3
PING IN COLD WWKE
SINGLE C
fALLINE MOLYB0ENU
^RVED WIT
1
1 1 1 e b *
r^ f ( l « L ^ if**
HELIUM TRAPPING IN COLD WORKED
SINGLE CRYSTALLINE MOLYBDENUM
OBSERVED WITH
HELIUM TRAPPING IN COLD WORKED
SINGLE CRYSTALLINE MOLYBDENUM
OBSERVED WITH
THERMAL HELIUM DESORPTION SPECTROMETRY
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR AAN DE TECHNISCHE UNIVERSITEIT DELFT, OP GEZAG VAN
DE RECTOR MAGNIFICUS, PROF. DR. J.M. DIRKEN, IN HET OPENBAAR TE VERDEDIGEN TEN OVERSTAAN VAN EEN COMMISSIE, AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN,
OP DONDERDAG 19 MAART 1987 TE 16.00 UUR.
DOOR
WILHELMUS THEODORUS MARIA BUTERS
NATUURKUNDIG INGENIEUR
GEBOREN TE WARMOND
Dit proefschrift is goedgekeurd door de promotor
Prof. dr.rr. A. van den Beukei
The work described in this thesis is part of the research programme of the Foundation for Fundamental Research on Matter (FOM) and was supported financially by the Netherlands Organization for the Advancement of Pure Research (ZWO).
It has been carried out in the Division of Physical Metallurgy at the Interdisciplinary Department of Metals Science and Technology of the Delft University of Technology.
Stellingen behorende bij het proefschrift
HELIUM TRAPPING IN COLD WORKED
SINGLE CRYSTALLINE MOLYBDENUM
OBSERVED WITH
Ik heb het gevoel dat
hoe meer woorden ik nu gebruik,
des te minder ik er straks kan hanteren
CONTENTS
Contents
General introduction 11
2. Technical requirements for Thermal Helium Desorption 17 Spectrometry
2.1. Introduction 17 2.2. Description of THDS technique 18
2.3- The equipment 21 2.3-1- The vacuum system 21 2.3-2. The specimen holder 23 2.3•3• The gas ion source 24 2.3-4. The mass spectrometer 26 2.3-5- The deformation device 27 2.3-6. Desorption, data acquisition and processing 31
3. Trapping and re-trapping of mobile particles by uniformly 39 distributed non-saturable traps
3.1. Introduction 39 3.2. The diffusion equation 42
3.2.1. Solution of the diffusion equation for a square source 43 function
3.2.2. Total trapped fraction of mobile particles 45 3.2.3- Re-distribution of trapped particles after release 47
4. Thermal helium desorption spectrometry on plastically 55 deformed molybdenum
4.1. Introduction 55 4.2. Experimental 56 4.3- Theory of helium trapping 59
4.3-1. Depth dependent trapping model 59 4.3.2. Monte Carlo simulations of helium trapping 60
4.4. Results and discussion 63
4.5- Conclusions 68
>. Some results on helium trapping in undeformed and cold 71
worked single crystalline copper: a comparison with molybdenum and nickel
5-1. Introduction 71 5.2. Experimental 72 5.3. Experimental results and discussion 73
5.3.I. Helium trapping as a function of the implantation 73 energy
5.3-2. More detailed peak assignment 76 5.3-3- Helium desorption spectra of plastically deformed 8l
copper
5.4. Conclusions 83
6. Evidence for helium pipe diffusion along dislocations
in 87molybdenum
6.1. Introduction 87 6.2. Experimental 90 6.3- Experimental results ' 91
6.3-1. Helium trapping as a function of the helium dose in 91 the as-deformed sample
6.3-2. Helium trapping at varying helium dose after an 94
intermediate anneal to 750 K
6.h. Discussion 97
6.4.1. Helium trapping by vacancies: a depth dependent 97 trapping model
6.4.2. Helium trapped by vacancy clusters 99
6.4.3- Preliminary conclusions 101
6.5- Drain experiments 101 6.5.1. Introduction 101 6.5-2. Principle of the measurements: ArV as a probe 101
6.5.3. Experimental results 104
6.5.4. Discussion 106 6.6. Conclusions and final remarks 110
7. A TEM study of helium trapping in cold worked single 115 crystalline molybdenum
7.1. Introduction 116 7.2. Experimental 117 7-3. Results of the cold worked samples with respect to 119
the dislocation structure
7-4. Results of helium implanted samples 121
7-5. Discussion and conclusions 123 7.6. Implications of the TEM results for the interpretation 126
of the helium trapping observed with THDS
7-6.1. Mechanisms to explain the observation of helium- 126 vacancy complexes in the desorption spectra
7.6.1.1. The first mechanism: Helium re-trapping at 127 vacancy clusters
7-6.1.2. The second mechanism: Vacancy trapping at 130 helium-filled monovacancies
Summary 139
Samenvatting 143
Nawoord 147
Curriculum vitae 149
Parts of this work have already been published:
Chapter
3-W.Th.M. Buters and A. van den Beukel J. Nucl. Mater. 137(1985)51.
Chapter 4.
W.Th.M. Buters and A. van den Beukel J . Nucl. Mater.
137(1985)57-Chapter
5-W.Th.M. Buters, A. van Veen and A. van den Beukel Subm. for publication Phys. Stat. Sol. (a).
Chapter 6.
W.Th.M. Buters and A. van den Beukel
Ace. for publication J. Nucl. Mater. (1986)
Ace. in short form as a contribution to the Second International Conference on Fusion Reactor Materials, Chicago (111.), USA 13-17 April 1986, J. Nucl. Mater. 141-143(1986) ■
Chapter 7•
W.Th.M. Buters, J.H. Evans, A. van Veen and A. van den Beukel Ace. for publication J. Nucl. Mater. 147(1986).
1
GENERAL INTRODUCTION
Helium in metals, or more general, helium in materials may seem a rather absurd subject to physicists. The extremely high heat of solution (3"5 eV per atom, depending on the host material) and the very small natural abundance of helium in the atmosphere does not seem to justify a world-wide effort to study the behaviour of helium in materials. An explanation is needed.
The stimulus to study the effect of helium on physical and mechanical properties of materials was given at the start of the nuclear energy era, which happened to coincide with the time the first electron microscopes were being developed. Detailed microscopic examination of partially burned-up fuel rods of nuclear fission reactors revealed the existence of small gas-filled cavities called 'bubbles' in the uranium matrix [1-3]- The gas inside the bubbles, mainly the heavy inert gases krypton and xenon [4], was formed as a transmutation product by (n,a) reactions or as a fission product in the material during reactor operation. The usual high operation temperature of nuclear reactors enabled the created gas atoms to accumulate at places where, due to lattice distortions, more space than usual is available. The capture of mobile vacancies by vacancy-gas agglomerates also appeared to promote the formation of larger bubbles
[5]-The first experiments to create helium bubbles deliberately were done by Barnes et al. [6]. They implanted a copper sample with alpha particles from a 30 MeV cyclotron. After a modest annealing treatment a high density of small helium bubbles was found at grain boundaries, with only a few larger bubbles within the grains. Apart from their observation of faceted bubbles, they also followed the growth of the observed bubbles during annealing of the sample. Once the accumulation of helium in voids, either in the matrix or at grain boundaries, was observed, it was realized that the effects of helium especially in fast fission, breeding or thermonuclear reactors would
GENERAL INTRODUCTION
be very strong due to two effects. First, in these reactors the fast neutron flux is a few orders of magnitude higher than in thermal
13 -2 -1
nuclear fission reactors (10 n cm s ) and second, in case of thermonuclear reactors helium produced by the T(d,n) He fusion reaction can escape from the plasma and impinge on the so-called first wall of the fusion reactor.
The problems arising when a large amount (10-100 appm) of helium is present in metals is manyfold, see e.g. [7]- The ductile to brittle transition temperature (DBTT) of metals is elevated from temperatures below room temperature to a few hundred degrees centigrade, mainly as a result of helium accumulation at grain boundaries. When for servicing or maintainance of the reactor the temperature of core elements would drop below the DBTT, serious mechanical problems could arise. Another practical problem is the dimensional stability of core components. Displacement rates for first wall components are expected
-6 -k
to ly in the range of 10 -10 dpa/s (displacements per atom per second). The high operation temperature of fusion reactors allows created vacancies to form small vacancy clusters (microvoids) in the material. Since helium prevents small voids from collapsing to dislocation loops, void formation seems to be promoted by the presence of large amounts of helium. Volume swellings of the order of 10% are predicted and have been observed. From constructive point of view a maximum swelling of less than 2% is allowed. At this point it
will be clear that a fundamental approach is needed to understand the atomic trapping processes finally leading to the formation of large gas-vacancy complexes in materials.
At the time fusion technology was being developed, another field of research started. The adsorption and desorption of various gases from solid surfaces was an unexplored area. Interest in the technique of ion pumping in ultra high vacuum systems [8] and gas reemission [9] finally led to the beginning of thermal desorption spectrometry
(TDS). Kornelsen [10] for the first time systematically measured the thermal desorption of inert gases implanted into a polycrystalline tungsten wire. Once the measured desorption peaks could be associated with the proper point defect reactions [11-16], Thermal Helium
GENERAL INTRODUCTION
Desorption Spectrometry (THDS) has become a very useful technique to study point defect interactions in solids
[17]-In 1974 the Reactor Physics Group (Delft University of Technology), started, in close cooperation with E.V. Kornelsen, to investigate the behaviour of helium in metals utilizing THDS. To be more specific, they studied the interaction between helium and point defects as a part of international research activities on material science for nuclear applications. The THDS technique yields not only information on the behaviour of helium in materials (bubble formation, blistering), but also on point defect interactions by using helium as a probe. Detailed helium desorption experiments have elucidated existing controverses such as the Stage III dilemma in molybdenum [13] and have revealed completely new features like trap-mutation [14,15] and, combined with transmission electron microscopy (TEM), the platelet-morphology of helium precipitates grown in molybdenum [18-20].
Finally in 1977 the Metal Physics Group (Delft University of Technology) started the project 'Gases in Metals'. One of the aims was to investigate the interaction between helium and dislocations by THDS and TEM. The dislocations are introduced by plastic deformation. It is well known that the mechanical strength of metals is strongly influenced by its microstructure (grain size, dislocation density).
5 -2 All metals contain dislocations with a density ranging from 10 cm
12 -2
for well annealed single crystals up to 10 cm for heavily deformed crystals. From numerous TEM studies (see e.g. [21-24]) it seems clear that dislocations play an important role in the transport of helium and the growth of helium bubbles. Therefore it seemed justified to start a detailed investigation to the trapping of helium at dislocations. At this point THDS seems to be an excellent tool to study the very beginning of helium trapping at dislocations finally leading to helium bubble formation. The reason for the choice of molybdenum is twofold. Firstly, there is already a vast amount of THDS data on molybdenum available, so that peak assignment is easy. Secondly, molybdenum is still considered as a long term candidate material for plasma facing components such as limiters, diverters etc.
GENERAL INTRODUCTION
It must be mentioned that the work described in this thesis will be presented in chronological order, the first chapters reporting rather basic work. Ideas originating in the early part of this work are worked out in more detail in Chapters 4,5.6 and
7-To learn something from thermal helium desorption experiments it is inevitable to be familiar with certain aspects of the technique. That is why Chapter 2 gives a brief explanation of some features of the technique and the equipment. An excellent general description of THDS has been given by Van Gorkum [17]. Subsequently in Chapter 3 a short treatment is given of the trapping and re-trapping of interstitial helium at defects. A relation between helium trapping probability and trap concentration is given, whereas for a very simple case re-trapping of helium at defects is calculated. A few basic relations emerging from this chapter will be used in subsequent chapters.
The first systematic THDS study on plastically deformed single crystalline molybdenum (bcc) is presented in Chapter k. The thermal
annealing has been followed with THDS. For comparison similar experiments performed on single crystalline copper (fee) are reported as well in Chapter 5- The absence of a clear dislocation related contribution in the spectra was an impetus to study the effect of the magnitude of the helium dose on the observed desorption spectra.
Chapter 6 reports on a detailed series of experiments on plastically deformed molybdenum, post-implanted with varying helium dose. The hypothesis of helium drain by pipe diffusion at room temperature along dislocations is postulated, tested and confirmed by accurate experiments.
A detailed TEM investigation, reported in Chapter 7. to visualize the trapping of helium in plastically deformed molybdenum confirms the hypothesis of helium pipe diffusion and reveals the strongly inhomogeneous production of point defects during plastic deformation. A hybrid Monte Carlo/Diffusion Theory model appears to be very successful in describing the observed trapping of helium at point defects in molybdenum.
GENERAL INTRODUCTION
References Chapter 1
[1] L.M. Wyatt, Harwell Report M/R1750U955) • [2] A.J.E. Foreman, Harwell Report T/M134(1956). [3] J.A. Enderby, UKAEA Report IGR-R/R198U956). [4] A.H. Cottrell, Metall. Rev.
1(1956)479-[5] D.E. Rimmer and A.H. Cottrell, Phil. Mag. 2_( 1957) 1345-[6] R.S. Barnes, Phil. Mag.
3.(1958)97-[7] Proc. First Topical Meeting on Fusion Reactor Materials, Miami Beach 1979, J. Nucl. Mater. 85&86(1979)•
[8] D. Alpert, J. Appl. Phys. 24_(1953)860.
[9] R.B. Burtt, J.S. Colignon and J.H. Leek, Brit. J. Appl. Phys. 12.(1961)396.
[10] E.V. Kornelsen, Can. J. Phys. 4_2_( 1964)364.
[11] E.V. Kornelsen and M.K. Sinha, J. Appl. Phys. 40(1969)2888. [12] E.V. Kornelsen, Rad. Effects 13_( 1972)227.
[13] L.M. Caspers, A. van Veen, A.A. van Gorkum, A. van den Beukel and C M . van Baal, Phys. Stat. Sol. (a) 21(1969)371.
[14] A. van Veen, L.M. Caspers, E.V. Kornelsen, R.H.J. Fastenau, A.A. van Gorkum and A. Warnaar, Phys. Stat. Sol.(a) 40(1977)235. [15] L.M. Caspers, R.H.J. Fastenau, A. van Veen and W.F.W.M.
van Heugten, Phys. Stat. Sol. (a) 46.(1978)541. [16] G.J. van der Kolk, Dr. thesis Delft (1984). [17] A.A. van Gorkum, Dr. thesis Delft (1981).
[18] J.H. Evans, A. van Veen and L.M. Caspers, Nature 291(1981)310. [19] A. van Veen, L.M. Caspers and J.H. Evans, J. Nucl. Mater.
103&104(1981)1181.
[20] A. van Veen, J.H. Evans, W.Th.M. Buters and L.M. Caspers, Rad. Effects 7_8(1983) 105.
[21] A.I. Ryazanov, G.A. Arutyunova, V.A. Borodin, Yu.N. Sokursky and V.I. Chuev, J. Nucl. Mater.
110(1982)65-[22] P.L. Lane and P.J. Goodhew, Phil. Mag.A 48_(1983)965. [23] B.N. Singh, T. Leffers, W.V. Green and M. Victoria,
J. Nucl. Mater.
125(1984)287-[24] J.H. Evans, A. van Veen, J.Th.M. de Hosson, R. Bullough and J.R. Willis, J. Nucl. Mater. 125(1984)298.
2
TECHNICAL REQUIREMENTS FOR THERMAL
HELIUM DESORPTION SPECTROMETRY
2.1. Introduction
The history of Thermal Helium Desorption Spectrometry (THDS) goes back to the early sixties when Kornelsen [1] measured the thermal desorption of helium implanted into polycrystalline tungsten. For a better interpretation of the results it soon became clear that it was necessary to work with atomically clean surfaces, not or hardly covered by (residual) gas atoms. Therefore in practice experiments were carried out under ultra high vacuum (UHV) conditions. The first experiments were performed on resistance-heated tungsten wires conventionally used in radio tubes. The helium ion implantation was carried out with an ill-defined helium glow discharge. Soon it was obvious that more massive samples with well defined and well known surface orientation and surface coverage made the theoretical description of the experiments much easier.
Up to now, THDS has not yet reached the status of a widely spread technique, although it has proved its unique value in several fields of research (on the trapping of helium in tungsten [2], on the stage III dilemma in molybdenum [3], measuring vacancy fractions in III-V semiconductors [ 4 ] , and in a study of the helium clustering and subsequent helium platelet formation in molybdenum [5]). The group of physicists having THDS facilities is very limited (Kornelsen and co-workers (National Research Council, Ottawa, Canada), Carter and Armour (Salford University, U K ) , Van Veen and co-workers
(Interuniversity Reactor Institute, Delft, The Netherlands) and Van den Beukel and co-workers (Delft University of Technology, Delft, The Netherlands)). The interesting thing about THDS is that helium is both a means (probe) to study defects, as the subject to study (helium trapping at defects for the better understanding of irradiation effects in materials).
TECHNICAL REQUIREMENTS
Industry (Leybold Heraeus) once started the development of commercial desorption equipment, but they never succeeded in bringing standard desorption equipment on the market. It is therefore that thermal helium desorption equipment has to be build up partly from standard available UHV products and partly from well-designed special purpose components, build by craftsmen in local workshops. Since all desorption equipment is unique and specifically designed for the applications of interest, a concise description will be given of the equipment used for the work described in this thesis.
2.2. Description of THDS technique
The physical basis of controlled thermal helium desorption spectrometry is the general high mobility (at room temperature) of helium in metals combined with an extremely low solubility. At room temperature, helium was found to diffuse in most metals as an interstitial [2], All rare gases except helium desorb, after implantation, by a multi-step process, first a single jump out of the trap, then a vacancy assisted diffusion to the nearest surface. Although it is often suggested to perform nitrogen or hydrogen desorption experiments as well to complement the insight in atomic trapping processes in metals, there are however severe experimental problems. Firstly, the natural background pressure of helium in UHV equipment usually is very low, typically being of the order of 10 Pa, depending a little on the pumps used (selective pumping) . Therefore any desorbing helium can easily be detected with sensitive detectors, this in contrast to hydrogen and nitrogen which form a substantial part of the rest gas in UHV equipment. Secondly, the sticking of hydrogen and nitrogen to metal surfaces disguises the true desorption process if the sticking energy exceeds the helium-defect dissociation energy. In other terms, after the hydrogen or nitrogen dissociates from traps, it sticks to the surface from which it dissociates later on at a higher temperature. In practice only high temperature desorption processes can be studied.
TECHNICAL REQUIREMENTS
The basic scheme for a THDS experiment is the following. A sample (usually a metal single crystal) is implanted with a low dose of
12 -2
helium ions. A typical dose is 5*10 He cm with an energy chosen so that no atomic displacement occurs as a result of a collision between a helium ion and a matrix atom (this corresponds to a 150 eV ion energy for helium implanted into molybdenum specimens). The sub-threshold implantation energy E. follows from the classical two-particle collision description where the transferred energy is given by
4M M2
Et = = x E. < E,. (2.1)
tr ,,, ,, ,2 ion dis (M1+M2)
where M. stands for the ion mass, M_ for target mass, E,. for
1 d dis
displacement energy and E for transferred energy.
Helium ions neutralise very quickly upon entering metals due to the overwhelming amount of conduction band electrons, thus forming atomic helium. At low implantation energy the average depth of deposition of the helium ions is very small (typically a few nanometers) and from thereon they perform a random walk in the lattice until they
a) find a trap, or,
b) leave the sample via diffusion to the surface (this will be the nearest crystal surface).
Usually the majority of the sub-threshold implanted helium atoms (=95#) escapes via the surface: the trapped fraction of helium is
only a few percent. The trap can be any kind of lattice distortion vacancies [3], impurities [6], dislocations (jogs) [7], bubbles [5], voids, precipitates and grain boundaries [7]- Upon a subsequent ramp anneal of the crystal, helium is released from traps and can be detected as a function of the crystal temperature. The observed desorption temperatures indicate the kind of trap the helium desorbs from and the magnitude of the desorption peak is a direct measure of the trap concentration. An excellent basic description of many theoretical and experimental features of THDS is given by Van Gorkum [8]. To give an idea of the time required to do an experiment a time
TECHNICAL REQUIREMENTS
schedule of a typical helium desorption experiment is given in Fig. 2.1.
PROCESS TIME
Fig. 2.1. Typical times in a standard thermal helium desorption experiment.
There are at least three parameters that can be varied systematically to study the defect nature and the helium-defect interaction:
- the defect concentration,
- the anneal temperature between defect creation and helium decoration (filling),
- the helium filling dose.
Especially the latter two have been used extensively in this study to get information about the identity and quantity of the defects formed by plastic deformation of metals and about the interaction of helium with these defects.
TECHNICAL REQUIREMENTS
2.3. The equipment
2.3-1- The vacuum system
Since THDS is one of the modern (sub)surface techniques, a clean sample surface is required. This invokes the use of an ultra high vacuum system. A scheme of the vacuum system designed for the desorption equipment is given in Fig. 2.2. The central part is a small (0.7 1) vacuum vessel containing the sample holder and sample heater (electron impact heater, 2.5kV 40 mA). The gas ion source is mounted on one of the flanges and a quadrupole mass spectrometer is mounted on a second one. The vacuum vessel is pumped via a throttle valve (to adjust the pumping speed) by a turbomolecular (TM) pump (220 1/s) for its high pumping speed and hydrocarbon-free operation. The TM pump is backed by an oil diffusion pump (DP) to reduce the partial helium pressure at the outlet port of the TM pump, and finally at the atmospheric side there is a rotary roughing pump (RP,
o _ Q
16 m / h r ) . After baking, a base pressure of less than 2x10 Pa is reached. At this base pressure it takes at least 1 hour for a mono-layer of gas atoms to cover the specimen surface. Thus it is ensured that during a desorption experiment the specimen surface is nearly free from any undesired and unknown contamination.
Note that no surface analysis equipment is available in the sample chamber to analyse the crystal surface condition. The only check on the purity of the sample material indirectly comes from desorption experiments themselves. In a special experiment the sample was implanted with sub-threshold helium ions up to a well known (high) dose. The total helium trapping measured afterwards is an indication of the impurity concentration, in the first microns of the sample material, provided they trap helium. Via a simple relation between total helium trapping and defect concentration (Chapter 3) the latter can be calculated easily. It was concluded from such experiments that the impurity level did not exceed 0.1 appm which is sufficiently low for our experiments.
TECHNICAL REQUIREMENTS QMS
[}&y-A
BAKEABLE MM t&h-Did-,—r-@ He ArFig. 2.2. The vacuum system used for the experiments. The upper part in the dashed box is the bakeable UHV part. The
abbreviations stand for:
QMS quadrupole mass spectrometer SC sample chamber
IS ion source
TM turbo molecular pump DP diffusion pump RP roughing pump IN, liquid nitrogen trap MM membrane manometer
TECHNICAL REQUIREMENTS
2.3-2. The specimen holder
On designing the specimen holder, we had to conform to several, as usual contradictory specifications. Mechanical stability, even after repeated temperature ramps up to 0.75 T (ranging from 85O K for copper, 2200 K for molybdenum, up to 2700 K for tungsten), had to be combined with a high thermal isolation but still with some flexability since the sample has to be deformed in the UHV chamber.
THERMO-COUPLE
«rMo-WIRE CRYSTAL
Fig. 2.3. The sample holder, frontview (a) and crosssection (b).
The final geometry, a typical product of the 'trial and error method', is shown in Fig. 2.3. Although not very 'sophisticated', considering all specifications this design proved to be a good compromise.
The disc shaped specimens were cut by a diamond saw from a single crystalline molybdenum rod (99-999% nominal purity). They were ground
TECHNICAL REQUIREMENTS
and polished mechanically with diamond powder down to 0.25 um grain size. They were polished electrolytically with a solution of 25$ H?SCv/75# methanol. Finally in the UHV equipment they were annealed a
-7 few hours at 2000 K at a pressure of 10 Pa.
2.3•3• The gas ion source
The gas ion source (Fig. 2.4) is of an axial ionizer type with a magnetic field around the ionization chamber. It is a slightly modified version of an ion gun designed by A. van Veen [9]
(Interuniversity Reactor Institute, Delft) and built by technicians of our laboratory. It consists of an ionizer (IC), followed by a Pierce extractor (PE), then a transport section (ELI) (transport energy variable, but usually set at 400 eV) leading to a Wien velocity filter section (WF). A Wien filter is an electro-magnetic filter, where the electric field, the magnetic field and the ion trajectory form a orthogonal system. All ions enter the Wien filter with the same energy, therefore a velocity filter can be seen as a mass filter. Ions passing the filter must obeye the equation
q(E+v*B) = 0 (2.2a) yielding qE and v = — (2.2b) 1 2 ;niv = E. = constant (2.2c) 2 ion ' finally we get m = 2E. B2/ ( q E )2 (2.2d) ion ' v^ v '
TECHNICAL REQUIREMENTS
where we have put
q = ion charge, v = ion velocity, E. = ion energy, ion E = electric field, B = magnetic field, m = ion mass.
When leaving the Wien filter section, the ions are either accelerated or decelerated to the chosen ion energy by the Einzel lens section EL2. The beam is wobbled in two directions by two pairs of sweeping plates (SP) to ensure a uniform implantation of the sample area
2
behind the last diaphragm (0.2 cm ). Finally the beam is deflected a few degrees by two deflection plates (DP) to remove the neutral particles from the ion beam, which is usually a very small fraction. In Fig. 2.4 a view of the ion optics is given.
F*:r
D
"ÏC
^
EL1 W F EL2 SP DP
Fig. 2,4, An overview of the optics in the ion source. The abbreviations stand for:
F filament IC ionization chamber PE Pierce extractor E H first Einzellens WF wien filter section EL2 second Einzellens SP sweeping plates DP deflection plates
TECHNICAL REQUIREMENTS
The purity of the ion beam is assured by the use of high purity (99.998%) helium gas, feeding the ion source at a typical operating pressure of 2x10 Pa, and also by the Wien filter section. Although the ion gun has been designed to operate at a pressure of about 2x10 Pa, in this study it was operated at a much lower pressure to limit the partial helium pressure in the vacuum vessel during implantation. This facilitates the helium outgassing of the equipment's interior, prior to the desorption step. The ion energy can be chosen anywhere between 50 eV and 3 keV. Finally the typical ion yield for helium and argon at several energies is given in Table 2.1.
Table 2.1. Typical ion yield (nA)
Ion energy Helium Argon
150 eV 300 eV 500 eV 750 eV 1 keV 1.5 keV 2 keV 2.5 keV 3.0 keV
3
4
8
10
13 15 1518
20
6
9
20
■ 304o
45
55
60
70
2.3.4. The mass spectrometer
The mass spectrometer is a commercial available quadrupole mass spectrometer (Riber QX-200) with a modified ion source of the Bayard-Alpert type. The rod diameter is 1/4" and the filter length is 5 Ö " • It was operated with a dynode multiplier used in the pulse counting mode. A typical detection efficiency of 1 pulse per 3*10 released helium atoms was obtained upon optimizing the quadrupole system performance. During desorption the vacuum vessel was pumped at such a
TECHNICAL REQUIREMENTS
rate that the average residence time T for helium in the vessel was 0.35 s. Immediately after each desorption experiment, the detection efficiency of the quadrupole system was measured. This was done by injecting a known amount of gas into the vacuum vessel followed by integrating the quadrupole response on the inlet of the gas (usually
12
about 1x10 atoms). This amount of gas was measured by filling a 0.834 cc volume out of a 1 litre supply vessel filled up to a well known pressure, measured by an absolute membrane manometer (accuracy
1%). It appeared that in most series of measurements as presented in
this thesis, the measured variation in quadrupole sensitivity did not exceed 5#• Furthermore the quadrupole ion source efficiency proved to be very insensitive to background pressure rises three decades above the partial pressure to be measured.
The above described method of calibration was checked as well by an independent straightforward experiment. A Mo-(100) crystal was
l4 -2
implanted with a high dose 3 keV helium (2x10 He cm ) . The measured total helium trapping should be high, about 95% [10]. By integrating the helium desorption spectrum a total helium trapping of
S8% was found, which is within the limits of accuracy in good
agreement with ref. [10]. We therefore concluded that the calibration method was reliable.
2.3-5- The deformation device
For the in situ plastic deformation of a single crystal of molybdenum, a special device had to be constructed. The most obvious question was how to deform a sample without touching the front side of it, since the front side of the sample will be implanted afterwards with helium to decorate the defects created by plastic deformation. Samples commonly used for in situ straining in an electron microscope could not be used, because those samples do not allow a fast and well defined temperature ramp anneal as needed for THDS. Therefore was chosen for the geometry as shown in Fig. 2.5-Only an outer circle of the front side of the sample is damaged by
TECHNICAL REQUIREMENTS
the impact of the dies, leaving a fairly large undamaged area for implantation later on.
CRYSTAL
Fig. 2.5. The geometry of deformation.
Next the dimensions of the crystal and the deformation device were considered. In Table 2.2 the advantages of a large crystal versus those for a small crystal are summarized.
Table 2.2. Crystal size.considerations
Large crystal Small crystal
-relatively easy to deform -large area for implantation
and therefore more desorption signal
-easy to heat -easy to polish -cheap
One of the requirements of the crystal heater is that it must be able to heat samples up to 0.75 T , i.e. around 2200 K for molybdenum. The power required to heat a disc-shaped crystal to 2200K can be calculated easily. Let D be the crystal diameter, and d the crystal thickness. At high temperatures, certainly above 1200K, most heat is lost by radiation. The radiative power loss P for given crystal
TECHNICAL REQUIREMENTS
dimensions, and hence surface area S, can be written as a function of the temperature :
P = carS(T/*-T^) (2.3)
where we have put
o = 5.67x10 (J s"1 K m "2) , S = nD2/2+nDd ( m2) ,
e = 0.28 (Mo [11]), T = 2200 (K), TQ= 300 (K).
It follows from work by Van Gorkum [8] that the crystal thickness should be at least 20# of the diameter, otherwise there would be an unadmissable radial temperature gradient across the crystal surface, causing a severe disturbance of the shape of the measured desorption peaks. If the maximum available heating power is 100W, then we can calculate the maximum diameter of crystals that can be heated sufficiently. From eq.(2.3) it follows that the maximum diameter to be used is 1 cm. This crystal size was a good compromise between large and small crystals as explained in Table 2.2.
Finally it was calculated whether the force to deform these crystals could be achieved with a device as proposed in the foregoing. Therefore a simplification of the situation of the crystal in the deformation device is given in Fig. 2.6. The problem of an elastic disc clamped between to dies has already been analysed by Nadai [12] in 1925- The equation for the force required to give a stress equal to the yield stress at the convex surface of the crystal is given by 2 co. sinh 10. ona 1 1
F = — [Z "j
~
2 r] (2.4)
p i J„ (A .) (sinh (o.-oo.) 1 1 1 1where we have put
TECHNICAL REQUIREMENTS F = exerted force, v = Poisson ratio, P a = crystal radius, o). = A.d/a, d = crystal thickness,
A. = i root of zero order Bessel function,
1 8 - 2
a = yield stress = 6x10 N m
J1(x) = Bessel function of the first order
Fig. 2.6. The force on a disc supported on the outer edge only.
For several crystal radii a plot is made of this force (Fig. 2.7) as a function of the crystal thickness. From this figure it is clear that for large crystals it is relatively easy to reach the yield stress, whereas for smaller crystals of equal thickness extraordinary large forces are needed.
TECHNICAL REQUIREMENTS
Note that these calculations are based on an isotropic elastic medium. They only serve to estimate the force required to deform specimens, which is of interest for the design of the deformation device.
1.0 1.2 U 1.6 1.É CRYSTAL THICKNESS (mm)
2.0
Fig. 2 . 7 . The force required to cause a s t r e s s equal to the yield s t r e s s at the convex side of the c r y s t a l as a function of the c r y s t a l thickness, calculated for a few c r y s t a l r a d i i .
During o p e r a t i o n , the force e x e r t e d on t h e sample was measured v i a four s t r a i n gauges connected t o an AC-resistance b r i d g e . The maximum a p p l i c a b l e load i s 10 kN. P r i o r to a l l measurements t h e s t r a i n gauge response a s a function of the a p p l i e d force was measured i n a t e n s i l e machine.
2 . 3 . 6 . D e s o r p t i o n , data a c q u i s i t i o n and p r o c e s s i n g
The p r o c e s s t h a t i s t o be followed i s the thermal d e s o r p t i o n of g a s , u s u a l l y helium, from t r a p s i n a metal sample. The r a t e equation
TECHNICAL REQUIREMENTS
of this process, regarded as a single step process, can be written as follows dN dt = -Nve ■Ed/kT(t) (2.5a) where T(t) = TQ + pt, (2.5b)
N = number of helium decorated defects, v = attempt frequency, E_ = dissociation energy, k = Boltzmann's constant, T = temperature, t = time, p = heating rate, T- = temperature of surroundings (RT).
This rate equation can not be solved analytically. Measured desorption peaks were fitted by computer generated first order desorption peaks. The three parameters in the fitting process obviously were E,, v and the peak population. However an alternative set of parameters can also be chosen: peak temperature, FWHM and peak height.
The desorbed amount of gas is recorded as a function of the sample temperature. We have chosen for the dynamical mode of measuring; the desorbed helium atoms spend an average (small) time x in the desorption chamber before they are pumped away. A typical value for the helium residence time is x=0.35 s. Note that Kornelsen in his experiments has chosen for the statical mode of measuring, so (almost) no pumping is involved. Due to the pumping, the relation between the true helium desorption rate L(t) and the measured partial helium pressure P(t) is given by the differential equation
TECHNICAL REQUIREMENTS
where
V = desorption volume, T = average residence time, t = time.
The average helium residence time is determined experimentally by measuring the exponential decrease of the partial helium pressure after a sudden closure of a helium inlet valve. All measured desorption spectra were corrected numerically for the finite residence time t by a proper deconvolution algorithm.
Ifil. -2.5 keV
nsample chamber
I250>
Fig. 2.8. A scheme of the data acquisition and control system.
As s t a t e d above, the desorbed gas i s measured as a function of the sample t e m p e r a t u r e . Therefore a WRe3#-WRe25% thermocouple was connected to t h e sample. The s y s t e m a t i c e r r o r i n the thermocouple r e s p o n s e i s e s t i m a t e d t o be l e s s than 1% according t o the m a n u f a c t u r e r ' s s p e c i f i c a t i o n s . Due t o the r e g u l a r check and c a l i b r a t i o n of t h e AD- and DA-converters, the o v e r a l l s y s t e m a t i c
TECHNICAL REQUIREMENTS
error in the recorded temperature is estimated to be also less than
1%.
The complete block scheme of the equipment is given in Fig. 2.8. The crystal heating and control circuits were developed by G.J. van der Kolk and J. de Roode (Philips Research Laboratories, Eindhoven and Interuniversity Reactor Institute, Delft respectively). The performance of the temperature control system is shown in Fig. 2.9.
80 6 0 -■i/i Ü 40Q: z X 20 "0 10 20 30 40 50" TIME (s)
Fig. 2.9. The performance of the temperature control c i r c u i t s , plotted are the temperature and heating r a t e as a function of time. The heating r a t e was s e t at hO Ks" with a maximum heating temperature of 2000 K.
All parameters such as sample r a t e (O.25-3OO Hz), h e a t i n g r a t e (1-100 - 1
Ks ) and anneal temperature (300-2200 K) a r e parameters i n t h e c o n t r o l software.
A l l equipment i s c o n t r o l l e d by a 16 b i t , microcomputer c o n t r o l l e d (HP 9835A), d a t a a c q u i s i t i o n system (HP 6940B). In each sample p e r i o d two s i g n a l s a r e sent out t o c o n t r o l the c r y s t a l h e a t i n g , and two i n p u t s i g n a l s a r e s t o r e d (measured c r y s t a l temperature and helium d e s o r p t i o n r a t e ) . The d a t a a c q u i s i t i o n software and hardware a l l o w s sample r a t e s up t o 330 Hz, which i s more than s u f f i c i e n t f o r s t a n d a r d
TECHNICAL REQUIREMENTS
desorption experiments, which are carried out at a sample rate of 10 Hz.
One of the standard helium desorption experiments, usually done as a check on the equipment, is the implantation and subsequent
12 -2
desorption of 9-6x10 cm 1 keV helium in molybdenum. With such an experiment the vacancy creation by energetic helium ion impact and the helium decoration of defects occur simultaneously and at such a rate that a very pronounced desorption spectrum can be measured afterwards.
To illustrate the performance of the equipment, finally a series of experiments is shown in Fig. 2.10. In this figure several helium desorption spectra are plotted after implantation with helium of
12 -2
different energies at a helium dose of 9-6x10 cm . In the spectra with an implantation energy roughly below 1.5 keV, only monovacancy desorption peaks (E,F ,F_,G and H) are seen. At a higher implantation energy, contributions of small vacancy clusters (I-peaks) can be seen as well.
TECHNICAL REQUIREMENTS
0 k 8 12 16 20 2k CRYSTAL TEMPERATURE (100 K)
Fig. 2.10. A series of helium desorption spectra at constant helium dose but with different implantation energies, indicated in the figure. The evolution of the spectra for increasing energy is clearly seen. At the lowest energy (250 eV) almost no trapping of helium is observed.
TECHNICAL REQUIREMENTS
References Chapter 2
[1] E.V. Kornelsen, Can. J. Phys. 4_2_( 1964)364. [2] E.V. Kornelsen, Rad. Eff. 13J 1972)227.
[3] L.M. Caspers, A. van Veen, A.A. van Gorkum, A. van den Beukel and C M . van Baal, Phys. Stat. Sol. (a)
21(1976)371-[4] E.V. Kornelsen, A. van Veen, L.M. Caspers and H. Bakker, Phys. Stat. Sol. (a) 29_(1977)Kl43.
[5] A. van Veen, J.H. Evans, W.Th.M. Buters and J.Th.M. de Hosson, Rad. Eff.
28(1983)53-[6] G.J. van der Kolk, Thesis Delft (1984).
[7] J.H. Evans, A. van Veen, J.Th.M. de Hosson, R. Bullough and J.R. Willis, J. Nucl. Mater. 125(1984)298.
[8] A.A. van Gorkum, Thesis Delft (198l).
[9] A. van Veen, A. Warnaar and L.M. Caspers, Vacuum 30(1980)109. [10] A. van Veen and L.M. Caspers, Harwell Symposium on Inert Gases
in Metals and Ionic Solids (1979), ed. S.F. Pugh, AERE Report 9733, P491*.
[11] R.C. Weast, Handbook of Chemistry and Physics, CRC Press, Cleveland Ohio (1976).
[12] A. Nadai, Die Elastischen Platten, Springer Verlag, Berlin (1925).
3
TRAPPING AND RE-TRAPPING OF MOBILE PARTICLES
BY UNIFORMLY DISTRIBUTED NON-SATURABLE TRAPS
W.Th.M. Buters and A. van den Beukel
Laboratory of Metallurgy, Delft University of Technology Rotterdamseweg 137, 2628 AL Delft
The Netherlands
Abstract
The trapping and re-trapping of mobile particles by uniformly distributed non-saturable traps in solids have been calculated by solving the steady-state diffusion equation for mobile particles deposited in a thin layer just beneath the surface.
As an extension of earlier work on the trapping of mobile particles, in more detail the probability for
re-trapping of earlier trapped mobile particles after release from the traps has been calculated. The consequences of trapping and especially of re-trapping as described here have been discussed in view of the application of this theory to Thermal Helium Desorption Spectrometry (THDS) on defects in plastically deformed metals.
3.1. Introduction
The trapping of mobile particles by immobile traps has been the subject of many papers (Kelly and Matzke [1], Gaus [2], Van Veen et al. [ 3 ] , Van Gorkum and Kornelsen [4] and Lin and Johnson [5])- The interest mainly stems from experimental studies on the diffusion of implanted noble gases (like helium) in metals. Interstitial helium,
TRAPPING AND RE-TRAPPING
and probably also other rare gases, migrate freely in metals like Mo, W, and Ni at room temperature.
The calculations of Kelly et al.[l] and Gaus [2] on the trapping of mobile particles are both based on a uniform trap concentration extending to infinite depth. The models of Van Veen et al.[3] and Van Gorkum and Kornelsen [4] have been developed to explain their results obtained by Thermal Helium Desorption Spectrometry (THDS) on trapping of helium by sinks in the vicinity of a metal surface. They showed that vacancies as well as implanted gas atoms act as non-saturable traps for diffusing helium in tungsten [6], molybdenum [7] and nickel [8]. Metallic implants can also act as non-saturable traps in tungsten [9] and probably in other metals too. Therefore their models treat the trapping of mobile particles by a relatively thin layer of immobile non-saturable traps.
When THDS is used to study the trapping and de-trapping (thermal desorption) of helium by a uniform concentration of non-saturable traps, a model must be set up incorporating these features. Uniform trap concentrations arise for instance by homogeneous plastic deformation of metals. During plastic deformation, dislocations and point defects are created in the bulk of the lattice. Although no proof has been given of dislocations being non-saturable traps, it is most likely that they behave as such, as can be concluded from several studies on helium bubble growth at dislocations [10-13]. Uniform trap concentrations are also found in alloys where a solute atom can act as a trap for diffusing mobile particles.
Thermal helium desorption spectrometry is a technique using helium as an atomic probe to detect the presence of defects in a solid. The helium is implanted with low energy into the solid creating little or no extra damage. An estimate of the deposition depth profile of 150 eV helium in molybdenum is given by Schiott [14], yielding a value of approximately 12 A for projected range and 21 A for range straggling (see Fig. 3-1)• This sub-surface injected helium starts to diffuse through the lattice. Part of the helium will be trapped but most helium diffuses out through the crystal surface. Upon subsequent heating of the crystal, trapped helium is released at temperatures characteristic for its binding state to the trap.
TRAPPING AND RE-TRAPPING LÜ
<
oro
CL LÜ Qy
t— GO O —square function -Schitftt theory 1 2 3 DEPTH (100 A)Fig. 3 . 1 . Helium implantation p r o f i l e for 150 eV helium implanted into molybdenum according to Schiott [14] (dashed line) and square function approximation (solid line) used as source Function in the diffusion model.
The aim of t h i s paper i s to derive, for a uniform distribution of
non-saturable traps, analytical expressions for the re-distribution
over the depth of trapped mobile particles i f during release (crystal
heating) deeper traps are present capable of trapping them again
(re-trapping) . Since calculations on the re-trapping of mobile p a r t i c l e s
are an extension of calculations on the trapping, prior to the
section on re-trapping effects, a short treatment will be given of
calculations on the trapping of mobile p a r t i c l e s by a uniform trap
concentration extending to i n f i n i t e depth. I t i s only for reasons of
r e a d a b i l i t y of t h i s paper that e a r l i e r work of for instance Kornelsen
[15] and Kelly and Matzke [1] i s described but now in the same units
as used in this paper.
TRAPPING AND RE-TRAPPING
3.2. The diffusion equation
In ion bombardment experiments, the ion beam diameter (0.1 - 1 cm) is in all cases much larger than the average ion penetration depth
-7 -k
( 1 0 - 1 0 c m ) . Hence the three dimensional diffusion problem reduces to a one dimensional problem. In the following only the dimension perpendicular to the surface of the solid and only jumps between octahaedral positions in a bcc lattice will be considered, describing the diffusion of mobile particles (like helium) in the lattice.
The steady-state diffusion equation describing the diffusion and trapping of mobile particles injected into a solid is
d2c (x) m k c ( x ) c (x) + S(x) = 0 (3.1) with , 2 t m d x 2 2 -1 D = vA /6 diffusivity of the mobile particles (cm s ) , c (x) = the concentration of the mobile particles (at.fr.),
x = the depth beneath the surface (cm), k = zv (s ) ,
z = rate constant,
v = frequency factor (s ) , c (x) = trap concentration (at.fr.),
-1 S(x) = deposition rate of mobile particles (s ) ,
A = an/2 = jump distance of mobile particles (cm),
a. = lattice constant (cm).
The depth dependent deposition rate S(x) is approximated by a square function (see Fig. 3.1)
S(x) = sQ x<=LQ (3.2a)
S(x) = 0 x>LQ (3-2b)
TRAPPING AND RE-TRAPPING note that S(x)dx = s^L- (cm s~ ) (3-2c) Boundary c o n d i t i o n s a r e cm(x=0) = 0 (3-3a) dcm(x) Urn —^— = 0 (3-3b) x->»
Integrating eq.(3-l) over x using boundary condition (3-3b) yields
dc (x)
dx x=0
k |ct(x)cm(x)dx = js(x)dx = sQL0 (3.4)
The first term in eq.(3.4) gives the loss through the surface by diffusion, the right hand term is the integral injection rate, so the total trapped fraction or trapping probability is the ratio f (eq. 3-5).
ft = k |ct(x)cm(x)dx/ |s(x)dx (3.5)
Since in the following a uniform trap concentration is assumed, c (x) reduces to c . Note that in all equations it is not only c that determines the trapping rate, but in fact the product zc , defining a
'trapping strength'.
3.2.1. Solution of the diffusion equation for a square source function
The diffusion equation (3-1) can easily be solved with a square source function (eq.(3.2a-3-2b)). The solution of eq.(3-l) is
TRAPPING AND RE-TRAPPING
c (x) = Aexp(x/L) + Bexp(-x/L) + sQL2/D x<=LQ (3-6a) cm(x) = Cexp(-(x-L0)/L) x>LQ (3.6b) with L2 = D/kc (3-6c) L = diffusion length (cm)
A,
A = - ^ - exP(-L0/L) (3.6d) L 2 SO 1 B = — j j — (-1 + 2e xP ( "Lo/ L ) ) ( 3 > 6 e ) C = -Aexp(L0/L) + Bexp(-L0/L) (3.6f)Note that continuity of both c and its first derivative at x=L_ is
m 0 another condition.
TRAPPING AND RE-TRAPPING Z3 < c_> z o o LU _ l
y
t—<
Q. O U 6 DEPTH (100 A) 10Fig. 3*2. Mobile p a r t i c l e concentration during implantation and subsequent diffusion as a function of depth, calculated with e q . ( 3 . 6 a - f ) , c i s parameter. The dashed l i n e s are l i n e a r approximations of the mobile p a r t i c l e
concentration for depth as used in eq.(3-10c).
concentration for depth x<L~ a t low trap concentrations,
In Fig. 3-2 the mobile p a r t i c l e concentration as a function of
depth following from equations (3-6a-f) i s plotted with c as
parameter. A value for L
nof kO A was taken (see Fig. 3-1)•
3.2.2. Total trapped fraction of mobile p a r t i c l e s
The trapping probability or t o t a l trapped fraction of mobile
p a r t i c l e s now follows from eq.(3-5) combined with e q . ( 3 . 6 a - f ) . I t can
be written as
TRAPPING AND RE-TRAPPING
ffc = [kct/s0][AL/L0(exp(L0/L)-l) + BL/L0(l-exp(-L0/L)) +
+ s0L^/D + CL/LQ]
(3-7)
For low trap concentrations eq.(3.7) reduces to
ft = 0.5/(L0/L) = (L0/2A)/(6zct)
(3-8)
which is a similar result as obtained by Kornelsen [15] and Kelly and Matzke [1]. This means that f is proportional to Jc and to thedepth of deposition L. as follows from eq.(3-6c). A plot of eq.(3-7) (solid line) and eq.(3-8) (dashed line) are shown in Fig. 3-3- The values used were as follows: L.=4oA, A=1.57A (1 half lattice unit, Mo) and z=l. 1 10
-2
o Q: Q-o Z Q_ a. < IX. -2 10 -3 1(1 10 . . I . . I . . , . . , . 1 I I 1 / (/
/ >
/
--.—
/ . . 1 . . 1 . . 1 . . 1 . . 1 . . eq. eq. ' ' (3.8) -(3.7) i . . i . . -9 -7 -5 -3 -1 10 10 10 10 10 TRAP CONCENTRATION cf (at.fr.)Fig- 3.3- Trapping probability for mobile particles as a function of the trap concentration c (eq.(3.7)) (solid line) ani low trap concentration limit (eq.(3-8)) (dashed line).
TRAPPING AND RE-TRAPPING
3.2.3. Re-distribution of trapped particles after release
In most practical situations there is not only one, but there are several types of traps present in the solid. After high energy ion implantation in general, vacancies, vacancy clusters, substitutional and interstitial impurities are introduced in the lattice. During plastic deformation, dislocations and point defects are formed.
Thermal helium desorption spectrometry has become a useful technique because in general different kind of traps also exhibit a different helium binding energy and therefore lead to different release temperatures. However, when the most weakly bound helium is released from traps and if deeper traps, i.e. with higher helium binding energies, are present, it could occur that the released helium falls into deeper traps. This effect, called re-trapping, obscures the original binding state of helium to traps in THDS experiments. To some extent Roodbergen et al. [16] have treated the problem of re-trapping numerically in the case of near-surface vacancies multiply filled with helium. In situations were the mutual distance between defects is comparable to, or smaller than their distances to the surface, this re-trapping effect must be taken into account. This is the case for (a) high trap concentrations (b) traps extending to large depth or both (a) and (b) simultaneously.
To set up a simple analytical model giving an estimate of re-trapping effects, a few assumptions are made
1) only two types of traps are present in the lattice labelled tl and t2,
2) the two types of traps have different binding energies for B B
mobile particles (helium), E .<< E _,
3) tl and t2 are both non-saturable traps and distributed uniformly over the depth,
4) the total trap concentration is defined as c = c .+ c _,
5) both types of traps have the same rate constant z for mobile particle trapping.
First of all the original depth distribution of trapped particles must be calculated. The trapped mobile particle concentration during implantation is proportional to the mobile particle concentration
TRAPPING AND RE-TRAPPING
since c is independent of depth. The mobile particle concentration has been calculated in Section 3-2.2.. In Fig. 3.2 it can be seen that for x<=L„ and especially for low trap concentrations c <10 the depth profile can be approximated by a linear function. For x>L_ the exponential form of eq.(3-6b) will be used. In case of re-trapping, the earlier trapped particles form the new source of diffusing particles, so the shape of trapping profile of eq.(3-6a-f) now determines the shape of the new source function. The equation to be solved is d2c (x) m , 2 t^ m d x 2 kc. c (x) + S(x) = 0 (3.9) This can be w r i t t e n as d2cm(x) Y~ - krcf ccm(x) + S(x) = 0 (3-lOa) d x
where we have put
T = ct /ct (3.10b)
S(x) = SQX/L. X < = = LO (linear> approximation) (3.10c)
S(x) = s0exp(-(x-L0)/L) x>LQ. (3-lOd)
Note that
Js(x)dx = (|LQ + L)s0 (3.10e)
Solving again the diffusion equation (3.10a) yields
cm(x) = Eexp(x/T/L) + Fexpf-x/T/L) + s0L2x/(YDL0) x<=LQ (3.11a)
cm(x) = Gexp(-x/Y/L) - s0L2/(D(l-T)) x>LQ (3-Hb)
TRAPPING AND RE-TRAPPING
with
E = S0L2/(2DT2)(-(1+/Y)"1- L/L0)exp(-L0/T/L) (3.11c)
F = -E (3-Hd)
G = [2Esinh(LQ/Y/L) + sQL2/(DY(1-Y))]exp(L0/Y/L)
(3-He)
Analogous to eq.(3-5). the the probability for re-trapping of a released particle is given by
a> a>
fr = k|rctcm(x)dx /J S(x)dx (3.12)
0 0
From an evaluation of eq.(3-12) combined with eq.(3-lla-e) we get
_1
fr = kYct/((ÏL0+L)s0)[2ELY 2(cosh(L0/Y/L)-l) +
+ L2LQs0/(2YD) +
♦ GLY 2exp(-L0/Y/L)-L3s0/(D(l-Y))] (3.13)
In Fig. 3-^ plots of eq.(3.13) are shown with Y as parameter. It can be seen that for Y approaching unity, the probability of re-trapping f approaches 0.5 at low trap concentrations.
TRAPPING AND RE-TRAPPING
1.0 r-r
10 10 10 10 10 TRAP CONCENTRATION'ct (at.fr.)
Fig. 3.4- The re-trapping probability f for mobile particles function of the total trap concentration with Ï as parameter (see also Section 3-3.)•
If T approaches unity then the vast majority of traps is of type t2. This implies that the depth profile of trapped particles after trapping (Section 3-2.1.) is almost completely governed by the presence of type t2 traps. If the mobile particles, trapped by type tl traps, are released from the traps (Section 3-2.3-) (analogous to helium desorption from traps during crystal heating), they still see a trap concentration of c *c and have a probability of 50% of being trapped again (re-trapped). When the trap concentration c _ and hence the parameter "1 is decreased, one can see that even for T = 0.1, i.e.
c -= 0.9c and c = 0.1c , re-trapping effects are still of the order of 25%. This means for THDS experiments that the relative
contribution of the desorption peak due to helium desorbing from type tl traps is only 0.75*0.9 = 0.675 and the relative contribution of the desorption peak due to helium desorbing from type t2 traps is 0.1+0.25x0.9 = O.325 of the total trapped amount of helium. These results differ significantly from the results if re-trapping was not
TRAPPING AND RE-TRAPPING
corrected for (0.9 vs. 0.1). Finally, in Fig. 3-5 crosssections through Fig. 3-^ at constant c are plotted.
10°
CO<
00o
DC 0_ CDz
Q-<
a:
10 en 10Fig. 3-5. The re-trapping probability F For a mobile particle as a Function oF
Section 3.3'
Function of 7 = c ,/c , now with c as parameter (see also
3-3- Discussion and conclusions
In this paper the trapping and especially the re-trapping effects of mobile particles by non-saturable traps have been calculated. It should be mentioned again that results, obtained here, are directly applicable in case of low energy 'sub-threshold' helium implantations into metals at room temperature (THDS technique).
It has been shown that for uniformly distributed low trap concentrations, typically below 10 appm, the trapped fraction of mobile particles is proportional both to the depth of deposition of the mobile particles and to the square root of the trap concentration (eq.(3-8)). A straightforward application of eq.(3-8) i s t o measure
TRAPPING AND RE-TRAPPING
trapped fraction of helium. In most THDS experiments up to now, traps were distributed in a thin layer just beneath the surface. However, as presented in a following paper [17], in THDS experiments, performed on plastically deformed molybdenum single crystals, traps
(like dislocations, vacancies and small vacancy clusters) were distributed uniformly in the lattice. By measuring total trapped fractions of helium, trap concentrations could be deduced from THDS experiments. Furthermore it can be seen from eq. (3-8) that with THDS the detection limit for trap concentrations is of the order 0.1 appm if it is assumed that the experimental detection limit is 1% total
helium trapping.
In THDS experiments it is desirable to eliminate re-trapping effects of helium which in general obscure the original helium binding state to the trap. If re-trapping effects cannot be eliminated, it is important to give an accurate estimate of this effect. In Section 3-2.3- the case is treated of two different types of traps tl and t2 present in the lattice, where tl is the weakly binding trap and t2 is the strongly binding trap. It has been shown that, for low trap concentrations, the probability for mobile particles, released from trap tl, to trap again, but now at trap t2 approaches 50% if the majority of traps is of type t2 (Fig. 3.5). In
case of equal concentrations of traps of type tl and type t2 this re-trapping effect is of the order of k0%. An application of this is
also found in ref.[17] where is is assumed that in a plastically deformed metal the concentration of traps of type tl (dislocation line segments) equals the concentration of traps of type t2
(vacancies). This implies that of all mobile particles (helium atoms), released from type tl traps (dislocations), l\0% will be trapped again, but now at traps of type t2 (vacancies). So, due to re-trapping, the vacancy related contribution in thermal helium desorption spectra wil be larger than expected from simple trapping theory as presented in Section 3-2.1..
TRAPPING AND RE-TRAPPING
References Chapter 3
[1] R. Kelly and H.-J. Matzke, J. Nucl. Mater. 20.(1966)171. [2] H. Gaus, Z.Naturf.(a) 20(1965)1298.
[3] A. van Veen, L.M. Caspers, E.V. Kornelsen, R.H.J. Fastenau, A.A. van Gorkum and A. Warnaar, Phys. Stat. Sol.(a)
40(1977)235.
[4] A.A. van Gorkum and E.V. Kornelsen, Rad. Effects 42.(1979)93-[5] R.-W. Lin and H.H. Johnson, Acta Metall. 2P_(1982)l8l9. [6] E.V. Kornelsen and A.A. van Gorkum, J. Nucl. Mater.
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[9] G.J. van der Kolk, Dr. Thesis Delft (1984) [10] G.Z. Ganeyev, J. Nucl. Mater. 114(1983)150.
[11] P.L. Lane and P.J. Goodhew, Phil. Mag.A 48_(1983)965. [12] J. Rothaut, H. Schroeder and H. Ullmaier, Phil. Mag. A
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4
THERMAL HELIUM DESORPTION SPECTROMETRY
ON PLASTICALLY DEFORMED MOLYBDENUM
W.Th.M. Buters and A. van den Beukel
Laboratory of Metallurgy, Delft University of Technology Rotterdamseweg 137, 2628 Al Delft
The Netherlands
Abstract
Thermal helium desorption spectrometry (THDS) has been applied to study the effect of plastic deformation on the trapping of low energy helium implanted into molybdenum single crystals. The analysis of the desorption spectra shows the presence of monovacancies at a concentration of 1.6 appm per % strain, which anneal out in the recovery
stage III. No contribution of single helium atoms bound to the dislocations was observed. The high temperature part of the spectra might contain a contribution of helium clusters bound to dislocations. However, after an anneal beyond stage III the main contribution in the desorption spectra is ascribed to helium desorbing from vacancy clusters.
4.1. Introduction
Several investigations have been done on the trapping of helium implanted into metals. A review of experimental work on helium in metals is recently given by Thomas [1]. Almost no experimental studies have been published on the binding energy of helium to extended defects, like dislocations. Knowledge of the binding energy
THERMAL HELIUM DESORPTION
of helium to extended defects is of great value in kinetic models of high temperature behaviour of metals under irradiation.
Many experimental studies on helium in metals are performed using high energy helium implantation into metals, which are often polycrystalline samples. In austenitic steels bubbles were found to nucleate preferentially on dislocations [2] and at grain boundaries [3]. However it is still not clear how the first helium atoms are bound to dislocations.
In order to separate the effects of vacancy creation and helium introduction duripg implantation, decay of thermally dissolved tritium [4] or sub-threshold helium implantation [5] is applied. Furthermore, if effects of grain boundaries have to be excluded, one is restricted to using single crystalline samples. In that case a well defined amount of dislocations can be introduced by in situ straining of the samples.
Up to now especially Thermal Helium Desorption Spectrometry (THDS) [6] has been used to determine the binding energies of helium to various point defects [7]- These studies were mainly done on metal single crystals with low dislocation density. In this paper the first results of thermal helium desorption spectrometry on in situ plastically deformed molybdenum single crystals will be presented. In order to facilitate the analysis of the spectra, first some theoretical considerations will be given (Section 4.3-) on the trapping and re-trapping of helium by vacancies and dislocations.
k.2. Experimental
Molybdenum-(100) single crystals were cut from a molybdenum single crystalline rod of 99-999 % nominal purity. Subsequently the crystals
(1 cm in diameter and approximately 0.2 cm thickness) were ground and polished with diamond powder with a grain size of 1 u m ) . Finally the crystals were polished electrolytically using a solution of
25XH SO(,/75# methanol. Laue back-reflection revealed a perfect Mo-(100) single crystalline surface. After mounting the crystal in
_o
THERMAL HELIUM DESORPTION
several hours in UHV at 2000 K. High dose (5*10 cm" ) 150 eV helium implantation in the as-received samples followed by standard THDS showed a total helium trapping of less than 0.5 %, indicating an
impurity concentration, capable of trapping helium , of less than 0.05 appm. For a detailed description of the technique we refer to Van Veen et al. [8].
A standard helium desorption experiment typically consists of three steps. In the first step damage is introduced into the crystal, for instance by high energy ion bombardment or, as in this work, by in situ plastic deformation (bending of the sample) at room temperature. Subsequently in the second step the damage is 'probed' by helium by means of a 'soft' sub-threshold helium ion implantation. The helium is deposited in a very thin layer just beneath the surface. When thermalized, the helium atoms start a random walk until they diffuse out again through the surface or until they are trapped at defects. In general, different types of defects exhibit different binding energies for helium. For molybdenum the implantation energy was chosen at 150 eV, so that even for central collisions the maximum energy transferred is below the displacement energy (3^ eV for molybdenum).
'CRYSTAL
Fig. <t.l. The geometry of in situ deformation. Crystal thickness d and curvature after bending R.
THERMAL HELIUM DESORPTION
Finally, during a linear temperature ramp anneal (40 K/s) of the crystal, the number of desorbing helium atoms against temperature is recorded and stored by a microcomputer for further processing and analysis. The desorbing helium is detected by a quadrupole mass spectrometer used in the pulse counting mode and the crystal temperature is measured by a WRe3#-WRe25# thermocouple.
Fig. h.1 shows a sketch of the geometry of deformation. Because the
crystal area to be examined is not to be touched, a pair of dies, one concave and one convex, is applied. Therefore, deformation of the crystal results in a circular symmetric bending. An estimate of the strain is based on the amount of bending of the crystal. We assumed pure tension at the front side of the crystal and pure compression at the back side. The strain follows from the simple expression
d
where we have put
E = strain,
d = crystal thickness,
R = crystal curvature after bending.
Deformation of metals produces dislocations, interstitials and vacancies. There are several mechanisms explaining the formation of point defects during plastic deformation of metals [10,11]. Non conservative motion of jogs in jogged dislocations produces point defects. Another more efficient mechanism is the mutual annihilation of two edge dislocations with Burgers vectors of opposite sign and placed on neighbouring glide planes, forming a row of either vacancies or interstitials. A third mechanism of point defect production during cold work is the intersection of dislocations, where vacancies and interstitials are produced in about the same amount.
