = 0.75 + 0.25 for all three metals. It should be noted that the data of Saint-Jacques et al. give A = 0.7 for Nb is fluence rather than their estimated retained dose is used to calculate the atomic concentration. Fenske et al. [2] have examined cross-sectional views of implanted foils by transmission electron microscopy and measured Av/ V as a function of depth in the foil. From these data A - 0.3 for 500 keV 4He in Ni and A - 0.5 for 20 keV 4He in Ni. Finally, the lateral stress measurements by EerNisse and Picraux [6] give values of 1.O, 2.4 and 3.9 for Al, MO and Nb respectively, but at fluences much smaller than 1O*’ /m*.Their values of A, for MO and Nb are unexpectedly large [6] and do not agree with the present work or that of ref. [5] for Nb. In summary, the present experimental technique gives a direct measurement of the change in density caused by impianting 3He into metals. When expressed in terms of volume swelling, the results are in reasonable agreement with other methods. By a suitable choice of the nuclear probe used, the technique could be applied to other implanted elements in other materials.
Acknowledgements
It is a pleasure to thank N.C. Bray and M. Steer for the design and construction of the target chamber, 0-M. Westcott for impl~t~g the targets with 3He and R.L. Brown for technical assistance with the electronics.
56
T.K. Alexander
et al. /A measurement
of the local density of 3He-implanted
References [l] J. Gittus, Irradiation Effects in Crystalline Solids (Applied Science Publishers, London, 1978). [2] G. Fe&e, SK. Das and M. Kaminsky, ANL 7866 Phys. Div. Ann. Rev. (1978); G. Fenske, S.K. Das, M. Kaminsky and C.H. MiJey, J. Nucl. Mater. 76177 (1978) 247. [3] D.J. Mazey, B.L. Eyre, J.H. Evans, S.K. Erents and G.M. McCracken, J. Nucl. Mater. 64 (1977) 145. [4] R.S. Blewer and W. Beezhold, Radiation Effects 19 (1973) 49. ] R.G. St-Jacques, G. Veilleux and B. Terreault, 8th Intern, Conf. on Atomic Collisions in Solids, Hamilton, Canada (1979). 81E.P. EerNisse and ST. Picraux, J. Appl. Phys. 48 (1977) 9. 1 T.K. Alexander and J.S. Forster, Advances in Nuclear Physics, Vol. 10, Eds. M. Baranger and E. Vogt (Plenum, New York, 1978) pp. 197-321.
metal foils
[8] J.S. Forster, T.K. Alexander, G.C. Ball, W.G. Davies, I.V. Mitchell and K.B. Winterbon, Nucl. Phys. A313 (1979) 397. [9] T.K. Alexander, G.C. Ball, W.G. Davies and J.S. Forster, Nucl. Phys. A313 (1979) 425. [lo] E.K. Warburton, J.W. Olness and C.J. Lister, Phys. Rev. C20 (1979) 619. [ 1 l] J.F. Ziegler, Helium: Stopping Powers and Ranges in All Elemental Matter (Pergamon, New York, 1977). [12] R. Behrisch, J. B&tiger, W. Eckstein, U. Littmark, J. Roth and B.M.U. Scherzer, Appl. Phys. Letters 27 (1975) 199. [ 131 J. B&tiger, P.S. Jensen and U. Littmark, J. Appl. Phys. 49 (1978) 965. [ 141 L.C. Northcliffe and R.F. Schilling, Nucl. Data Tables 7 (1970) 233. [15] D. Ward, J.S. Forster, H.R. Andrews, I.V. Mitchell,-G.C. Ball, W.G. Daviesand G.J. Costa, AECL5313 (1976).
A MEASUREMENT OF THE LOCAL DENSITY OF 3He-IMPLANTED DOPPLER SHIFT ATTENUATION METHOD T.K. ALEXANDER,
METAL FOILS BY THE
G.C. BALL, W.G. DAVIES and I.V. MITCHELL
Atomic Energy of Canada Limited, Chalk River Nuclear Laboratories,
Chalk River, Ontario, Canada KOJ lJ0
Received 27 May 1980
A new experimental method has been devised to measure density changes in the helium implanted region of metal foils. The principle is demonstrated for the case of 35 keV 3He ions implanted into Zr, Nb and Au foils, and it is shown that large swelling occurs for fluences from 2 to 7 X 1O*r ‘He/m*.
information about the rate of change of the recoil ion velocity. The technique essentially measures the deviations from the full unattenuated Doppler shifted energy for y-rays emitted by recoiling heavy ions produced within the implanted helium region. The magnitude of these deviations is dependent upon two factors: (1) the mean nuclear lifetime, 7, of the decaying ions, and (2) the rate of change of velocity, du/dt, of the recoiling ions in the stopping medium. The rate of change of velocity depends on the ion stopping power and the density of the material in which the ion is slowing down. The method is particularly sensitive to changes in the density of the implanted layer if a significant number of ions decay while traversing this region, i.e., when the “radiation length”, ur, is comparable to the width of the helium implant range profile. Here we show that the density of the target is lowered by helium implantation and that the experimental method gives quantitative information on the swelling responsible for the reduced density.
1. Introduction The phenomenon of material swelling caused by the bombardment of metals by electrons, neutrons or energetic ions is well-known [l]. The behaviour of metals subjected to high fluences (lO*l to lo** ions/ m”) of energetic helium ions is of particular interest. This interest has gained momentum through the research into surface blistering and erosion, both possible problems in fusion reactor technology. Some of the techniques for determining the swelling of helium implanted foils are electron microscopy of the metal [2,3], optical interferometry to determine the surface expansion [4,5] and the observation of foil bending induced by stress build-up [6]. In this paper, we describe a new experimental method that provides quantitative information on changes in the density of the layer where the helium resides in the metal. Our interest in the subject of metal swelling arose from a project to develop a reliable technique of measuring nuclear mean lifetimes in the few femto second (10-l ’ s) region. The Doppler-shift attenuation method [7] has been used in conjunction with helium implanted targets, to deduce the lifetime of recoiling, yemitting nuclei formed by nuclear reactions between the implanted helium target atoms and a beam of high velocity heavy ions [8,9]. Through the Doppler effect, the energy spectrum of the emitted y-rays gives direct
2. Experimental The principle is demonstrated for the case of “C ions excited to the 2.000 MeV level by the 3He(12C, a)’ ‘C reaction. The “C ions have a radiation length UT (the recoil velocity u being about 4.7% the velocity of light and the lifetime T about 10 fs) comparable 51
T.K. Alexander
52
et al. /A measurement
of the local density of 3He-implanted
metal foils
APERTURES PARTICLE TELESCOPE VACUUM CHAMBER
SHRQUD COOLED LN TEMPERATURE To
\
TO
l5E 1
Pb
ABSORBER Ge
:
/
(LI 1 DETECTOR II
(COUNTER
APERTURES (3mlpl
\
/COOLED TARGET FOIL IMPLANTED WITH 35 keV 3He
Ge ii-i)
DETECTOR
(COUNTER
2
1
Fig. 1. A schematic diagram of the apparatus used. The inset shows a typical range dis~bution of 35 keV 3He in a metal foil and compares its width with a vector representation of the “radiation length” VTfor ’ 'C (2.000 MeV). The vector starts at the centre of the distribution where most of the *‘C ions originate and the vector length equals UT.
with the profde width of 35 keV 3He ions implanted in Au, Zr (625 @g/cm’ on Au) or Nb. The inset in fig. 1 shows schematically the relationship between UT and the range distribution of 35 keV 3He in Au. The vector length equals ur and starts at the centre of the distribution where most of the “C ions originate from the reaction, It is seen that ur is appro~mately equal to the fwhm of the 3He concentration profile, a condition that results in good sensitivity. The characteristics of the 3He implanted targets are summarized in table 1. The targets were prepared under high vacuum conditions using the CRNL 70 kV isotope separator. The 3He was implanted unifo~y into an
area of 1 cm2 in each foil. A ba~kscatter~g analysis using the 3He(d, p) o reaction confirmed that the retained 3He and the fluence of 3He were linearly related for all the targets listed in table 1. Fig. 1 shows a schematic diagram of the apparatus used to bombard the various targets of 3He with 39 MeV “C ions. Alpha particles from the 3He(‘2C, ar)“C reaction were detected in the AE-E surface barrier counter telescope at OO.Coincident Dopplershifted 2.000 MeV Frays were detected in a Ge(Li) detector also positioned at 0’ as shown in fig. 1. A second Ge(Li) detector (counter 2 in fig. 1) was shielded from reaction y-rays and was used to detect
53
TX. Alexander et al. /A measurement of the local density of 3He-implanted metal foils Table 1 Characteristics of targets implanted with 35 keV 3He+ ions Material
Thickness (pm)
Dose a) (10Z1/m2)
R b, (urn)
0 b) (pm)
co c, (at%)
$-p:
Au Au Nb Zr
25 25 25 630 ccg/cm* on 25 pm Au
2 6 I
0.120 0.120 0.093
0.062 0.062 0.071
22 65 69
1.944 1.944 1.417
1.02 1.06 1.074
4
0.128
0.074
51
1.074
1.055
(1 + 6) e,
a) The retained 3He and the fluence of 3He are linearly related for all targets (see text). b, The projected range R and variance o are adopted values based on those given in ref. [ 111, [ 121 and [ 131. The values correspond to normal density. c, co is the peak atomic concentration of 3He in the material assuming a Gaussian range distribution and 100% retention. d, The slowing down parameter for 1 ‘C at u = 0.047 c in the unimplanted material calculated from the stopping powers of ref. [ 141 modified as outlined in ref. [ 151. e, The correction to ’ 'C stopping power for the 3He in the material at concentration co.
88Y source -y-ray s in coincidence with counter 1 for stabilization of the energy measuring electronics. Considerable care was taken to ensure that the targets were kept cool and free of condensable conA cooled taminants during the ‘*C bombardment. shroud surrounded the target ladder and the beam path in front of it. Differential pumping was employed to decouple the vacuum system from the beam transport vacuum system preceding the target chamber. The targets were also cooled by conduction to the liquid nitrogen reservoir (see fig. 1). It is estimated that in ah cases the target foil temperature was 5250 K and no loss of 3He was observed during the ‘*C bombardment at a beam power of ~0.5 watt. Fig. 2 shows parts of the coincident y-ray spectra in the region of the Doppler-shifted 2.000 MeV fullenergy peak for three different targets. The top panel shows the spectrum obtained from an Au foil implanted with 6 X lO*l/m * 3He, the middle from a Nb foil implanted with 7 X lO*l/m* 3He and the bottom spectrum from a Zr foil, 4 X 1021/m2. In addition, spectra were also obtained for the 6 X 1021/m2 3He Au foil rotated through 45” (to increase the range profile depth) and for a 2 X lo* l/m* 3He Au foil (to reduce the density effect). The centroids of these y-ray peaks were taken from the data and used to determine the lifetime of the 2.000 MeV level in ’ 'C and the density change within the target foils following an analysis procedure based on that described by Warburton et al. [lo]. For
short lifetimes, the average gamma-ray energy observed at 0” for the case of a homogeneous medium is given by [lo]: (E,) =E,(r
= 0) -A&o&
(1)
where E,(t = 0) is the fully shifted y-ray energy, A& is the full Doppler shift and 0;;’ = (l/u)(du/dt) is the characteristic slowing down time of the material. If it is assumed that the fluence of 3He swells the material according to [S] : AV
y=Ac
where c is the local atomic concentration and A is a material dependent proportionality constant then the characteristic slowing down time becomes a-1
=
1+6 oil 1 +Ac
(3)
where 1 t 6 is the correction factor to the stopping power for the added ‘He. The factor 1 t 6 is the ratio of the stopping power of the compound material (host atom t c 3He) to that of the host metal alone. Furthermore, if the target is approximated by a two-layer medium, in which the Gaussian implant profile with peak concentration co and variance CJis .assumed to be a rectangular profile with a constant atomic concentration co and a width of fi u, then (E,) = E,(r
= 0) - AE+Y&
(4)
T.K. Alexander
54
et al. /A measurement
of the local density of 3He-implanted
metal foils
1 +Aco + 1+6 exp(-@‘td~)Q ..,
I i Au
( 3He,
6x
IO”/
m2
i i
I --I 3. t . -I
’t
Nbf
‘lie,
-I- =10.6
7x102’/m2
and To = fi a/2u is the average time for the ions to traverse the layer containing the 3He in the absence
of swelling. Here C& is an effective slowing down parameter that depends on the swelling parameter, A, and on the ratio of 7’e to the nuclear lifetime 7. The centroid data were analyzed by calculating CY.&for each implanted target for an assumed value of T close to the actual value and for various values of A assumed to be material independent. The procedure was iterated once r was known. For each value of A the measured CEy>values were fitted to -eq. (4) and x2 evaiulated. The best fit (x2 = 0.75) was obtained with A = 0.75 + 0.25 as shown in fig. 3b (curve 1). The fit to the data points is shown in fig. 3a and the slope of the line gives T = 10.9 + 1.5 fs. The sensitivity of the value of A to the assumed
f “C’
rr
f 1.5 fs
1 INTERCEPT
*
(5)
:
’ ’ keV) ’ (2000
2095
26
+ 0
14
’
i
i
‘I
(0)
keV
t 1 Zr
‘OO! i
Zrf
3He,
T = IO.2
Nb
4 xlO”/m’) + 2.4
fs
L-L-.-L-
O
10
20
(b) Ii
A(Zr) A(Au)
21
A(Zr) A(Au)
CHANNEL Fig. 2. Doppler broadened gamma-ray lineshapes in various targets for the 2.000 --t 0 MeV transition in r ‘C. The dispersion is 1 keV/channel. The solid lines are best fits to the lineshapes for the lifetime values shown.
where 1+6
( )(
f& =aI;’
-
1
+Aco
1 - exp(-(T&)(1
+-Ace))
= AfNb)
= A
= A = A(Nb)
=
II
= A
Fig. 3. (a) A plot of the average gamma-ray energy Er as a function of & for the targets listed in tables 1 and 2. The best fit to the data is for A = 0.75 * 0.25 and is shown as the straight line. tb) The value of x2 is plotted as a function of A, the swelling parameter. For curve 1 it is assumed that A is the same for all metals. For curve 2, it was assumed that A = 1.1 for Zr and Nb and A for Au was varied.
T.K. Alexander et al. /A measurement of the locai density of 3He-im~~a~tedmetal folk Table 2 Summary of lifetime lineshape analysis of the “C, MeV level Target
Dose (lO*l/m*)
7 (fs)
Au Au Au at 45” Average of Au targets Nb Zr Average from lineshape analysis
2 6 6
8.9 11.9 9.8 10.2 10.6 10.2
7 4
Centroid shift analysis Average
2.000
* l.l(l.0) a) t 1.2(1.0) f 1.2(1.1) 2 0.8(0.6) f. l.S(l.4) + 2.4c2.3)
10.3 r 0.7 10.9 t: 1.5 10.4 + 0.6
a) Values in brackets are combined uncertainties including statistical uncertainties, uncertainties in A, in the recoil distribution, and in the counter response function. The full uncertainties in&de an additional 5% uncertainty in 02.
widths, u, of the implanted 3He distributions (see table 1) was investigated by varying the widths while keeping a c0 constant, A change of +20% in u changed the best value of A by only +7%, and indicates the value of A is not too sensitive to the detailed assumed shape of the implant distribution but to the total amount of 3He. The experimental Doppler broadened lineshapes presented in fig. 2 were also analyzed with the computer program described in ref. [8] and [9]. The calculated lineshapes took into account the measured velocity distribution of the 1‘C ions, the gamma-ray detector response function and the swelling of the target layer (where the same two layer target approximation with A = 0.75 was used). Representative best fits are shown as solid lines in fig. 2 and a summary of the results is given in table 2. The lifetimes obtained are consistent with each other and the weighted average T = 10.3 ?r 0.7 fs is in good agreement with the value +f= 10.9 + 1.5 fs obtained from the centroid shift analysis.
3. Results and discussion In the present experiment, the density change in the material has been assumed to arise from expan-
55
sion in the direction normal to the foil surface. It has also been assumed that A is the same for the three metals used: however, the present experimental value is weighted in favour of that for Au because of its large I$ and the three data points (see fig. 3). The value obtained, A = 0.75 f 0.25, is in reasonable accord with the values from other techniques and from theoretical estimates [lo]. Saint-Jacques et al. [5] have measured a value of A = 1.l for 5-25 keV 4He in Nb by surface step-height measurements. A similar value has been measured for 160 keV 4He in Er by Blewer and Beezhold [4] using the same technique, If we assume A = I .l for Nb and Zr, then A for gold is 0.95 +_0.25, T = 10.4 fs, but x2 = 1.25 (curve 2 of Ag. 3b) compared to x2 = 0.75 when A = 0.75 + 0.25 for all three metals. It should be noted that the data of Saint-Jacques et al. give A = 0.7 for Nb is fluence rather than their estimated retained dose is used to calculate the atomic concentration. Fenske et al. [2] have examined cross-sectional views of implanted foils by transmission electron microscopy and measured Av/ V as a function of depth in the foil. From these data A - 0.3 for 500 keV 4He in Ni and A - 0.5 for 20 keV 4He in Ni. Finally, the lateral stress measurements by EerNisse and Picraux [6] give values of 1.O, 2.4 and 3.9 for Al, MO and Nb respectively, but at fluences much smaller than 1O*’ /m*.Their values of A, for MO and Nb are unexpectedly large [6] and do not agree with the present work or that of ref. [5] for Nb. In summary, the present experimental technique gives a direct measurement of the change in density caused by impianting 3He into metals. When expressed in terms of volume swelling, the results are in reasonable agreement with other methods. By a suitable choice of the nuclear probe used, the technique could be applied to other implanted elements in other materials.
Acknowledgements
It is a pleasure to thank N.C. Bray and M. Steer for the design and construction of the target chamber, 0-M. Westcott for impl~t~g the targets with 3He and R.L. Brown for technical assistance with the electronics.
56
T.K. Alexander
et al. /A measurement
of the local density of 3He-implanted
References [l] J. Gittus, Irradiation Effects in Crystalline Solids (Applied Science Publishers, London, 1978). [2] G. Fe&e, SK. Das and M. Kaminsky, ANL 7866 Phys. Div. Ann. Rev. (1978); G. Fenske, S.K. Das, M. Kaminsky and C.H. MiJey, J. Nucl. Mater. 76177 (1978) 247. [3] D.J. Mazey, B.L. Eyre, J.H. Evans, S.K. Erents and G.M. McCracken, J. Nucl. Mater. 64 (1977) 145. [4] R.S. Blewer and W. Beezhold, Radiation Effects 19 (1973) 49. ] R.G. St-Jacques, G. Veilleux and B. Terreault, 8th Intern, Conf. on Atomic Collisions in Solids, Hamilton, Canada (1979). 81E.P. EerNisse and ST. Picraux, J. Appl. Phys. 48 (1977) 9. 1 T.K. Alexander and J.S. Forster, Advances in Nuclear Physics, Vol. 10, Eds. M. Baranger and E. Vogt (Plenum, New York, 1978) pp. 197-321.
metal foils
[8] J.S. Forster, T.K. Alexander, G.C. Ball, W.G. Davies, I.V. Mitchell and K.B. Winterbon, Nucl. Phys. A313 (1979) 397. [9] T.K. Alexander, G.C. Ball, W.G. Davies and J.S. Forster, Nucl. Phys. A313 (1979) 425. [lo] E.K. Warburton, J.W. Olness and C.J. Lister, Phys. Rev. C20 (1979) 619. [ 1 l] J.F. Ziegler, Helium: Stopping Powers and Ranges in All Elemental Matter (Pergamon, New York, 1977). [12] R. Behrisch, J. B&tiger, W. Eckstein, U. Littmark, J. Roth and B.M.U. Scherzer, Appl. Phys. Letters 27 (1975) 199. [ 131 J. B&tiger, P.S. Jensen and U. Littmark, J. Appl. Phys. 49 (1978) 965. [ 141 L.C. Northcliffe and R.F. Schilling, Nucl. Data Tables 7 (1970) 233. [15] D. Ward, J.S. Forster, H.R. Andrews, I.V. Mitchell,-G.C. Ball, W.G. Daviesand G.J. Costa, AECL5313 (1976).