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The annealing of copper after radiation damage at low temperatures
THE ANNEALING
OF COPPER AFTER RADIATION A’k LOW TEMPERATURES*
DAMAGE
R. R. EGGLESTONt Resistance measurements at the boiling point of liquid helium have been made on copper which was damaged at temperatures below - 150°C by an exposure to 35 Mev alpha particles and then annealed at higher temperatures. The activation energy for the process active at annealing temperatures between - 65°C and - 20°C is 0.717 ev. At temperatures between 250°C and 325°C the activation energy describing the annealing is 2.12 ev. The activation energy obtained at the lower temperatures is in agreement with the value of 0.672 ev for copper cold-worked in liquid helium, and the value of 0.68 ev obtained by Overhauser on copper irradiated in a similar manner and annealed in the same low temperature range. Cold-work and radiation damage in copper were compared qualitatively by making similar constant time anneals at progressively higher temperatures on specimens irradiated at temperatures below - 150°C and specimens cold-worked.in liquid helium. Up to about - 80°C the rate of annealing of the two specimens was similar, but at room temperature about 25 per cent of the radiation damage remained compared to 50 per cent remaining in the cold-worked specimen. LE
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Des mesures de rCsistance, au point d’Cbullition de l’hilium liquide, ont 6th effect&es sur du cuivre endommagi: & des tempkratures en dessous de - 150°C par des particules alpha de 35Mev et ensuite recuit P des tempkratures plus blev&es. L’energie d’activation du processus de recuit aux temperatures allant de - 65°C & 20°C est de 0,717 ev. Aux tempkratures variant de 250°C B 325°C l’&ergie d’activation du recuit est de 2,12 ev. L’energie d’activation obtenue aux basses tempCratures est en accord avec les 0.672 ev obtenus pour du cuivre &roui dans l’hhlium liquide, et les 0,68 ev obtenus par Overhauser sur du cuivre irradik d’une fafon similaire et recuit dans le meme intervalle de basses tempbratures. Les deggts provoquCs dans le cuivre par I’Ccrouissage et par l’irradiation ont et6 cornpar& qualitativement, en effectuant des recuits similaires, de m&me durite, & des tempCratures de plus en plus itle&es, sur des &hantillons irradiirs a des tempkratures infbrieures B - 150°C et sur des &chanti!lons Ccrouis dans I’h&lium liquide. Jusqu’environ - 80°C la vitesse de recuit des deux &chantillons Ctait similaire, alors qu’8 la temp(trature ambiante le dCgat ritsiduel &tait de 25 pour cent danc le cas des Cchantdlone irradiiis et de 50 pour cent dans le cas des Cchantillons itcrouis. ;2USGLiiHEN
VON
KUP+ER TIEFEN
NACH STRAHLUNGSSCHi;DIGUNG TEMPERATUREN
BE1
Der Widerstand von Kupfer, das der Bestrahlung mit 35 MeV Alpha Teilchen bei einer Temperatur unterhalb von - 150°C ausgesetzt und dann ausgegliiht worden war, wurde am Siedepunkt des fliissigen Heliums gemessen. Die Aktivierungsenergie fiir den bei der Gltihtemperatur zwi:chen - 65°C und - 20°C stattfindenden Vorgang betrggt 0.717 eV. Bei Temperaturen zwischen 250°C und 325’C betr?igt die dem Ausgliihen zugeschriebene ilktivierungsenergie 2.12 eV. Der bei tieferen Temperaturen erhaltene Wert der Aktivierungsenergie stimmt zufriedenstellend mit dem Wert mit 0:672 e\J fiir in fliissigem Helium kaltbearbeitetem Kupfer iiberein, ebenso wie mit den 0,68 eV, die Overhauser fiir Kupfer, das in zhnlicher Weise bestrahlt und in gleichem tiefen Temperaturbereich ausgegliiht wurde, angegeben hat. Kaltbearbeitung und Strahlungssch&digung von Kupfer wurden quantitativ verglichen, indem entsprechende Gliihungen (mit konstanter Gliihzeit) bei fortschreitend haheren Tempzraturen an Proben, die unterhalb van - 150°C bestrahlt oder in fliissigem Helium kalt bearbeitet worden waren, durchgefiihrt wurden. Bis ZLI - 80°C war das Verhgltnis des Ausheilens bei beiden Proben das gleiche, bei Zimmertemperatur verblieben jedoch 25 prozent der Strahlungsschgdigung im Vergleich zu 50 prozent der Kaltbearbeitung.
Introduction Changes in physical properties take place when metals are exposed either to a neutron flux or to a charged particle bombardment [l, 21. In the case of a pure metal such as copper, the amount of damage as observed by resistivity measurements is dependent on the thermal history of the bombarded specimen, both during the bombardment and prior to observation. It is the purpose of this paper to describe measurements of electrical resistance made on *Received June 6, 1953. tNorth American Aviation, Inc., Atomic Department, Downey, California. ACTA
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copper irradiated at temperatures below - 15O”C, then subjected to controlled heat treatments. These treatments were first carried out in the range of temperatures from - 65°C to 0°C and then between 250°C and 300°C. These results will be compared with the annealing behavior of copper which was cold-worked at the liquid helium temperature. The comparison will be made on the basis of activation energies determined by making the assumption that within each temperature range considered the annealing process can be described by a single, well-defined activation energy. The determination of the energy of activation for annealing active in different temperature ranges
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for material damaged in a variety of ways may aid in the identification of the various possible lattice defects. The electrical resistance measurements were made at the boiling point of liquid helium, and will be referred to hereafter as residual resistance measurements. Since there is no temperature dependence of the extra resistance due to defects at measurement temperatures below 18”K, it was assumed that Matthiessen’s rule holds for measurements made at 4.2’K. Thus the extra resistance measured due to the damage may be assumed proportional to the number of defects. Results of previous work [3] indicate that there is a slight temperature dependence of the resistivity due to defects at other temperatures of measurement. By making measurements of residual resistivity, the possibility of identifying the annealing mechanisms is improved.
Experimental
Procedure
The measurement of residual resistivity by standard potentiometric methods was used to detect changes due to thermal treatments in all of the following experiments. The temperature of measurement differed from the thermal treatment temperature; therefore in order to know the time of anneal accurately the specimen had to be taken up to, and lowered from, the thermal treatment temperature rapidly. This method of annealing at a higher temperature and taking measurements at a more desirable or convenient temperature has been called a pulse annealing technique [4]. There are experimental advantages in using residual resistance measurements, in addition to the theoretical advantages discussed above. These advantages are that the temperature coefficient of resistance is small at this temperature, the temperature of measurement is reproducible, and the relative changes arising from the annealing are larger. In the thermal treatments, the individual specimens were either at a constant temperature or at progressively higher temperatures for a constant time at each temperature. The former treatment will be called an isothermal anneal and the latter a tempering anneal. Constant temperature baths of large heat capacity were used for these anneals. Commercial O.F.H.C. copper wire of 3-mil diameter was used for these studies; the exact purity was unknown, but from maximum and minimum assays of copper plus silver that were available it is probably safe to assume that the
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purity was at least 99.9 per cent. For the tempering anneals, a wire about 8.5 cm long was wound on a thin mica strip so that its entire length was evenly bombarded. The isothermal specimens, approximately 0.7 cm long, were mounted similarly, but without a supporting mica strip. The specimen mountings were small enough so that as many as four specimens could be bombarded simultaneously and still receive nearly identical irradiations. The 60-inch cyclotron of the Cracker Radiation Laboratory at the University of California in Berkeley was used for the alpha-particle irradiations. The energy of the particles at the target was 35 Mev. The range of the particles of this energy in copper is approximately 7 mils so that there should be no inhomogeneities in the samples due to end of range effects in the isothermal samples. The specimens were kept at temperatures below - 150°C during the irradiation by flowing refrigerated helium past the specimen and by limiting the beam current. After the irradiation it was possible to transfer the specimens rapidly, without warming, .to liquid nitrogen, in which they were stored before annealing. The exposures of the isothermal samples, tabulated in Table I, TABLE
I
Annealing temperature
- fJ5T
- 5OT
- 35°C
-
Exposure (aahrs/cm*
13.3
13.0
13.1
13.3
in Residual resistance arbitrary units after irradiation
1570.9,
1455.0s
1515.0”
1433.81
After long time at room temperature
460.71
464.91
473.45
431.9j
Annealing temperature
3OOT
275T
25OT
resistance in Residual arbitary units after Specimen anneal 5OOT. 2 hr. broke
98.2,
100.72
95.76
Values of residual resistivity due to defects produced by irradiation
0.0777
0.0778
0.0782
0.0782
2OT
varied slightly from sample to sample. These exposures were determined from a beam profile distribution obtained by counting st:rips from a monitoring foil placed between the specimen and the cyclotron. Before irradiation the specimens were annealed in a vacuum at temperatures of at least 780°C for 10 minutes and above 400°C for 105 minutes.
Results An exploratory
tempering
anneal curve, which
EGGLESTON:
ANNEALING
AFTER
is presented in Figure 1, shows that the most rapid annealing occurs between - 70°C and 0°C. Hence, the temperatures chosen for the i~thermal annPals were - 65”C, - 5O”C, - 35°C and - 20°C. Between - 70°C and 0°C the tempering curve
FIGURE1. Result of tempering anneal on copper irradiated at temperatures below - 15O’C to an exposure of 17.2 rahrs/ cm2 with 34.5 Mev alpha particles.
does not exhibit any properties that would indicate more than a single active annealing process. After the isothermal data were taken, each of the four specimens was allowed to stand at ambient room temperature for a period of 12 days. In Table I the data of residual resistance in arbitrary units has been collected at several times during the thermal history together with the exposures and annealing temperatures for each of the specimens. There are several possible ways to reduce or normalize the data and thus make direct comparisons of the isothermal curves. Since the radiation exposures and lengths of the samples are different, this procedure is of necessity complicated. The normalization procedure to be described was found to yield activation energies that were quite well defined and nearly constant. The residual resistance values attributed to the defect being annealed were first obtained for each from the resistances specimen by subtracting measured during the annealing a value obtained after a long anneal at room temperature. This value was used since the room temperature anneal resulted in a nearly complete disappearance of the defects under study, leaving relatively undisturbed the defects that anneal at higher temperatures. Curves of change in resistivity versus exposure under similar irradiation conditions give us
RADIATION
DAMA%GE
681
information to allow us to make the small relative corrections needed for the normalization, though they are not reliable absolutely. These curves show that at the exposures encountered here, the change of residual resistivity with exposure is 1.71 X 10P3 ~&m/~ahr/cm”, and at an exposure of 12~ahrs/cm2, the total change of residual resistivity is 0.076~~cm. In order to get relative values of residual resistivity the above slope was multiplied by the extra exposure given each sample over 12pahrs/cm2 and then added to the value given above for an exposure of 12pahrs/cm2. The values of residual resistivity due to the defects introduced by the irradiation are also tabulated in Table I ; these values are accurate relatively but not absolutely. The residual resistance data for each specimen were then normalized by multiplying by the ratio of relative residual resistivity values tabulated above to the extra resistance due to the defects after irradiation. Thus it was possible to correct for slight length and exposure differences from specimen to specimen. The normalized annealing curves are displayed in Figure 2. The phenomenological activation
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FIGURE 2. Normalized isothermal annealing curves for temperatures of anneal between - 65°C and - 20°C. In order to obtain an approximate value of residual resistivity change in micro ohm cm due to the irradiation, multiply the arbitrary scale by 0.018. Residual resistivity may then be obtained by adding this value to the annealed residual resistivity which is approximately 0.015 @cm.
energy can easily be obtained from these curves. When the logarithms of the times to reach equal property values of the helium point resistance along several isothermal curves is plotted against the corresponding reciprocal absolute temperature of the isothermals the points define a line whose slope determines the activation energy. In Figure
682
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3 the results of making several equal property cuts on the curves in Figure 2 are given. The activation energy is seen to be quite well defined. The average energy is 0.717 ev while the spread is from 0.707 ev to 0.742 ev. There is no obvious trend in these values which would indicate that
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deuterons for an exposure of I. 1 X 1 OLi pnrticles,/ cm2 and found an activation energy of 0.68 ev for the annealing occurring above - 50°C‘ which is in agreement with both of the above values. After the above specimens had annealed at room temperature they were then further annealed isothermally at 25O”C, 275°C and 300°C, after which they were annealed at 500°C for two hours to completely remove the defects caused by the irradiation. The normalized annealing curves are shown in Figure 4. In this case the normal-
FIGURE 4. Normalized isothermal annealing curves for temperatures of anneal between 250°C and 3OOT. In order to obtain an approximate value of residual resistivity change in micro ohm cm due to the irradiation, multiply the arbitrary scale by 0.018. Residual resistivity may then be obtained by adding this value to the annealed residual resistivity which is approximately 0.015 @cm. FIGURE 3. Phenomenological determination of activation energy for the annealing process active in the temperature range between - 65°C and - 20°C.
this spread is due to other than experimental uncertainties. Since both the lengths and the exposure did not vary greatly among the specimens it is possible to use other logical normalization procedures based on the assumption that these slight differences did not exist. Isothermal curves compared after normalization by these assumptions yielded values that differed from the above average value by less than 10 per cent. This is not surprising, since both the lengths and the exposures did not vary greatly among the specimens; thus the normalization corrections should be small as also should be the variation in determined activation energies. An activation energy of 0.672 ev has been reported previously [5] for copper that had been cold-worked by twisting at liquid helium temperatures and annealed at temperatures between - 50°C and - 10°C. This is not too different from the value found for the irradiated copper. This agreement may indicate that the annealing process is similar in the two cases. Overhauser [6] has irradiated copper at - 180°C with 12 Mev
ization was made by assuming that all three of the specimens had identical residual resistivities after the 500°C anneal. The other specimens were normalized to the residual resistance of the specimen annealed at 300°C. The determination of activation energies was made in the same way as for the earlier annealing data. The results of making several equal property cuts on the normalized isothermal curves in Figure 3 are shown in Figure 5. The activation energy is seen to be fairly well defined, the average value being 2.12 ev while the spread is from 2.09 ev to 2.18 ev. The data for this annealing range were not taken over as wide a temperature range as the data at lower temperatures; thus the values of activation energy are less reliable. The activation energy of 2.12 ev is in agreement with values of the copper self-diffusion activation energy, given as 2.1 ev by Seitz [7] and a slightly lower value of 2.02 ev by Mott [8]. In Figure 6, tempering curves for irradiated and for cold-worked copper are compared on a percentage basis, allowing several qualitative features of the annealing to be noted. The final resistivities of the damaged specimens were 21.01 and 15.3 X 10-?&m respectively. Initially these specimens had resistivities of 1.56 and 1.37 X l0-80cm respectively.
EGGLESTON:
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RADIrZTION
683
DALIAGE
to about 50 per cent for the cold-worked material. As the temperature is raised above 100°C the damage finally anneals completely, that due to the cold-work annealing more rapidly than that due to irradiation. If the agreement in activation energies obtained for the temperature range from - 70°C to 0°C for cold-worked and for irradiated copper is indicative of motion or annihilation of the same defect then the above qualitative features show that this defect is produced in quite different concentrations in the two methods of damage. The isothermal annealing curves may be described empirically by using a kinetic rate equation,
d(P - PO)-___-dt
(p -
po)ae-E’gT
where the resistivity change undergoing is annealing, t is the time, a! is the order of the reaction and is restricted to integer values, E is the activation energy, K is the Boltzmann constant and T is the absolute temperature. A third order of reaction is needed to fit the isothermal data between - 65°C and - 2O’C. For the isothermal annealing between 250°C and 300°C a fourth order of reaction is needed to fit the data. P
FIGURE 5. Phenomenological determination of activation energy for the annealing process active in the temperature range between 250°C and 300°C.
The irradiated specimen had been exposed at temperatures below 150°C to 17.2pahr/cm2 of 34.5 Mev alpha particles, and the coldworked specimen had been twisted while immersed in liquid helium, after which the specimens were similarly tempered from temperatures near their damage temperature to 100°C. Up to about - 80°C the rate of annealing is nearly equal for the two types of damage; about 75 per cent of the damage still remains. From this temperature to near room temperatures however, the irradiated material anneals to a greater extent than the cold-worked copper so that at room temperature there is only approximately 25 per cent of the radiation damage still present compared
-
PO
Acknowledgments The author wishes to acknowledge the help of C. R. Davidson and Lyle Glasgow of the Irradiation Physics Group at Berkeley for supervising and performing the required irradiations and to thank Miss Sonja Hanjian for patient help in performing the required annealings. This work was based on studies conducted for the Atomic Energy Commission under Contract AT-1 l-lGEN-8.
References
FICUKE 6. Tempering annealing curves for irradiated and for cold-worked copper on a percentage basis. The irradiated specimen received an exposure of 17.2 Fahrs/cm2 with 34.5 Mev alpha particles at temperatures below - 150°C. The cold-worked specimen had been cold-worked by twisting while immersed in liquid helium.
1. MARTIN, A. B., et al. Phys. Rev. 81 (1951) 664. 2. MARX, J. W., COOPER, H. G., and HENDERSON, J. W. Phys. Rev. 88 (1952) 106. 3. BOWEN, DWAIN, EGGLESTON,R. R., and KROPSCHOT,R. H. J. Appl. Phys: 23 (1952) 630. 4. PARKINS, W. E., DIENES, G. J., and BROWN, F. W. J. Appl. Phys. 22 (1951) 1012. 5. EGGLESTON,R. R. J. Appl. Phys. 23 (1952) 1400. Bull. Am. Phys. Sot., December 6. OVERHAUSER, A. W. 1952. 7. SEITZ, F. Adv. in Physics, Quart. Supp. Phil. Mag. 1 (1952) 43. 8. MOTT, N. F. Phil. Mag. 43 (1952) 1151.
OF COPPER AFTER RADIATION A’k LOW TEMPERATURES*
DAMAGE
R. R. EGGLESTONt Resistance measurements at the boiling point of liquid helium have been made on copper which was damaged at temperatures below - 150°C by an exposure to 35 Mev alpha particles and then annealed at higher temperatures. The activation energy for the process active at annealing temperatures between - 65°C and - 20°C is 0.717 ev. At temperatures between 250°C and 325°C the activation energy describing the annealing is 2.12 ev. The activation energy obtained at the lower temperatures is in agreement with the value of 0.672 ev for copper cold-worked in liquid helium, and the value of 0.68 ev obtained by Overhauser on copper irradiated in a similar manner and annealed in the same low temperature range. Cold-work and radiation damage in copper were compared qualitatively by making similar constant time anneals at progressively higher temperatures on specimens irradiated at temperatures below - 150°C and specimens cold-worked.in liquid helium. Up to about - 80°C the rate of annealing of the two specimens was similar, but at room temperature about 25 per cent of the radiation damage remained compared to 50 per cent remaining in the cold-worked specimen. LE
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R4DIATIONS
Des mesures de rCsistance, au point d’Cbullition de l’hilium liquide, ont 6th effect&es sur du cuivre endommagi: & des tempkratures en dessous de - 150°C par des particules alpha de 35Mev et ensuite recuit P des tempkratures plus blev&es. L’energie d’activation du processus de recuit aux temperatures allant de - 65°C & 20°C est de 0,717 ev. Aux tempkratures variant de 250°C B 325°C l’&ergie d’activation du recuit est de 2,12 ev. L’energie d’activation obtenue aux basses tempCratures est en accord avec les 0.672 ev obtenus pour du cuivre &roui dans l’hhlium liquide, et les 0,68 ev obtenus par Overhauser sur du cuivre irradik d’une fafon similaire et recuit dans le meme intervalle de basses tempbratures. Les deggts provoquCs dans le cuivre par I’Ccrouissage et par l’irradiation ont et6 cornpar& qualitativement, en effectuant des recuits similaires, de m&me durite, & des tempCratures de plus en plus itle&es, sur des &hantillons irradiirs a des tempkratures infbrieures B - 150°C et sur des &chanti!lons Ccrouis dans I’h&lium liquide. Jusqu’environ - 80°C la vitesse de recuit des deux &chantillons Ctait similaire, alors qu’8 la temp(trature ambiante le dCgat ritsiduel &tait de 25 pour cent danc le cas des Cchantdlone irradiiis et de 50 pour cent dans le cas des Cchantillons itcrouis. ;2USGLiiHEN
VON
KUP+ER TIEFEN
NACH STRAHLUNGSSCHi;DIGUNG TEMPERATUREN
BE1
Der Widerstand von Kupfer, das der Bestrahlung mit 35 MeV Alpha Teilchen bei einer Temperatur unterhalb von - 150°C ausgesetzt und dann ausgegliiht worden war, wurde am Siedepunkt des fliissigen Heliums gemessen. Die Aktivierungsenergie fiir den bei der Gltihtemperatur zwi:chen - 65°C und - 20°C stattfindenden Vorgang betrggt 0.717 eV. Bei Temperaturen zwischen 250°C und 325’C betr?igt die dem Ausgliihen zugeschriebene ilktivierungsenergie 2.12 eV. Der bei tieferen Temperaturen erhaltene Wert der Aktivierungsenergie stimmt zufriedenstellend mit dem Wert mit 0:672 e\J fiir in fliissigem Helium kaltbearbeitetem Kupfer iiberein, ebenso wie mit den 0,68 eV, die Overhauser fiir Kupfer, das in zhnlicher Weise bestrahlt und in gleichem tiefen Temperaturbereich ausgegliiht wurde, angegeben hat. Kaltbearbeitung und Strahlungssch&digung von Kupfer wurden quantitativ verglichen, indem entsprechende Gliihungen (mit konstanter Gliihzeit) bei fortschreitend haheren Tempzraturen an Proben, die unterhalb van - 150°C bestrahlt oder in fliissigem Helium kalt bearbeitet worden waren, durchgefiihrt wurden. Bis ZLI - 80°C war das Verhgltnis des Ausheilens bei beiden Proben das gleiche, bei Zimmertemperatur verblieben jedoch 25 prozent der Strahlungsschgdigung im Vergleich zu 50 prozent der Kaltbearbeitung.
Introduction Changes in physical properties take place when metals are exposed either to a neutron flux or to a charged particle bombardment [l, 21. In the case of a pure metal such as copper, the amount of damage as observed by resistivity measurements is dependent on the thermal history of the bombarded specimen, both during the bombardment and prior to observation. It is the purpose of this paper to describe measurements of electrical resistance made on *Received June 6, 1953. tNorth American Aviation, Inc., Atomic Department, Downey, California. ACTA
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Research
copper irradiated at temperatures below - 15O”C, then subjected to controlled heat treatments. These treatments were first carried out in the range of temperatures from - 65°C to 0°C and then between 250°C and 300°C. These results will be compared with the annealing behavior of copper which was cold-worked at the liquid helium temperature. The comparison will be made on the basis of activation energies determined by making the assumption that within each temperature range considered the annealing process can be described by a single, well-defined activation energy. The determination of the energy of activation for annealing active in different temperature ranges
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for material damaged in a variety of ways may aid in the identification of the various possible lattice defects. The electrical resistance measurements were made at the boiling point of liquid helium, and will be referred to hereafter as residual resistance measurements. Since there is no temperature dependence of the extra resistance due to defects at measurement temperatures below 18”K, it was assumed that Matthiessen’s rule holds for measurements made at 4.2’K. Thus the extra resistance measured due to the damage may be assumed proportional to the number of defects. Results of previous work [3] indicate that there is a slight temperature dependence of the resistivity due to defects at other temperatures of measurement. By making measurements of residual resistivity, the possibility of identifying the annealing mechanisms is improved.
Experimental
Procedure
The measurement of residual resistivity by standard potentiometric methods was used to detect changes due to thermal treatments in all of the following experiments. The temperature of measurement differed from the thermal treatment temperature; therefore in order to know the time of anneal accurately the specimen had to be taken up to, and lowered from, the thermal treatment temperature rapidly. This method of annealing at a higher temperature and taking measurements at a more desirable or convenient temperature has been called a pulse annealing technique [4]. There are experimental advantages in using residual resistance measurements, in addition to the theoretical advantages discussed above. These advantages are that the temperature coefficient of resistance is small at this temperature, the temperature of measurement is reproducible, and the relative changes arising from the annealing are larger. In the thermal treatments, the individual specimens were either at a constant temperature or at progressively higher temperatures for a constant time at each temperature. The former treatment will be called an isothermal anneal and the latter a tempering anneal. Constant temperature baths of large heat capacity were used for these anneals. Commercial O.F.H.C. copper wire of 3-mil diameter was used for these studies; the exact purity was unknown, but from maximum and minimum assays of copper plus silver that were available it is probably safe to assume that the
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purity was at least 99.9 per cent. For the tempering anneals, a wire about 8.5 cm long was wound on a thin mica strip so that its entire length was evenly bombarded. The isothermal specimens, approximately 0.7 cm long, were mounted similarly, but without a supporting mica strip. The specimen mountings were small enough so that as many as four specimens could be bombarded simultaneously and still receive nearly identical irradiations. The 60-inch cyclotron of the Cracker Radiation Laboratory at the University of California in Berkeley was used for the alpha-particle irradiations. The energy of the particles at the target was 35 Mev. The range of the particles of this energy in copper is approximately 7 mils so that there should be no inhomogeneities in the samples due to end of range effects in the isothermal samples. The specimens were kept at temperatures below - 150°C during the irradiation by flowing refrigerated helium past the specimen and by limiting the beam current. After the irradiation it was possible to transfer the specimens rapidly, without warming, .to liquid nitrogen, in which they were stored before annealing. The exposures of the isothermal samples, tabulated in Table I, TABLE
I
Annealing temperature
- fJ5T
- 5OT
- 35°C
-
Exposure (aahrs/cm*
13.3
13.0
13.1
13.3
in Residual resistance arbitrary units after irradiation
1570.9,
1455.0s
1515.0”
1433.81
After long time at room temperature
460.71
464.91
473.45
431.9j
Annealing temperature
3OOT
275T
25OT
resistance in Residual arbitary units after Specimen anneal 5OOT. 2 hr. broke
98.2,
100.72
95.76
Values of residual resistivity due to defects produced by irradiation
0.0777
0.0778
0.0782
0.0782
2OT
varied slightly from sample to sample. These exposures were determined from a beam profile distribution obtained by counting st:rips from a monitoring foil placed between the specimen and the cyclotron. Before irradiation the specimens were annealed in a vacuum at temperatures of at least 780°C for 10 minutes and above 400°C for 105 minutes.
Results An exploratory
tempering
anneal curve, which
EGGLESTON:
ANNEALING
AFTER
is presented in Figure 1, shows that the most rapid annealing occurs between - 70°C and 0°C. Hence, the temperatures chosen for the i~thermal annPals were - 65”C, - 5O”C, - 35°C and - 20°C. Between - 70°C and 0°C the tempering curve
FIGURE1. Result of tempering anneal on copper irradiated at temperatures below - 15O’C to an exposure of 17.2 rahrs/ cm2 with 34.5 Mev alpha particles.
does not exhibit any properties that would indicate more than a single active annealing process. After the isothermal data were taken, each of the four specimens was allowed to stand at ambient room temperature for a period of 12 days. In Table I the data of residual resistance in arbitrary units has been collected at several times during the thermal history together with the exposures and annealing temperatures for each of the specimens. There are several possible ways to reduce or normalize the data and thus make direct comparisons of the isothermal curves. Since the radiation exposures and lengths of the samples are different, this procedure is of necessity complicated. The normalization procedure to be described was found to yield activation energies that were quite well defined and nearly constant. The residual resistance values attributed to the defect being annealed were first obtained for each from the resistances specimen by subtracting measured during the annealing a value obtained after a long anneal at room temperature. This value was used since the room temperature anneal resulted in a nearly complete disappearance of the defects under study, leaving relatively undisturbed the defects that anneal at higher temperatures. Curves of change in resistivity versus exposure under similar irradiation conditions give us
RADIATION
DAMA%GE
681
information to allow us to make the small relative corrections needed for the normalization, though they are not reliable absolutely. These curves show that at the exposures encountered here, the change of residual resistivity with exposure is 1.71 X 10P3 ~&m/~ahr/cm”, and at an exposure of 12~ahrs/cm2, the total change of residual resistivity is 0.076~~cm. In order to get relative values of residual resistivity the above slope was multiplied by the extra exposure given each sample over 12pahrs/cm2 and then added to the value given above for an exposure of 12pahrs/cm2. The values of residual resistivity due to the defects introduced by the irradiation are also tabulated in Table I ; these values are accurate relatively but not absolutely. The residual resistance data for each specimen were then normalized by multiplying by the ratio of relative residual resistivity values tabulated above to the extra resistance due to the defects after irradiation. Thus it was possible to correct for slight length and exposure differences from specimen to specimen. The normalized annealing curves are displayed in Figure 2. The phenomenological activation
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00
iN MINIJTES
FIGURE 2. Normalized isothermal annealing curves for temperatures of anneal between - 65°C and - 20°C. In order to obtain an approximate value of residual resistivity change in micro ohm cm due to the irradiation, multiply the arbitrary scale by 0.018. Residual resistivity may then be obtained by adding this value to the annealed residual resistivity which is approximately 0.015 @cm.
energy can easily be obtained from these curves. When the logarithms of the times to reach equal property values of the helium point resistance along several isothermal curves is plotted against the corresponding reciprocal absolute temperature of the isothermals the points define a line whose slope determines the activation energy. In Figure
682
ACTA
METALLURGICA,
3 the results of making several equal property cuts on the curves in Figure 2 are given. The activation energy is seen to be quite well defined. The average energy is 0.717 ev while the spread is from 0.707 ev to 0.742 ev. There is no obvious trend in these values which would indicate that
L’OL.
1,
1953
deuterons for an exposure of I. 1 X 1 OLi pnrticles,/ cm2 and found an activation energy of 0.68 ev for the annealing occurring above - 50°C‘ which is in agreement with both of the above values. After the above specimens had annealed at room temperature they were then further annealed isothermally at 25O”C, 275°C and 300°C, after which they were annealed at 500°C for two hours to completely remove the defects caused by the irradiation. The normalized annealing curves are shown in Figure 4. In this case the normal-
FIGURE 4. Normalized isothermal annealing curves for temperatures of anneal between 250°C and 3OOT. In order to obtain an approximate value of residual resistivity change in micro ohm cm due to the irradiation, multiply the arbitrary scale by 0.018. Residual resistivity may then be obtained by adding this value to the annealed residual resistivity which is approximately 0.015 @cm. FIGURE 3. Phenomenological determination of activation energy for the annealing process active in the temperature range between - 65°C and - 20°C.
this spread is due to other than experimental uncertainties. Since both the lengths and the exposure did not vary greatly among the specimens it is possible to use other logical normalization procedures based on the assumption that these slight differences did not exist. Isothermal curves compared after normalization by these assumptions yielded values that differed from the above average value by less than 10 per cent. This is not surprising, since both the lengths and the exposures did not vary greatly among the specimens; thus the normalization corrections should be small as also should be the variation in determined activation energies. An activation energy of 0.672 ev has been reported previously [5] for copper that had been cold-worked by twisting at liquid helium temperatures and annealed at temperatures between - 50°C and - 10°C. This is not too different from the value found for the irradiated copper. This agreement may indicate that the annealing process is similar in the two cases. Overhauser [6] has irradiated copper at - 180°C with 12 Mev
ization was made by assuming that all three of the specimens had identical residual resistivities after the 500°C anneal. The other specimens were normalized to the residual resistance of the specimen annealed at 300°C. The determination of activation energies was made in the same way as for the earlier annealing data. The results of making several equal property cuts on the normalized isothermal curves in Figure 3 are shown in Figure 5. The activation energy is seen to be fairly well defined, the average value being 2.12 ev while the spread is from 2.09 ev to 2.18 ev. The data for this annealing range were not taken over as wide a temperature range as the data at lower temperatures; thus the values of activation energy are less reliable. The activation energy of 2.12 ev is in agreement with values of the copper self-diffusion activation energy, given as 2.1 ev by Seitz [7] and a slightly lower value of 2.02 ev by Mott [8]. In Figure 6, tempering curves for irradiated and for cold-worked copper are compared on a percentage basis, allowing several qualitative features of the annealing to be noted. The final resistivities of the damaged specimens were 21.01 and 15.3 X 10-?&m respectively. Initially these specimens had resistivities of 1.56 and 1.37 X l0-80cm respectively.
EGGLESTON:
ANNEALING
AFTER
RADIrZTION
683
DALIAGE
to about 50 per cent for the cold-worked material. As the temperature is raised above 100°C the damage finally anneals completely, that due to the cold-work annealing more rapidly than that due to irradiation. If the agreement in activation energies obtained for the temperature range from - 70°C to 0°C for cold-worked and for irradiated copper is indicative of motion or annihilation of the same defect then the above qualitative features show that this defect is produced in quite different concentrations in the two methods of damage. The isothermal annealing curves may be described empirically by using a kinetic rate equation,
d(P - PO)-___-dt
(p -
po)ae-E’gT
where the resistivity change undergoing is annealing, t is the time, a! is the order of the reaction and is restricted to integer values, E is the activation energy, K is the Boltzmann constant and T is the absolute temperature. A third order of reaction is needed to fit the isothermal data between - 65°C and - 2O’C. For the isothermal annealing between 250°C and 300°C a fourth order of reaction is needed to fit the data. P
FIGURE 5. Phenomenological determination of activation energy for the annealing process active in the temperature range between 250°C and 300°C.
The irradiated specimen had been exposed at temperatures below 150°C to 17.2pahr/cm2 of 34.5 Mev alpha particles, and the coldworked specimen had been twisted while immersed in liquid helium, after which the specimens were similarly tempered from temperatures near their damage temperature to 100°C. Up to about - 80°C the rate of annealing is nearly equal for the two types of damage; about 75 per cent of the damage still remains. From this temperature to near room temperatures however, the irradiated material anneals to a greater extent than the cold-worked copper so that at room temperature there is only approximately 25 per cent of the radiation damage still present compared
-
PO
Acknowledgments The author wishes to acknowledge the help of C. R. Davidson and Lyle Glasgow of the Irradiation Physics Group at Berkeley for supervising and performing the required irradiations and to thank Miss Sonja Hanjian for patient help in performing the required annealings. This work was based on studies conducted for the Atomic Energy Commission under Contract AT-1 l-lGEN-8.
References
FICUKE 6. Tempering annealing curves for irradiated and for cold-worked copper on a percentage basis. The irradiated specimen received an exposure of 17.2 Fahrs/cm2 with 34.5 Mev alpha particles at temperatures below - 150°C. The cold-worked specimen had been cold-worked by twisting while immersed in liquid helium.
1. MARTIN, A. B., et al. Phys. Rev. 81 (1951) 664. 2. MARX, J. W., COOPER, H. G., and HENDERSON, J. W. Phys. Rev. 88 (1952) 106. 3. BOWEN, DWAIN, EGGLESTON,R. R., and KROPSCHOT,R. H. J. Appl. Phys: 23 (1952) 630. 4. PARKINS, W. E., DIENES, G. J., and BROWN, F. W. J. Appl. Phys. 22 (1951) 1012. 5. EGGLESTON,R. R. J. Appl. Phys. 23 (1952) 1400. Bull. Am. Phys. Sot., December 6. OVERHAUSER, A. W. 1952. 7. SEITZ, F. Adv. in Physics, Quart. Supp. Phil. Mag. 1 (1952) 43. 8. MOTT, N. F. Phil. Mag. 43 (1952) 1151.