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Vacancy annealing in He and H2 irradiated Mo observed by thermal helium desorption spectrometry
journal of nuclear ~~~
Journal of Nuclear Materials 203 (1993) 189-195 North-Holland
Vacancy annealing in He and H, irradiated MO observed by thermal helium desorption sp~ctro~et~ T.R. Armstrong
I, H.A. Filius, A. van Veen and J.R. Heringa
Interfaculty Reactor Institute, De@ University of Technology, Mekelweg IS, 2629 JB De& The Netherlands Received 4 April 1993; accepted 20 April 1993
Thermal helium desorption spectrometty (THDS) provides a sensitive technique for measuring the concentration of vacancy type defects at low defect concentrations. This technique has been utilized to measure vacancy annealing curves for single crystalline Mo(l10) irradiated with 3 keV He, I keV He and 3 keV H, ions. In order to extract the vacancy migration energy Ev from the measured data, the annealing curves have been analysed by using a simple diffusion model. The value of Ey obtained is 1.23i:O.OS eV. In addition, an attempt has been made to examine the influence of hydrogen on the annealing behaviour of vacancies in MO. It appears that hydrogen does not have any measurable influence on the vacancy annealing curves. The dissociation energy of hydrogen bound to vacancies in MO is found to be less than 1.4 eV.
1. Introduction The properties of vacancies in MO have been studied by several authors employing a variety of experimental techniques both to create the initial vacancy population and to measure the resulting concentrations. For example, Schwirtlich and Schultz [l] have used electrical resistivity annealing measurements to determine the monovacancy formation energy (3.20 eV), the monovacancy formation entropy (l.Sk) and the monovacancy migration energy (1.35 eV> in single crystalline molybdenum. The vacancies were produced by quenching the sample in superfluid helium from high temperatures. More recent measurements of stage III recovery of electron irradiated molybdenum yielded a value for the migration energy of 1.30 F 0.02 eV [2]. Measurements with hyperfine techniques [3] on vacancies in molybdenum suggest an upper limit to the monovacancy migration energy of 1.35 eV. Maier et al. ]4] have also derived the monovacan~ formation energy for a range of bee metals by carrying out positron annihilation measurements. For molybdenum they found a monovacancy formation energy of 3.0 & 0.2 eV.
r Present address: N.Z. Institute of Industrial Research, P.O. Box 31-310, Lower Hatt, New Zealand. 0022-3115/93/$06.00
In this work it is shown how thermal helium desorption spectromet~ is utilized to measure the vacancy migration energy in single crystalline MO irradiated with low energy (I 3 keV) helium ions. For an overview of the technique see ref [5]. Since the THDS technique is extremely sensitive to vacancies, low defect concentrations can be used and therefore phenomena such as retrapping [6] and vacancy clustering can be neglected in determining the vacancy migration energy Ey. Moreover, Ev can be derived from the experimental data without assuming a vacancy sink strength, since all of the damage is created close to the sample surface and the surface acts as an infinite sink once the vacancies become mobile. There are however disadvantages to the THDS technique. Firstly, it is necessary to know the distribution of the vacancies produced during the initial damaging irradiation. Secondly, because the technique is destructive (i.e. the vacancy population is destroyed during the measurement), it is necessary to create a new vacancy population for each annealing step. These vacancy populations are not always identical, and therefore a certain amount of scatter occurs in the data points. Both the advantages and the disadvantages are illustrated in the next sections. Section 2 gives a brief description of the experimental technique. Section 3 describes a simple diffusion model which has been
0 1993 - Elsevier Science Publishers B.V. All rights reserved
190
T.R. Armstronget al. / Vacancy annealing in He and H, irradiated MO observed by THDS
used to extract the vacancy migration energy Ev from the experimental results. Subsection 4.1 presents the experimental results obtained from experiments in which the initial vacancy populations were created by helium irradiation, and in subsection 4.2 it is considered how sensitive the obtained value for Ev is to variations in the fitting parameters. To investigate whether the presence of hydrogen has any measurable effect on the vacancy annealing curves, and to examine whether the THDS technique can be used to determine the hydrogen-vacancy dissociation energy in molybdenum, THDS experiments have been carried out in which the molybdenum sample was irradiated with Hz ions. The results of these experiments are described in section 5.2 and discussed in section 5.3.
3. Data analysis The annealing curves obtained from the experiments have been analysed by solving the one-dimensional diffusion equation $(x,
t)
D,=DF
2. Experimental
technique
Full details of the experimental technique and the experimental apparatus have been published previously [7-91, so only a brief description of the relevant details are reported here. The apparatus consists of a UHV chamber with a sample mounted opposite an ion gun capable of producing mass and energy analysed ion beams with energies ranging from - 100 eV to - 4 keV. The ion gun can thus be used both to create defects within the sample and for filling the sample with low energy helium without producing further damage. The sample used was the same Mo(l10) sample which has been used for experiments reported previously [9,10]. In the experiments described here, the MO sample was damaged with helium ions and then annealed by heating the sample to the desired annealing temperature (the sample was heated at a controlled rate of 40 K/s by 2 keV electron bombardment on the rear face of the sample). When the desired temperature was reached, the heater was switched off and the sample was immediately allowed to cool to room temperature. Helium was then added by irradiating the sample with 150 eV He. After this, the sample was heated again and the partial pressure of the released helium was monitored with a mass spectrometer. The partial pressure spectrum was converted to a helium desorption spectrum [ll] from which the concentration of vacancies remaining in the sample was deduced. This procedure has been repeated for a series of annealing temperatures in order to obtain plots of the vacancy concentration as a function of annealing temperature.
=D,
~*c”(x, t)
(1) a.2 ’ where cv(x, t) is the depth distribution of the vacancies created during the initial irradiation and D, is the vacancy diffusion coefficient. The initial depth distribution c,(x, 0) of the vacancies created by ion irradiation has been obtained from MARLOWE calculations [12]. At both surfaces the vacancy concentration equals zero, and the boundary conditions are therefore: c,(O, t) = 0 and cv(m, t> = 0. D, can be expressed in terms of Ev through the equation at
exp(-Ey/kT),
(2)
where Dcy is the preexponential factor for vacancy migration. In order to obtain a value for Ey from the measured data, eq. (1) has been solved for different E$’ values by using Gear’s method [13]. Although mainly Ey has been adjusted to match the experimental data, it is important to note that in fact D, is measured, which involves another parameter, viz Dr (see eq. (2)). Without performing a large number of separate experiments which might allow the exact temperature dependence of D, to be determined, it is necessary to know Dt. In the present work, D,,M has been obtained from the following relationships: DF = $2v,
exp Sy/k,
(3)
DSD = iA*v,, exp(S5 + Sy)/k,
(4)
where A and Y,, denote respectively the average jump distance and the average jump frequency, Sv and SC are the entropy of vacancy migration and vacancy formation, and DSD is the preexponential factor for selfdiffusion. Combining eqs. (3) and (4) gives Dy in terms of DSD and SC, which can be found in the literature. Using a value of 0.13 X 10m4 mz s-’ for DSD [14] and a value of 1.5k for SC [1,15] gives Df=3x10P6 m* s-i. Apart from fitting Ey, the effect of vacancy clustering on the annealing curves has been examined. In order to do so, the following set of coupled equations has been solved:
ac”
-_=D
at a+, -=D at
a*c, -_
” ax2 -a*+, “2 ax*
2 K,c:, + 2K2cvL, + K,c:
- K2cv2,
T.R. hnstrorq
191
et al. / Vacancy a~al~~g in He and Hz irradiated MO obserl~d by THUS
where the subscript V refers to monovacancies and the subscript V, to divacancies. K, is the rate at which monovacancies combine to form divacancies and K, is the rate at which the divacancies dissociate [16]. Both K, and K, have been calculated by using K = rv(, es/k e-E/kr,
(7)
with .z = 1 [17], ve= lOi s-l, S-k [14,151, and the activation energy E = Ev for K, and E = Ev -I-E$*” = E$’ + 0.44 [17] for K,, where Ev is the binding energy of a vacancy in a divacancy.
k? $ l.O2 ’
0.8 -
3 !5 0.6 -
annealing molybdenum
4. The
4. I. Experimental
behaviour
of monovacancies
in
:
cn
I results
4 He
->
Mo(llO)
5
F 5
H
3-
n
z
G
F 2
2-
p
0
0.4 0.2 __________________._______
Fig. 1 shows a typical helium desorption spectrum obtained from a MO sample which has been irradiated with 3 keV helium ions. The broad peak between 300 and 650 K is due to the release of helium trapped near the sample surface. The peaks labelled E, F, G and H have been shown previously 181to represent the amount of helium released from respectively He,_,V (a complex of n helium atoms in a vacancy, with 5 in I 9), He,_,V, He,V and HeV defects. It is important to note that the release of helium from defects containing more than one helium per vacancy occurs in several steps [7]. A vacancy containing two helium atoms for 7
ii 1
500
1000
TEMPERATURE
1500 f
2000 K
Fig. 1. A typical helium desorption spectrum obtained for a Mo(llO) single crystal which had been irradiated with 9.0x 10” cme2 3 keV helium ions and subsequently 5 X lOI 150 eV He ions.
0.0 I
300 ’
400 ’
5k
sbo
0
7bo
&I
TEMPERATURE (K)
Fig. 2. Number of vacancies left after annealing versus annealing temperature. The initial vacancy distribution has been produced by 9X 10” cm-* 1 keV He irradiation. The squares represent the experimental data measured by the helium desorption technique. The solid curve has been calculated with EF = 1.23 eV. instance will release one helium atom at a temperature of 970 K (which will contribute to the peak iabelled G), while an HeV defect will remain in the sample. When the temperature is further increased, the He atom from the HeV defect will contribute to the peak labelled H. Consequently, the vacancy concentration can be derived from the helium population of the H peak. The present experiments have been performed on a MO sample which was initially irradiated with a fluence of 9 X 10” cm-’ 1 keV helium ions to create vacancies, then annealed to a certain temperature, and finally irradiated with 4 x lOI cmP2 150 eV helium to probe the remaining vacancies. In the case of saturation of the vacancies the H peak population equals the vacancy population. Fig. 2 shows the vacancy concentration as a function of the annealing temperature. The solid CUNe has been calculated using the diffusion model based on eq. (1). It can be seen in fig. 2 that the initial damaging 1 keV He irradiation produced 1.43 x 10” cm-’ vacancies (corresponding to _ 0.16 vacancies per incident he&urn ion), and that the vacancy concentration remains relatively constant for annealing temperatures below 480 IL. Above this temperature the vacancy concentration drops rapidly with increasing temperature until at _ 700 K almost ali of the vacancies have left the sample. The maximum in the anneal-
T R. Armstrong et al. / Vacancy annealing in He and H2 irradiated MO obserued by THDS
I
3ccl400
500
800
TEMPERATURE
700
floe
(K)
Fig. 3. Number of vacancies left after annealing versus annealing temperature. The initial vacancy distribution has been produced by 9X 10” cm-’ 3 keV He irradiation. The squares represent the experimental data measured by the helium desorption technique. The solid curve has been calculated with Ev = 1.23 eV.
ing rate occurs at a temperature of 560 K and the annealing step has a full width at half m~mum of 5.5 K. A very small number of vacancies remains at - 800 K because some of the vacancies trap a helium atom during the initial 1 keV irradiation. The trapped helium atom stabilizes the vacancy until it is released at - 1170 K, when it contributes to the H peak. Fig. 3 shows similar data as fig, 2 but for an initial irradiation with 3 keV instead of 1 keV helium ions. Again, the solid curve has been calculated using the diffusion model. The general features of the data are similar to the data from the 1 keV irradiation although the unannealed vacancy concentration differs ( - 0.76 vacancies per helium ion instead of - 0.16). It can be deduced from fig. 3 that in the 3 keV experiment approximately 15% of the vacancies remain at temperatures above 700 K (cf. 7% in the 1 keV experiment). These are vacancies immobilized by helium atoms. A certain fraction of the projectiles is trapped in the vacancies produced by the projectiles. 4.2. Discussion It can be observed in figs. 2 and 3 that there is good agreement between the experimental data and the
calculated curve. In the calculations, EF has been adjusted to match the experimental curves for the value of Dr derived in section 3, and the most suitable value of Ev, determined by least squares fitting, is found to be 1.23 + 0.05 eV. It has already been remarked however that the Ev value obtained depends on the value of DC? used in the calculations. To check whether the value of DF obtained from the literature yields the best fitting result, the calculations have been repeated for several other values of Df, ranging from 10-s to 10m4 m2 S -l. It turned out that the best least square fit was indeed obtained with the literature value for Qy = 3 x 10eh m2 s-t and the value for Ev of 1.23 eV. The only other variable in the data analysis is the depth distribution of the vacancies produced by the helium irradiation. To examine the sensitivity of Ey to changes in the vacancy depth distribution, annealing curves have been calculated for depth distributions with ranges differing by 33% and stragglings by 20% from those given by the MARLOWE program. It was found that this produces a variation in Ey of approximately 4%. Thus, the calculated value of Ev is not very sensitive to variations in the assumed vacancy depth distribution. In all of the present experiments the vacancy concentrations were low and the damage was created close to the sample surface. This means that the probability of a free interstitial atom annihilating a vacancy other than its own is virtually negligible (Hou et al. [ZS] have calculated the effective recombination radius for correlated vacancy-interstitial recombination to be - 1.16 nml. Vacancy annealing curves for empty vacancies have previously been measured in THDS studies on Kr and Xe in W (see ref. [16] and references cited therein) and Ar [19] and N [9,10] in MO. The width of the annealing stages derived from these curves however are much smaller than those presented here. It is believed that this is due to the trapping of the vacancies at substitutional noble-gas defects and other impurities, which prevent the vacancies from reaching the sample surface. The comparatively large widths of the recovery stage in the annealing curves presented here are taken as evidence that the sample used was relatively free from impurities during the course of the experiments. To estimate the effect of vacancy clustering on the annealing curves, calculations have been performed which were based on the eqs. (5) and (6). Dv, was chosen to be 0 to obtain maximum effect. The results showed that in the present experiments an effect of vacancy clustering was negligible: the maximum num-
193
T.R. Armstrong et al. / Vacancya~nea~~gin He and Hz irradiatedMOobserved by THDS
ber of divacancies was found to be a factor 104 lower than the number of monovacancies. This can be attributed to the small number of vacancies present in the sample. The obtained value of 1.23 * 0.05 eV for the monovacancy migration energy is in agreement with the values reported in ref. [2] and the references cited therein (see table II in ref. [2]) and is consistent with the upper bound provided by ref. 131.
1.8-
’
f
8
I
t
I
l.i?t_ 1.2 1.3 1.4 1.5
eV eV eV eV
5. The interaction between monovacancies and hydrogen in MO 5.1. Introduction 0.2 -
To investigate whether the presence of hydrogen has a measurable effect on the vacancy annealing curves, and to examine whether the THDS technique can be used to determine the hydrogen-vacancy dissociation energy in molybdenum E$!A’, experiments have been carried out on a Mo(ll0) sample irradiated with hydrogen. In section 5.2 the experimental results are described and in section 5.3 the results are discussed. It should be noted that direct thermal hydrogen desorption experiments are quite difficult to perform since hydrogen is always present as a background gas in the vacuum system. Moreover, hydrogen is chemisorbed on a Mo(ll0) surface in two states from which desorption as molecules occurs with desorption energies of 1.2 and 1.5 eV [20]. Thus, surface retrapping obscures all processes below the surface having lower activation energies. In the experiments reported here, helium was therefore used as a probe.
Fig. 4 shows a vacancy annealing curve similar to those in figs. 2 and 3 but now for an initial irradiation of 2.8 x 1013 cm-’ 3 keV H, ions instead of He ions (this dose is approximately equivalent to 5.6 X 1013 crnm2 1.5 keV protons). As before, the initial irradiation was followed by annealing and a 4 X lOi cme2 150 eV helium irradiation. The general features of the experimental data in fig. 4 are similar to those in figs. 2 and 3. The only difference is that in the hydrogen experiment all vacancies have gone at a temperature of 700 K. To study the effect of adding hydrogen to empty vacancies, the experiment of fig. 3 was repeated but with an additional hydrogen irradiation step. The vacancies, created by 9 x 10” cm-’ 3 keV He irradia-
0.0
’ 3004bo TEMPERATURE (K)
Fig. 4. Numner of vacancies left after annealing versus annealing temperature. The initial vacancy distribution has been produced by 2.8~ lOI cm -’ 3 keV H, irradiation. The squares represent the experimental data measured by the helium desorption technique. The curves have been calcutated with a reaction diffusion equation for the indicated values of Eg$ with EvM - 123 . eV.
tion, were filled with hydrogen by exposing the sample to a fluence of 2 x 10” cm-’ 0.7 keV Hz ions. An energy of 0.7 keV is sufficiently low to assure that no additional damage is created in the sample. After the 0.7 keV H, irradiation the sample was annealed and filled with low energy helium, exactly the same as in the experiment of fig. 3. The presence of additional hydrogen in the vacancies did not have a measurable effect upon the annealing curve however: no significant difference was found with fig. 3. 5.3. Discussion The fact that the influence of hydrogen is not reflected in the annealing curves implies that the exact value of Egt cannot be extracted from the measured data. Nonetheless, it is possible to make an estimate of the smallest hydrogen-vacancy dissociation energy which should have been observed in the annealing curves. In order to do so, caI~ulat~ons have been performed for different dissociation energies. In these calculations it was assumed that the vacancies were initially filled with hydrogen and the hydrogen filled
194
7X. Armstrong et al. / Vacancy annealing in He and H, irradiated MO observed by THDS
vacancies were taken immobile. The following set of equations was applied:
v = v.
exp( -EHD;“/kT),
(IO)
where the subscript HV refers to hydrogen filled vacancies. The results of some of the calculations are shown in fig. 4. Examination of the curves shows for example that a dissociation energy of 1.5 eV should have produced a delay in the recovery of - 100 K. Bearing this in mind, it can be deduced from fig. 4 that the dissociation energy of a hydrogen atom bound to a vacancy must be less than 1.4 eV. This is in agreement with experimentally and theoretically obtained dissociation energies of 1.38 and 1.31 eV, respectively, reported by Myers and Besenbacher [21] (in which a deuterium migration energy of 0.35 eV was assumed). It is also in agreement with the hydrogen dissociation energy of 1.19 eV reported by Doyle and Brice [22]. Abd El Keriem et al. 1231 found a dissociation energy of 1.42 f 0.03 eV, that may be influenced by the probing indium atom next to the vacancy in their experiments. This value agrees with our upper limit, if one takes into account the attempt frequency of 2 x lOi s-r. Zhu et a1.1241, Linderoth et al. [25] and Hansen et al. [26J have carried out positron experiments on the hydrogen-vacancy interaction in molybdenum. They observed a delay in vacancy clustering due to hydrogen of about 2.5 K and reported a maximum value of 1.7 eV for the hydrogen-vacancy dissociation energy, which is higher than our value of 1.4 eV. The value of 1.7 eV however is ascribed to hydrogen release from small clusters rather than from single vacancies. Although it may not seem especially surprising that the dissociation energy of a hydrogen atom bound to a vacancy in molybdenum is less than 1.4 eV, it is worth noting that the binding of a hydrogen atom to a very large vacancy cluster is higher in MO than in most other metals, and that it is higher than the value of Ey measured here. If the surface of a large cluster is considered simply as a free surface, then the energy Edcs required to release the hydrogen atom can be calculated from &es = Eads + &,, + Ei% (11) where Ed_ is the energy required to release the H atom, E,, is the energy of adsorption to the surface,
and E,, and Eg are the energies of solution and migration for a hydrogen atom in MO, respectively. Values of Eads, E,, and EC: have been reported by Toyoshima and Somorjai [27] and EsO, and Eg by Tanabe et al. [28], and thus it can be caiculated that the dissociation energy of a hydrogen atom bound to a very large vacancy cluster is in the order of 0.8 + 0.4 + 0.2 = 1.4 eV. Of the more common metals, only W has a higher binding energy. This makes it possible to observe the dissociation of hydrogen from large defects in tungsten unobstructed by retrapping at the surface. Examples of hydrogen desorption experiments on tungsten are given in refs. [29,30].
6. Conclusions The THDS method has been shown to be useful in measuring vacancy migration energies. Since the technique is mainly sensitive to vacancies THDS can easily identify vacancy migration, and activation energies can be determined using less assumptions than in, for example, resistivity annealing experiments. In the present work, the vacancy migration energy Ey in MO has been found to be 1.23 f 0.05 eV. This value could be derived assuming only the surface is a sink for mobile vacancies. The only quantities required in the analysis which could not be measured, were the parameters characterising the initial depth distribution of the vacancies, but the obtained result proved to be relatively insensitive to variations in this parameter. The results of an attempt to measure the dissociation energy of a hydrogen atom to a vacancy showed that this dissociation energy is less than 1.4 eV.
References [I] LA. Schwi~iich and Ft. Schultz, Philos. Mag. A42 (1980)
121~‘~amakaw~ II. Kugier and H. Schultz, Radiat. Eff. 105 (1988) 171: [3] A. Weidinger, R. Wessner, E. Recknagel and Th. Wichert, Nucl. Instr. and Meth. 182-183 (1981) 509. [4] K. Maier, M. Peo, B. Saile, H.E. Schaefer and A. Seeger, Philos. Mag. A40 (1979) 701. [51 A. van Veen, Proc. NATO Advanced Research Workshop on Fundamental Aspects of Inert Gas Behaviour in Solids, Bonas, France (Plenum, New York, 1991) p. 41. [6] W.Th.M. Buters and A. van den Beukel, J. Nucl. Mater. 137 (1985) 51. 171 E.V. Komelsen, Radiat. Eff. 13 (1972) 227.
T. R. Armstrong et ai. / Vacancy annealing in He and Hz irradiated MO observed by THDS [S] A. van Veen and L.M. Caspers, Proc. Consultants
Symp. on Inert Gases in Metals, AERE Report 9733 (1980) p. 517. [9] A. van Veen and L.M. Caspers, Solid State Commun. 30 (1979) 761. [lo] H.A. Filius and A. van Veen, J. Nucl. Mater. 144 (1987) 1. [ll] A. van Veen, A.A. van Gorkum, L.M. Caspers, J. Nihoul, L. Stab and J. Cornelis, Phys. Status Soiidi A32 (1975) K123. [12] M.T. Robinson and I. Torrens, Phys. Rev. B9 (1974) 5008. [13] P.M. Dew and J.E. Walsh, ACM Trans. Math. Softw. 7 (1981) 295. [14] K. Maier, H. Mehrer and G. Rein, Z. Metallk. 70 (1979) 271. [15] A. Seeger and H. Mehrer, Proc. Int. Conf. on Vacancies and Interstitials in Metals, eds. A. Seeger, D. Schumacher, W. Schilling and J. Diehl (North-Holland, Amsterdam, 19691 p. 1. [16] A. van Veen, Mater. Sci. Forum 15-18 (19871 3. [17] R.H.J. Fastenau, A. van Veen, P. Penning and L.M. Caspers, Phys. Status Solidi A47 (19781577. fl8] M. Hou, A. van Veen, L.M. Caspers and M.R. Ypma, Nucl. Instr. and Meth. 209/210 (1983) 19. [19] A. van Veen, W.Th.M. Buters, G.J. van der Kolk, L.M.
19.5
Caspers and T.R. Armstrong, Nucl. Instr. and Meth. 194 (1982) 485. 1201 M. Mahning and L.D. Schmidt, Z. Phys. Chem. N.F. 80 (1971171. [21] SM. Myers and F. Besenbacher, J. Appl. Phys. 60 (1986) 3499. [22] B.L. Doyle and D.K. Brice, J. Nucl. Mater. 122 & 123 (19841 1523. [23] MS. Abd El Keriem, D.P. van der Werf and F. Pleiter, J. Phys. Cond. Matter. 5 (1993) 1801. [24] Z. Zhu, X. Chen, J. Chen, R. Xu and Z. Wang, Nucl. Instr. and Meth. B61 (1991) 72. 1251 S. Linderoth, H. Rajainmaki, B. Nielsen, H.E. Hansen, R.M. Nieminen and K. Petersen, Mater. Sci. Forum 1.5-18 (1987) 751. [26] H.E. Hansen, R. Talja, H. Rajainm~ki, H.K. Nielsen, B. Nielsen and R.M. Nieminen, Appl. Phys. A36 (19851 81. [27] I. Toyoshima and G.A. Somorjai, Catal. Rev. Sci. Eng. 19 (1979) 105. 1281T. Tanabe, Y. Yamanishi and S. fmoto, J. Nuct. Mater. 191-194 (1992) 439. [29] H. Ele-;eld and A. van Veen, J. Nucl. Mater. 191-194 (1992) 433. [30] H. Eleveld, A.T. Dijksman and A. van Veen, Proc. 16th Symp. on Fusion Technology, SOFT-16, London, 1990, p. 376.
Journal of Nuclear Materials 203 (1993) 189-195 North-Holland
Vacancy annealing in He and H, irradiated MO observed by thermal helium desorption sp~ctro~et~ T.R. Armstrong
I, H.A. Filius, A. van Veen and J.R. Heringa
Interfaculty Reactor Institute, De@ University of Technology, Mekelweg IS, 2629 JB De& The Netherlands Received 4 April 1993; accepted 20 April 1993
Thermal helium desorption spectrometty (THDS) provides a sensitive technique for measuring the concentration of vacancy type defects at low defect concentrations. This technique has been utilized to measure vacancy annealing curves for single crystalline Mo(l10) irradiated with 3 keV He, I keV He and 3 keV H, ions. In order to extract the vacancy migration energy Ev from the measured data, the annealing curves have been analysed by using a simple diffusion model. The value of Ey obtained is 1.23i:O.OS eV. In addition, an attempt has been made to examine the influence of hydrogen on the annealing behaviour of vacancies in MO. It appears that hydrogen does not have any measurable influence on the vacancy annealing curves. The dissociation energy of hydrogen bound to vacancies in MO is found to be less than 1.4 eV.
1. Introduction The properties of vacancies in MO have been studied by several authors employing a variety of experimental techniques both to create the initial vacancy population and to measure the resulting concentrations. For example, Schwirtlich and Schultz [l] have used electrical resistivity annealing measurements to determine the monovacancy formation energy (3.20 eV), the monovacancy formation entropy (l.Sk) and the monovacancy migration energy (1.35 eV> in single crystalline molybdenum. The vacancies were produced by quenching the sample in superfluid helium from high temperatures. More recent measurements of stage III recovery of electron irradiated molybdenum yielded a value for the migration energy of 1.30 F 0.02 eV [2]. Measurements with hyperfine techniques [3] on vacancies in molybdenum suggest an upper limit to the monovacancy migration energy of 1.35 eV. Maier et al. ]4] have also derived the monovacan~ formation energy for a range of bee metals by carrying out positron annihilation measurements. For molybdenum they found a monovacancy formation energy of 3.0 & 0.2 eV.
r Present address: N.Z. Institute of Industrial Research, P.O. Box 31-310, Lower Hatt, New Zealand. 0022-3115/93/$06.00
In this work it is shown how thermal helium desorption spectromet~ is utilized to measure the vacancy migration energy in single crystalline MO irradiated with low energy (I 3 keV) helium ions. For an overview of the technique see ref [5]. Since the THDS technique is extremely sensitive to vacancies, low defect concentrations can be used and therefore phenomena such as retrapping [6] and vacancy clustering can be neglected in determining the vacancy migration energy Ey. Moreover, Ev can be derived from the experimental data without assuming a vacancy sink strength, since all of the damage is created close to the sample surface and the surface acts as an infinite sink once the vacancies become mobile. There are however disadvantages to the THDS technique. Firstly, it is necessary to know the distribution of the vacancies produced during the initial damaging irradiation. Secondly, because the technique is destructive (i.e. the vacancy population is destroyed during the measurement), it is necessary to create a new vacancy population for each annealing step. These vacancy populations are not always identical, and therefore a certain amount of scatter occurs in the data points. Both the advantages and the disadvantages are illustrated in the next sections. Section 2 gives a brief description of the experimental technique. Section 3 describes a simple diffusion model which has been
0 1993 - Elsevier Science Publishers B.V. All rights reserved
190
T.R. Armstronget al. / Vacancy annealing in He and H, irradiated MO observed by THDS
used to extract the vacancy migration energy Ev from the experimental results. Subsection 4.1 presents the experimental results obtained from experiments in which the initial vacancy populations were created by helium irradiation, and in subsection 4.2 it is considered how sensitive the obtained value for Ev is to variations in the fitting parameters. To investigate whether the presence of hydrogen has any measurable effect on the vacancy annealing curves, and to examine whether the THDS technique can be used to determine the hydrogen-vacancy dissociation energy in molybdenum, THDS experiments have been carried out in which the molybdenum sample was irradiated with Hz ions. The results of these experiments are described in section 5.2 and discussed in section 5.3.
3. Data analysis The annealing curves obtained from the experiments have been analysed by solving the one-dimensional diffusion equation $(x,
t)
D,=DF
2. Experimental
technique
Full details of the experimental technique and the experimental apparatus have been published previously [7-91, so only a brief description of the relevant details are reported here. The apparatus consists of a UHV chamber with a sample mounted opposite an ion gun capable of producing mass and energy analysed ion beams with energies ranging from - 100 eV to - 4 keV. The ion gun can thus be used both to create defects within the sample and for filling the sample with low energy helium without producing further damage. The sample used was the same Mo(l10) sample which has been used for experiments reported previously [9,10]. In the experiments described here, the MO sample was damaged with helium ions and then annealed by heating the sample to the desired annealing temperature (the sample was heated at a controlled rate of 40 K/s by 2 keV electron bombardment on the rear face of the sample). When the desired temperature was reached, the heater was switched off and the sample was immediately allowed to cool to room temperature. Helium was then added by irradiating the sample with 150 eV He. After this, the sample was heated again and the partial pressure of the released helium was monitored with a mass spectrometer. The partial pressure spectrum was converted to a helium desorption spectrum [ll] from which the concentration of vacancies remaining in the sample was deduced. This procedure has been repeated for a series of annealing temperatures in order to obtain plots of the vacancy concentration as a function of annealing temperature.
=D,
~*c”(x, t)
(1) a.2 ’ where cv(x, t) is the depth distribution of the vacancies created during the initial irradiation and D, is the vacancy diffusion coefficient. The initial depth distribution c,(x, 0) of the vacancies created by ion irradiation has been obtained from MARLOWE calculations [12]. At both surfaces the vacancy concentration equals zero, and the boundary conditions are therefore: c,(O, t) = 0 and cv(m, t> = 0. D, can be expressed in terms of Ev through the equation at
exp(-Ey/kT),
(2)
where Dcy is the preexponential factor for vacancy migration. In order to obtain a value for Ey from the measured data, eq. (1) has been solved for different E$’ values by using Gear’s method [13]. Although mainly Ey has been adjusted to match the experimental data, it is important to note that in fact D, is measured, which involves another parameter, viz Dr (see eq. (2)). Without performing a large number of separate experiments which might allow the exact temperature dependence of D, to be determined, it is necessary to know Dt. In the present work, D,,M has been obtained from the following relationships: DF = $2v,
exp Sy/k,
(3)
DSD = iA*v,, exp(S5 + Sy)/k,
(4)
where A and Y,, denote respectively the average jump distance and the average jump frequency, Sv and SC are the entropy of vacancy migration and vacancy formation, and DSD is the preexponential factor for selfdiffusion. Combining eqs. (3) and (4) gives Dy in terms of DSD and SC, which can be found in the literature. Using a value of 0.13 X 10m4 mz s-’ for DSD [14] and a value of 1.5k for SC [1,15] gives Df=3x10P6 m* s-i. Apart from fitting Ey, the effect of vacancy clustering on the annealing curves has been examined. In order to do so, the following set of coupled equations has been solved:
ac”
-_=D
at a+, -=D at
a*c, -_
” ax2 -a*+, “2 ax*
2 K,c:, + 2K2cvL, + K,c:
- K2cv2,
T.R. hnstrorq
191
et al. / Vacancy a~al~~g in He and Hz irradiated MO obserl~d by THUS
where the subscript V refers to monovacancies and the subscript V, to divacancies. K, is the rate at which monovacancies combine to form divacancies and K, is the rate at which the divacancies dissociate [16]. Both K, and K, have been calculated by using K = rv(, es/k e-E/kr,
(7)
with .z = 1 [17], ve= lOi s-l, S-k [14,151, and the activation energy E = Ev for K, and E = Ev -I-E$*” = E$’ + 0.44 [17] for K,, where Ev is the binding energy of a vacancy in a divacancy.
k? $ l.O2 ’
0.8 -
3 !5 0.6 -
annealing molybdenum
4. The
4. I. Experimental
behaviour
of monovacancies
in
:
cn
I results
4 He
->
Mo(llO)
5
F 5
H
3-
n
z
G
F 2
2-
p
0
0.4 0.2 __________________._______
Fig. 1 shows a typical helium desorption spectrum obtained from a MO sample which has been irradiated with 3 keV helium ions. The broad peak between 300 and 650 K is due to the release of helium trapped near the sample surface. The peaks labelled E, F, G and H have been shown previously 181to represent the amount of helium released from respectively He,_,V (a complex of n helium atoms in a vacancy, with 5 in I 9), He,_,V, He,V and HeV defects. It is important to note that the release of helium from defects containing more than one helium per vacancy occurs in several steps [7]. A vacancy containing two helium atoms for 7
ii 1
500
1000
TEMPERATURE
1500 f
2000 K
Fig. 1. A typical helium desorption spectrum obtained for a Mo(llO) single crystal which had been irradiated with 9.0x 10” cme2 3 keV helium ions and subsequently 5 X lOI 150 eV He ions.
0.0 I
300 ’
400 ’
5k
sbo
0
7bo
&I
TEMPERATURE (K)
Fig. 2. Number of vacancies left after annealing versus annealing temperature. The initial vacancy distribution has been produced by 9X 10” cm-* 1 keV He irradiation. The squares represent the experimental data measured by the helium desorption technique. The solid curve has been calculated with EF = 1.23 eV. instance will release one helium atom at a temperature of 970 K (which will contribute to the peak iabelled G), while an HeV defect will remain in the sample. When the temperature is further increased, the He atom from the HeV defect will contribute to the peak labelled H. Consequently, the vacancy concentration can be derived from the helium population of the H peak. The present experiments have been performed on a MO sample which was initially irradiated with a fluence of 9 X 10” cm-’ 1 keV helium ions to create vacancies, then annealed to a certain temperature, and finally irradiated with 4 x lOI cmP2 150 eV helium to probe the remaining vacancies. In the case of saturation of the vacancies the H peak population equals the vacancy population. Fig. 2 shows the vacancy concentration as a function of the annealing temperature. The solid CUNe has been calculated using the diffusion model based on eq. (1). It can be seen in fig. 2 that the initial damaging 1 keV He irradiation produced 1.43 x 10” cm-’ vacancies (corresponding to _ 0.16 vacancies per incident he&urn ion), and that the vacancy concentration remains relatively constant for annealing temperatures below 480 IL. Above this temperature the vacancy concentration drops rapidly with increasing temperature until at _ 700 K almost ali of the vacancies have left the sample. The maximum in the anneal-
T R. Armstrong et al. / Vacancy annealing in He and H2 irradiated MO obserued by THDS
I
3ccl400
500
800
TEMPERATURE
700
floe
(K)
Fig. 3. Number of vacancies left after annealing versus annealing temperature. The initial vacancy distribution has been produced by 9X 10” cm-’ 3 keV He irradiation. The squares represent the experimental data measured by the helium desorption technique. The solid curve has been calculated with Ev = 1.23 eV.
ing rate occurs at a temperature of 560 K and the annealing step has a full width at half m~mum of 5.5 K. A very small number of vacancies remains at - 800 K because some of the vacancies trap a helium atom during the initial 1 keV irradiation. The trapped helium atom stabilizes the vacancy until it is released at - 1170 K, when it contributes to the H peak. Fig. 3 shows similar data as fig, 2 but for an initial irradiation with 3 keV instead of 1 keV helium ions. Again, the solid curve has been calculated using the diffusion model. The general features of the data are similar to the data from the 1 keV irradiation although the unannealed vacancy concentration differs ( - 0.76 vacancies per helium ion instead of - 0.16). It can be deduced from fig. 3 that in the 3 keV experiment approximately 15% of the vacancies remain at temperatures above 700 K (cf. 7% in the 1 keV experiment). These are vacancies immobilized by helium atoms. A certain fraction of the projectiles is trapped in the vacancies produced by the projectiles. 4.2. Discussion It can be observed in figs. 2 and 3 that there is good agreement between the experimental data and the
calculated curve. In the calculations, EF has been adjusted to match the experimental curves for the value of Dr derived in section 3, and the most suitable value of Ev, determined by least squares fitting, is found to be 1.23 + 0.05 eV. It has already been remarked however that the Ev value obtained depends on the value of DC? used in the calculations. To check whether the value of DF obtained from the literature yields the best fitting result, the calculations have been repeated for several other values of Df, ranging from 10-s to 10m4 m2 S -l. It turned out that the best least square fit was indeed obtained with the literature value for Qy = 3 x 10eh m2 s-t and the value for Ev of 1.23 eV. The only other variable in the data analysis is the depth distribution of the vacancies produced by the helium irradiation. To examine the sensitivity of Ey to changes in the vacancy depth distribution, annealing curves have been calculated for depth distributions with ranges differing by 33% and stragglings by 20% from those given by the MARLOWE program. It was found that this produces a variation in Ey of approximately 4%. Thus, the calculated value of Ev is not very sensitive to variations in the assumed vacancy depth distribution. In all of the present experiments the vacancy concentrations were low and the damage was created close to the sample surface. This means that the probability of a free interstitial atom annihilating a vacancy other than its own is virtually negligible (Hou et al. [ZS] have calculated the effective recombination radius for correlated vacancy-interstitial recombination to be - 1.16 nml. Vacancy annealing curves for empty vacancies have previously been measured in THDS studies on Kr and Xe in W (see ref. [16] and references cited therein) and Ar [19] and N [9,10] in MO. The width of the annealing stages derived from these curves however are much smaller than those presented here. It is believed that this is due to the trapping of the vacancies at substitutional noble-gas defects and other impurities, which prevent the vacancies from reaching the sample surface. The comparatively large widths of the recovery stage in the annealing curves presented here are taken as evidence that the sample used was relatively free from impurities during the course of the experiments. To estimate the effect of vacancy clustering on the annealing curves, calculations have been performed which were based on the eqs. (5) and (6). Dv, was chosen to be 0 to obtain maximum effect. The results showed that in the present experiments an effect of vacancy clustering was negligible: the maximum num-
193
T.R. Armstrong et al. / Vacancya~nea~~gin He and Hz irradiatedMOobserved by THDS
ber of divacancies was found to be a factor 104 lower than the number of monovacancies. This can be attributed to the small number of vacancies present in the sample. The obtained value of 1.23 * 0.05 eV for the monovacancy migration energy is in agreement with the values reported in ref. [2] and the references cited therein (see table II in ref. [2]) and is consistent with the upper bound provided by ref. 131.
1.8-
’
f
8
I
t
I
l.i?t_ 1.2 1.3 1.4 1.5
eV eV eV eV
5. The interaction between monovacancies and hydrogen in MO 5.1. Introduction 0.2 -
To investigate whether the presence of hydrogen has a measurable effect on the vacancy annealing curves, and to examine whether the THDS technique can be used to determine the hydrogen-vacancy dissociation energy in molybdenum E$!A’, experiments have been carried out on a Mo(ll0) sample irradiated with hydrogen. In section 5.2 the experimental results are described and in section 5.3 the results are discussed. It should be noted that direct thermal hydrogen desorption experiments are quite difficult to perform since hydrogen is always present as a background gas in the vacuum system. Moreover, hydrogen is chemisorbed on a Mo(ll0) surface in two states from which desorption as molecules occurs with desorption energies of 1.2 and 1.5 eV [20]. Thus, surface retrapping obscures all processes below the surface having lower activation energies. In the experiments reported here, helium was therefore used as a probe.
Fig. 4 shows a vacancy annealing curve similar to those in figs. 2 and 3 but now for an initial irradiation of 2.8 x 1013 cm-’ 3 keV H, ions instead of He ions (this dose is approximately equivalent to 5.6 X 1013 crnm2 1.5 keV protons). As before, the initial irradiation was followed by annealing and a 4 X lOi cme2 150 eV helium irradiation. The general features of the experimental data in fig. 4 are similar to those in figs. 2 and 3. The only difference is that in the hydrogen experiment all vacancies have gone at a temperature of 700 K. To study the effect of adding hydrogen to empty vacancies, the experiment of fig. 3 was repeated but with an additional hydrogen irradiation step. The vacancies, created by 9 x 10” cm-’ 3 keV He irradia-
0.0
’ 3004bo TEMPERATURE (K)
Fig. 4. Numner of vacancies left after annealing versus annealing temperature. The initial vacancy distribution has been produced by 2.8~ lOI cm -’ 3 keV H, irradiation. The squares represent the experimental data measured by the helium desorption technique. The curves have been calcutated with a reaction diffusion equation for the indicated values of Eg$ with EvM - 123 . eV.
tion, were filled with hydrogen by exposing the sample to a fluence of 2 x 10” cm-’ 0.7 keV Hz ions. An energy of 0.7 keV is sufficiently low to assure that no additional damage is created in the sample. After the 0.7 keV H, irradiation the sample was annealed and filled with low energy helium, exactly the same as in the experiment of fig. 3. The presence of additional hydrogen in the vacancies did not have a measurable effect upon the annealing curve however: no significant difference was found with fig. 3. 5.3. Discussion The fact that the influence of hydrogen is not reflected in the annealing curves implies that the exact value of Egt cannot be extracted from the measured data. Nonetheless, it is possible to make an estimate of the smallest hydrogen-vacancy dissociation energy which should have been observed in the annealing curves. In order to do so, caI~ulat~ons have been performed for different dissociation energies. In these calculations it was assumed that the vacancies were initially filled with hydrogen and the hydrogen filled
194
7X. Armstrong et al. / Vacancy annealing in He and H, irradiated MO observed by THDS
vacancies were taken immobile. The following set of equations was applied:
v = v.
exp( -EHD;“/kT),
(IO)
where the subscript HV refers to hydrogen filled vacancies. The results of some of the calculations are shown in fig. 4. Examination of the curves shows for example that a dissociation energy of 1.5 eV should have produced a delay in the recovery of - 100 K. Bearing this in mind, it can be deduced from fig. 4 that the dissociation energy of a hydrogen atom bound to a vacancy must be less than 1.4 eV. This is in agreement with experimentally and theoretically obtained dissociation energies of 1.38 and 1.31 eV, respectively, reported by Myers and Besenbacher [21] (in which a deuterium migration energy of 0.35 eV was assumed). It is also in agreement with the hydrogen dissociation energy of 1.19 eV reported by Doyle and Brice [22]. Abd El Keriem et al. 1231 found a dissociation energy of 1.42 f 0.03 eV, that may be influenced by the probing indium atom next to the vacancy in their experiments. This value agrees with our upper limit, if one takes into account the attempt frequency of 2 x lOi s-r. Zhu et a1.1241, Linderoth et al. [25] and Hansen et al. [26J have carried out positron experiments on the hydrogen-vacancy interaction in molybdenum. They observed a delay in vacancy clustering due to hydrogen of about 2.5 K and reported a maximum value of 1.7 eV for the hydrogen-vacancy dissociation energy, which is higher than our value of 1.4 eV. The value of 1.7 eV however is ascribed to hydrogen release from small clusters rather than from single vacancies. Although it may not seem especially surprising that the dissociation energy of a hydrogen atom bound to a vacancy in molybdenum is less than 1.4 eV, it is worth noting that the binding of a hydrogen atom to a very large vacancy cluster is higher in MO than in most other metals, and that it is higher than the value of Ey measured here. If the surface of a large cluster is considered simply as a free surface, then the energy Edcs required to release the hydrogen atom can be calculated from &es = Eads + &,, + Ei% (11) where Ed_ is the energy required to release the H atom, E,, is the energy of adsorption to the surface,
and E,, and Eg are the energies of solution and migration for a hydrogen atom in MO, respectively. Values of Eads, E,, and EC: have been reported by Toyoshima and Somorjai [27] and EsO, and Eg by Tanabe et al. [28], and thus it can be caiculated that the dissociation energy of a hydrogen atom bound to a very large vacancy cluster is in the order of 0.8 + 0.4 + 0.2 = 1.4 eV. Of the more common metals, only W has a higher binding energy. This makes it possible to observe the dissociation of hydrogen from large defects in tungsten unobstructed by retrapping at the surface. Examples of hydrogen desorption experiments on tungsten are given in refs. [29,30].
6. Conclusions The THDS method has been shown to be useful in measuring vacancy migration energies. Since the technique is mainly sensitive to vacancies THDS can easily identify vacancy migration, and activation energies can be determined using less assumptions than in, for example, resistivity annealing experiments. In the present work, the vacancy migration energy Ey in MO has been found to be 1.23 f 0.05 eV. This value could be derived assuming only the surface is a sink for mobile vacancies. The only quantities required in the analysis which could not be measured, were the parameters characterising the initial depth distribution of the vacancies, but the obtained result proved to be relatively insensitive to variations in this parameter. The results of an attempt to measure the dissociation energy of a hydrogen atom to a vacancy showed that this dissociation energy is less than 1.4 eV.
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121~‘~amakaw~ II. Kugier and H. Schultz, Radiat. Eff. 105 (1988) 171: [3] A. Weidinger, R. Wessner, E. Recknagel and Th. Wichert, Nucl. Instr. and Meth. 182-183 (1981) 509. [4] K. Maier, M. Peo, B. Saile, H.E. Schaefer and A. Seeger, Philos. Mag. A40 (1979) 701. [51 A. van Veen, Proc. NATO Advanced Research Workshop on Fundamental Aspects of Inert Gas Behaviour in Solids, Bonas, France (Plenum, New York, 1991) p. 41. [6] W.Th.M. Buters and A. van den Beukel, J. Nucl. Mater. 137 (1985) 51. 171 E.V. Komelsen, Radiat. Eff. 13 (1972) 227.
T. R. Armstrong et ai. / Vacancy annealing in He and Hz irradiated MO observed by THDS [S] A. van Veen and L.M. Caspers, Proc. Consultants
Symp. on Inert Gases in Metals, AERE Report 9733 (1980) p. 517. [9] A. van Veen and L.M. Caspers, Solid State Commun. 30 (1979) 761. [lo] H.A. Filius and A. van Veen, J. Nucl. Mater. 144 (1987) 1. [ll] A. van Veen, A.A. van Gorkum, L.M. Caspers, J. Nihoul, L. Stab and J. Cornelis, Phys. Status Soiidi A32 (1975) K123. [12] M.T. Robinson and I. Torrens, Phys. Rev. B9 (1974) 5008. [13] P.M. Dew and J.E. Walsh, ACM Trans. Math. Softw. 7 (1981) 295. [14] K. Maier, H. Mehrer and G. Rein, Z. Metallk. 70 (1979) 271. [15] A. Seeger and H. Mehrer, Proc. Int. Conf. on Vacancies and Interstitials in Metals, eds. A. Seeger, D. Schumacher, W. Schilling and J. Diehl (North-Holland, Amsterdam, 19691 p. 1. [16] A. van Veen, Mater. Sci. Forum 15-18 (19871 3. [17] R.H.J. Fastenau, A. van Veen, P. Penning and L.M. Caspers, Phys. Status Solidi A47 (19781577. fl8] M. Hou, A. van Veen, L.M. Caspers and M.R. Ypma, Nucl. Instr. and Meth. 209/210 (1983) 19. [19] A. van Veen, W.Th.M. Buters, G.J. van der Kolk, L.M.
19.5
Caspers and T.R. Armstrong, Nucl. Instr. and Meth. 194 (1982) 485. 1201 M. Mahning and L.D. Schmidt, Z. Phys. Chem. N.F. 80 (1971171. [21] SM. Myers and F. Besenbacher, J. Appl. Phys. 60 (1986) 3499. [22] B.L. Doyle and D.K. Brice, J. Nucl. Mater. 122 & 123 (19841 1523. [23] MS. Abd El Keriem, D.P. van der Werf and F. Pleiter, J. Phys. Cond. Matter. 5 (1993) 1801. [24] Z. Zhu, X. Chen, J. Chen, R. Xu and Z. Wang, Nucl. Instr. and Meth. B61 (1991) 72. 1251 S. Linderoth, H. Rajainmaki, B. Nielsen, H.E. Hansen, R.M. Nieminen and K. Petersen, Mater. Sci. Forum 1.5-18 (1987) 751. [26] H.E. Hansen, R. Talja, H. Rajainm~ki, H.K. Nielsen, B. Nielsen and R.M. Nieminen, Appl. Phys. A36 (19851 81. [27] I. Toyoshima and G.A. Somorjai, Catal. Rev. Sci. Eng. 19 (1979) 105. 1281T. Tanabe, Y. Yamanishi and S. fmoto, J. Nuct. Mater. 191-194 (1992) 439. [29] H. Ele-;eld and A. van Veen, J. Nucl. Mater. 191-194 (1992) 433. [30] H. Eleveld, A.T. Dijksman and A. van Veen, Proc. 16th Symp. on Fusion Technology, SOFT-16, London, 1990, p. 376.