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Deuterium-defect trapping in ion-irradiated zirconium
152
Journal
of Nuclear
Materials 125 (1984) 152-159 North-Holland, Amsterdam
DEUTERIUM-DEFECT TRAPPING IN ION-IRRADIATED ZIRCONIUM * M.B. LEWIS Metals and Ceramics Division, Oak Ridge National Laborarmy, Received
1 November
1983; accepted
16 February
Oak Ridge, TN 37831, USA
1984
Trapping of ion-implanted deuterium by lattice defects in zirconium has been investigated. The lattice defects were generated by 4 MeV Zr+ (self ion) irradiation of pure zirconium metal at 750 K. Following 100 keV deuterium implantation of the predamaged zirconium, concentration versus depth profiles were measured by a method of nuclear microanalysis. The specimens were aged at a variety of temperatures and further profiles were measured. The measured migration of the deuterium was analyzed by solving a system of differential equations involving a diffusion and reversible trapping term. The results indicate that most of the deuterium is retained in traps with binding enthalpy approximately (0.28 f 0.06) eV below that for normal equilibrium sites. Evidence also suggests some defect trapping at other binding enthalpies. The solubility of deuterium in zirconium at T=473 K was also measured on a specimen exposed to deuterium gas; the value obtained by nuclear microanalysis was determined to be (OSOrfrO.10) at%.
1. Introduction Interest
in the
behavior
of hydrogen
in metals
has
been increasing over the past few years due to the technological need for such information and the rise of new techniques to study it. In particular, for nuclear pressurized water reactors, there exists the problem of excessive hydrogen absorption in zirconium alloys found in fuel cladding, heat shields and various support structures. Zirconium alloys are important because of their low neutron activation cross section and good mechanical and co~osion-resist~t properties in high temperature water. The presence of excessive hydrogen, however, limits the usefulness of zirconium alloys by causing ebrittlement. Recently, measurements of the concentration of hydrogen present in a zircaloy corrosion film produced by water have been made by a nuclear microanalysis technique [l]. Concentrations as high as 4.5 at% were measured near the surface of the corrosion film. However, these measurements were carried out in the absence of radiation and with materials which had not been previously irradiated. It is clearly important to study the
* Research sponsored by the Division of Materials Sciences, US. Department of Energy under contract W-7405-eng-26 with the Union Carbide Corporation.
0022-3115/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
migration of hydrogen in irradiated zirconium. Such studies will assist the design of zirconium alloys with desired corrosion resistant properties for reactors. In this work we have utilized ion beam techniques for the irradiation of zirconium, the implantation of hydrogen into zirconium and the measurement of the mobility of the hydrogen in the irradiated metal.
2. Experimental procedure Disks of 5 mm diameter and 0.5 mm thickness were punched from cold-rolled iodide zirconium sheet. They were annealed by heating for 30 min at 900 K at a pressure of about 1O-5 Pa. The specimens were mechanically polished with 0.1 pm diamond paste. Approximately 1 pm of surface was then removed by electropolishing (87% methyl alcohol, 12.7% H,SO,, 0.3% HF) at a temperature of 243 K. The prepared specimens were mounted in an ultrahigh vacuum target chamber. The chamber was cryopumped to 10m6 Pa. The specimens were then heated by contact with a back plate which was heated by an electron gun. Further details of the target chamber can be found in ref. [Z]. After the targets were heated to a temperature of 750 K, they were irradiated with a beam of 4 MeV Zr+ ions in order to create a specific depth profile of high density defects discussed in the following B.V.
M. B. Lewis / Deuterium - defect trapping in ion -irradiated zirconium section. The Zr+ ion flux was maintained at 5 X 10” ions/cm2 s for lo4 s. Following the irradiation, the targets were immediately allowed to cool. Individual specimens were transferred to a scattering chamber for deuterium implantation and analysis. Deuterium was implanted at room temperature or 253 K at an energy of 100 keV. In addition an unirradiated specimen was implanted with 60 keV deuterium. In both cases the beams impinged at an angle of 45” to the surface normal and were collimated to dimensions of 1 mm X 2 mm by an aperture which was much smaller than the beam diameter. This technique ensured a uniform beam intensity over the surface of implantation. The 60 keV implantation was carried out at a flux of 7 X 1013 ions/cm2 s. The 100 keV implantation was made at a lower flux of 7 X lOI ions/cm2 s. In both cases the total fluence was 7 X 1016 ions/cm2. In addition to injecting deuterium into zirconium by ion implantation, one sample (not irradiated) was annealed at 473 K at 10s Pa of deuterium gas for a period of about 20 h in order to examine hydrides of zirconium near the specimen surface. In another experiment the electropolishing step mentioned above in the sample preparation was carried out using D,SO, (in place of H2S04) in order to measure (as described below) possible hydrogen pickup from the electropolishing solution. All samples were aged at various temperatures. Following each aging step a depth versus concentration profile was made to determine the migration of the deuterium in the Zr-irradiated region of the specimens. The profiles were measured by a technique of nuclear microanalysis utilizing the D(d, p)T reaction. A beam of 0.5 MeV deuterium was steered onto the target at 45’ from the surface normal and made to overlap the previously implanted region. The collimation of the 0.5 MeV beam was the same as that for the lower energy implanted beam. A second insulated (antiscattering) collimator of slightly larger size was positioned down stream from the defining collimator and negatively charged to repel stray electrons from striking the target. A positive bias was applied to the target so that secondary electrons created by the ion beam stopping in the target could not escape the target surface. This ensured that the integrated electrical current on the target was true beam current which was used as the primary method to normalize the data. A surface barrier detector was used to measure the energy of the D(d, p)T reaction products. A Mylar widow was placed in front of the detector to suppress low energy particles from striking the detector and causing pulse pile up. A small hole in the Mylar allowed enough elastically scattered deuterons from the target to be measured as a secondary method of normal-
153
izing the data. This method was useful when the target was cooled since in this case the target could not be electrically insulated. As an energy calibration check for the D(d, p)T reaction data, a standard spectrum using a deuterated polyethylene target was taken. Further details of the scattering chamber and electronics can be found in ref. (31. Data obtained by nuclear microanalysis consists of energy dispersive spectra of the proton yield from the D(d, p)T reaction. These spectra are normalized by dividing the proton yield by the integrated current. The normalized spectra must be converted into concentration versus depth profiles of the deuterium. This has been carried out by calculating convolution integrals of the type Y( E)/AE
= C/Pipa,P, s
dS.
(1)
In this equation the subscripts i and r refer, respectively, to the incident and reaction ion involved in the nuclear reaction; Y( E)/AE is the yield of the (proton) reaction product and C is the normalizing constant including the beam fluence on the target; the P’s are Gaussian probability functions whose widths are determined by the overall resolution while ua is the nuclear reaction cross section [4] and S represents the mathematical space of energy and volume over which the reaction takes place. The stopping powers on which the P’s in eq. (1) depend were taken from ref. [5]. The (deuterium) concentration profile, p, was extracted by an iteration procedure; the details of the calculations are given in ref. [6] (in ref. [6] measurements of electropolished specimens are unpublished). This nuclear microanalysis method is nondestructive with an absolute accuracy of about 15% in concentration, a depth resolution of about 0.1 pm, and a profile sensitivity of about 500 appm [3,6]. Finally, in this type of reaction where the probing beam is composed of the same atoms as profile atoms, the background from the beam has to be measured. This was determined by analyzing an unirradiated sample and found to be less than 100 appm for our analysis.
3. Experimental
results
3.1. Electropolishing The sample which had been electropolished using deuterated acid D,SO, in place of the commonly used H,SO, was examined within 10 min after polishing. These results showed no appreciable deuterium beyond that of the probing beam mentioned above, i.e., Q 100
M.B. Lewis / Deurerium-defecttrappingin
154
3.2. Thermal absorption result and its implications The deuterium concentration profile measured on the unirradiated sample which had been “hydrogenated” with deuterium gas for 20 h at 473 K is shown in fig. 1. The profile in fig. 1, shows a high concentration of deuterium in the first 0.4 pm of the surface, beyond which the concentration is essentially uniform and relatively low, = 0.005 atom fraction (D/Zr). This behavior implies that precipitation of hydrides near the surfaces takes place under the applied temperature and pressure conditions [7]. The near surface region is expected to consist of S and y type deuteride particles dispersed in the alpha zirconium matrix. Deeper below the surface the deuterium concentration is less than the solubility limit and deuterides cannot form until the specimen is
THERMAL 2
-.-
lo-’ Y N
a
10-s
A profile of a 60 keV, room temperature implantation of deuterium in unirradiated zirconium is shown 60 keV
D+-Zr
ZIRCONIUM
I
I
I
INITIAL 473K AGED 1000s REGION OF DEUTERIDE
5
3.3. Ion implantation
ABSORPTION OVER
I
I
I
-irradiatedzirconium
allowed to cool down. As the temperature just begins to drop the saturated solution region also precipitates and is thus “frozen in” allowing the depth profile to be measured. The solubility limit for deuterium in alpha zirconium at 473 K occurs at the discontinuity in the profile, and in fig. 1 this would be about 0.5 at% at the depth of about 0.4 pm. This value is in good agreement with the recent measurement of Cann and Atrens [8] as well as the earlier work of Kearns [9]. Also shown in fig. 1 is the concentration profile after the sample was aged in vacuum at 473 K for a period of 1000 s. It can be expected that the precipitates begin to dissolve, and some desorption begins to take place. However the precipitates cannot reform at this temperature since there is no deuterium overpressure (any desorbed gas is pumped away). After the specimen again cools and is reexamined, the interface between the hydride region and the solution or precipitate free region is less distinct.
appm, in the first half micrometer of surface depth. These kinds of measurements had been previously carried out on nickel and stainless steel samples commonly used in this laboratory and measured both with the D(d, p)T and D(3He, a)P reactions [6]. In all cases the concentrations found were less than 100 appm in the surface regions with values as low as 30 appm using the D( 3He, a)P reaction probe on the austenitic samples polished at 223 K.
DEUTERIUM
ion
IO4
PRECIPITATES
I=-.. \
0
I
I
0.2
0.4
I 0.6 DEPTH
I 0.6 Ipm)
I I.0
I 1.2
1 I.4
Fig. 1. Concentration versus depth profiles for a zirconium sample which had been initially heated to 473 K in one atmosphere of deuterium for 20 h and subsequently allowed to cool to ambient temperature. Also shown is the profile obtained after further aging the initial sample for 1000 s at 473 K in vacuum.
10-4
0
I 0.2
I 0.4
I
I
I
0.6
0.6
1.0
DEPTH
1.2
(pm)
Fig. 2. Concentration versus depth profile for a zirconium sample irradiated with 60 keV deuterium ions at ambient temperature. Also shown is the profile after the specimen was aged at 473 K for 1000 s. For comparison, theoretical values of the range (R) and width (horizontal arrow) are also given.
155
M. B. Lewis / Deuterium - defect trapping in ion -irradiated zirconium
in fig. 2. Typical uncertainties in this kind of data are given by the error bars for concentration (D/Zr) and depth (pm). Also shown in the figure are the theoretical values for the range, R, and full width at half maximum (horizontal arrow) for this implantation condition taken from the systematic compilation in ref. [S]. While agreement between measured values and theory is good for the range, some deviations exists in the shape. The standard deviation near the mean range is slightly larger than the theoretical value (given by the horizontal arrow in the figure). Also the deep lying tail of the measured distribution is larger than expected, exhibiting a nongaussian shape. A series of profiles taken on samples which had been
100 keV D++Zr-ION I I 1 k -
IRRADIATED I I MEASURED3
predamaged and then implanted with 100 keV D are shown in fig. 3. The curve labeled 253 K is the profile resulting from the implantation carried out on the target held at 253 K without aging at any other temperature. The remaining curves labeled 373 K, 423 K and 473 K represent measurements made following implantation at room temperature and subsequent aging for 1000 s in isochronal temperature steps at 333 K, 353 K, 373 K, 423 K and 473 K up to a value indicated on the curve. The 253 K curve, like the curve in fig. 2 exhibits a non-gaussian tail which is enhanced in the deeper regions beyond the mean range of the profile. The 100 keV profiles measured in this work were found to be relatively stable near room temperature or below. The samples which were aged near 373 K or above exhibited profiles which indicated considerable migration of the deuterium away from the mean range (0.4 pm). This is in contrast to the 60 keV implantation of undamaged Zr which still retained most of its gaussian shape after aging at 473 K as indicated by the broken curve in fig. 2.
4. Analysis of ion implantation The theoretical defect profile produced by 4 MeV Zr+ of zirconium is given in fig. 4. Also shown is the 4 MeV ENERGY
I
473K
o-
100
I
keV
Zr+--
Zr
DEPOSITION
I
PROFILE
I
I
I
1.0
1.2
0 -Zr
-1
‘0-4
1.2 DEPTH
(mm)
Fig. 3. Concentration versus depth profiles of zirconium samples irradiated with 100 keV deuterium ions and subsequently aged at various temperatures to the maximum temperature shown in the figure. Also shown in relative units is the defect profile. The broken line curves are calculated profiles explained in the text.
0.6
DEPTH
0.6
1.4
(pm)
Fig. 4. Energy deposition profile used in the diffusion and trapping calculations. Also shown is the range profile for 4 MeV Zr ion irradiated Zr in arbitrary units.
156
hf. B. Lewis / Deutekm
-defect trapping in ion -irradiated zirconium
range profile of Zr implantation in arbitrary units. These curves were generated from the energy deposition code EDEP-1 [lo]. The depth region within the first 0.8 pm is expected to be relatively free of implanted interstitials, and where found, the implanted interstitials are the same atomic type as the substrate. This type of irradiation is expected to produce an atomic displacement type defect density in the specimen of the order of 1 at.%, depending upon the recombination rate of vacancies and interstitials. The deuterium profiles in the irradiated samples were analyzed using a model for the migration of gases in metals suggested by McNabb and Foster [ll] in which the gas atoms move between normal atomic sites and lower energy sites or traps caused by impurity atoms or crystal defects. Their differential equation involves a diffusive and a trap term:
(2) where C is the concentration of dissolved gas atoms, D is the normal diffusion coefficient, N is the density of traps, n is the fractional occupation of the traps, G is the generator (ion beam flux) and t is time. We have applied this approach in a manner similar to that of Myers and Picraux 1121by numerically solving eq. (2). In this case the fractional occupation of the traps is explicitly parameterized by an/ar=4sRND[C(l-n)-nzexp(-Q,/kT)].
(3)
Where R is the trapping radius and Qr is the trap enthalpy, i.e., the energy below that of normal (equilibrium) atomic sites of density z. The exponential term in eq. (3) is the usual Boltzmann factor. The parameters in eqs. (2) and (3) are determined as follows: the diffusion constant was taken as L) = 0.7 X 10-s exp(0.5/kT) [13]. The accuracy of this value is not very important since any similar number will give very rapid diffusion to trap sites which themselves determine the profile characteristics. The initial concentration of the dissolved gas C is taken as zero. The shape of the ion flux (G) as a function of depth is simply the semi-empirical range profile of 100 keV deuterium [5] (corrected for the angle of implantation). The capture radius A was taken as 4 x lo-’ cm which is approximately the average lattice constant of HCP zirconium. The normal hydrogen site density was taken to be that of the tetrahedral sites (I = 2) [14]. The product RN and Q.,. are important in the determination of the deuterium profiles. Electron microscopy studies 1151on irradiated zirconium alloys indicate that there is not a large number of voids produced under the Zr irradiation condi-
tions applied here. Therefore the choice of R having a value near the lattice size is reasonable. Although this choice of R ignores coarsening of the defect structure beyond simple Frenkel pairs, such coarsening implies a decrease in N as well as an increase in R so that the product RN changes only slightly; this fact increases confidence in the value of Q, which is to be extracted from the solutions of eqs. (2) and (3). If we write the trap density N(x) = N,f( x) such that /f(x) dx = 1, where x is the depth, N, becomes the total number of traps. If F is the predamage ion fluence then g = NO/F is the number of traps generated per incident ion. In our earlier work [3] we found g = 15 for 2 MeV Ni ion irradiation of stainless steel at room temperature. In order to estimate g for the case of 4 MeV Zr’ ions in zirconium, the usual formula for atomic displacement based on the modified Kinchin-Pease relationship was used (the choice of the input parameter Ed = 40 eV is based on the Annual Book of ASTM Standards [lo]), P(x)=0.8(dE/‘dx)+,‘2E,N,.
(4)
In eq. (4) the atomic displacements per atom (dpa), P, is determined by the nuclear displacement energy loss factor, dE/dx, given by the EDEP-1 code, the ion fluence, 6, the atomic density NA, and the threshold energy displacement factor Ed, Assuming Ed = 40 eV [lo] we find that Pz, = 2.0 P,, which implies g = 30. Using eq. (4), we estimate that the Zr ion fluence produced about 3 dpa at the peak of the damage distribution in fig. 4. This derivation of g is uncertain since it is uncertain if the recombination of Frenkel pair defects in zirconium is similar to that in nickel. However, there is experimental evidence to suggest that damage saturation does not occur below about 1 dpa (or 102’ neutrons cme2) [l&17]. Therefore our estimate of the trap density should be the proper order of magnitude. The implanted deuterium also creates additional displacement damage (although much less than that of the Zr ions) which cannot be distinguished from the Zr ion damage. While the atomic displacement energy density of the D-ion irradiation is negligible compared to that of Zr-ion bomb?rdment, the vacancy-interstitial recombination rate is expected to be much less for D-ions due to the larger average separation between the defects. Thus the surviving Frenkel pairs or residual damage from the light-ion irradiation becomes significant. For example in the case of charged particle irradiation of stainless steel at 900 K, the swelling rate (X swelling per dpa) of 0.75 MeV protons was found to be about 100 times larger than that of 3.5 MeV nickel ions (181. Based
M.B.
Lewis / Beuterium - deject trapping in ion - irradiated zirconium
on the EDEP-1 calculations and the work in refs. [19] and [20], we expect g = 3 for 100 keV deuterium ions in Zr. The functional form, f(x), for both Zr-ions and D-ions is given by the EDEP-1 code. As an aid to understanding the significance of the calculations, the sensitivity of the enthalpy parameter Q, to various values of Na (the most uncertain of the fixed parameters) was determined. The results are shown in fig. 5. The upper portion of the figure shows two curves calculated using different values of the D-defect enthalpy Qr and defect density parameter No. The
5
I
I
---No=O.Of
0
I
I
, Q,=O.33eV
0.4
0.6 OEPTX
0.26
I
curves are sufficiently similar compared to the uncertainty in the data that the calculations do not have a unique solution. The lower portion of the figure summarizes the problem by plotting values of Qr and N,, all of which lead to similar calculated curves. Before eqs. (2) and (3) can be solved, the boundary conditions must be set. Since the equations are solved nume~c~ly with 200 grid points, it is not practical to solve the equations throughout the entire depth (0.5 mm) of the sample. Therefore, an approximate analytical form of the solution is set well beyond the region of
Q,=O.Z8eV
-N0=0.04,
0.8
157
1.0
!
3.2
( pm 1
* 0.01
0.02
0.03
0.04
NO/Zr Fig. 5. An example of two calculated depth profiles which are similar due to the choices of the trap density parameter No and trap strength QT. Also shown is a graph of No versus QT values which all lead to similar curves when used in the diffusion and trapping equations.
158
M. B. Lewis / Deuierium -defect trapping in ion -irradiatedzirconium
interest. We have used the form erfc(x/2L). For the boundary condition we have calculated the gradient of this form at x,,, where x,+, is the deepest grid point (10 pm) and L is the diffusion length during the last aging step. This type of boundary condition with the choice of xN is important for the computational stability of the solutions of equations for values of T > 400 K. The calculations near the surface (Q 0.2 pm) are sensitive to the boundary condition imposed at the specimen surface. None of profiles shown in fig. 3 show zero deuterium concentration at the surface. This is indicative of restricted surface permeation and/or deuteric formation; this follows from the fact that there is no significant deuterium overpressure for these specimens at any time of their history. Myers and collaborators [12,20] have measured the surface permeability directly by ion beam methods for ion implanted nickel and iron. They find that the permeability was low for Fe and high for Ni presumably because of excessive surface oxide in the case of iron. Similarly in our case the chemically active zirconium specimens, having been exposed to air, are expected to have surface oxide and exhibit low deuterium permeability. Therefore we have set the boundary condition aC/ax = 0 at x = 0. Although this choice of boundary condition is somewhat arbitrary, the solutions of eqs. (2) and (3) in the deeper region of interest (x = 0.5 pm) were found to be rather insensitive to the degree of surface permeability.
5. Computational results and conclusions Allowing Qr, the trap enthalpy, to be the adjustable parameter in the solution of eqs. (2) and (3) a set of curves was obtained which best represents the data in fig. 3. These curves calculated with a binding enthalpy of Qr = 0.28 eV are shown as the broken lines in the figure. At the lowest temperature (253 K), the dominant shape of the profiles is that of the initial range profile of the deuterium implantation [5]. At higher temperatures, the deuterium distribution broadens to a degree resembling or decorating the defect profile itself as shown at the top of the figure. While the shape of the measured profiles is generally accounted for by the calculated curves, some significant discrepancies can be observed. It is clear that the deuterium concentration in the region of x Q 0.1 pm cannot be accounted for by simple ion implantation even when, as in our case, we apply the boundary condition aC/ax = 0 at x = 0. We suggest that the oxygen on the specimen surface is acting like a trap for deuterium so that during the implantation, when the surface region is highly ionized, the
oxygen-deuterium bond is formed. We have observed stronger evidence of this phenomenon in deuterium implanted uranium [21]. The solubility of hydrogen in zirconium is about 10e4 atomic fraction near ambient temperature [8], and our observed concentrations are much higher. However, the (100 keV) deuterium implantation rate was maintained at low6 atomic fraction per second, so that in the absence of trapping centers we calculate, using the quoted value of D, that the maximum concentration (say at 0.4 pm) would be only 4 x lo-’ atomic fraction. Therefore, since our sample contained irradiation defects prior to implantation, deuterium defect trapping was much more likely than hydride formation. Of course, this fact does not preclude the possibility of hydride-defect complexes forming during the aging process. For our implantation at 100 keV the peak concentration is expected at 0.4 pm, but there is little evidence (based on the observed deuterium mobility) to suggest that stable hydrides formed in that region as opposed to the 0.6 pm region where the concentration is much lower. However, the 60 keV implantation rate was carried out at 10 times the 100 keV rate and on unirradiated material. We observe for this case much less deuterium mobility as shown in fig. 2. The similarity of the deuterium mobilities between the thermal absorption in fig. 1 and the high rate implantation in fig. 2 implies that much of the trapping in the 60 keV implantation is due to hydride formation. It has already been pointed out that the 300 K curve in fig. 2 as well as the 253 K curve in fi. 3 show excessive deuterium in the deeper regions of the profile. Since the samples were well annealed it appears unlikely that pipe-diffusion along grain boundaries would be important. It may be significant that the predamaged specimen although implanted at a low temperature contains excess deuterium in its tail region. If we assume the existence of a secondary type of trap such as a dislocation which is weaker (say Qr < 0.10 eV) [22] than the primary trap, such lower energy traps would be occupied with a relatively high probability at a relatively low temperature [12]. Since ion irradiated specimens are observed [15] to contain dislocations well beyond the mean range of the incident ions, the existence of weak dislocation trapping could qualitatively explain the deuterium rich tails. While the details of the experimental curves are not reproduced by the solutions to eqs. (2) and (3) the uncertainty in the value determined for the binding enthalpy, Qr, remains small. This follows from the high sensitivity of the solutions to Q-r as illustrated in fig. 6. At elevated temperatures (> 350 K) where the diffusion
M. B. Lewis / Deuterium - defect trapping in ion -irradiated zirconium 100 keV D+--Zr 473 L
I
I
(Zr
ION IRRADIATED)
159
Acknowledgments
K MAXIMUM
I
I
I
II
The author would like to acknowledge the helpful discussions with K. Farrell regarding the microstructure of irradiated zirconium.
References VI IS. Woolsey and J.R. Morris, Corrosion 37 (1981) 575. 121M.B. Lewis; N.H. Packan, G.F. Wells and R.A. Buhl, Nucl. Instr. Meths. 167 (1979) 233. Advanced Techniques for Characterizing Microstructures, eds., F.W. Wiffen and J.A. Spitznagel (AIME, New York, 1982) p. 487. 141L. Ruby and R.B. Crawford, Nucl. Instr. and Meth. 24 (1963) 413; R.B. Theus, W.J. McGarry and L.A. Beach, Nucl. Phys. 8 (1966) 273. Stopping 151H.H. Andersen and J.F. Ziegler, Hydrogen Powers and Ranges (Pergamon Press, New York, 1977). WI M.B. Lewis, Nucl. Instr. Meths. 190 (1981) 605. Hydrogen-Metal Systems Databook, [71 M.A. Galaktionowa, ed., A. Abraham (Ordentlich, 1980). 181C.D. Cann and A. Atrens, J. Nucl. Mater. 88 (1980) 42. 191J.J. Keams, J. Nucl. Mater. 22 (1967) 292. Wl I. Manning and G.P. Mueller, Comp. Phys. Comm. 7 (1974) 85; Annual Book of ASTM Standards, Part 45, Nuclear Standards, Section E-521 (ASTM, Philadelphia, PA, 1977) p. 991. 1111A. McNabb and P.K. Foster, Trans. AIME 227 (1963) 618. WI SM. Myers and S.T. Picraux, J. Appl. Phys. 50 (1979) 5710. P31 E.A. Gulbransen and K.F. Andrew, J. Electrochem, Sot. 101 (1954) 560. 1141A.C. Chami, J.P. Bugeat and E. Ligeon, Radiat. Eff. 37 (1978) 73. 1151K. Farrell, unpublished. WI D. Fulkner and M.P. Puls, Fundamental Aspects of Radiation Damage in Metals, Vol. II, Proc. of Conf., Gatlinburg, TN, USA, October 1975, CONF 751006-P2 USERDA, p. 1287. P71 D.O. Northwood, Atomic Energy Review 154 (1977) 547. WI F.A. Gamer, R.W. Powell, D.W. Keefer, A.G. Pard, K.R. Garr, M.M. Nakata, T. Lauritzen, W.L. Bell, W.G. Johnston, W.K. Appleby, S. Diamond, M. Baron, R. Chickering, R. Bajaj, M.L. Bleiberg, J.A. Sprague, F.A. Smidt and J.E. Westmoreland, Proceedings of the Workshop on Correlation of Neutron and Charge Particle Damage, ed., J.O. Stiegler, ERDA CONF 760673, Oak Ridge (1976) p. 147. 1191S.T. Picraux, Nucl. Instr. Meths. 182/183 (1981) 413. PO1 F. Besenbacher, J. Bottiger and S.M. Myers, J. Appl. Phys. 53 (1982) 3536. WI M.B. Lewis, J. Nucl. Mater. 88 (1980) 23. WI A. Atrens and N.F. Fiore, J. Appl. Phys. 48 (1977) 4247. ~31 K.L. Wilson and M.I. Baskes, J. Nucl. Mater. 76/77 (1978) 291.
[31 M.B. Lewis and K. Farrell,
tt 0
-I I __
OZ
I _.
0.4
I __
I
0.6
DEPTH
0.8
I
1.0
II 1.2
(pm)
Fig. 6. Concentration versus depth profiles calculated with three Qr values without changing other parameters in the equations. The data for the 473 K aged specimen is shown. The width of the data curve represents the absolute uncertainty.
length (Dt)“’ of the deuterium during the aging is long (2 5 pm) compared to the thickness of the damaged region (= 1 pm) the release of the deuterium is a sharp function of temperature due to the Boltzmann factor, exp( - Q,/kT), in eq. (3). The error in the derived value of Qr is estimated to be no more than 20%. The binding enthalpy found for zirconium is similar to the value (Qr = 0.33 eV) found for defects in stainless steel [3,23], and values (Qr = 0.48 eV and Qr = 0.24 eV) for what are believed to be monovacancy traps in iron and nickel found by Myers and Collaborators [12,20]. In addition they find evidence for at least two distinct trap energies. These values for the hydrogen-defect binding enthalpy are believed to be theoretically related to the chemisorption of hydrogen to the internal (quasi) surfaces created by vacancies and vacancy clusters [19]. In summary, we have introduced deuterium into zirconium both by aging in a deuterium atmosphere and by ion implantation. Deuterium concentration profiles of these specimens were measured by the technique of nuclear microanalysis. The solubility of deuterium in zirconium at 473 K was determined as (0.50 f 0.10) at!%. By aging the irradiated specimens the primary deuterium-defect-binding enthalpy was determined as (0.28 + 0.06) eV below normal equilibrium sites.
Journal
of Nuclear
Materials 125 (1984) 152-159 North-Holland, Amsterdam
DEUTERIUM-DEFECT TRAPPING IN ION-IRRADIATED ZIRCONIUM * M.B. LEWIS Metals and Ceramics Division, Oak Ridge National Laborarmy, Received
1 November
1983; accepted
16 February
Oak Ridge, TN 37831, USA
1984
Trapping of ion-implanted deuterium by lattice defects in zirconium has been investigated. The lattice defects were generated by 4 MeV Zr+ (self ion) irradiation of pure zirconium metal at 750 K. Following 100 keV deuterium implantation of the predamaged zirconium, concentration versus depth profiles were measured by a method of nuclear microanalysis. The specimens were aged at a variety of temperatures and further profiles were measured. The measured migration of the deuterium was analyzed by solving a system of differential equations involving a diffusion and reversible trapping term. The results indicate that most of the deuterium is retained in traps with binding enthalpy approximately (0.28 f 0.06) eV below that for normal equilibrium sites. Evidence also suggests some defect trapping at other binding enthalpies. The solubility of deuterium in zirconium at T=473 K was also measured on a specimen exposed to deuterium gas; the value obtained by nuclear microanalysis was determined to be (OSOrfrO.10) at%.
1. Introduction Interest
in the
behavior
of hydrogen
in metals
has
been increasing over the past few years due to the technological need for such information and the rise of new techniques to study it. In particular, for nuclear pressurized water reactors, there exists the problem of excessive hydrogen absorption in zirconium alloys found in fuel cladding, heat shields and various support structures. Zirconium alloys are important because of their low neutron activation cross section and good mechanical and co~osion-resist~t properties in high temperature water. The presence of excessive hydrogen, however, limits the usefulness of zirconium alloys by causing ebrittlement. Recently, measurements of the concentration of hydrogen present in a zircaloy corrosion film produced by water have been made by a nuclear microanalysis technique [l]. Concentrations as high as 4.5 at% were measured near the surface of the corrosion film. However, these measurements were carried out in the absence of radiation and with materials which had not been previously irradiated. It is clearly important to study the
* Research sponsored by the Division of Materials Sciences, US. Department of Energy under contract W-7405-eng-26 with the Union Carbide Corporation.
0022-3115/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
migration of hydrogen in irradiated zirconium. Such studies will assist the design of zirconium alloys with desired corrosion resistant properties for reactors. In this work we have utilized ion beam techniques for the irradiation of zirconium, the implantation of hydrogen into zirconium and the measurement of the mobility of the hydrogen in the irradiated metal.
2. Experimental procedure Disks of 5 mm diameter and 0.5 mm thickness were punched from cold-rolled iodide zirconium sheet. They were annealed by heating for 30 min at 900 K at a pressure of about 1O-5 Pa. The specimens were mechanically polished with 0.1 pm diamond paste. Approximately 1 pm of surface was then removed by electropolishing (87% methyl alcohol, 12.7% H,SO,, 0.3% HF) at a temperature of 243 K. The prepared specimens were mounted in an ultrahigh vacuum target chamber. The chamber was cryopumped to 10m6 Pa. The specimens were then heated by contact with a back plate which was heated by an electron gun. Further details of the target chamber can be found in ref. [Z]. After the targets were heated to a temperature of 750 K, they were irradiated with a beam of 4 MeV Zr+ ions in order to create a specific depth profile of high density defects discussed in the following B.V.
M. B. Lewis / Deuterium - defect trapping in ion -irradiated zirconium section. The Zr+ ion flux was maintained at 5 X 10” ions/cm2 s for lo4 s. Following the irradiation, the targets were immediately allowed to cool. Individual specimens were transferred to a scattering chamber for deuterium implantation and analysis. Deuterium was implanted at room temperature or 253 K at an energy of 100 keV. In addition an unirradiated specimen was implanted with 60 keV deuterium. In both cases the beams impinged at an angle of 45” to the surface normal and were collimated to dimensions of 1 mm X 2 mm by an aperture which was much smaller than the beam diameter. This technique ensured a uniform beam intensity over the surface of implantation. The 60 keV implantation was carried out at a flux of 7 X 1013 ions/cm2 s. The 100 keV implantation was made at a lower flux of 7 X lOI ions/cm2 s. In both cases the total fluence was 7 X 1016 ions/cm2. In addition to injecting deuterium into zirconium by ion implantation, one sample (not irradiated) was annealed at 473 K at 10s Pa of deuterium gas for a period of about 20 h in order to examine hydrides of zirconium near the specimen surface. In another experiment the electropolishing step mentioned above in the sample preparation was carried out using D,SO, (in place of H2S04) in order to measure (as described below) possible hydrogen pickup from the electropolishing solution. All samples were aged at various temperatures. Following each aging step a depth versus concentration profile was made to determine the migration of the deuterium in the Zr-irradiated region of the specimens. The profiles were measured by a technique of nuclear microanalysis utilizing the D(d, p)T reaction. A beam of 0.5 MeV deuterium was steered onto the target at 45’ from the surface normal and made to overlap the previously implanted region. The collimation of the 0.5 MeV beam was the same as that for the lower energy implanted beam. A second insulated (antiscattering) collimator of slightly larger size was positioned down stream from the defining collimator and negatively charged to repel stray electrons from striking the target. A positive bias was applied to the target so that secondary electrons created by the ion beam stopping in the target could not escape the target surface. This ensured that the integrated electrical current on the target was true beam current which was used as the primary method to normalize the data. A surface barrier detector was used to measure the energy of the D(d, p)T reaction products. A Mylar widow was placed in front of the detector to suppress low energy particles from striking the detector and causing pulse pile up. A small hole in the Mylar allowed enough elastically scattered deuterons from the target to be measured as a secondary method of normal-
153
izing the data. This method was useful when the target was cooled since in this case the target could not be electrically insulated. As an energy calibration check for the D(d, p)T reaction data, a standard spectrum using a deuterated polyethylene target was taken. Further details of the scattering chamber and electronics can be found in ref. (31. Data obtained by nuclear microanalysis consists of energy dispersive spectra of the proton yield from the D(d, p)T reaction. These spectra are normalized by dividing the proton yield by the integrated current. The normalized spectra must be converted into concentration versus depth profiles of the deuterium. This has been carried out by calculating convolution integrals of the type Y( E)/AE
= C/Pipa,P, s
dS.
(1)
In this equation the subscripts i and r refer, respectively, to the incident and reaction ion involved in the nuclear reaction; Y( E)/AE is the yield of the (proton) reaction product and C is the normalizing constant including the beam fluence on the target; the P’s are Gaussian probability functions whose widths are determined by the overall resolution while ua is the nuclear reaction cross section [4] and S represents the mathematical space of energy and volume over which the reaction takes place. The stopping powers on which the P’s in eq. (1) depend were taken from ref. [5]. The (deuterium) concentration profile, p, was extracted by an iteration procedure; the details of the calculations are given in ref. [6] (in ref. [6] measurements of electropolished specimens are unpublished). This nuclear microanalysis method is nondestructive with an absolute accuracy of about 15% in concentration, a depth resolution of about 0.1 pm, and a profile sensitivity of about 500 appm [3,6]. Finally, in this type of reaction where the probing beam is composed of the same atoms as profile atoms, the background from the beam has to be measured. This was determined by analyzing an unirradiated sample and found to be less than 100 appm for our analysis.
3. Experimental
results
3.1. Electropolishing The sample which had been electropolished using deuterated acid D,SO, in place of the commonly used H,SO, was examined within 10 min after polishing. These results showed no appreciable deuterium beyond that of the probing beam mentioned above, i.e., Q 100
M.B. Lewis / Deurerium-defecttrappingin
154
3.2. Thermal absorption result and its implications The deuterium concentration profile measured on the unirradiated sample which had been “hydrogenated” with deuterium gas for 20 h at 473 K is shown in fig. 1. The profile in fig. 1, shows a high concentration of deuterium in the first 0.4 pm of the surface, beyond which the concentration is essentially uniform and relatively low, = 0.005 atom fraction (D/Zr). This behavior implies that precipitation of hydrides near the surfaces takes place under the applied temperature and pressure conditions [7]. The near surface region is expected to consist of S and y type deuteride particles dispersed in the alpha zirconium matrix. Deeper below the surface the deuterium concentration is less than the solubility limit and deuterides cannot form until the specimen is
THERMAL 2
-.-
lo-’ Y N
a
10-s
A profile of a 60 keV, room temperature implantation of deuterium in unirradiated zirconium is shown 60 keV
D+-Zr
ZIRCONIUM
I
I
I
INITIAL 473K AGED 1000s REGION OF DEUTERIDE
5
3.3. Ion implantation
ABSORPTION OVER
I
I
I
-irradiatedzirconium
allowed to cool down. As the temperature just begins to drop the saturated solution region also precipitates and is thus “frozen in” allowing the depth profile to be measured. The solubility limit for deuterium in alpha zirconium at 473 K occurs at the discontinuity in the profile, and in fig. 1 this would be about 0.5 at% at the depth of about 0.4 pm. This value is in good agreement with the recent measurement of Cann and Atrens [8] as well as the earlier work of Kearns [9]. Also shown in fig. 1 is the concentration profile after the sample was aged in vacuum at 473 K for a period of 1000 s. It can be expected that the precipitates begin to dissolve, and some desorption begins to take place. However the precipitates cannot reform at this temperature since there is no deuterium overpressure (any desorbed gas is pumped away). After the specimen again cools and is reexamined, the interface between the hydride region and the solution or precipitate free region is less distinct.
appm, in the first half micrometer of surface depth. These kinds of measurements had been previously carried out on nickel and stainless steel samples commonly used in this laboratory and measured both with the D(d, p)T and D(3He, a)P reactions [6]. In all cases the concentrations found were less than 100 appm in the surface regions with values as low as 30 appm using the D( 3He, a)P reaction probe on the austenitic samples polished at 223 K.
DEUTERIUM
ion
IO4
PRECIPITATES
I=-.. \
0
I
I
0.2
0.4
I 0.6 DEPTH
I 0.6 Ipm)
I I.0
I 1.2
1 I.4
Fig. 1. Concentration versus depth profiles for a zirconium sample which had been initially heated to 473 K in one atmosphere of deuterium for 20 h and subsequently allowed to cool to ambient temperature. Also shown is the profile obtained after further aging the initial sample for 1000 s at 473 K in vacuum.
10-4
0
I 0.2
I 0.4
I
I
I
0.6
0.6
1.0
DEPTH
1.2
(pm)
Fig. 2. Concentration versus depth profile for a zirconium sample irradiated with 60 keV deuterium ions at ambient temperature. Also shown is the profile after the specimen was aged at 473 K for 1000 s. For comparison, theoretical values of the range (R) and width (horizontal arrow) are also given.
155
M. B. Lewis / Deuterium - defect trapping in ion -irradiated zirconium
in fig. 2. Typical uncertainties in this kind of data are given by the error bars for concentration (D/Zr) and depth (pm). Also shown in the figure are the theoretical values for the range, R, and full width at half maximum (horizontal arrow) for this implantation condition taken from the systematic compilation in ref. [S]. While agreement between measured values and theory is good for the range, some deviations exists in the shape. The standard deviation near the mean range is slightly larger than the theoretical value (given by the horizontal arrow in the figure). Also the deep lying tail of the measured distribution is larger than expected, exhibiting a nongaussian shape. A series of profiles taken on samples which had been
100 keV D++Zr-ION I I 1 k -
IRRADIATED I I MEASURED3
predamaged and then implanted with 100 keV D are shown in fig. 3. The curve labeled 253 K is the profile resulting from the implantation carried out on the target held at 253 K without aging at any other temperature. The remaining curves labeled 373 K, 423 K and 473 K represent measurements made following implantation at room temperature and subsequent aging for 1000 s in isochronal temperature steps at 333 K, 353 K, 373 K, 423 K and 473 K up to a value indicated on the curve. The 253 K curve, like the curve in fig. 2 exhibits a non-gaussian tail which is enhanced in the deeper regions beyond the mean range of the profile. The 100 keV profiles measured in this work were found to be relatively stable near room temperature or below. The samples which were aged near 373 K or above exhibited profiles which indicated considerable migration of the deuterium away from the mean range (0.4 pm). This is in contrast to the 60 keV implantation of undamaged Zr which still retained most of its gaussian shape after aging at 473 K as indicated by the broken curve in fig. 2.
4. Analysis of ion implantation The theoretical defect profile produced by 4 MeV Zr+ of zirconium is given in fig. 4. Also shown is the 4 MeV ENERGY
I
473K
o-
100
I
keV
Zr+--
Zr
DEPOSITION
I
PROFILE
I
I
I
1.0
1.2
0 -Zr
-1
‘0-4
1.2 DEPTH
(mm)
Fig. 3. Concentration versus depth profiles of zirconium samples irradiated with 100 keV deuterium ions and subsequently aged at various temperatures to the maximum temperature shown in the figure. Also shown in relative units is the defect profile. The broken line curves are calculated profiles explained in the text.
0.6
DEPTH
0.6
1.4
(pm)
Fig. 4. Energy deposition profile used in the diffusion and trapping calculations. Also shown is the range profile for 4 MeV Zr ion irradiated Zr in arbitrary units.
156
hf. B. Lewis / Deutekm
-defect trapping in ion -irradiated zirconium
range profile of Zr implantation in arbitrary units. These curves were generated from the energy deposition code EDEP-1 [lo]. The depth region within the first 0.8 pm is expected to be relatively free of implanted interstitials, and where found, the implanted interstitials are the same atomic type as the substrate. This type of irradiation is expected to produce an atomic displacement type defect density in the specimen of the order of 1 at.%, depending upon the recombination rate of vacancies and interstitials. The deuterium profiles in the irradiated samples were analyzed using a model for the migration of gases in metals suggested by McNabb and Foster [ll] in which the gas atoms move between normal atomic sites and lower energy sites or traps caused by impurity atoms or crystal defects. Their differential equation involves a diffusive and a trap term:
(2) where C is the concentration of dissolved gas atoms, D is the normal diffusion coefficient, N is the density of traps, n is the fractional occupation of the traps, G is the generator (ion beam flux) and t is time. We have applied this approach in a manner similar to that of Myers and Picraux 1121by numerically solving eq. (2). In this case the fractional occupation of the traps is explicitly parameterized by an/ar=4sRND[C(l-n)-nzexp(-Q,/kT)].
(3)
Where R is the trapping radius and Qr is the trap enthalpy, i.e., the energy below that of normal (equilibrium) atomic sites of density z. The exponential term in eq. (3) is the usual Boltzmann factor. The parameters in eqs. (2) and (3) are determined as follows: the diffusion constant was taken as L) = 0.7 X 10-s exp(0.5/kT) [13]. The accuracy of this value is not very important since any similar number will give very rapid diffusion to trap sites which themselves determine the profile characteristics. The initial concentration of the dissolved gas C is taken as zero. The shape of the ion flux (G) as a function of depth is simply the semi-empirical range profile of 100 keV deuterium [5] (corrected for the angle of implantation). The capture radius A was taken as 4 x lo-’ cm which is approximately the average lattice constant of HCP zirconium. The normal hydrogen site density was taken to be that of the tetrahedral sites (I = 2) [14]. The product RN and Q.,. are important in the determination of the deuterium profiles. Electron microscopy studies 1151on irradiated zirconium alloys indicate that there is not a large number of voids produced under the Zr irradiation condi-
tions applied here. Therefore the choice of R having a value near the lattice size is reasonable. Although this choice of R ignores coarsening of the defect structure beyond simple Frenkel pairs, such coarsening implies a decrease in N as well as an increase in R so that the product RN changes only slightly; this fact increases confidence in the value of Q, which is to be extracted from the solutions of eqs. (2) and (3). If we write the trap density N(x) = N,f( x) such that /f(x) dx = 1, where x is the depth, N, becomes the total number of traps. If F is the predamage ion fluence then g = NO/F is the number of traps generated per incident ion. In our earlier work [3] we found g = 15 for 2 MeV Ni ion irradiation of stainless steel at room temperature. In order to estimate g for the case of 4 MeV Zr’ ions in zirconium, the usual formula for atomic displacement based on the modified Kinchin-Pease relationship was used (the choice of the input parameter Ed = 40 eV is based on the Annual Book of ASTM Standards [lo]), P(x)=0.8(dE/‘dx)+,‘2E,N,.
(4)
In eq. (4) the atomic displacements per atom (dpa), P, is determined by the nuclear displacement energy loss factor, dE/dx, given by the EDEP-1 code, the ion fluence, 6, the atomic density NA, and the threshold energy displacement factor Ed, Assuming Ed = 40 eV [lo] we find that Pz, = 2.0 P,, which implies g = 30. Using eq. (4), we estimate that the Zr ion fluence produced about 3 dpa at the peak of the damage distribution in fig. 4. This derivation of g is uncertain since it is uncertain if the recombination of Frenkel pair defects in zirconium is similar to that in nickel. However, there is experimental evidence to suggest that damage saturation does not occur below about 1 dpa (or 102’ neutrons cme2) [l&17]. Therefore our estimate of the trap density should be the proper order of magnitude. The implanted deuterium also creates additional displacement damage (although much less than that of the Zr ions) which cannot be distinguished from the Zr ion damage. While the atomic displacement energy density of the D-ion irradiation is negligible compared to that of Zr-ion bomb?rdment, the vacancy-interstitial recombination rate is expected to be much less for D-ions due to the larger average separation between the defects. Thus the surviving Frenkel pairs or residual damage from the light-ion irradiation becomes significant. For example in the case of charged particle irradiation of stainless steel at 900 K, the swelling rate (X swelling per dpa) of 0.75 MeV protons was found to be about 100 times larger than that of 3.5 MeV nickel ions (181. Based
M.B.
Lewis / Beuterium - deject trapping in ion - irradiated zirconium
on the EDEP-1 calculations and the work in refs. [19] and [20], we expect g = 3 for 100 keV deuterium ions in Zr. The functional form, f(x), for both Zr-ions and D-ions is given by the EDEP-1 code. As an aid to understanding the significance of the calculations, the sensitivity of the enthalpy parameter Q, to various values of Na (the most uncertain of the fixed parameters) was determined. The results are shown in fig. 5. The upper portion of the figure shows two curves calculated using different values of the D-defect enthalpy Qr and defect density parameter No. The
5
I
I
---No=O.Of
0
I
I
, Q,=O.33eV
0.4
0.6 OEPTX
0.26
I
curves are sufficiently similar compared to the uncertainty in the data that the calculations do not have a unique solution. The lower portion of the figure summarizes the problem by plotting values of Qr and N,, all of which lead to similar calculated curves. Before eqs. (2) and (3) can be solved, the boundary conditions must be set. Since the equations are solved nume~c~ly with 200 grid points, it is not practical to solve the equations throughout the entire depth (0.5 mm) of the sample. Therefore, an approximate analytical form of the solution is set well beyond the region of
Q,=O.Z8eV
-N0=0.04,
0.8
157
1.0
!
3.2
( pm 1
* 0.01
0.02
0.03
0.04
NO/Zr Fig. 5. An example of two calculated depth profiles which are similar due to the choices of the trap density parameter No and trap strength QT. Also shown is a graph of No versus QT values which all lead to similar curves when used in the diffusion and trapping equations.
158
M. B. Lewis / Deuierium -defect trapping in ion -irradiatedzirconium
interest. We have used the form erfc(x/2L). For the boundary condition we have calculated the gradient of this form at x,,, where x,+, is the deepest grid point (10 pm) and L is the diffusion length during the last aging step. This type of boundary condition with the choice of xN is important for the computational stability of the solutions of equations for values of T > 400 K. The calculations near the surface (Q 0.2 pm) are sensitive to the boundary condition imposed at the specimen surface. None of profiles shown in fig. 3 show zero deuterium concentration at the surface. This is indicative of restricted surface permeation and/or deuteric formation; this follows from the fact that there is no significant deuterium overpressure for these specimens at any time of their history. Myers and collaborators [12,20] have measured the surface permeability directly by ion beam methods for ion implanted nickel and iron. They find that the permeability was low for Fe and high for Ni presumably because of excessive surface oxide in the case of iron. Similarly in our case the chemically active zirconium specimens, having been exposed to air, are expected to have surface oxide and exhibit low deuterium permeability. Therefore we have set the boundary condition aC/ax = 0 at x = 0. Although this choice of boundary condition is somewhat arbitrary, the solutions of eqs. (2) and (3) in the deeper region of interest (x = 0.5 pm) were found to be rather insensitive to the degree of surface permeability.
5. Computational results and conclusions Allowing Qr, the trap enthalpy, to be the adjustable parameter in the solution of eqs. (2) and (3) a set of curves was obtained which best represents the data in fig. 3. These curves calculated with a binding enthalpy of Qr = 0.28 eV are shown as the broken lines in the figure. At the lowest temperature (253 K), the dominant shape of the profiles is that of the initial range profile of the deuterium implantation [5]. At higher temperatures, the deuterium distribution broadens to a degree resembling or decorating the defect profile itself as shown at the top of the figure. While the shape of the measured profiles is generally accounted for by the calculated curves, some significant discrepancies can be observed. It is clear that the deuterium concentration in the region of x Q 0.1 pm cannot be accounted for by simple ion implantation even when, as in our case, we apply the boundary condition aC/ax = 0 at x = 0. We suggest that the oxygen on the specimen surface is acting like a trap for deuterium so that during the implantation, when the surface region is highly ionized, the
oxygen-deuterium bond is formed. We have observed stronger evidence of this phenomenon in deuterium implanted uranium [21]. The solubility of hydrogen in zirconium is about 10e4 atomic fraction near ambient temperature [8], and our observed concentrations are much higher. However, the (100 keV) deuterium implantation rate was maintained at low6 atomic fraction per second, so that in the absence of trapping centers we calculate, using the quoted value of D, that the maximum concentration (say at 0.4 pm) would be only 4 x lo-’ atomic fraction. Therefore, since our sample contained irradiation defects prior to implantation, deuterium defect trapping was much more likely than hydride formation. Of course, this fact does not preclude the possibility of hydride-defect complexes forming during the aging process. For our implantation at 100 keV the peak concentration is expected at 0.4 pm, but there is little evidence (based on the observed deuterium mobility) to suggest that stable hydrides formed in that region as opposed to the 0.6 pm region where the concentration is much lower. However, the 60 keV implantation rate was carried out at 10 times the 100 keV rate and on unirradiated material. We observe for this case much less deuterium mobility as shown in fig. 2. The similarity of the deuterium mobilities between the thermal absorption in fig. 1 and the high rate implantation in fig. 2 implies that much of the trapping in the 60 keV implantation is due to hydride formation. It has already been pointed out that the 300 K curve in fig. 2 as well as the 253 K curve in fi. 3 show excessive deuterium in the deeper regions of the profile. Since the samples were well annealed it appears unlikely that pipe-diffusion along grain boundaries would be important. It may be significant that the predamaged specimen although implanted at a low temperature contains excess deuterium in its tail region. If we assume the existence of a secondary type of trap such as a dislocation which is weaker (say Qr < 0.10 eV) [22] than the primary trap, such lower energy traps would be occupied with a relatively high probability at a relatively low temperature [12]. Since ion irradiated specimens are observed [15] to contain dislocations well beyond the mean range of the incident ions, the existence of weak dislocation trapping could qualitatively explain the deuterium rich tails. While the details of the experimental curves are not reproduced by the solutions to eqs. (2) and (3) the uncertainty in the value determined for the binding enthalpy, Qr, remains small. This follows from the high sensitivity of the solutions to Q-r as illustrated in fig. 6. At elevated temperatures (> 350 K) where the diffusion
M. B. Lewis / Deuterium - defect trapping in ion -irradiated zirconium 100 keV D+--Zr 473 L
I
I
(Zr
ION IRRADIATED)
159
Acknowledgments
K MAXIMUM
I
I
I
II
The author would like to acknowledge the helpful discussions with K. Farrell regarding the microstructure of irradiated zirconium.
References VI IS. Woolsey and J.R. Morris, Corrosion 37 (1981) 575. 121M.B. Lewis; N.H. Packan, G.F. Wells and R.A. Buhl, Nucl. Instr. Meths. 167 (1979) 233. Advanced Techniques for Characterizing Microstructures, eds., F.W. Wiffen and J.A. Spitznagel (AIME, New York, 1982) p. 487. 141L. Ruby and R.B. Crawford, Nucl. Instr. and Meth. 24 (1963) 413; R.B. Theus, W.J. McGarry and L.A. Beach, Nucl. Phys. 8 (1966) 273. Stopping 151H.H. Andersen and J.F. Ziegler, Hydrogen Powers and Ranges (Pergamon Press, New York, 1977). WI M.B. Lewis, Nucl. Instr. Meths. 190 (1981) 605. Hydrogen-Metal Systems Databook, [71 M.A. Galaktionowa, ed., A. Abraham (Ordentlich, 1980). 181C.D. Cann and A. Atrens, J. Nucl. Mater. 88 (1980) 42. 191J.J. Keams, J. Nucl. Mater. 22 (1967) 292. Wl I. Manning and G.P. Mueller, Comp. Phys. Comm. 7 (1974) 85; Annual Book of ASTM Standards, Part 45, Nuclear Standards, Section E-521 (ASTM, Philadelphia, PA, 1977) p. 991. 1111A. McNabb and P.K. Foster, Trans. AIME 227 (1963) 618. WI SM. Myers and S.T. Picraux, J. Appl. Phys. 50 (1979) 5710. P31 E.A. Gulbransen and K.F. Andrew, J. Electrochem, Sot. 101 (1954) 560. 1141A.C. Chami, J.P. Bugeat and E. Ligeon, Radiat. Eff. 37 (1978) 73. 1151K. Farrell, unpublished. WI D. Fulkner and M.P. Puls, Fundamental Aspects of Radiation Damage in Metals, Vol. II, Proc. of Conf., Gatlinburg, TN, USA, October 1975, CONF 751006-P2 USERDA, p. 1287. P71 D.O. Northwood, Atomic Energy Review 154 (1977) 547. WI F.A. Gamer, R.W. Powell, D.W. Keefer, A.G. Pard, K.R. Garr, M.M. Nakata, T. Lauritzen, W.L. Bell, W.G. Johnston, W.K. Appleby, S. Diamond, M. Baron, R. Chickering, R. Bajaj, M.L. Bleiberg, J.A. Sprague, F.A. Smidt and J.E. Westmoreland, Proceedings of the Workshop on Correlation of Neutron and Charge Particle Damage, ed., J.O. Stiegler, ERDA CONF 760673, Oak Ridge (1976) p. 147. 1191S.T. Picraux, Nucl. Instr. Meths. 182/183 (1981) 413. PO1 F. Besenbacher, J. Bottiger and S.M. Myers, J. Appl. Phys. 53 (1982) 3536. WI M.B. Lewis, J. Nucl. Mater. 88 (1980) 23. WI A. Atrens and N.F. Fiore, J. Appl. Phys. 48 (1977) 4247. ~31 K.L. Wilson and M.I. Baskes, J. Nucl. Mater. 76/77 (1978) 291.
[31 M.B. Lewis and K. Farrell,
tt 0
-I I __
OZ
I _.
0.4
I __
I
0.6
DEPTH
0.8
I
1.0
II 1.2
(pm)
Fig. 6. Concentration versus depth profiles calculated with three Qr values without changing other parameters in the equations. The data for the 473 K aged specimen is shown. The width of the data curve represents the absolute uncertainty.
length (Dt)“’ of the deuterium during the aging is long (2 5 pm) compared to the thickness of the damaged region (= 1 pm) the release of the deuterium is a sharp function of temperature due to the Boltzmann factor, exp( - Q,/kT), in eq. (3). The error in the derived value of Qr is estimated to be no more than 20%. The binding enthalpy found for zirconium is similar to the value (Qr = 0.33 eV) found for defects in stainless steel [3,23], and values (Qr = 0.48 eV and Qr = 0.24 eV) for what are believed to be monovacancy traps in iron and nickel found by Myers and Collaborators [12,20]. In addition they find evidence for at least two distinct trap energies. These values for the hydrogen-defect binding enthalpy are believed to be theoretically related to the chemisorption of hydrogen to the internal (quasi) surfaces created by vacancies and vacancy clusters [19]. In summary, we have introduced deuterium into zirconium both by aging in a deuterium atmosphere and by ion implantation. Deuterium concentration profiles of these specimens were measured by the technique of nuclear microanalysis. The solubility of deuterium in zirconium at 473 K was determined as (0.50 f 0.10) at!%. By aging the irradiated specimens the primary deuterium-defect-binding enthalpy was determined as (0.28 + 0.06) eV below normal equilibrium sites.