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Positron annihilation measurements of quenched-in defects in Ni
Volume 138, number 1,2
PHYSICS LETTERS A
12 June 1989
POSITRON ANNIHILATION MEASUREMENTS OF QUENCHED-IN DEFECTS IN Ni T. TROEV, Ch. ANGELOY and I. MINCOV Institute/br Nuclear Research and Nuclear Energy, Bulgarian Academy ofSciences, Sofia 1184, Bulgaria Received 6 February 1989; accepted for publication 12 April 1989 Communicated by D. Bloch
Positron lifetime and Doppler broadening have been measured in Ni between 925 and 1700 K. The positron trapping is used as a defect indicator. The values obtained for the vacancy formation energy in nonequilibrium conditions are ~ = 1.6 ±0.1 eV from positron lifetime and H~.= 1.7 ±0.1 eV from Doppler broadening of the annihilation gamma-line.
A considerable effort has been undertaken in Fecent years for the investigation of defects and the de-’ termination of vacancy formation and migration
After the subtraction of the source component, the spectra were analysed as a sum of the two components r1 and r2 and a constant background. From the
energies in Ni. A few experimental studies [1—8]using different techniques were carried out for the investigation of point defects in Ni. Nevertheless, the uncertainties in the value of the formation energy of vacancies Ni are between 1.54and andbetween 1.8 eV 1.39 obtamed frominexperimental studies and 1.45 eV obtained from theoretical calculations [9,10]. The present study was carried out for the determination of the vacancy formation energy in nonequilibrium experiments in Ni by measurements of positron lifetime and Doppler broadening of the annihilation gamma-line. The Ni samples used for quenching experiments had 99.999% purity. The samples were annealed prior to the quenching ternperature procedure. They were heated for two hours at a temperature below the melting point at 1683 K in a vacuum chamber at l0—~Torr. The samples of Ni had a cylindrical shape 2x 10 mm with a central hole, which is bored along the axis. The aqueous solution of the 22NaCl source, 37x l0~Bq, was injected in the sample. A vertical furnace was used for heating the samples. They were moving rapidly, when entered into the quench bath. The quenching rate was of the order of 8 x I o~K The positron lifetime spectra were measured with a fast—slow coincidence system with a time resolulion FWHM of 290 ps. The spectra were evaluated with the POSITRONFIT EXTENDED program.
analysed lifetimes and relative intensities we calculated the average lifetime of the positrons. Doppler broadening of the annihilation gammaline was carried out by a Ge(Li) detector, which85Sr. has 1.3 keV at the 514tokeV gamma-line We usedresolution the S parameter characterize theof measured energy distribution. The positron lifetime and Doppler-effect results as a function of temperature are shown in fig. 1. The lifetime spectra above 1180 K yielded two components. The second one is due to the presence of vacancy trapping centres. This component increases up to 210 ps and its relative intensity changes from 4 to 62%. This shows a strong positron trapping. As a result of the quenching, ~increased from the bulk value of Fb=98 ps to 149 ps. This increase in the average positron lifetime occurred when the measurement temperature of the sample was raised from 1100 to 1700 K. The average lifetime and S parameter were found to have a strong increase above 1250 K as shown in fig. 1. The results also show that saturation of the S parameter value occurs above 1450 K. The obtained values of the lineshape parameters were discussed according to the two-state trapping model. The changes in average positron lifetime and S parameter are associated with quench-in vacancies. They are quite comparable with corresponding results from other positron studies [1—5,7], see fig. 2.
~ — ~.
0375-9601/89/$ 03.50 © Elsevier Science Publishers By. (North-Holland Physics Publishing Division)
65
Volume 138. number 1,2
PHYSICS LETTERS A
12 June 1989
P 3.47
PS 150
-.
A~ IA
3.46
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AA
LA
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A
I
140
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____I
k..—
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1 _____
______
1150
1300
.1
___
1450 TEMPERATURE
1600
K
Fig. I. Temperature dependence of the average positron lifetime and S parameter in nickel.
Thereisfortheaveragelifetimeonlyanapparentselfconsistency between the results of the equilibrium measurements and the present quenching data. At a temperature between 925 and 1250 K the results of the ~ are remarkably similar, while in the region 1280—1570 K they are quite different. This anomaly between the results of the average positron lifetime from earlier equilibrium experiments [1] and the quenching data of positron annihilation in Ni found here is puzzling. We attributed the observed effect to the specific positron trapping rate. In our study we measured the changes in the trapping rate ofthe positrons and in this way on the basis of the obtained results we determined the vacancy formation energy in Ni. By analysing the data we assumed the presence only of the monovacancies as positron traps. In fig. 3 we show the points in the temperature region 1180—1450 K which are used for determination of ~ by linear regression of the data. The obtained value is 1.6 ±0.1 eV. The value of the formation energy of vacancies determined by means of the S parameter, obtained by measurement of Doppler broadening of the annihilation gamma-line is 66
1.7±0.1eV. The results ofWycisk and Kniepmeier [8] on measurements of the resistivity recovery after quenching of Ni show that the energy for self-diffusion is equal to 2.88 eV. The simplest and most precise method for determining the migration energy of vacanciesis based on the well-known relationship between the energy for migration of vacancies, the energy for self-diffusion H~ and the energy for formation of vacancies ~ H~.~=H~ —H~~ (I .
In this way, from sufficiently accurate determination of H~ reported in the present paper and H~Yobtamed in (8), we may deduce H~,which is equal to 1.2 ±0.2 eV. This value is in good agreement with the values reported in the papers published earlier [11,121. Our results of the vacancy formation energy ~ are compared in table 1 with the results obtamed in earlier studies. From the present quenching experiments and the comparison with the results presented in the literature [1—6,81we may conclude that positrons are trapped into vacancies in Ni in the temperature region 1180—1700 K. The increase of ~ and S param-
Volume 138, number 1,2
Pcc
i -
140—
PHYSICS LETTERS A
12 June 1989
1 / ~V
urft~
[arbitrary 1300
V ~
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I
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-
6.00
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0730
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Fig. 2. Comparison of positron experimental data in Ni obtained as a function of temperature: (~)for ~ [11; PCC [5]; (ix) for 1/W 121; (V) forPCC [4]; (A) forS, presentwork; (~)fort, present work.
(x)
for F [3];
(•)
for
Table 1 H~’.values compared with values published by other authors.
> .
~ (eV) Method References ________________________________________________________
22
Ni 21
211
1.54±0.2 1.55±0.05
positron lifetime PCC
1.68 1.73±0.1 1.73 1.8±0.1 1.58—1.63 I .6 ±0. 1 1.7±0.1
PCC DBAGL DBAGL DBAGL electric resistivity
[11 [4] [5] [6] [2] [3] [8]
positron lifetime
present work
DBAGL
presentwork
19-~____________________________ ~1•
6 •
6.5
•
I
7
7.5 TEMPERATURE
~
,
~4
~
I
1)trapping for determination offrom the vacancy formation enFig. 3. Positron rate derived the lifetime data versus I0~/ ergy in nickel. T (K
eter reflects the increase of vacancy concentration, e.g. the positron traps. The obtained values for the tamed, another energy independent method, electrivacancybyformation are close to the by values obcal resistivity measurements of quenched Ni samples. 67
Volume 138, number 1,2
PHYSICS LETTERS A
References [1] KG. Lynn, CL. Snead and J.J. Hurst. J. Phys. F 10 (1980) 1753. [2]J.L.Campbell,C.W.SchulteandJ.A. Jackman.J. Phys. F7 (1977) 1985. [3] L.C. Smedskjaer, M.J. Fluss, D.C. Legnini. M.K. Chason and R.W. Siegel, J. Phys. F 11(1981) 2221. [4] H. Matter, J. Winter and W. Triftshauser, Appl. Phys. 20 (1979) 135. [5]S. Nanao, K. Kuribayashi, S. Tanigawa and M. Doyama. J. Phys. F 7 (1977)1403.
68
12 June 1989
[6] K. Maier, G. Rein. B. Saile. P. Valenta and HE. Schaefer, in: Proc. 5th mt. Conf. on Positron annihilation. Japan (l979)p. 101. [7] M. Fluss. L.C. Smedskjaer. B Chakraborty and M K Chason.J. Phys. F 13(1983)817. [8]W. Wycisk and M Fcller-Kniepmeier. Phys Stat Sol (a) 37(1976)183. [9]A. Seeger and H. Mehrer, in: Vacancies and interstitials of metals (North-Holland, Amsterdam, 1970) p. 1. [l0]Y. Nakamura,J Phys. Soc. Japan l6 (1961) 2167. [Il] Y.V. Konobeev. V.1. Bykov and A.V. Subbotin. Phys. Stat. Sol. (a) 40 (1977) K89 [121 M.H. Yoo and JO. Stiegler. Philos. Mag. 36 (1977) 1305.
PHYSICS LETTERS A
12 June 1989
POSITRON ANNIHILATION MEASUREMENTS OF QUENCHED-IN DEFECTS IN Ni T. TROEV, Ch. ANGELOY and I. MINCOV Institute/br Nuclear Research and Nuclear Energy, Bulgarian Academy ofSciences, Sofia 1184, Bulgaria Received 6 February 1989; accepted for publication 12 April 1989 Communicated by D. Bloch
Positron lifetime and Doppler broadening have been measured in Ni between 925 and 1700 K. The positron trapping is used as a defect indicator. The values obtained for the vacancy formation energy in nonequilibrium conditions are ~ = 1.6 ±0.1 eV from positron lifetime and H~.= 1.7 ±0.1 eV from Doppler broadening of the annihilation gamma-line.
A considerable effort has been undertaken in Fecent years for the investigation of defects and the de-’ termination of vacancy formation and migration
After the subtraction of the source component, the spectra were analysed as a sum of the two components r1 and r2 and a constant background. From the
energies in Ni. A few experimental studies [1—8]using different techniques were carried out for the investigation of point defects in Ni. Nevertheless, the uncertainties in the value of the formation energy of vacancies Ni are between 1.54and andbetween 1.8 eV 1.39 obtamed frominexperimental studies and 1.45 eV obtained from theoretical calculations [9,10]. The present study was carried out for the determination of the vacancy formation energy in nonequilibrium experiments in Ni by measurements of positron lifetime and Doppler broadening of the annihilation gamma-line. The Ni samples used for quenching experiments had 99.999% purity. The samples were annealed prior to the quenching ternperature procedure. They were heated for two hours at a temperature below the melting point at 1683 K in a vacuum chamber at l0—~Torr. The samples of Ni had a cylindrical shape 2x 10 mm with a central hole, which is bored along the axis. The aqueous solution of the 22NaCl source, 37x l0~Bq, was injected in the sample. A vertical furnace was used for heating the samples. They were moving rapidly, when entered into the quench bath. The quenching rate was of the order of 8 x I o~K The positron lifetime spectra were measured with a fast—slow coincidence system with a time resolulion FWHM of 290 ps. The spectra were evaluated with the POSITRONFIT EXTENDED program.
analysed lifetimes and relative intensities we calculated the average lifetime of the positrons. Doppler broadening of the annihilation gammaline was carried out by a Ge(Li) detector, which85Sr. has 1.3 keV at the 514tokeV gamma-line We usedresolution the S parameter characterize theof measured energy distribution. The positron lifetime and Doppler-effect results as a function of temperature are shown in fig. 1. The lifetime spectra above 1180 K yielded two components. The second one is due to the presence of vacancy trapping centres. This component increases up to 210 ps and its relative intensity changes from 4 to 62%. This shows a strong positron trapping. As a result of the quenching, ~increased from the bulk value of Fb=98 ps to 149 ps. This increase in the average positron lifetime occurred when the measurement temperature of the sample was raised from 1100 to 1700 K. The average lifetime and S parameter were found to have a strong increase above 1250 K as shown in fig. 1. The results also show that saturation of the S parameter value occurs above 1450 K. The obtained values of the lineshape parameters were discussed according to the two-state trapping model. The changes in average positron lifetime and S parameter are associated with quench-in vacancies. They are quite comparable with corresponding results from other positron studies [1—5,7], see fig. 2.
~ — ~.
0375-9601/89/$ 03.50 © Elsevier Science Publishers By. (North-Holland Physics Publishing Division)
65
Volume 138. number 1,2
PHYSICS LETTERS A
12 June 1989
P 3.47
PS 150
-.
A~ IA
3.46
I
AA
LA
A
I
A
I
140
A
I
A A lfortt
~
AforS
130
A
0.45
A
I
120
A 0.44
A
I
A AA A 0.43
A
1000
no
~._-_
ioo
A
AAA
____I
k..—
I
1 _____
______
1150
1300
.1
___
1450 TEMPERATURE
1600
K
Fig. I. Temperature dependence of the average positron lifetime and S parameter in nickel.
Thereisfortheaveragelifetimeonlyanapparentselfconsistency between the results of the equilibrium measurements and the present quenching data. At a temperature between 925 and 1250 K the results of the ~ are remarkably similar, while in the region 1280—1570 K they are quite different. This anomaly between the results of the average positron lifetime from earlier equilibrium experiments [1] and the quenching data of positron annihilation in Ni found here is puzzling. We attributed the observed effect to the specific positron trapping rate. In our study we measured the changes in the trapping rate ofthe positrons and in this way on the basis of the obtained results we determined the vacancy formation energy in Ni. By analysing the data we assumed the presence only of the monovacancies as positron traps. In fig. 3 we show the points in the temperature region 1180—1450 K which are used for determination of ~ by linear regression of the data. The obtained value is 1.6 ±0.1 eV. The value of the formation energy of vacancies determined by means of the S parameter, obtained by measurement of Doppler broadening of the annihilation gamma-line is 66
1.7±0.1eV. The results ofWycisk and Kniepmeier [8] on measurements of the resistivity recovery after quenching of Ni show that the energy for self-diffusion is equal to 2.88 eV. The simplest and most precise method for determining the migration energy of vacanciesis based on the well-known relationship between the energy for migration of vacancies, the energy for self-diffusion H~ and the energy for formation of vacancies ~ H~.~=H~ —H~~ (I .
In this way, from sufficiently accurate determination of H~ reported in the present paper and H~Yobtamed in (8), we may deduce H~,which is equal to 1.2 ±0.2 eV. This value is in good agreement with the values reported in the papers published earlier [11,121. Our results of the vacancy formation energy ~ are compared in table 1 with the results obtamed in earlier studies. From the present quenching experiments and the comparison with the results presented in the literature [1—6,81we may conclude that positrons are trapped into vacancies in Ni in the temperature region 1180—1700 K. The increase of ~ and S param-
Volume 138, number 1,2
Pcc
i -
140—
PHYSICS LETTERS A
12 June 1989
1 / ~V
urft~
[arbitrary 1300
V ~
for
~
Lynn ct
at
~
I
•
~
-
A
F 0.7578
-
VA •
x
.
For F 130_ 1250
Present
A for ~
0JiOO..
et at
•
A
A
x
A~
—
~
6.9085
-
X
-
0.750
X
A
67019
-
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•
A
work
x ix xx
0
A
A
oeoo
A ~
•
.
v
work
Present
V •
A
for FCC MattCr et at for ~
E
Spi.dskjaer
Lv A~A t~
A
for 1/V PtC Campbell et at
A V
NanaO et at
for FCC
~ A
X
-
X
.
1
6.50
A~
L
c$
-
01
I H iv
A
VA
=
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~.
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A A
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I
6.30
—
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H iv 1.55 eV Matter et at F H iv = 1.70 cv Precent work
A
I~i.~II
=1.8 ~V 9MedskJaer e~tat
I
I
I~.I I
I
I
14~I
I
TEMPERATURE
I
Ii4~SI
-
6.00
I
-
0730
-
I
K
Fig. 2. Comparison of positron experimental data in Ni obtained as a function of temperature: (~)for ~ [11; PCC [5]; (ix) for 1/W 121; (V) forPCC [4]; (A) forS, presentwork; (~)fort, present work.
(x)
for F [3];
(•)
for
Table 1 H~’.values compared with values published by other authors.
> .
~ (eV) Method References ________________________________________________________
22
Ni 21
211
1.54±0.2 1.55±0.05
positron lifetime PCC
1.68 1.73±0.1 1.73 1.8±0.1 1.58—1.63 I .6 ±0. 1 1.7±0.1
PCC DBAGL DBAGL DBAGL electric resistivity
[11 [4] [5] [6] [2] [3] [8]
positron lifetime
present work
DBAGL
presentwork
19-~____________________________ ~1•
6 •
6.5
•
I
7
7.5 TEMPERATURE
~
,
~4
~
I
1)trapping for determination offrom the vacancy formation enFig. 3. Positron rate derived the lifetime data versus I0~/ ergy in nickel. T (K
eter reflects the increase of vacancy concentration, e.g. the positron traps. The obtained values for the tamed, another energy independent method, electrivacancybyformation are close to the by values obcal resistivity measurements of quenched Ni samples. 67
Volume 138, number 1,2
PHYSICS LETTERS A
References [1] KG. Lynn, CL. Snead and J.J. Hurst. J. Phys. F 10 (1980) 1753. [2]J.L.Campbell,C.W.SchulteandJ.A. Jackman.J. Phys. F7 (1977) 1985. [3] L.C. Smedskjaer, M.J. Fluss, D.C. Legnini. M.K. Chason and R.W. Siegel, J. Phys. F 11(1981) 2221. [4] H. Matter, J. Winter and W. Triftshauser, Appl. Phys. 20 (1979) 135. [5]S. Nanao, K. Kuribayashi, S. Tanigawa and M. Doyama. J. Phys. F 7 (1977)1403.
68
12 June 1989
[6] K. Maier, G. Rein. B. Saile. P. Valenta and HE. Schaefer, in: Proc. 5th mt. Conf. on Positron annihilation. Japan (l979)p. 101. [7] M. Fluss. L.C. Smedskjaer. B Chakraborty and M K Chason.J. Phys. F 13(1983)817. [8]W. Wycisk and M Fcller-Kniepmeier. Phys Stat Sol (a) 37(1976)183. [9]A. Seeger and H. Mehrer, in: Vacancies and interstitials of metals (North-Holland, Amsterdam, 1970) p. 1. [l0]Y. Nakamura,J Phys. Soc. Japan l6 (1961) 2167. [Il] Y.V. Konobeev. V.1. Bykov and A.V. Subbotin. Phys. Stat. Sol. (a) 40 (1977) K89 [121 M.H. Yoo and JO. Stiegler. Philos. Mag. 36 (1977) 1305.