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Low-temperature electron radiation damage in scandium
Volume 107A, number 3
PHYSICS LETTERS
21 January 1985
LOW-TEMPERATURE ELECTRON RADIATION DAMAGE IN SCANDIUM J.N. DAOU, P. VAJDA, A. LUCASSON l , p. LUCASSON and J.P. BURGER 2 E.R.A. No. 720 du CNRS, Bdtirnent 350, Universitd Paris.Sud, F-91405 Orsay, France
Received 30 October 1984
Electron irradiation of hcp scandium at T ~ 12 K allowed to determine the energy threshold for Frenkel-palr creation, Td = 13.8 ± 0.5 eV, and the defect resistivity, PF ~ 5 X 10-a S2 cm/F.P. The annealing spectrum exhibits four substages between 20 and 70 K, a broad substage centered at 105 K attributed to interstitial long-range migration, and a stage III between 240 and 300 K.
In the past few years, a systematic investigation o f radiation damage in the metals o f the rare earth series has been conducted in our laboratory [ I - 8 ] , in order to establish eventual regularities in the creation and the behaviour o f point defects in these elements. Scandium, Z = 21, (and y t t r i u m ) being situated in the same group IIIb of the periodic table as the lanthanides can be considered as a light analog o f the latter. Moreover, as we have started studying the properties of the system S c - H under irradiation, it was important to determine specific defect characteristics o f the pure metal, such as the threshold energy for the creation o f the Frenkel pairs and their annealing behaviour. 25 ~tm thick Sc foils o f 4N-grade quality had been purchased from Rare Earth Products Ltd. (Great Britain) containing 30 at p p m AI, 7 p p m Y, 5 p p m Lu as main metallic impurities. No gaseous impurities had been announced, b u t we have degassed the foils at 1000°C for several hours in a vacuum o f 10 - 7 Torr. The samples prepared from them o f resistivity measurements has a resistance ratio o f R 295 K/R 4.2 K = 6.7 and a residual resistivity o f P4.2 K = 8.0/a~2 cm. The irradiation was performed at liquid helium temperatures using electrons from our C o c k r o f t - W a l t o n accelerator in the energy range E = 3 0 0 - 1 0 0 0 keV. 1 Eeole Normale Sup6rieure de Jeunes Filles, F-92129 Montrouge, France. 2 Laboratoire de Physique du Sohde, Bitiment 510, Universit~ Paris-Sud, F-91405 Orsay, France.
142
152
363
i
63t~ 965
i
i
Tmax/ev
i
o/b
h1
i
p.
03 131
i:=
[ %,5
r I.v
~
l.o (220KeV)
d_
o
e .S'~o= al÷a 2
.100
(3:
50
01 ,,'~L 05
~ , 10 E/MeV
Fig. 1. Residual-resistivity change rates per incident electron
fluence as a function of electron energy, the upper abscissa indicating the transmitted energies. The drawn curves (righthand axis) are calculated best-fit cross sections for different thresholds using the probability step functions depicted in the insert, broken line - one step, full hne - two steps. Fig. 1 shows the residual-resistivity change rates,
A p/n, per incident electron fluence as a function of their energy, with the corresponding maximum transmittable energy to a Sc atom, Tmax/eV = (560.8/A) × e (e + 2), being plotted on the upper edge of the figure; A = 44.956 is the atomic mass of Sc and e = E/mc 2 the reduced electron energy. We have fitted the experimental data with atomic displacement cross sections o, such that 0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 107A, number 3
Ap(E)/n O(E)PF,
PHYSICS LETTERS
(1)
=
where PF is the electrical resistivity of a Frenkel pair. O(E) is obtained by integration of the differential scattering cross section, do/dT, over the transmitted energy T, taking into account straggling and energy degradation:
Tmax
21 January 1985
The value of Td ~ 14 eV can be compared with the empirical expression derived for other hop rare earths [5] :
TRE/eV= 75 {2.65(c/a) [rl(A)] -1
_ 1},
giving, with rl(SC) = a = 3.309 g and c/a = 1.5917, TdRE(Sc) = 20.6 eV. Another phenomenological formula for Td has been proposed by Jung [10] :
74dur~/eV= 0.022 Br 1 exp(1.18rl), rd (The procedure has been outlined in the earlierpapers, e.g. in ref. [5] .)Pd(T) is the displacement probability and T d the atomic displacement threshold energy. The best fit using a single-stepprobability function yielded the curve labelled o(220 keV), i.e.for an incident electron ofE d = 220 keV as threshold. The corresponding step function with a step height 0 < h ~< I is drawn as a broken line in the insert: PFPd = 2.5 X 10 -3 I2cm, for
13.1 e V < T~< 96.5 eV.
Here, Td = 13.1 4. 0.7 eV is the displacement threshold related t o e d = 220 + 10 keV, and T = 96.5 eV corresponds to the highest incident electron energy of E = 1 MeV. The fit is quite satisfactory for energies E 2 0.4 MeV, but passes above the experimental points for lower energies. An improvement is achieved with a two-step probability function, the best fit being represented by the full line o and the corresponding Pd in the insert: PFPd(T) = 1.5 X 10 . 3 ~2cm, for
13.8 eV < 7"~< 14.5 eV,
= 2.4 X 10 . 3 12cm, for
14.5 eV < T~< 96.5 eV,
with the two thresholds of Tdl = 13.8 4- 0.5 eV and Td2 14.5 -+ 0.5 eV representing the two "easiest" displacement mechanisms in the Sc lattice. From geometrical considerations and by analogy with other hcp metals, we would suggest for them displacements along the close packed (1120) directions and through one of the open lenses along (2022) or (2023) (e.g. ref. [9] ). At the same time, the single-step fit does not necessarily mean just one principal collision mechanism but rather two (or more) displacement processes having the same energy threshold.
(3)
(4)
containing the bulk modulus B(101°pa). Using for B = 5.66 X 1010pa [11] ,we obtain TadUng(Sc)= 20.4 eV, in close agreement with T~aE(Sc), but about 50% higher than the experimental result. The Frenkel pair resistivity PF can be obtained from the results assuming a certain step height for Pd(10. In the transmitted energy range of our experiment, Tmax(1MeV) = 96.5 eV ~ 7Td, a reasonable choice is [3] Pd ~ I/2, which gives PF(SC) ~. 5 X 10 -3 I2 cm/FP, good to maybe -+ 30%. A relationship suggested by Benedek [12] between PF and the lattice resistivity at the melting point (generalized later by Jung [13] to include low melting point metals) pFB = 17.5p(Tf),
(5)
gives, with p(Tf = 1814 K) = 325/zI2cm extrapolated from ref. [14] ,pBF(SC) = 5.7 X 10 -3 I2cm/FP, in good agreement with our proposed value. An exploration of the isochronal annealing behaviour was undertaken subsequently to the irradiation: the results of two runs using electrons of various energy ranges are presented in fig. 2. The main features can be summarized as follows: 0 10
F%
APLrr/~cm E;/MeV 08.10 03to07
30
=
7C 9C lo ' ;;o ~o ~o
,
100
t
.'m
200 300 fQnn/K
Fig. 2. Damage recovery in scandium irradiated with electrons of different energies at T~ ~ 12 K.
143
Volume 107A, number 3
PHYSICS LETTERS
(1) several simple annealing substages centered at ~ 2 0 K, 36 K, 48 K, 70 K, covering together ~ 3 0 % of the induced damage, probably due to close-pair recovery; (2) a big complex stage between 80 and 130 K covering another 50% o f the damage; the peak temperature o f this stage, T ~ 105 K, is in good agreement with the migration temperature o f the interstitial, T m, when compared to the empirical relation derived in refs. [4,6]:
Tm/T f = 1.1 1(8/3) 1/2 - c/aL + 7.2 × 10 - 3 ,
(6)
which gives T m = 95.5 K - we suggest long-range interstitial migration for this substage; (3) about 10% recovery spread over an interval o f I00 K, possibly a stage II analog due to the anneal o f various complexes; (4) a final stage centered around 270 K and finishing at room temperature, stage III - tentatively assigned to vacancy recovery.
144
21 January 1985
References [1] J.N. Daou, J.E. Bonnet, P. Valda, M Blget, A. Lucasson and P Lucasson, Phys. Stat. Sol. 40a (1977) 101. [2] J.N. Daou, J.E. Bonnet, P Vajda, A. Lucasson and P. Lucasson, Phys. Lett. 63A (1977) 158. [3] J.N. Daou, P. Va]da, A. Lucasson and P. Lucasson, Radlat. Eft. 39 (1978) 3 [4] P. Vajda, J.N Daou, A. Lucasson and P. Lucasson, Solid State Commun 27 (1978) 1317. [5] J.N. Daou, E.B. Hannech, P. Valda, A. Lucasson and P. Lucasson, Philos. Mag. A41 (1980) 225. [6[ J.N. Daou, P. Vajda, A. Lucasson and P. Lucasson, J. Phys. F10 (1980) 583. [7] J.N. Daou, P. Vajda, A. Lucasson and P. Lucasson, Radiat. Eft. 61 (1982) 93. [8] J.N. Daou, P. Vajda, A. Lucasson and P. Lucasson, Radmt. Eft., to be published [9] P. Vajda, Rev. Moo. rhys. 49 (1977) 481. [10] P. lung, Radlat. Eft. 35 (1978) 155. [11 ] Handbook on the physics and chenustry of rare earths, Vol. 1, eds. K.A. Gschneidner and L. Eyring (NorthHoUand, Amsterdam, 1978) p. 701. [12] R. Benedek, J. Appl. Phys. 48 (1977) 3832. [13] P. lung, Radiat. Eft. 51 (1980) 249. [14] F.H. Spedding, D.Cress and B.J Beaudry, J. Less Common Met. 23 (1971) 263.
PHYSICS LETTERS
21 January 1985
LOW-TEMPERATURE ELECTRON RADIATION DAMAGE IN SCANDIUM J.N. DAOU, P. VAJDA, A. LUCASSON l , p. LUCASSON and J.P. BURGER 2 E.R.A. No. 720 du CNRS, Bdtirnent 350, Universitd Paris.Sud, F-91405 Orsay, France
Received 30 October 1984
Electron irradiation of hcp scandium at T ~ 12 K allowed to determine the energy threshold for Frenkel-palr creation, Td = 13.8 ± 0.5 eV, and the defect resistivity, PF ~ 5 X 10-a S2 cm/F.P. The annealing spectrum exhibits four substages between 20 and 70 K, a broad substage centered at 105 K attributed to interstitial long-range migration, and a stage III between 240 and 300 K.
In the past few years, a systematic investigation o f radiation damage in the metals o f the rare earth series has been conducted in our laboratory [ I - 8 ] , in order to establish eventual regularities in the creation and the behaviour o f point defects in these elements. Scandium, Z = 21, (and y t t r i u m ) being situated in the same group IIIb of the periodic table as the lanthanides can be considered as a light analog o f the latter. Moreover, as we have started studying the properties of the system S c - H under irradiation, it was important to determine specific defect characteristics o f the pure metal, such as the threshold energy for the creation o f the Frenkel pairs and their annealing behaviour. 25 ~tm thick Sc foils o f 4N-grade quality had been purchased from Rare Earth Products Ltd. (Great Britain) containing 30 at p p m AI, 7 p p m Y, 5 p p m Lu as main metallic impurities. No gaseous impurities had been announced, b u t we have degassed the foils at 1000°C for several hours in a vacuum o f 10 - 7 Torr. The samples prepared from them o f resistivity measurements has a resistance ratio o f R 295 K/R 4.2 K = 6.7 and a residual resistivity o f P4.2 K = 8.0/a~2 cm. The irradiation was performed at liquid helium temperatures using electrons from our C o c k r o f t - W a l t o n accelerator in the energy range E = 3 0 0 - 1 0 0 0 keV. 1 Eeole Normale Sup6rieure de Jeunes Filles, F-92129 Montrouge, France. 2 Laboratoire de Physique du Sohde, Bitiment 510, Universit~ Paris-Sud, F-91405 Orsay, France.
142
152
363
i
63t~ 965
i
i
Tmax/ev
i
o/b
h1
i
p.
03 131
i:=
[ %,5
r I.v
~
l.o (220KeV)
d_
o
e .S'~o= al÷a 2
.100
(3:
50
01 ,,'~L 05
~ , 10 E/MeV
Fig. 1. Residual-resistivity change rates per incident electron
fluence as a function of electron energy, the upper abscissa indicating the transmitted energies. The drawn curves (righthand axis) are calculated best-fit cross sections for different thresholds using the probability step functions depicted in the insert, broken line - one step, full hne - two steps. Fig. 1 shows the residual-resistivity change rates,
A p/n, per incident electron fluence as a function of their energy, with the corresponding maximum transmittable energy to a Sc atom, Tmax/eV = (560.8/A) × e (e + 2), being plotted on the upper edge of the figure; A = 44.956 is the atomic mass of Sc and e = E/mc 2 the reduced electron energy. We have fitted the experimental data with atomic displacement cross sections o, such that 0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 107A, number 3
Ap(E)/n O(E)PF,
PHYSICS LETTERS
(1)
=
where PF is the electrical resistivity of a Frenkel pair. O(E) is obtained by integration of the differential scattering cross section, do/dT, over the transmitted energy T, taking into account straggling and energy degradation:
Tmax
21 January 1985
The value of Td ~ 14 eV can be compared with the empirical expression derived for other hop rare earths [5] :
TRE/eV= 75 {2.65(c/a) [rl(A)] -1
_ 1},
giving, with rl(SC) = a = 3.309 g and c/a = 1.5917, TdRE(Sc) = 20.6 eV. Another phenomenological formula for Td has been proposed by Jung [10] :
74dur~/eV= 0.022 Br 1 exp(1.18rl), rd (The procedure has been outlined in the earlierpapers, e.g. in ref. [5] .)Pd(T) is the displacement probability and T d the atomic displacement threshold energy. The best fit using a single-stepprobability function yielded the curve labelled o(220 keV), i.e.for an incident electron ofE d = 220 keV as threshold. The corresponding step function with a step height 0 < h ~< I is drawn as a broken line in the insert: PFPd = 2.5 X 10 -3 I2cm, for
13.1 e V < T~< 96.5 eV.
Here, Td = 13.1 4. 0.7 eV is the displacement threshold related t o e d = 220 + 10 keV, and T = 96.5 eV corresponds to the highest incident electron energy of E = 1 MeV. The fit is quite satisfactory for energies E 2 0.4 MeV, but passes above the experimental points for lower energies. An improvement is achieved with a two-step probability function, the best fit being represented by the full line o and the corresponding Pd in the insert: PFPd(T) = 1.5 X 10 . 3 ~2cm, for
13.8 eV < 7"~< 14.5 eV,
= 2.4 X 10 . 3 12cm, for
14.5 eV < T~< 96.5 eV,
with the two thresholds of Tdl = 13.8 4- 0.5 eV and Td2 14.5 -+ 0.5 eV representing the two "easiest" displacement mechanisms in the Sc lattice. From geometrical considerations and by analogy with other hcp metals, we would suggest for them displacements along the close packed (1120) directions and through one of the open lenses along (2022) or (2023) (e.g. ref. [9] ). At the same time, the single-step fit does not necessarily mean just one principal collision mechanism but rather two (or more) displacement processes having the same energy threshold.
(3)
(4)
containing the bulk modulus B(101°pa). Using for B = 5.66 X 1010pa [11] ,we obtain TadUng(Sc)= 20.4 eV, in close agreement with T~aE(Sc), but about 50% higher than the experimental result. The Frenkel pair resistivity PF can be obtained from the results assuming a certain step height for Pd(10. In the transmitted energy range of our experiment, Tmax(1MeV) = 96.5 eV ~ 7Td, a reasonable choice is [3] Pd ~ I/2, which gives PF(SC) ~. 5 X 10 -3 I2 cm/FP, good to maybe -+ 30%. A relationship suggested by Benedek [12] between PF and the lattice resistivity at the melting point (generalized later by Jung [13] to include low melting point metals) pFB = 17.5p(Tf),
(5)
gives, with p(Tf = 1814 K) = 325/zI2cm extrapolated from ref. [14] ,pBF(SC) = 5.7 X 10 -3 I2cm/FP, in good agreement with our proposed value. An exploration of the isochronal annealing behaviour was undertaken subsequently to the irradiation: the results of two runs using electrons of various energy ranges are presented in fig. 2. The main features can be summarized as follows: 0 10
F%
APLrr/~cm E;/MeV 08.10 03to07
30
=
7C 9C lo ' ;;o ~o ~o
,
100
t
.'m
200 300 fQnn/K
Fig. 2. Damage recovery in scandium irradiated with electrons of different energies at T~ ~ 12 K.
143
Volume 107A, number 3
PHYSICS LETTERS
(1) several simple annealing substages centered at ~ 2 0 K, 36 K, 48 K, 70 K, covering together ~ 3 0 % of the induced damage, probably due to close-pair recovery; (2) a big complex stage between 80 and 130 K covering another 50% o f the damage; the peak temperature o f this stage, T ~ 105 K, is in good agreement with the migration temperature o f the interstitial, T m, when compared to the empirical relation derived in refs. [4,6]:
Tm/T f = 1.1 1(8/3) 1/2 - c/aL + 7.2 × 10 - 3 ,
(6)
which gives T m = 95.5 K - we suggest long-range interstitial migration for this substage; (3) about 10% recovery spread over an interval o f I00 K, possibly a stage II analog due to the anneal o f various complexes; (4) a final stage centered around 270 K and finishing at room temperature, stage III - tentatively assigned to vacancy recovery.
144
21 January 1985
References [1] J.N. Daou, J.E. Bonnet, P. Valda, M Blget, A. Lucasson and P Lucasson, Phys. Stat. Sol. 40a (1977) 101. [2] J.N. Daou, J.E. Bonnet, P Vajda, A. Lucasson and P. Lucasson, Phys. Lett. 63A (1977) 158. [3] J.N. Daou, P. Va]da, A. Lucasson and P. Lucasson, Radlat. Eft. 39 (1978) 3 [4] P. Vajda, J.N Daou, A. Lucasson and P. Lucasson, Solid State Commun 27 (1978) 1317. [5] J.N. Daou, E.B. Hannech, P. Valda, A. Lucasson and P. Lucasson, Philos. Mag. A41 (1980) 225. [6[ J.N. Daou, P. Vajda, A. Lucasson and P. Lucasson, J. Phys. F10 (1980) 583. [7] J.N. Daou, P. Vajda, A. Lucasson and P. Lucasson, Radiat. Eft. 61 (1982) 93. [8] J.N. Daou, P. Vajda, A. Lucasson and P. Lucasson, Radmt. Eft., to be published [9] P. Vajda, Rev. Moo. rhys. 49 (1977) 481. [10] P. lung, Radlat. Eft. 35 (1978) 155. [11 ] Handbook on the physics and chenustry of rare earths, Vol. 1, eds. K.A. Gschneidner and L. Eyring (NorthHoUand, Amsterdam, 1978) p. 701. [12] R. Benedek, J. Appl. Phys. 48 (1977) 3832. [13] P. lung, Radiat. Eft. 51 (1980) 249. [14] F.H. Spedding, D.Cress and B.J Beaudry, J. Less Common Met. 23 (1971) 263.