70-14,012
FAIRAND, Barry Philip, 1934- FAST NEUTRON SPUTTERING FROM POLYCRYSTALLINE AND MONOCRYSTALLINE GOLD CRYSTALS.
The Ohio State University, Ph.D., 1969 Physics, radiation
University Microfilms, Inc., Ann Arbor, Michigan
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED FAST NEUTRON SPUTTERING FROM POLYCRYSTALLINE
AND MONOCRYSTALLINE GOLD CRYSTALS
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
Barry Philip Fairand, B.Sc., M.Sc,
Vc -k * * * *
The Ohio State University 1969
Approved by
(~rn> Adviser Department of Physics ACKNOWLEDGMENT
The author wishes to express his appreciation to Dr. M. L.
Pool of The Ohio State University for his encouragement and guidance in the pursuit of this research. In addition the author wishes to thank Dr. E. M. Baroody of Battelle Memorial Institute for his helpful suggestions in the preparation of this manuscript.
The author is also indebted to Battelle Memorial Institute for the Battelle Fellowship given to support his research.
ii VITA
May 20, 1934 . . . Born - Watertown, New York
1955 B.Sc., LeMoyne College, Syracuse, New York
1957 M.Sc., The University of Detroit, Detroit Michigan
1957-1969 Physicist, Battelle Memorial Institute, Columbus, Ohio
PUBLICATIONS
"Least Square Matrix Method for Analyzing Neutron Spectra", American Nuclear Society Transactions, Volume 7, p. 371 (1964).
"Sputtering of Polycrystalline Gold by Fast Neutrons", Journal of Applied Physics, Volume 37, pp. 621-623 (1966).
FIELDS OF STUDY
Major Field: Physics
Studies in Mathematics. Professor Zuber
Studies in Classical Mechanics. Professors Wave H. Shaffer and Jan Korringa
Studies in Quantum Mechanics. Professor Andrew Sessler
Studies in Electromagnetism. Professor Albert L. Prebus
Studies in Thermodynamics. Professor Clifford V. Heer
Studies in Modern Physics. Professor Marion L. Pool
iii TABLE OF CONTENTS
Page
ACKNOWLEDGMENT ...... ii
VITA ...... iii
LIST OF TABLES ...... vi
LIST OF ILLUSTRATIONS ...... vii
INTRODUCTION ...... 1
I. THEORY OF HIGH ENERGY NEUTRON INTERACTIONS IN GOLD AND SPUTTERING MODELS ...... 6
Primary Knock-On Atom (PKA) Energy Spectrum .... 6
Displacement Cascade Model in Gold ...... 10
Sputtering Models ...... 17
II. FAST NEUTRON SPUTTERING FROM A POLYCRYSTALLINE GOLD TARGET AND A MONOCRYSTALLINE GOLD TARGET WITH THE <100> DIRECTION NORMAL TO THE TARGET SURFACE ...... 22
Introduction ...... 22
Experimental Procedure ...... 22
Experimental Results ...... 35
Discussion of Results ...... 41
Discussion of Experimental Error ...... 52
III. FAST NEUTRON SPUTTERING FROM A MONOCRYSTALLINE GOLD TARGET WITH THE <111> DIRECTION NORMAL TO THE TARGET SURFACE ...... 56
Introduction ...... 56
Experimental Procedure ...... 57
iv Page
Experimental Results ...... 64
Discussion of Results ...... 68
Discussion of Experimental Error ...... 72
IV. C O N C L U S I O N S ...... 74
APPENDIX
A DISCUSSION OF SPUTTERING MODELS DEVELOPED BY THOMPSON . . . 77
B LEAST SQUARE MATRIX METHOD FOR ANALYZING NEUTRON SPECTRA ...... 85
BIBLIOGRAPHY ...... 89
v LIST OF TABLES
Table Page
1 Results of Neutron Energy Spectrum Measurements Above 0.4 M e V ...... 37
2 Results of Thermal Neutron Flux and Gold Activity Measurements ...... 39
3 Parameters Used in the Calculation of the Sputtering R a t i o s ...... 40
4 Estimated Errors in Factors Determining the Poly crystalline Sputtering Ratio ...... 53
5 Estimated Errors in Factors Determining the Mono crystalline Sputtering Ratio ...... 54
6 Parameters Used in the Calculation of the Sputtering Ratios ...... 67
7 Specified Impurity Contents in Spectrosil ...... 71
8 Estimated Errors in Factors Determining the Sputtering Ratio ...... 73
9 Methods for Finding Fast Neutron Spectra From Activation Experiments...... 86
vi LIST OF ILLUSTRATIONS
Figure Page
1 Diameter of Displacement Cascade Based on Von Jan Model and Vector Range of Gold Atoms in G o l d ...... 15
2 Vacuum Facility ...... 23
3 Sputtering Chamber for One of the Gold Targets ...... 27
4 Quartz Plate Holder for Thermal Neutron Activation E x p e r i m e n t ...... 32
5 Fast Neutron Energy Spectrum ...... 36
6 Primary Knock-On Atom Spectrum in Gold Crystals .... 43
7 In-Pile Vacuum System ...... 58
8 Sputtering Chamber for Gold Target ...... 61
9 Integral Fast Neutron Energy Spectrum ...... 65
vii INTRODUCTION
This dissertation describes experimental studies of atom ejec
tion (sputtering) from the surface of polycrystalline and monocrystal
line gold targets when these targets are bombarded by high energy
neutrons that are produced in a nuclear reactor. These studies repre
sent an extension of earlier work that was confined to fast neutron
sputtering of polycrystalline gold.^ In these more recent experiments
sputtering ratios (atoms of gold sputtered per fast-neutron-crossing
the surface of the target) were measured for gold targets with the
< 100> and < 111> crystallographic direction normal to the target sur
face. Another measurement of the polycrystalline sputtering ratio was
obtained by irradiating a polycrystalline gold target with the < 100>
monocrystalline gold target.
The present experiments were undertaken in order to study
possible differences in the sputtering due to the crystalline state of
the target. It was hoped in this manner to obtain additional informa
tion on the mechanisms responsible for the number of sputtered atoms
observed in the initial experiment. The sputtering ratio of
-4 (1.0 + 0.3) x 10 observed in that experiment was much larger than would be expected on the basis of theory of sputtering by high energy
^D. W. Norcross, B. P. Fairand, and J. N. Anno, J. Appl. Phys. 37, 621 (1966). 1 ions (> 50 keV) developed by Goldman and Simon and modified for fast 3 neutron bombardment by Taimuty. Since no adequate theory to explain the magnitude of the observed sputtering ratio existed at the time these experiments were performed, an experimental study designed to provide additional information on the nature of the sputtering process was considered to be important.
Ejection of atoms from a metal surface by high energy neutrons may provide a useful tool for studying the secondary collision pro cesses which occur in a collision cascade in the bulk of the material.
This may be the case since the primary knock-on atoms (PKA) resulting from neutron interactions in the solid are formed as a volumetric source rather than as a distribution near the target surface. There fore, events occurring near the target surface which lead to atom sputtering may be similar in nature to those events occurring in the bulk."*
^D. T. Goldman and A. Simon, Phys. Rev. 14, 383 (1958).
^S. I. Taimuty, Nucl. Sci. Eng., JJ3, 403 (1961).
4 A collision cascade develops in the material when a neutron interaction in the solid creates a recoil atom (usually referred to as the PKA or primary knock-on atom) which in turn interacts with other atoms in the solid creating additional knock-on atoms.
"*The sputtering ratio by itself can only provide rather limited information as to the details of the collision cascade. However, once a satisfactory theory of sputtering has been developed, data on sputtering ratios together with data on the spatial distri bution and energy spectra of ejected atoms can lead to a comprehensive understanding of secondary collisions. Sputtering of atoms from a material under fast neutron bombard ment is also of interest in thermonuclear research and may be applied to problems encountered in atom ejection from surfaces in the vicinity of high power fast reactor systems.
In addition to the work reported in this dissertation and an earlier publication on fast neutron sputtering in polycrystalline gold the author is aware of only three other investigations of neutron
7 8 9 sputtering in gold. ’ * Two experiments involved the use of a 14 MeV beam of neutrons and a Pu-Be neutron source was employed in the other experiment.
Within the context of the present understanding of fast neutron
sputtering the difference in the sputtering ratios for gold when bom barded by a 14 MeV neutron beam and the neutrons from a reactor source is not unreasonable. However no'satisfactory explanation could be
found to describe the difference in the sputtering ratio in gold for fast neutrons from the Pu-Be source and the other neutron sources.^
Possible theories to explain the observed sputtering ratios are discussed in this dissertation. These theories focus on the
^D. W. Norcross, B. P. Fairand, and J. N. Anno, J. Appl. Phys.
. I. Garber, G. P. Dolya, V. M. Kolyada, A. A. Modlin, and A. I. Fedorenko, J. Exp. and Theo. Phys. (letters), 7, 296 (1968).
^K. Keller and R. V. Lee, J. Appl. Phys., 37, 1890 (1966).
^K, Keller, Plasma Phys., _10, 195 (1968).
^This measurement of the sputtering ratio is thought to be in error. K. Keller, Plasma Phys., p. 198. relative importance of a random sputtering mechanism which does not depend on the particular crystalline state of the target, and an ordered sputtering mechanism which depends on correlated atom colli sion sequences owing to the particular crystalline makeup of the material. The theories which appear to best treat the problem were 11 12 developed by Thompson. *
13 A displacement spike concept similar to Brinkman's model and subsequently improved by Von Jan^4,'*'3,'''^ appears to best describe the interaction of a primary knock-on atom (PKA) in gold. Results
17 18 of work by Merkle ’ where he used an electron microscope to study fission fragment and fast neutron irradiation in gold agree in general
^M. W. Thompson, Phil. Mag., l!8, 377 (1968).
12 Recently Sigmund published a theory of sputtering which is used to estimate the fast neutron sputtering yield based on a random sputtering mechanism. The sputtering yield is developed from the general Boltzman transport equation and appears to provide a more detailed analysis of the random sputtering mechanism than Thompson's work. Because of the late date of publication of Sigmund's work, it was not possible to integrate his analysis into the dissertation. However the sputtering yields predicted by Sigmund's model do not appear to differ by more than a factor of about two from values pre dicted by Thompson's model. This difference does not alter the con clusions of this dissertation. Peter Sigmund, Phys. Rev., 184, 383 (1969).
13J. A. Brinkman, Amer. J . Phys., 24, 246 (1956).
14r. V. Jan, Phys. Stat. Sol., 6, 925 (1964).
15r. V. Jan, Phys. Stat. Sol., 7, 299 (1964).
16r. V. Jan, Phys. Stat. Sol., 8 , 331 (1965).
17k. L. Merkle, J. Appl. Phys., 38[, 301 (1967).
18 M. J. Makin (ed.), The Nature of Small Defect Clusters (Atomic Energy Research Establishment, Harwell, 1966), Vol. I, pp. 8-37. with this model. Models derived by Thompson to explain the sputter
ing ratios for solids when bombarded by high energy ions are modified
to treat the fast neutron sputtering problem.
This dissertation is organized in four main sections. The 20 first is a review of the theory of high energy neutron interactions
in gold and a discussion of possible models to account for the sput
tering of atoms from the gold surface. The theory of high energy
neutron interactions in gold includes a discussion of the primary
knock-on atom (PKA) energy spectrum and the displacement cascade cre
ated when the PKA slows down in gold. The first section is followed
by two presentations where one treats the experiment on sputtering
from the surface of a polycrystalline target and a monocrystalline
gold target with its < 100> crystallographic direction normal to the
target surface and the other presentation is devoted to the experiment
on sputtering from the surface of the monocrystal with its < 111> crys
tallographic direction normal to the target surface. The fourth
section of the dissertation presents the principal conclusions drawn
from this study.
Details of the derivations of equations used in determining
the sputtering ratios and the procedure used to calculate the neutron
energy spectrum are given in appendixes.
^M. W. Thompson, Phil. Mag., 18. 20 The Battelle Research Reactor was used as the source of high energy (fast) neutrons where most fast neutrons have energies between 0.1 MeV and 10 MeV. I. THEORY OF HIGH ENERGY NEUTRON INTERACTIONS IN GOLD AND SPUTTERING MODELS
Primary Knock-On Atom (PKA) Energy Spectrum
For the nuclear reactor neutron source used in the experiments the major source of high energy primary knock-on atoms in gold are elastic (n,n) and inelastic (n,n') scattering collisions with the neu trons. The differential cross section for a neutron having an initial energy in the laboratory coordinate system of E , to produce a recoil atom with energy between T and T + dT is
K
q(T) = N f K(T,E ) cp (E ) dE (2) o° ii xi n n
where N q is the number of atoms per unit volume in gold.
The energy transferred to a gold atom (neglecting crystal binding energies) in an elastic or inelastic scattering collision from a neutron having an energy En is
6 where A is the mass ratio of the gold atom to neutron, e is the energy of the outgoing neutron expressed in the center-of-mass coordinate system, and 0 is the scattering angle in the center-of-mass coordinate 2 2 system. For elastic scattering e = (A /(A+l) ) En and Equation (3) reduces to the more familiar form
4 A E n 2 ft T = r sin — . (4) (A+l) Z
The value of (T,En) is given by
Kel <5> where da^/dQ is the cross section per unit solid angle for scattering at angle 9 into solid angle dfi. Using Equation (4), Equation (5) can be rewritten as
j. i,v 2 da K CT E ) = -- Kel' ’ n' A E df) * ( ' n
21 From known values of da ,/dQ the elastic cross section is el found from Equation (6).
For inelastic scattering events a spectrum of possible neutron energies, as viewed in the center of mass system, may be emitted by
21 M. D. Goldberg, V. M. May, and J. R. Stehn, Angular Distri buttons in Neutron-Induced Reactions, BNL 400, Vol. II, 2nd ed. (October, 1962). the gold nucleus for a given incident neutron energy. The energy spectrum for the emitted neutrons is described approximately by the
Maxwell evaporation spectrum
_ £
N(e) = e * (7) x where h is a nuclear temperature which depends on the incident neutron 22 energy. The calculation of *-s simplified by the fact that for gold *-s approximately independent of the scattering angle 0 and can be set equal to c^Att where is the total inelastic 23 scattering cross section at a given incident neutron energy. For a given E r and e the spectrum of possible recoil energies observed in the laboratory coordinate system will be uniformly distributed between the limits
AF ^2 2 AF ^2 2 i r n - «1/2ff ST* 1 + €I/21 (8) A L(A + 1) J A L(A + 1) J
The inelastic cross section is given by
e CTT I* n dQ K
A 2 The upper limit on the integral is e = ----- ~ E and is the n (A+ir n same as the energy transferred to the outgoing neutron in an elastic
22D. B. Thomson, Phys. Rev., 129, 1649 (1963).
23_. . . Ibid. scattering collision. The lower limit on the integral depends on the particular value of T. Based on Equation (8) the maximum and minimum values for T are expressed in terms of e by
AT - (1 + x)2 n £ x £ ( ) and 0 1 10
AT . 0 m n - (1 - X )2 e 1 n .2 where X = (e/e1}* For a glven value of T the corresponding value for e is found from that expression given by Equation (10) which satisfies the condition 0 ^ X 5 !•
Equation (9) may be rewritten as
(A+l) p n i/o -e/jt K
N(e) is given by Equation (7). From known values of a the inelastic 24 cross section is found from Equation (11).
The sum of Equations (6) and (11) is used in Equation (2) to evaluate the PKA energy spectrum.
24 M. D. Goldberg, S. F. Mughabghab, S. N. Purohit, B. A. Magurno, and V. M. May, Neutron Cross Sections, BNL 325, Vol. IIC, 2d ed., Supp. 2 (August, 1966). 10
Displacement Cascade Model in Gold
The primary knoclc-on atoms created by interactions with the fast neutrons produced in the nuclear reactor source typically have energies that range from a few keV to several tens of keV. Over this energy range the PKA transfers most of its energy to other gold atoms in the form of atom motion. Energy losses through excitation and ionization of electrons are negligible for PKA energies less than
25 100 keV. The PKA, in slowing down, sets atoms in the gold lattice into motion. These atoms in turn share their energy with other atoms.
If the energy transferred to a struck atom is greater than E^, which is the energy required in order to remove the struck atom from its lattice site, it will move in the lattice and possibly displace other atoms. In this manner a cascade of displaced atoms (displacement cas cade) can develop inside the gold lattice. In general the equations governing the motion of these atoms can be treated quite accurately using classical scattering theory. The ability to approximate the quantum mechanical treatment by classical methods and the range of 26 validity of this approximation is discussed by Carter and Colligon.
If an adequate expression for the interatomic potential is available then the detailed motions occurring within the displacement cascade
25 R. S. Nelson, The Observation of Atomic Collisions In Crystalline Solids, edited by S. Amelinckx, R. Gevers, and J. Nihoul (John Wiley and Sons, Inc., New York, 1968), Vol. I, pp. 35-37.
26 G. Carter, and J. S. Colligon, Ion Bombardment of Solids. (American Elsevier Publishing Co. Inc., New York, 1968), pp. 27-30. 11 can in principle be determined. Because the problem is many bodied it normally is not tractable by any reasonable hand calculational schemes.
In order to avoid difficulties associated with the treatment of a many-body collisional problem, analytical models for predicting the effects of a PKA moving in a crystal lattice have evoked various simplifying assumptions which limit the problem to isolated binary collisions, the interaction of an atom with its nearest neighbors, or smear out the details of the atom motions through statistical processes.
An early model to account for the interaction of high energy
PKA's in heavy metals was proposed by Brinkman and is commonly 27 referred to as the displacement spike model. According to Brinkman, a displacement spike occurs when the knock-on atom's mean-free-path between collisions is less than the atom diameter. Under these circum stances a vacancy rich region is created in the metal which is sur rounded by a mantle rich in interstitial atoms. This produces a highly unstable region in the metal which forces the atoms to rapidly recombine. Brinkman estimated that knock-on atoms in gold with ener gies between about 400 eV and 80 keV would produce a displacement spike. This model did not take into account atom collision effects that could be caused by the crystal lattice structure.
Silsbee was one of the first people to look at the effect of 28 the ordered crystal lattice on atom collisions in solids. He
27 J. A. Brinkman, Amer. J. Phys.
^ R . H. Silsbee, J. Appl. Phys., 28, 1246 (1957). 12
pointed out that under certain conditions the momentum of a knock-on atom could be efficiently focused along close packed crystal direc
tions over many interatomic distances. In this manner an atom could be removed from its lattice.site even though it was far removed from
the major disturbance created by the displacement cascade.
Since Silsbee's work there has been numerous studies on various types of correlated collisions sequences that may occur when
the ordered nature of the crystal lattice is taken into account. Much 29 30 of this work is summarized in the references listed here. * In
gold, focusing events which occur along the close packed crystal directions appear to be the dominate source of correlated collision
sequences^.
Numerical schemes based on the use of high speed computers have provided one method for examining in detail the trajectories of many atoms at one time. Gibson, and his co-workers, were the first
to use this approach to study the dynamics of radiation damage in
31 copper. Correlated collision sequences arising from the ordered nature of the crystal lattice were clearly evidenced. The develop ment of a displacement cascade with some regions in the crystal
29 R. S. Nelson, The Observation of Atomic Collisions in Crystalline Solids, pp. 170-195.
30 M. W. Thompson, Defects and Radiation Damage in Metals, edited by A. Herzenberg and J. M. Ziman (Cambridge University Press, London, England, 1969), pp. 167-225.
31 J. B. Gibson, A. N. Goland, M. Milgram, and G. H. Vineyard, Phys. Rev., 120, 1229 (1960). 13
lattice being left depleted in atoms while other regions were rich in interstitial atoms was also evidenced. Beeler, using a somewhat dif ferent approach and emphasizing higher knock-on atom energies, arrived 32 at similar conclusions.
Von Jan has studied the spatial distribution of vacancies and 3 3 3^, ^ ^ interstitial atoms produced in a displacement cascade. * * He
36 used the work of Holmes and Leibfried on range calculations and added a displacement model in order to separately calculate mean values for the vacancy and interstitial distributions. Von Jan found that in gold there is a tendency for vacancies to accumulate at the center of the displacement cascade even when the cascade is initiated by ener getic primary knock-on atoms. Before recombination processes occur, the damaged region is envisioned as an irregularly shaped vacancy zone
surrounded by a region that is rich in interstitial atoms. This is 37 quite similar to Brinkman's displacement spike concept. Unlike
Brinkman's concept, however, spontaneous recombination may not be com
plete and a center vacancy region remains after the damage event has
subsided. The Von Jan model predicts that the displacement cascade consists of a single damaged region and splitting into subcascades
■^J. R. Beeler, Jr., Phys. Rev., 150, 470 (1966). 33 R. v. Jan, Phys. Stat. Sol., £. 34 R. v. Jan, Phys. Stat. Sol., 1_.
35 R. v. Jan, Phys. Stat. Sol., 8>.
D. K. Holmes and G. Leibried, J. Appl. Phys., 31^, 1046 (1960).
37 J. A. Brinkman, Amer. J. Phys. 14 does not occur even for maximum primary recoil energies that are expected in the reactor irradiation. However, Von Jan felt that for primary recoil energies greater than about 10 keV, recombination processes may divide the central vacancy region into several smaller regions.
Merkle *has irradiated thin films of gold in a fast neutron 38 39 environment similar to the one used in this experiment. ’ He examined the damage to the gold samples by transmission electron microscopy. He observed defect clusters under the electron microscope which he attributed to the creation of small vacancy zones with only one defect cluster formed for each energetic atom recoil produced by a scattering event with a fast neutron. These vacancy zones are pre
sumably formed during the development of the displacement cascade and not by homogeneous nucleation processes. These results agree with the model proposed by Von Jan for gold except that a single vacancy zone remains after spontaneous recombination, and any splitting into
smaller zones occurs at energies considerably greater than 10 keV.
The Von Jan prediction for the diameter of the disturbed region in the crystal lattice which contains 91 percent of the defects is shown in
Figure 1 as a function of PKA energy. Since only one displacement
38 Radiation Effects, edited by W. F. Sheely (Gordon and Breach Science Publishers, Inc., New York, 1967), Vol. 37, pp. 173-181.
on K. L. Merkle, The Nature of Small Defect Clusters, pp. 173 181. CASCADE DIAMETER OR VECTOR RANGE, angstroms 200 160 120 80 FIGURE 1. DIAMETER OF DISPLACEMENT CASCADE BASED ON VON JAN VON ON BASED CASCADE DISPLACEMENT OF DIAMETER 1. FIGURE 40 060 20 MODEL AND VECTOR RANGE OF GOLD ATOMS IN GOLD IN ATOMS GOLD OF RANGE VECTOR AND MODEL RMR KOKO AO EEG, keV ENERGY, ATOM KNOCK-ON PRIMARY PRIMARY 080 40 ATOM ACD DIAMETER CASCADE ETR RANGE VECTOR ENERGY 100 120 15 140 cascade is formed in gold per energetic PKA, the vector range of the primary recoil atom (the vector distance between the starting point and the point where the particle comes to rest) should provide an approximate lower limit on the diameter of this disturbed region.
The vector range for gold atoms in gold is also shown in Figure 1.
For energies less than 20 keV the curve is a theoretical fit to experi- 40 mental data. The curve above 20 keV is a linear extrapolation of the theoretical curve between 15 keV and 20 keV where the vector range increases approximately linearly with increasing PKA energy.
It is envisioned that two mechanisms, both generated by the displacement cascade, may contribute to the number of atoms sputtered from the gold surface. In one mechanism a displacement cascade is formed near enough to the surface so that secondary and higher order knock-on atoms are directly sputtered from the surface. This is referred to as the random sputtering model. Long range focusing o events Oc 100 A) specifically along close packed crystal directions may contribute to the observed number of sputtered atoms. This is referred to as the ordered sputtering model.
40 Solid State Physics, edited by Frederick Seitz and David Turnbull (Academic Press, New York, 1966), Vol. 18, p. 31. 17
Sputtering Models
Sputtering Models Based on Thompson Work
To assist in the interpretation of the energy spectrum of ejected atoms during the sputtering of gold by high energy A+ ions ■f 41 and Xe ions, Thompson developed theoretical models in which atom ejection may result from either a random sputtering mechanism or the generation of focused collision sequences. Since the basic assump tions that were made in deriving these models are equally applicable to fast neutron sputtering in gold, Thompson's models are used in this work in order to provide estimates for the fast neutron sputtering 42 ratios. The essential relationships used in the derivation of these models are discussed on the following pages. Additional details on
the derivation of the relationships for the sputtering ratios are pre
sented in Appendix A.
Random Model for Sputtering
Assume that atoms in a solid, which is effectively infinite in
size, recoil from some primary event with energy T. An expression for
41 M. W. Thompson, Phil. Mag., 18.
42 Only the random model and the model for focusing along the close packed crystal directions are used in the interpretation of the fast neutron sputtering ratios. Thompson also developed a model based on what is termed assisted focusing collisions. This type of colli sion occurs along the < 100> and < 111> crystal directions and focusing is assisted by rings of atoms surrounding the atom path. In gold, simple focusing is much more probable than assisted focusing. For this reason sputtering by the assisted focusing mechanism is not considered. the flux of atoms in the energy interval dE ' at E* crossing any inter nal surface in the solid and traveling into a solid angle dQ in direction x' is
CO cos 9 dQ/dE/ cp(E ', r')dE'dQ' = T) — f q(T)TdT (12) 4tt ( E ' ) 2 JE, where D is the nearest neighbor spacing in gold, q(T) is the density of primary knock-on atoms at energy T, 8 is the angle between the sur- face normal and r /, and T) is a constant of order unity.
It is now assumed that the infinite solid is cut in half and the flux of atoms emerging from the surface in the energy interval dE at E is observed. The surface effect on the flux of sputtered atoms is taken into account by assuming that a binding force acts normal to the surface. The surface therefore has a refractive effect where a sputtered atoms velocity component normal to the surface will be reduced by subtracting the binding energy E^ from that part of its kinetic energy. When this surface effect is taken into account the flux of sputtered atoms in the energy interval dE at E and traveling into a solid angle dfi is
00
Tq(T)dT (13)
b where T is the angle between the surface normal and the sputtered atom trajectory.
Thompson contends that this assumption will lead to an over estimate of ejection, particularly at low energies. 19
In subsequent estimates of the sputtering ratio the PKA energy spectrum is approximated by a set of monoenergetic source where
q(T) = E q. 6 (Ti - E) (14) i and the summation is over all sources. After substitution of this expression into Equation (13) and integration over dT, df2, and dE, the total flux of sputtered atoms is given by
"’-'"sirb i ?"iTi • <15)
In the calculation of the sputtering ratio it is assumed that the neutron flux environment at the surface of the gold target is isotropic. The number of neutrons crossing the target surface per unit area and time is w^ere 'Pp *s t^ie fast neutron flux at the location of the sputtering experiment. Based on the expression for the total flux given by Equation (15) the sputtering ratio is
A*, ~ T] t t 2 — E q. T. (16) R ^ b ^ F i 1 1
Ordered Model for Sputtering From Focused Collision Sequences
The type of collision sequence considered here occurs along the closest packed atom row in the gold lattice. In a face centered cubic crystal such as gold this is the <110> crystal direction. For this type of collision sequence the flux of atoms sputtered from the surface with energy in the interval dE at E and directed along a particular close packed crystal direction is given by 20
cp(E,Y)dE = J q(T) J X(T,E') cos y dr dT dE ' . (17) T o
In this equation X(T,E/) dE* is the number of secondary recoils with energy in the interval dE; at E ; generated by a primary knock-on of energy T and moving so as to initiate a focused sequence along a particular close packed crystal direction.
The source of these collision sequences is a slab of thickness drcos Y at a depth rcos Y from the solid surface. The integration over dr extends from the surface to ? which is the maximum range for ejection of atoms with energy E. Following the rationale developed by Thompson and using the expression for XCTjE7) derived by Sanders 44 and Thompson the expression for the flux of sputtered atoms in a particular close packed crystal direction is
L/ct _ o»r cp(E,Y)dE = J q(T) J L|c,|sY(l-grJ__ g 2 dr dT dE . (18) j q 2DEj (E *t E^)
45 In this equation E^ is the focusing energy threshold, E^ the effec tive surface binding energy, D the nearest neighbor interatomic spacing in gold, and B is the exponential parameter in the Born-Mayer
_r /B interatomic potential of the form e . The quantity L /a is given by {1/a) ln^E^/CE-tE^)^ where a approximately equals (1/39D) lnCE^/E^).
44 J. B. Sanders and M. W. Thompson, Phil. Mag., T7, 211 (1968).
45 A knock-on atom cannot initiate a focusing sequence unless its energy is equal to or less than E^. Substitution of Equation (14) into Equation (18) and integration over dT and dr gives
E q£ Tt BcosY 3/2 E ,E+E .1/2 . ,,(Ej,)dE, „ 2— ( _ j _ ) { ln( _ x . ) + 2( _ b ) .2} dE . (19)
Equation (19) is integrated over dE from zero to E^ - E^. Carrying out this integration Equation (19) becomes
78 BcosY E q± T. £ 1/2 4£ 1/2
» ( » ------^ — - { [ i + ( $ ./^j ^ (20) b “ f
This is the total flux leaving the surface along a close packed crys tal direction whose angle to the surface normal is Y. The total flux of sputtered atoms is obtained from Equation (20) by summing over all close packed crystal directions which are directed out of the target surface. Based on a focusing mechanism the sputtering ratio is
v 1/2 aw lf2 A = E 1. cos f. E q. T. {l + (=~) - . F EFtpF J 3 3 i 1 b ln(Ef/Eb) \^Vi ' ^lTl] } (21) % E f where cp_ is the fast neutron flux and 1 . is summed over all close TF j packed directions which lead out of the target surface at angle Y . II. FAST NEUTRON SPUTTERING FROM A POLYCRYSTALLINE GOLD TARGET AND A MONOCRYSTALLINE GOLD TARGET WITH THE <100> DIRECTION NORMAL TO THE TARGET SURFACE
Introduction
Battelle Memorial Institute's research reactor was used as the source of high energy neutrons. This facility is a light-water moderated swimming pool reactor with a normal operating power of two- megawatts. The reactor core which is located approximately 20 feet below the surface of the water consists of highly enriched uranium-235 fuel elements. The experiment was performed a few inches from the reactor core where the neutron environment consists of a fast compo nent approximated by a fission neutron energy spectrum and a slowing down component whose energy spectrum varies approximately as one over the neutron energy.
Experimental Procedure
Description of Vacuum Facility
Figure 2 is a schematic of the vacuum facility that housed the experimental apparatus. This facility consisted of a 5-in. diam eter aluminum pipe welded shut at the bottom. The outside of this pipe was covered on the bottom and over a length of 49 inches with a
0.060-in. thick sheet of cadmium. This assembly was placed into a
22 23
TO VACUUM PUMP
132
8"0IA. LEAD OUT PIPE
INTERMEDIATE SPACE CADMIUM FILLED WITH BAC COVER
APPROXIMATE v REACTOR \ LOCATION OF \ C 0 R E \ EXPERIMENT PACKAGE
*
FIGURE 2. VACUUM FACILITY concentric aluminum pipe with a 7-in. diameter and the intermediate space was filled with B^C powder compacted to a density of approxi- 3 mately 1.5 gm/cm . The two pipes were mated at a flange located 49.5 inches from the bottom of the assembly. This portion of the vacuum facility was located approximately two and one-half inches from the reactor core face. An 8 -in. diameter aluminum lead-out pipe con nected the core end of the vacuum facility with a fore pump and dif fusion pump which were located above the surface of the water. This system was able to maintain a vacuum of about 10 "* torr. in the irradiation chamber.
The part of the vacuum facility containing the target assembly was covered with cadmium and B.C in order to absorb the thermal neu- 4 trons and reduce the neutron flux at the 4.9 eV resonance peak of gold. This was done in order to confirm an earlier conclusion that neutron sputtering by gold recoils from (n,y) interactions is much 46 less than sputtering by fast neutrons.
Measurement of the Neutron Environment Inside the Vacuum Facility
The neutron energy spectrum at the core end of the vacuum facility was measured at the approximate position that would be occu pied by the experimental apparatus. These measurements were made at reduced reactor power and normalized to the experiment irradiation
46 D. W. Norcross, B. P. Fairand, and J. N. Anno, J. Appl. Phys., p. 623. 25
power by use of the reactor power monitor and the measured activity
of nickel dosimeter wires irradiated with the gold targets.
The fast neutron energy spectrum above 0.4 MeV was measured with threshold radioactivants where a least square over-determined 47 matrix method was utilized in the data analysis (Appendix B). This
technique resolves the neutron spectrum above 0.4 MeV into six energy
groups.
The fast neutron spectrum was calculated from the measured 239 237 activities of the following reactions: Pu(n,f), Np(n,f),
115t , /Nt 115m 238,.. 58.,’ 58 32_, .,,32 28... . In(n,n )In , U(n,f), Ni(n,p)Co , S(n,p)P , Si(n,p)
Al^, ^Al(n,p)Mg^, ^Al(n,or)Na^, and *^I(n,2n)I*^. All of these 239 detectors except for Pu were used in the least square over
determined matrix method to calculate the neutron energy spectrum
above 0.4 MeV. 239 The Pu detector was used to estimate the total flux greater
than 0.01 MeV. An effective threshold concept was used where the
energy dependent cross section is approximated by a step function. 239 The parameters selected for the Pu detector were an effective
energy threshold of 0.01 MeV and an energy independent cross section
-24 2 above this energy of 1.8 x 10 cm .
The intermediate neutron energy spectrum at the specimen loca
tion would normally approximate the 1/En slowing down spectrum where
En is the neutron energy. However, it was anticipated that the cadmium
47 H. M. Epstein, B. P. Fairand, and B. L. Schrock, American Nuclear Society Transactions, T_, No. 2, 371 (1964). 26 and B^C shielding would not only absorb the thermal neutrons but in
addition significantly reduce the unperturbed neutron flux up to ener-
48 gies of several eV. Therefore, a thick foil method was used to measure the neutron flux at the 4.9 eV gold resonance and the 132 eV
cobalt resonance. A 1/En spectrum was assumed for energies above the cobalt resonance at 132 eV and this spectrum was matched to the fast neutron spectrum at 0.4 MeV.
Description of the Experimental Apparatus and Gold Targets
In this experiment the sputtering ratios for a polycrystalline
gold target and a monocrystalline gold target with the < 100> crystal
direction normal to the surface were measured. A schematic of the
sample holder for one of these gold targets is shown in Figure 3. An
identical holder positioned directly on top of the assembly shown in
Figure 3 was used for the other gold target. The completed assembly
resembled a pillbox arrangement where the sputtered gold atoms were
collected on a thin quartz collector plate. Since some atoms arriving
at the collector plate may be reflected back to the plane of the tar
get, a quartz reflector plate was placed around the gold target. The
target was positioned on an aluminum pedestal which protruded through
^G. Ehret, Atompraxis, 393 (1961), Trans. F. Lachman (Atomic Energy Research Establishment, Harwell, England), AERE- Trans-906. 27
ALUMINUM COVER ' PLATE
QUARTZ COLLECTOR
ALUMINUM SPACER RING
QUARTZ REFLECTOR
GOLD TARGET NICKEL DOSIMETER WIRE
-ALUMINUM MOUNT
F-IGURE 3. SPUTTERING CHAMBER FOR ONE OF THE GOLD TARGETS 28
49 a hole centered in the quartz reflector. A 0.009-in. thick aluminum cap with a 3/16-in. diameter hole was placed over the pedistal. This cap positioned the targets on the pedistal and exposed a 3/16-in. diameter circular target surface to the sputtering chamber. The dis tance from the target surface to the quartz collector plate was 0.268 in. and the effective diameter of the quartz collector and reflector plates was 4.00 in. As noted earlier the fast neutron flux during the irradiation was monitored by means of a nickel wire wrapped around the base of the aluminum pedistal. The apparatus was mounted in the vacuum facility so that the surface of the gold target was normal to the reactor core face.^
49 The collector plates were made from high purity synthetic fused quartz. These collectors are not discolored by neutron bombard ment during the irradiation and after the irradiation any visible deposition of sputtered atoms on the collector plates could easily be seen. The reflector plates were made from natural quartz. All quartz plates were obtained from the Thermal American Fused Quartz Company in Montville, N.J.
50 In the calculation of the sputtering ratio it is assumed that the fast neutron flux environment at the surface of the gold targets is isotropic. Since the exterior wall of the vacuum facility is only separated from the reactor core face by approximately two and one-half inches of water, some anisotropy in the neutron environment at the target surface is expected. However, the correction to the sputtering ratio which accounts for the anisotropy in the neutron environment should not be too large. This is based on the fact that the gold targets are located at least one scattering mean free path (2 MeV neutrons) from the neutron source, and the reactor core face can be effectively treated as an infinite slab which isotropically emits neutrons. 29
The polycrystalline gold target was taken from a sheet of
99.999 percent pure 0.0005-in. thick gold foil. The monocrystal tar
get was grown epitaxially on a sodium chloride substrate. In this
technique gold is evaporated onto a cleaved NaCl crystal at 400°C whose <100> axis is normal to the crystal surface. The entire proce
dure is conducted in a vacuum of about 10 torr."** After the epitax
ial deposition of the gold film on the NaCl substrate the monocrystal-
linity of the gold crystal was checked by X-ray diffraction and it was determined that the gold target had its principal orientation with the
{l00} planes in the surface. The gold monocrystal was removed from
the NaCl substrate by immersing the gold film-substrate composite into distilled water. After the NaCl substrate had dissolved, the monocrys
tal was transferred to the aluminum pedistal in the experimental
apparatus. The thickness of the monocrystal was not determined. How
ever it was conservatively estimated to be greater than 1000 angstroms
thick.
After the experimental apparatus was inserted into the vacuum
facility and the system was assembled it was pumped with a fore pump
and diffusion pump and allowed to outgas for approximately 24 hours.
The facility containing the experimental apparatus was then moved into
the vicinity of the reactor core.
The pressure at the pump end of the vacuum system after it was moved into the vicinity of the core was 2 x 10 ^ torr. This measure ment was made with an ionization gauge. The pressure at the core end
W. Pashley, Advan. Phys., Jj, 173 (1956). 30 of the vacuum system was estimated to be between 7 x 10 and 8 x 10 torr. This was based on later measurements of the pressure at the core end of the system and comparison to measurements at the pump end of the vacuum facility. Approximately 18 hours after initiation of the irradiation the pressure at the core end of the vacuum facility was measured with an ionization gauge to be 3.3 x 10 ^ torr. During the remainder of the irradiation the pressure varied between the maxi mum value of 3.3 x 10 torr and a minimum of 2 x 10 ^ torr. The total irradiation time was 284.8 hours. Temperatures in the experi mental apparatus should not have exceeded about 50°C. This is based on the good thermal contact of the experimental apparatus with the walls of the vacuum facility which were maintained at about 45°C by the reactor pool water.
Procedure for Determining the Number of Sputtered Atoms
To measure the number of gold atoms sputtered onto the quartz plates a radioactive tracer technique was employed. In this method a known fraction of the gold atoms are made radioactive by activation with thermal neutrons. From a measurement of the induced activity it is possible to calculate the number of sputtered atoms. In earlier work the radioactive gold atoms were generated "in-pile" simultaneously
52 with sputtering by fast neutron irradiation of the target. In the present experiment the thermal neutron shield prevented "in-pile"
52 D. W. Norcross, B. P. Fairand, and J. N. Anno, J. Appl. Phys., p. 621. activation of the sputtered atoms. Since the radioactive tracer tech nique is used to determine the number of sputtered atoms, irradiation of the quartz plates in a thermal neutron flux was required. The irradiation was performed adjacent to the reactor core face in a 12 2 thermal neutron flux of about 5 x 10 n/(cm )(sec). The irradiation chamber was an aluminum parallelepiped 9-5/8-in. square by 8-in. high, fastened to an 8 -in. diameter aluminum pipe, 51-in. long. A flange sealed by a neoprene "0 "-ring connected the capsule to a 2-1/2-in. diameter lead tube. Above the water line the lead tube was connected to a fore pump which was used to evacuate the system to about 10 ^ torr. 53
A drawing of the holder which contained the quartz collectors is shown in Figure 4. It was held on edge in a cradle within the rectangular irradiation chamber. The quartz plates were irradiated for a total of 112 hours. The thermal neutron flux in the capsule was monitored during the irradiation with cobalt-aluminum wires (0.75 w/o cobalt). Three concentric dosimeter wires with respective diam eters of 0.536-in., 1.500-in., and 3.125-in. were located 0.040-in. from each quartz plate. The thermal neutron flux was calculated after the irradiation from a measurement of the ^ C o activity in the dosim eter wires. A 3-in. diameter well type Nal scintillation crystal and
512-channel Nuclear Data multichannel analyzer were used in this measurement.
53 This was done in order to minimize hazards from radioactive air which could escape from the system. 32
DOSIMETER WIRE GROOVES
QUARTZ PLATE \ ALUMINUM SPACER a. CROSS SECTION OF HOLDER
QUARTZ PLATE
DOSIMETER WIRE GROOVES
ALUMINUM
b. VIEW OF ONE HOLDER
FIGURE 4. QUARTZ PLATE HOLDER FOR THERMAL NEUTRON ACTIVATION EXPERIMENT The position of the quartz plates with respect to the reactor core was purposely selected to minimize the spatial variation in the thermal neutron flux over the surface of each quartz plate. After the irradiation the azimuthal variation in the thermal neutron flux in the plane of the quartz plates was checked by cutting one of the dosimeter wires in quadrants and counting the activity from a small piece of wire taken from the center of each quadrant. It was determined in this manner that the aximuthal variation in the neutron flux was less than two percent. In subsequent determinations of the dosimeter wire activities each concentric wire was counted in its entirety. This provided separate determinations of the thermal neutron flux over the face of each quartz plate at three radial positions corresponding to the respective radii of the concentric dosimeter wires. The thermal neutron flux was calculated from the measured ^ C o activity by the equation
Aa X c t c — CO 6 / o o \ 'Pth " N ct -X T ’ ^ ^ co o (i . e c )
60 Where A is the measured Co activity in dis/sec, N the number of co co cobalt atoms in the dosimeter wire, cjq the microscopic thermal neutron cross section for production of ^Co, X^ the decay constant for ^Co, t the cooling time from the end of the irradiation until count, and c T is the irradiation time.
The sputtering ratio (atoms of gold sputtered per fast neutron crossing the surface) is defined as where N g is the total number of atoms sputtered during the irradiation, 54 S is the target's surface area, and 5^ is the fast neutron fluence.
The number of sputtered atoms is related to the gold radioactivity
observed on the quartz collector and reflector by the expression
(24)
a
After substitution of Equation (24) into Equation (23) the
sputtering ratio is given by
(25)
The quantities A£ and A^ are respectively the measured activities in
disintegrations per second corrected to zero decay time on the quartz
collector and reflector. The thermal neutron fluxes to which the
collector and reflector were exposed are 9c and cp^, respectively,
is the microscopic neutron-activation cross section for Au, \ is
198 the decay constant for Au, and t is the irradiation time for the
gold targets. The quantity 6 is a factor accounting for resonance
activation of the gold, and F is a correction factor which accounts
for sputtered atoms which were not collected on the quartz plates.
The radioactivity of the sputtered atoms was determined by
direct counting of the 0.412-MeV gamma radiation accompanying the
198 2.70-day half-life decay of Au. A preliminary check of the
In an isotropic neutron flux environment the total number of neutrons crossing the target surface in both directions is 35
sputtered atom activity was made by counting the collectors on top of a 3-in. diameter Nal scintillation crystal. After these counts the
sputtered atoms were removed from the quartz plates by chemically etching the surface. The reverse side of the plates were first etched with HF acid to remove contamination. The plates were then separately
placed in an aqua regia solution with gold carrier (> 0.5 mg per ml) and the solution was heated to dissolve the gold. To ensure complete removal of the gold, the plates were etched with HF acid. The acid
solutions were diluted to a known volume and an aliquot was then taken
for analysis to which 20 mg of gold carrier was added. The gold was
separated from the solutions by addition of 0.5 gm of hydroquinone to
form dry samples. Each sample was counted several times in a 3-in.
diameter Nal well-type scintillation crystal which was used in conjunc
tion with a 512-channel Nuclear Data multichannel analyzer.
Experimental Results
The neutron energy spectrum above 0.1 MeV inside the vacuum
facility at the position occupied by the experimental apparatus is
shown in Figure 5. The curve is a smooth fit to the measured neutron
fluxes. The neutron flux at 4.9 eV and 132 eV was determined by the
thick foil method with gold and cobalt detectors.'*'’ The neutron flux
at 4.9 eV calculated from measured activities in the gold foils was
2.86 x 1014 n/(cm^)(sec)(MeV) and the neutron flux at 132 eV from the 13 2 measured activities in the cobalt foils was 9.80 x 10 n/(cm )(sec)
(MeV).
Ehret, Atompraxis. FAST NEUTRON FLUX, n/(cm2 )(see)(MeV) 0.1 IUE . ATNURNEEG SPECTRUM ENERGY NEUTRON FAST 5. FIGURE ETO EEG, M«V ENERGY, NEUTRON 1.0 MOH T TO IT F SMOOTH ESRD SPECTRUM MEASURED 10.0
36 100 . 37
The neutron flux per unit energy from the 132 eV cobalt reso nance up to 0.4 MeV was assumed to be given approximately by the relationship"*8
Cp(En ) = '•’o ^ n (26) where the parameter cp^ was found from the flux at the cobalt resonance 10 2 to be 1.28 x 10 n/(cm )(sec).
The neutron flux above 0.4 MeV was calculated for six energy
57 groups by use of the over-determined matrix method. These energy
groups and the corresponding neutron flux per unit energy for each
energy group are listed in Table 1.
TABLE 1
RESULTS OF NEUTRON ENERGY SPECTRUM MEASUREMENTS ABOVE 0.4 MeV
Energy Interval, Neutron Flux, MeV n / (cm2) (Sec)
0.40 - 1.25 6.10 X io10
1.25 - 3.00 2.22 X io11
3.00 - 5.50 5.37 X io10
5.50 - 7.75 2.07 X io10
7.75 - 10.25 4.25 X io9
10.25 - 14.00 6.23 X io8
88This is the standard slowing down spectrum for neutrons in a moderating medium where absorption processes are neglected.
"*^H. M. Epstein, B. P. Fairand, and B. L. Schrock, American Nuclear Society Transactions. 38
The integral neutron flux greater than 0.01 MeV determined from
239 11 2 the measured activity of the Pu detector was 5.1 x 10 n/(cm )(sec).
This compares favorably with the integral flux above 0.01 MeV of 11 2 4.1 x 10 n/(cm )(sec) obtained from the sum of the neutron fluxes above 0.4 MeV in Table 1 and the neutron flux between 0.01 MeV and
0.4 MeV found by integration of Equation (26).
The sputtering ratios are based on the integral neutron flux above 0.1 MeV. An energy threshold of 0.1 MeV was selected in order to be consistent with an earlier definition for the fast neutron 58 sputtering ratio. In addition, most energetic PKA's which are the generating source of the sputtered atoms are created by neutrons with energies above 0.1 MeV. The fast neutron fluence, which is the prod uct of the total fast neutron flux above 0.1 MeV and the irradiation time T, is used in the calculation of the sputtering ratios. Based on an irradiation time of 1.03 x 10^ secs and an integral neutron flux 11 2 above 0.1 MeV of 3.8 x 10 n/(cm )(sec) the fast neutron fluence is
3.90 x 1017 n/(cm^).
The maximum spatial variation in the calculated thermal neutron flux over the surface of each quartz collector was found from the measured ^ C o gamma activity in the dosimeter wires to be less than
+ 5 percent. A spatially averaged value of the thermal neutron flux over each collector was used in the calculation of the sputtering ratios.
58 N. W. Norcrofcs, B. P. Fairand, and J. N. Anno, J. Appl. Phys. 39
After the gold was chemically removed from the quartz collec- 198 tors, the Au was counted several times over a 3-day period. The average of the activities from the various counting times corrected for counter efficiency and corrected to zero decay time are given in
Table 2. The average thermal neutron flux over each of the quartz plates is also listed in Table 2.
TABLE 2
RESULTS OF THERMAL NEUTRON FLUX AND GOLD ACTIVITY MEASUREMENTS
Average Thermal Neutron Flux Over Surface 1 98Au A Activitya -4 . * Quartz Plate of Quartz Plate, on Quartz Plate, Identification 10^2 n/(cm2)(sec) Dis/(sec)
Monocrystal Collector 5.84 673
Monocrystal Reflector 5.82 501
Polycrystal Collector 5.38 1017
Polycrystal Reflector 5.27 861
The factor F which accounts for the sputtered atoms not col lected by the quartz plates was 1.08 for the monocrystal experiment and 1.15 for the polycrystal experiment.
The remaining parameters in Equation (25) which need to be specified in order to calculate the sputtering ratios are the target surface area, the epicadmium correction factor, the activation time 40 of the gold atoms on the quartz plates, the microscopic neutron acti-
198 vation cross section for gold, and the decay constant for Au.
These values are listed in Table 3.
TABLE 3
PARAMETERS USED IN THE CALCULATION OF THE SPUTTERING RATIOS
Parameter Value
Target Surface Area, S 0.178 cm2
Irradiation Time, t 111.94 hr -24 2b Cross Section, ct 98.8 x 10 cm ’ a Decay Constant, X 1.07 x 10"2/(hr)C .a Epicadmium Correction Factor, 6 1.11
S i CR The value of 6 is based on a cadmium ratio of 10 where 5 = T ^ T j T > and CR is the cadmium ratio.
^M. D. Goldberg, S. F. Mughabghab, S. N. Purohit, B. A. Magurno, and V. M. May, Neutron Cross Sections, p. 79-0-1.
CNuclear Data Sheets, 1959-1965,fAcademic Press, New York and London), p. 2390.
From the values listed in Tables 2 and 3, a fast neutron
17 2 fluence of 3.90 x 10 n/(cm ), and the F factor values of 1.08 and
1.15, the sputtering ratio for the polycrystal gold target is
-4 (1.5 + 0.4) x 10 , and the monocrystal sputtering ratio is (0.9 + 0.2) x 10 \ The uncertainty in the sputtering ratios is discussed in the section on experimental error. 41
Discussion of Results
Comparison With Earlier Experiment on Fast Neutron Sputtering From Polycrystalline Gold
The fast neutron sputtering ratio for the polycrystalline gold
-4 target of (1.5 + 0 . 4 ) x 10 that is reported in this dissertation is -4 59 in good agreement with an earlier measurement of (1.0 + 0.3) x 10
A basic difference between the two experiments is in the method for
activating the sputtered gold atoms. In the earlier experiment the
sputtered atoms were activated "in-pile" by thermal neutron irradia
tion of the gold target simultaneously with sputtering by fast neutron
irradiation of the target. In the present experiment the sputtering
apparatus was shielded from thermal neutrons by a cadmium and B^C
shield and activation of the sputtered gold atoms required a separate
experiment where the quartz plates were irradiated in a known thermal
neutron environment.
It was recognized in the earlier experiment there could be a
contribution to sputtering by recoil atoms generated in the thermal
197 (n,Y) reaction with Au. Based on a subsequent experiment (unpub
lished) where a cadmium sleeve was placed around the experiment
chamber and the sputtered gold atoms were activated in a separate
59 D. W. Norcross, B. P. Fairand, and J. N. Anno, J. Appl.
^The mean recoil energy for gold atoms from capture gamma emission in (n,y) events is 81 eV. Gold atoms with this energy can escape from their lattice sites and move in the gold lattice. R. R. Coltman, Jr., C. E. Klabunde, D. L. McDonald, and J. V. Redman, J. Appl. Phys., 33, 3509 (1962). 42 irradiation, it was concluded that recoil atoms from (n,y) events were not the predominant source of sputtered atoms. Unfortunately the results of the experiment were subject to rather large uncertainties.
The experiment reported in this dissertation provides conclusive evi dence that thermal neutron sputtering is not the predominant source of sputtered atoms.
Comparison of Observed Sputtering Ratios With Theoretical Predictions
The observed sputtering ratios can be compared with predic tions from theory for the two models developed by Thompson.^ In order to calculate the sputtering ratios it is necessary to determine the PKA energy spectrum in gold which results from the fast neutron bombardment. The PKA energy spectrum is calculated from Equation (2) where the neutron elastic and inelastic scattering cross sections in gold for producing energetic atom recoils are given in Equations (6) and (11) and the fast neutron energy spectrum is taken from Figure 5.
The PKA energy spectrum in the polycrystalline and monocrystalline gold targets is shown in Figure 6 . Contributions to the total PKA energy spectrum from elastic and inelastic neutron scattering in gold are shown separately. In the calculation of the sputtering ratios the PKA energy spectrum is approximated by a set of monoenergetic
sources. The procedure for replacing the PKA spectrum shown in
Figure 6 by a set of monoenergetic sources was to first approximate
^M. W. Thompson, Phil. Mag., 18. q (T) *3,24 X 10 1V 2 -3 7 .3 T 1 lMev'(toeV) > _ ( EXPONENTIAL FIT <20keV)
•TOTAL PKA ENERGY SPECTRUM
- INELASTIC COMPONENT
ELASTIC COMPONENT .13 -93.3T(Mev) . A — \q2(T)81.75 X 10 e \ \ \ (EXPONENTIAL FIT 20keV)
0 20 6040 80 100 PRIMARY KNOCK-ON ATOM ENERGY, keV
FIGURE 6. PRIMARY KNOCK-ON ATOM SPECTRUM IN GOLD CRYSTALS 44
the spectrum by two exponential functions where one function approxi mates the PKA spectrum for recoil energies less than 20 keV and the other function fits the PKA spectrum for recoil energies greater than
20 keV. These two functions, given respectively by q^(T) and q2 (T), are shown in Figure 6 . The energy spectrum is now conveniently divided into a set of monoenergetic sources where the energy of each
source is given by
J Tq (T) dT T. = --- , (27) J f q (T) dT AT 1 q^(T) refers either to q^(T) or q2 (T) an^ integration for each source is taken over AT. It was found that little error is introduced in the calculated values for the sputtering ratios when the spectrum is approximated by two monoenergetic sources. These sources have ener- 3 gies of 9.2 keV and 30.7 keV and the total number of recoils per cm — second corresponding to these energies were 6.7 x 10*^ and 2.9 x 10^, respectively.
The sputtering ratio based on the random model is calculated "8 from Equation (16). Using values of D = 2.88 x 10 cm, cp^, = 11 2 3.8 x 10 n/(cm )(sec), 1) ^ 1 and = 3.5 eV the calculated sputter- _5 62,63 ing ratio is 0.8 x 10 . This value should be equally applicable
to both the monocrystalline and polycrystalline targets.
62 "H is a constant of order unity whose value is taken equal to one in this calculation.
63 The effective surface binding energy in gold is approximated by the sublimation energy whose value is between 3 eV and 4 eV. D. R. Stull and G. C.Sinke, Thermodynamic Properties of the Elements (American Chemical Society, Washington, 1956), p. 18. 45
The sputtering ratio based on focusing collisions along the
<110> crystal directions is calculated from Equation (21). In the
< 100> monocrystal there are four close packed crystal directions which are directed out of the target surface. Each of these directions is inclined at an angle of 45 degrees to the surface normal. Using
-8 64. values of E^ = 167 eV, and B = 0.202 x 10 cms the calculated sput-
-4 tering ratio is 0.9 x 10 . It is not possible to perform a similar calculation for the polycrystalline gold target since the crystallites
in the target are oriented in a random manner. However, the focusing model will predict a sputtering ratio for the polycrystalline material
-4 of about 10 . This is easily seen by noting that the factor £ 1. j J cos Y, in Equation (21) will vary between approximately 2.8 and 3.0 depending on the particular angle the crystallites have with respect
to the surface normal, i.e., for the <100> orientation £ 1. cos Y. = j J J 2.88, for the <110> orientation £ 1. cos Y. =3, and for the <111> j J J orientation £ 1 cos Y. = 2.82. J The sputtering ratio predicted by the random model differs by more than an order of magnitude from the observed sputtering ratios while the focusing model is in surprisingly good agreement with the measured sputtering ratio for the < 100> monocrystal and polycrystal. .
Because of uncertainties in some of the parameters which enter into
the relationships for the sputtering ratios, the excellent agreement between the experimental sputtering ratios and the value predicted by
the ordered model may be somewhat fortuitous. For example, selection
64 M. W. Thompson, Phil. Mag., 18. 46 of a surface binding energy of 3 eV and a value for the Born-Mayer parameter determined by Abrahamson^ will change the calculated value for the sputtering ratio by more than a factor of 1.5. However the ordered model still predicts a sputtering ratio which is in substan tially better agreement with the experimental values than the value predicted by the random model. Comparison between the sputtering theory and experiment indicates that focusing, specifically along close packed crystal directions, is the major source of sputtered atoms.
A similar comparison between theory and the sputtering ratios observed when gold foils are bombarded by 14 MeV neutrons supports this conclusion. In this regard, it is of interest to consider the sputtering experiment reported by Garber, et a_l. for fast neutrons incident on a <100> monocrystal of gold.^^ They reported a sputtering
-3 ratio of 3 x 10 and furthermore observed preferred emission of the sputtered atoms which they contend confirms the existence of a colli sion focusing mechanism in neutron bombardment of crystals. The random and ordered sputtering models given by Equations (16) and (21) are applicable to this environment. The only change in the models other than the use of a different PKA energy spectrum rests in the definition of the sputtering ratio. In a neutron beam environment the sputtering ratio is defined as cp/cp^ rather than 2cp/cp^ which applies to an isotropic neutron flux environment.
^R. S. Nelson, The Observation of Atomic Collisions In Crys talline Solids, p. 12.
R. I. Garber, et al., j, Exp. and Theo. Phys. (letters). 47
For 14 MeV neutrons incident on gold the PKA energy spectrum can be approximated by two monoenergetic sources. The 14 MeV neutron cross section in gold is approximately equally divided between (n,2n) reactions and elastic scattering. Because of the relatively long half-life of the gold isotope produced by the (n,2n) reaction the PKA energy from this interaction is due to the recoil of the compound nucleus which has an energy of about 70 keV.^^ The PKA's from elastic scattering are assumed to be characterized by an average energy of
68 3 142 keV. The total number of recoils per cm -second from each of
1 3 these sources is — N a_cp„ where N is the atoms per cm in gold, 2 o TTF o T is the total neutron cross section at 14 MeV, and cp^ is the neutron flux at 14 MeV. These source densities and the PKA energies of 70 keV and 142 keV are used in Equations (16) and (21), after they are cor rected for the difference between a beam and isotropic neutron environ ment, to determine the sputtering ratios. The random model predicts a sputtering ratio of about 3 x 10 ^ and the ordered model predicts a
-4 sputtering ratio of about 4 x 10
In this case the ordered model does not provide the excellent agreement with the experimental sputtering ratio that was observed for
^This is determined from Equation (3) where e = 0.
68 This assumes isotropic neutron scattering in the center-of- mass coordinate system and therefore tends to overestimate the number of high energy recoils. The recoil energy is found from Equation (4) where 9 = 90°. Furthermore, PKA energy losses due to ionization are neglected. This energy loss is on the order of 10% of the initial PKA energy. R. S. Nelson, The Observation of Atomic Collisions In Crystal line Solids, p. 37. 48 the reactor neutron environment. However, in view of the approxima tions used in the derivation of the ordered model the agreement between theory and experiment is still considered reasonable.
Keller also has attempted to measure the fast neutron sputter ing ratio for 14 MeV neutrons incident on gold foils.^ Although
Keller does not specify whether he used polycrystalline or monocrystal line gold foils, it appears, from the content of his paper, that he used polycrystalline foils. Because of limitations in the detection capability of his system no sputtering was detected. However an upper
-4 limit for the sputtering ratio of 6 x 10 was estimated from the experimental data. The difference between the sputtering ratio ob served by Garber, e£ al. and the upper limit specified by Keller can not be explained on the basis of the reported information.^
Until additional information is obtained on 14 MeV neutron sputtering in gold, it can only be assumed that the sputtering ratio
-4 -3 has a value between 6 x 10 and 3 x 10 . It is obvious that the upper limit for the sputtering ratio specified by Keller agrees more favorably with the sputtering ratio predicted by the ordered model than the value reported by Garber and his co-workers.
Although it cannot be concluded that a focusing mechanism is the sole agent for fast neutron sputtering in gold, it does appear to
^K. Keller, Plasma Phys., 10.
^Based on the sputtering ratios for polycrystalline and mono crystalline gold foils reported in this disseration, it does not appear that a difference in the crystalline state of the target would be responsible for this large difference in sputtering ratios. be a significant source of sputtered atoms. This conclusion is
strengthened by the observation of a preferential pattern in the gold
atoms sputtered by 14 MeV neutrons. The random model underestimates
the sputtering ratios observed in a reactor neutron environment and a
14 MeV neutron environment by more than an order of magnitude. In
the case of the 14 MeV neutron environment this difference may be as
great as two orders of magnitude. This poor agreement between theory
and experiment and the fact that the model predicts sputtering ratios
in both cases which underestimate the observed values indicates that
the random sputtering mechanism considered by Thompson^* does not con
tribute significantly to the number of sputtered atoms.
It is implicit in the random model developed by Thompson that
sputtering occurs on a per atom basis. A random sputtering model which does not depend on single atom ejection is based on a cluster
sputtering mechanism. In this model displacement cascades produced
near the target surface could cause ejection of large clusters of
atoms as well as single atoms. Ejection of atom clusters has been 72 observed in fission-fragment damage in uranium. The source of these
sputtered atom clusters were thought to be due to displacement spikes
produced near the surface of the uranium. If these atom clusters are
ejected from displacement spikes then displacement spikes created by
fast neutron interactions in gold may produce similar results. Some
^M. W. Thompson, Phil. Mag., 18.
72 K. Verghese.and R. S. Piascik, J. Appl. Phys., 40, 1967 (1969). 50 similarities between fission-fragment and fast neutron damage in single crystal gold films have been observed by Merkle from electron micros- 73 copy studies. Defect clusters in the form of vacancy rich regions in the crystal lattice were observed in both cases. Merkle concludes that these defect clusters are produced directly in displacement cas cades initiated by energetic primary knock-on atoms. Because of these similarities between fission fragment and fast neutron damage in gold,
Merkle's results lend some support to the conclusion that cluster sputtering may occur in gold when it is bombarded by fast neutrons.
Unfortunately no quantitative theory exists which may be used to pre dict a sputtering ratio based on this type of mechanism.
Atom Collection Efficiency of Quartz Plates
The experimental apparatus was designed so that most of the sputtered atoms would be collected by the collector and reflector quartz plates. However, some atoms may undergo multiple reflections from the quartz plates and be lost to the aluminum spacer ring sur rounding the quartz plates or they may reflect from the collector plate back onto the target. In order to approximate this loss factor an estimate of the sticking probability for the sputtered gold atoms on the quartz plates is required. An estimate for this number may be found from the gold activities measured on the quartz plates. The values listed in Table 2 indicate that the sticking probability is rather low. Furthermore these values indicate that the number of
73 Radiation Effects, Vol. 37, pp. 173-181. 51
atoms reflecting off the collector plate back onto the target is not
too large. This is seen by noting that the sticking probability for
gold atoms onto gold should nearly be equal to one. Therefore the
ratio in activities on the collector and reflector plate would be con
siderably larger than the observed value if a significant number of
atoms reflected off the collector plate back onto the target.
An approximate expression for the sticking probability is
given by A - A
S ~ CA (28) c where Aand A^ are the measured gold activities on the collector and
reflector plates. From the monocrystal results this value is 0.25.
The polycrystal results predict a value of 0.15. However, this value
is subject to a large uncertainty because of the large uncertainty in
the measured activity on the polycrystal collector plate.
The number of sputtered atoms lost to the aluminum spacer ring will depend on the particular angle from the surface normal at which
atoms are ejected. In the case of the monocrystal, if it is assumed
most atoms are ejected along the closed packed crystal directions or
equivalently at 45 degrees to the surface normal, the atoms will
undergo four reflections from the collector plate and three reflec
tions from the reflector plate before they are incident on the
aluminum spacer ring. On this basis the fraction of atoms lost to
the spacer ring is (1-S)^ or 0.13. If atoms are randomly emitted
from the target surface their average angle to the surface normal is
still approximately 45 degrees. Therefore it is concluded that up to 52
13 percent of the sputtered atoms are not collected. For the poly
crystal target this number is approximately 0.19. In terms of the
correction factor used in Equation (25) this value could range from
1.00 to 1.15 in the monocrystal experiment or 1.00 to 1.24 in the
polycrystal experiment. Mean values of 1.08 and 1.12 were used
respectively for the correction factor in the monocrystal and poly
crystal sputtering ratios.
Discussion of Experimental Error
The principal sources of error in determining the sputtering
ratios from Equation (25) were due to the uncertainties in the mea- 198 sured Au activity of the sputtered atoms, the correction factor
for sputtered atoms not collected by the quartz plates, and uncertain
ties associated with the thermal neutron and fast neutron fluxes.
Uncertainties in the gold decay constant and microscopic absorption
cross section, the irradiation times, and target surface areas are
negligible compared to uncertainties in the above quantities. The
estimated errors in the factors used to determine the sputtering
ratios are summarized in Tables 4 and 5.
The uncertainty in the factor F was estimated by assuming its value could range from the extreme value of 1.00 up to 1.15 in the
monocrystal case and 1.00 up to 1.24 in the polycrystal case. There
fore based on a mean value over these ranges the F factors are given
by 1.08 + 0.08 and 1.12 + 0 .12. TABLE 4
ESTIMATED ERRORS IN FACTORS DETERMINING THE POLYCRYSTALLINE SPUTTERING RATIO
Estimated Error, Source of Error Percent Remarks
Fast Neutron Fluence, §p 11.8 Primarily due to uncertainties in radioactivant cross sections and activity determination.
Correction for Atom Collection Efficiency, F 10.7 Conservative estimate for atoms escaping quartz plates.
Collector Plate Thermal Neutron Flux, cpc 8.4 From standardized flux determination procedure at Battelle Research Reactor and uncertainty in spatial variation of thermal neutron flux over quartz plate.
Reflector Plate Thermal Neutron Flux, cpr 8.4 Sources of error same as for cp . Tc
Gold Activity on Collector Plate, A£ 33.2 High uncertainty primarily due to high background activity on quartz plate.
Gold Activity on Reflector Plate, A^ 11.4 From chemical separation procedure and calibration of counting facility.
Epicadmium Correction Factor, 6 1.8 From cadmium ratio determination.
<_n CO TABLE 5
ESTIMATED ERRORS IN FACTORS DETERMINING THE MONOCRYSTALLINE SPUTTERING RATIO3
Estimated Error, Source of Error Percent Remarks
Correction for Atom Collection Efficiency, F 7.4 Conservative estimate for atoms escaping quartz plates.
Gold Activity on Collector Plate, A£ 7.6 From chemical separation procedure and calibration of counting facility.
Gold Activation Reflector Plate, Ay 11.0 Sources of error same as for A . c
a Estimated errors in 5^, cpc, cpr, and 6 are the same as those listed in Table 4.
in The larger uncertainty in the measured gold activity on the
polycrystal collector plate compared to the uncertainty in the other activities listed in Table 2, was due to a difference in techniques
198 used for the determination of the Au activities. The standard
procedure for determining the gold activity was to remove the gold atoms from the "quartz plates by immersion in an acid bath, chemically
separate the gold atoms from the resultant solution and then determine
198 the Au activity by counting the 0.412-MeV gamma radiation. This
procedure eliminated most of the background activity. An improper method was used in the chemical separation of the gold atoms from the
polycrystal collector plate and it was necessary to use backup data
obtained from a count of the gold activity on the quartz plate before
the atoms were chemically removed. Due to large background activity
198 the Au activity on the collector plate could not be determined as
precisely as the activity measurements on the chemically separated
samples.
From the estimated uncertainties listed in Table 4 the com
pound error was determined from Equation (25) using
•* - [(i)2
The values for the polycrystal and monocrystal sputtering
ratios with their estimated uncertainties are respectively (1.5 + 0.4)
-4 ,„-4 III. FAST NEUTRON SPUTTERING FROM A MONOCRYSTALLINE GOLD TARGET WITH THE <111> DIRECTION NORMAL TO THE TARGET SURFACE
Introduction
This experiment was performed at Battelle Memorial Institute's research reactor a few inches from the reactor core. It was intended to provide sputtering ratio information in gold for a new crystal orientation. In addition an attempt was made to measure the deposi tion pattern of the sputtered atoms on the quartz collector. Informa tion on the sputtering ratio was obtained, but it was not possible to measure the distribution in the sputtered atoms. Based on analysis of results from this experiment it was concluded that this type of meas- urement cannot be practically performed at the research reactor facility.
In addition to the measurement of the fast neutron sputtering ratio, the method used to activate the sputtered atoms provided a method for placing an upper limit on the thermal neutron sputtering ratio.
56 57
Experimental Procedure
Description of Vacuum Facility
Figure 7 shows a schematic of the vacuum facility. The por tion of the vacuum facility containing the experimental apparatus consisted of an 8-in. diameter aluminum pipe 56-in. long. The bottom end of the pipe was welded shut and the top end connected to a flanged tee. One side of this tee contained thermocouple leads and heater leads which were removed from the vacuum system through a header plate and brought to the pool surface in an aluminum lead-out tube. The other side of the tee was a continuation of the 8 -in. diameter vacuum system and connected above the pool surface with the vacuum pumps.
The overall vacuum system is an oil free unit capable of vacuum levels in the low 10 ^ to high 10 ^ torr range (at the core end) with gas loads of about 2 x 10 ^ torr-liter/sec.
The pumping unit consists of (1) two 400 liter/sec triode-type ion pumps, (2) a titanium sublimation booster pump (7500 liter/sec) for intermittent duty, (3) a roots-type blower, and (4) a mechanical fore pump. A liquid nitrogen cold trap was located between the fore pump and roots blower. During operation, the system is roughed to _2 about 10 torr with the fore pump and the roots-blower is started
-4 which roughs the system to about 10 torr. At this point the ion pumps are started and the blower is valved off and removed from the
system. During the roughing phase a thermocouple gauge measured the vacuum at the pump end of the system. Once the vacuum exceeded about
-4 10 torr measurements were made with NRC type 527 ionization gauges. 58
VACUUM , PUMPING i UNIT
INSTRUMENTATION LEADS
VACUUM GAUGES
EXPERIMENTAL PACKAGE
CORE
FIGURE 7. IN-PILE VACUUM SYSTEM 59
One gauge was located at the pump end and two gauges were located at
the core end of the vacuum system. The vacuum system was able to “6 maintain a vacuum of about 10 torr. in the irradiation chamber.
Based on the first experiment it was concluded that thermal
neutrons are not the predominant source of sputtered atoms. For this
reason the experimental apparatus was not shielded from thermal neu
trons and sputtered atoms were activated "in-pile" simultaneously with
sputtering by the fast neutron irradiation of the target.
Measurement of the Neutron Environment Inside the Vacuum Facility
The neutron energy spectrum at the core end of the vacuum
facility was measured at the approximate location that would be occu
pied by the experimental apparatus. These measurements were made at
reduced reactor power and normalized to the experiment irradiation
power by use of the reactor power monitor and the measured activity
of an iron dosimeter wire irradiated with the gold target.
The fast spectrum above 0.1 MeV was measured with threshold
radioactivants where an effective threshold concept was used. In
this technique the energy dependent cross section is approximated by
a step function. A standard procedure for determining the threshold
foil parameters by a fission flux weighted, least-squares averaging 74 technique was developed at Battelle.
74 Fairand, B. P., and Epstein, H. M., American Nuclear Society Transactions, ,6, 33 (1963). 60
The fast neutron spectrum was calculated from the measured activities of the following reactions, ^^Pu(n,f), ^ “*In(n,n/)IN^^‘^m , 238,.. 58.,.. 58 32c . N„32 , 24x, , 24 U(n,f), Ni(n,p)Co , S(n,p)P , and Mg(n,p)Na
The fast neutron fluence during the irradiation was monitored by a iron dosimeter wire located beneath the gold target. After the irradiation, the fast neutron fluence was calculated from a measure- 54 ment of the Mn activity in the iron dosimeter wire from the
54 54 Fe(n,p)Mn reaction.
Description of the Experimental Apparatus and Gold Targets
A schematic of the sample holder which contained the <111> monocrystal gold target is shown in Figure 8 . The use of fired lavite instead of aluminum in the sample holder was intended to reduce the activity of the holder at completion of the irradiation. This was particularly desirable in this experiment since the sputtered atoms were activated "in-pile" and it was necessary to retrieve the quartz collectors soon after the end of the irradiation. The iron dosimeter was used to measure the fast neutron flux and the cobalt-aluminum wires were thermal neutron monitors. A mica sheet was used to isolate the dosimeter wires from the gold target. A piece of mica with a
0.25-in. diameter hole was placed over the target. This exposed a
0.25-in. diameter circular target surface to the sputtering chamber.
The distance from the target surface to the primary collector was
0.40-in. The reflector plate was natural quartz and the collector 61
LAVITE COVER PLATE
QUARTZ COLLECTOR
LAVITE SPACER RING
QUARTZ REFLECTOR
GOLD TARGET ON MICA SUBSTRATE
MICA
THERMOCOUPL DOSIMETERS
LAVITE MOUNT
FIGURE 8. SPUTTERING CHAMBER FOR GOLD TARGET 62 75 was very high purity synthetic quartz called "spectrosil". This material was selected since the planned procedure for obtaining the distribution of sputtered atoms on the collector was an autoradio graphic technique. In this technique beta and gamma radiation from the radioactive gold atoms on the collector plate expose a standard
X-ray film. Therefore background activity in the collector plate must be minimized. The effective diameter of the quartz collectors used to collect the sputtered atoms was 4.50-in. A 2KW stainless-steel sheath heater was wrapped concentrically around the specimen package. This heater was used to outgas the experimental package at temperatures up to 350°C prior to the irradiation. The temperature in the lavite at a position immediately below the gold target was measured with a chromal- alumal thermocouple.
The gold monocrystal was grown epitaxially on a white mica substrate. In this technique gold is evaporated onto a mica substrate at 400°C. The entire procedure was conducted in a vacuum of about
10 torr. After the gold crystal was grown on the mica substrate its monocrystallinity was verified by an X-ray diffraction analysis. The gold target was then transferred to the sample holder while still on the mica substrate. The experimental apparatus was mounted in the vacuum facility so that the surface of the gold target was normal to the reactor core face.
^"*The material was obtained from the Thermal American Fused Quartz Co., Montville, N.J. 63
After the experimental apparatus was inserted into the vacuum system the facility was evacuated until the pressure at the experiment
“6 end of the system was approximately 10 torr. The temperature in the experimental package was gradually raised over a period of 8 days from an ambient value of 50°C to approximately 300°C and then allowed to bake at this tejnperature for four days. The temperature was then re duced over a period of 14 days back to the ambient value of 50°C. The system was allowed to pump for an additional.17 days before the facil ity was moved into the vicinity of the reactor core.
In order to reduce gamma heating in the experimental package a lead shield was placed between the vacuum facility and the reactor core. This shield was a half cylinder, 30-in. high and 0.75-in. thick.
Gamma heating during the irradiation raised the temperature in the experimental package from an ambient value of about 50°C to 390°C.
The pressure at the experimental end of the system increased from 10 ^ torr to approximately 3 x 10 torr at the beginning of the irradiation after which it began to decrease. After approximately one day in-core the pressure was 5.9 x 10 ^ torr. The pressure continued to decrease "6 as the irradiation progressed finally stabilizing at about 10 torr.
The total irradiation time was 427.9 hours.
Procedure for Determining the Number of Sputtered Atoms
To measure the number of sputtered atoms a radioactive tech nique was used. The gold atoms were activated "in pile" simultaneously with sputtering by fast neutron irradiation of the target. 64
The thermal neutron flux over the quartz plates was monitored during the radiation with cobalt-aluminum wires (0.75 w/o cobalt).
The thermal neutron flux was calculated after the irradiation from a measurement of the ^ C o activity in the dosimeter wires. The dosim eter wires were counted with a 3-in. diameter cylindrical Nal scintil
lation crystal. The thermal neutron flux was determined at eight different positions distributed over the quartz plates. Maximum vari ation in the neutron flux was less than 13 percent and in the calcula tion of the sputtering ratio an average thermal neutron flux value over the eight different positions on the quartz plates was used.
The radioactivity of the sputtered atoms was determined by direct counting of the 0.412-MeV gamma radiation accompanying the 198 2.70-day half-life decay of Au. The quartz collector plate was counted several times on top of an 8 -in. diameter Nal crystal. Since the reflector plate was natural quartz the background radioactivity precluded its count with the 8 -in. diameter crystal. The gold was chemically removed from the quartz and placed in solution. A portion of this solution was counted in the 3-in. diameter well crystal.
The number of sputtered atoms was determined from Equation
(24) and the sputtering ratio was calculated from Equation (25).
Experimental Results
The neutron energy spectrum inside the vacuum facility at the position occupied by the experimental apparatus is shown in Figure 9. 65
CRANBERG FISSION SPECTRUM
..IRON OATUM POINT
NEUTRON ENERGY, MeV
FIGURE 9. INTEGRAL FAST NEUTRON ENERGY SPECTRUM 66
76 This is an assumed spectrum normalized to the neutron fluence above
5.1 MeV which was calculated from the measured activity in the iron dosimeter wire located beneath the gold target.
The remaining data points on the curve represent the results of the neutron spectrum measurement conducted prior to experiment irradiation. Tfiese points have been normalized to the experiment irra diation power and corrected for the irradiation time. The good agree ment of these data points with the curve in Figure 9 confirms the assumption that the fission neutron spectrum is a good approximation to the integral neutron spectrum for neutron energies above 0.1 MeV. 18 2 The neutron fluence above 0.1 MeV is 2.4 x 10 n/(cm ).
The remaining parameters used to calculate the sputtering ratio from Equation (25) are listed in Table 6 . Based on the values listed 18 2 in Table 6 and the fast neutron fluence of 2.4 x 10 n/(cm ) the -4 sputtering ratio for the <111> gold monocrystal is (0.8 + 0.4) x 10
7 The Cranberg fission spectrum integrated over energy has been assumed. L. Cranberg, g . Frye, N. Nereson, and L. Rosen, Phys. Rev., 103. 662 (1956). 67
TABLE 6
PARAMETERS USED IN THE CALCULATION OF THE SPUTTERING RATIOS
Parameter Value
Collector Plate Activity, Ac 5500 dis/sec
Reflector Plate Activity, A^ 4400 dis/sec
Average Thermal Neutron Flux over Both Quartz Plates, cpc and cp^ 3.4 x 10^2 n/(cm2)(sec)
Target Surface Area, S 0.316 cm2
Irradiation Time, t 427.9 hr -24 2 Cross Section, a 3 98.8 x 10 H cm a , a Decay Constant, X 1.07 x 10"2/(hr) b Epicadmium Correction Factor, 6 1.1 c Correction Factor, F 1.18
Q See Table 3 for references on these values.
^This is an estimated correction based on cadmium ratio measurements in a similar facility.
cProcedure for determining F is the same as used in the first experiment. 68
Discussion of Results
Comparison With Sputtering Ratio Results From First Experiment
The sputtering ratio for the <111> monocrystal is consistent with the result anticipated on the basis of the first experiment.
Focusing collisions along the close packed crystal directions should be a significant source of sputtered atoms and the ordered model should provide a reasonable estimate of the sputtering ratio.
In the <111> monocrystal there are three close packed crystal directions leading out of the target surface where each of these direc tions is inclined at an angle of 35.5. degrees to the surface normal.
In Equation (21) the sum E 1. Cos X. is 2.44 and the value for the i J J 1 .4 77 sputtering ratio predicted by the ordered model is 0.8 x 10 . In the growth of the gold monocrystal on mica twinning may occur in the gold film. This would result in six close packed crystal directions leading out of the target surface and a predicted sputtering ratio of -4 1.6 x 10 . If the softer nature of the neutron energy spectrum in the second experiment is taken into account the predicted value for
-4 the sputtering ratio is about 1.2 x 10 . In either case the predicted value for the sputtering ratio is in good agreement with the observed value.
^This number is based on the PKA energy spectrum determined in the first experiment. The fission neutron spectrum used to approxi mate the neutron energy spectrum in the second experiment has an aver age neutron energy of about 2 MeV while the average neutron energy in the first experiment is 2.5 MeV. In the softer neutron spectrum repre sented by the fission spectrum the predicted value for the sputtering ratio would be somewhat less than 0.8 x 10"4, i.e., ~ 0.6 x 10”4 . 69
Estimated Upper Limit for Thermal Neutron Sputtering Ratio
Because of the radioactivation technique used to analyze for the number of sputtered atoms, the thermal neutron sputtering ratio must be much less than the fast neutron sputtering ratio. This is seen by noting that each thermal neutron sputtered atoms is radio active whereas only a small fraction of the fast neutron sputtered atoms are radioactive. The thermal neutron sputtering ratio is given by the expression
L t t 4 th ’ ~7, 3 ? ---- (30) (l-a-U ) where A^, is the measured disintegration rate for fast neutron sput tered atoms, a the microscopic thermal neutron absorption cross cl section in gold, and § is the fast neutron fluence. r It has been concluded on the basis of the first experiment that thermal neutron sputtered atoms are not the major source of sputtered atoms. Therefore it is reasonable to assume that the mea sured activity on the collector plate due to thermal neutron sputtered 70 atoms is less than one half the total measured activity or in Equation (31) A^/Aj, < 0.5. From the measured values of A^ and Equation (31) -8 predicts that the thermal neutron sputtering ratio is less than 10 Discussion of the Attempt to Measure the Spatial Distribution in the Sputtered Atoms An autoradiographic technique was selected as the means for measuring the spatial distribution of atoms sputtered onto the collec tor. This technique has been successfully employed in ion sputtering „ 78 experiments. Since the total number of atoms deposited on a collector 14 during a typical fast neutron sputtering experiment is less than 10 atoms the collector material must have a very low impurity content and its major constituents must not lead to any long lived radioisotopes otherwise neutron induced radioactivity in the collector would mask any activity from the sputtered gold atoms. After a careful review of available materials it appeared that a super high purity synthetic quartz called "spectrosil" was the only acceptable candidate. A list of impurity contents determined for this material are listed in Table 7. -4 Based on an assumed sputtering ratio of 10 it was determined that none of the impurities listed in Table 7 would result in exces- 30 31 sive background activity. In addition, the Si(n,y)Si reaction 78 R. S. Nelson, The Observation of Atomic Collisions In Crystalline Solids, pp. 228-235. 71 arising from the silicon in SiC^ would not be troublesome, since the 31 2.65 hour half-life Si isotope could be allowed to decay before autoradiographs were taken. TABLE 7 SPECIFIED IMPURITY CONTENTS IN SPECTROSIL Element Parts per million Element Parts per million Aluminum < 0.02 Gallium < 0.004 Antimony < 0.0001 Iron < 0.1 Arsenic < 0.0002 Manganese < 0.001 Boron < 0.01 Phosphorus < 0.001 Calcium < 0.1 Potassium < 0.004 Copper < 0.0002 Sodium < 0.04 After the experiment irradiation was completed and the quartz collector retrieved, it was immediately determined from activity counts with the 8 -in. diameter Nal scintillation crystal that back ground activity in the quartz collector was excessively high and meaningful autoradiographs of the collector were not possible. From an analysis of the gamma spectrum the high background activity was found to be due to fission products. Based on background activity measurements the total uranium content in the quartz plate was esti mated to be less than one part per million. It could not be unambig uously determined why this impurity was not specified by the manufac turer of spectrosil. 72 Discussion of Experimental Error The estimated errors in the factors used to determine the sputtering ratio are summarized in Table 8 . From these errors the compound error was estimated using - [ (It)2 ( H : ) 2 < V 2 + (lt)2 From Equation (25) the value for the monocrystal sputtering -4 ratio with its estimated uncertainty is (0.8 + 0.4) x 10 TABLE 8 ESTIMATED ERRORS IN FACTORS DETERMINING THE SPUTTERING RATIO Estimated Error, Source Percent Remarks Fast Neutron Fluence, §_ 31 Primarily due to estimates of flux above r 0.1 MeV from iron dosimeter wire data. Correction for Atom Collection 15.2 Conservative estimate for atoms escaping Efficiency, F quartz plates. Thermal Neutron Flux Over Quartz Plates, 10.8 From standardized flux determination procedure at Battelle Research Reactor and uncertainty in spatial variation of thermal neutron flux over quartz plates. Gold Activity on Collector 21.8 Primarily due to correction for back Plate, Afi ground activity. Gold Activity on Reflector 29.6 Same as for Ac and additional uncertainty Plate, A in removal of gold atoms from quartz ’ r plate. Epicadmium Correction Factor, 6 5 Conservative estimate for possible vari- ation in cadmium ratio. IV. CONCLUSIONS From the results of the experiments presented in this disser tation and analysis thereof it is concluded that: 1) The fast neutron sputtering ratio in a polycrystalline gold target due to neutrons produced in a nuclear reac tor source with energies greater than 0.1 MeV is -4 (1.5 + 0.4) x 10 . The average neutron energy is 2.5 MeV. This value for the sputtering ratio is in good agreement with an earlier measurement of the neutron sputtering ratio in polycrystalline gold of (1.0 + 0.3) x -4 10 . The reactor source was used in the earlier experi ment and the average neutron energy was approximately 1.7 MeV. 2) The fast neutron sputtering ratio in a monocrystalline gold target (the < 100> crystallographic direction normal to the target surface) due to neutrons produced in a nuclear reactor source with energies greater than 0.1 MeV -4 is (0.9 + 0.2) x 10 . This target was irradiated simul taneously with the polycrystalline gold target. 3) The fast neutron sputtering ratio in a monocrystalline gold target (the < 111> crystallographic direction normal to the target surface) due to neutrons produced in a 74 75 nuclear reactor source with energies greater than 0.1 MeV -4 is (0.8 + 0.4) x 10 . The average neutron energy is 2.0 MeV. 4) The thermal neutron sputtering ratio in gold due to recoil 197 atoms generated in the thermal (n,y) reaction with Au *•8 is less than 10 5) The fast neutron sputtering ratios observed for both mono crystalline gold targets and the.polycrystalline gold target are reasonably well predicted by an ordered sput tering model where atom ejection is due to long range focusing collisions along close packed crystal directions, i.e., <110> directions. In gold this type of mechanism contributes significantly to the number of fast neutron sputtered atoms. This conclusion is strengthened by re ported results for 14 MeV neutron sputtering in gold. 6 ) A random sputtering model which neglects the ordered nature of the crystal lattice and treats sputtering on a single knock-on atom basis underestimates the observed sputtering ratios in gold for the reactor neutron bombard ment by more than an order of magnitude and the observed sputtering ratio in gold for 14 MeV neutron bombardment by as much as two orders of magnitude. This type of random sputtering mechanism is of secondary importance in fast neutron sputtering of gold. 76 7) A random sputtering model based on clusters of atoms being ejected from the surface may be an important fast neutron sputtering mechanism. This conclusion is based strictly on qualitative arguments involving similarities between fast neutron and fission fragment radiation damage in gold ancl the observation that fission fragments cause cluster sputtering in uranium metal. APPENDIXES APPENDIX A. DISCUSSION OF SPUTTERING MODELS DEVELOPED BY THOMPSON Both the random sputtering model and ordered model used in this dissertation to predict the fast neutron sputtering ratios are treated in detail by Thompson. However in the interest of complete ness and to clearly point out important assumptions or simplifying approximations used in the derivation of these models they are treated in some detail in this appendix. Random Model Consider an infinite solid where atoms recoil from some primary event with energy T and have a density of q(T)dT. In our case the PKA’s are created by fast neutron interactions in the solid. If it is assumed that each of the primary recoils generates a colli sions and the flux of knock-on atoms has an isotropic distribution, an expression for the flux of knock-on atoms in the energy interval d E 7 at E 7 crossing any internal surface in the solid and travelling into a solid angle at dQ 7 in direction r 7 which makes an angle 0 to the surface normal is d Q 7d E 7 dT cos 0 (33) 4 tt 77 78 where v(T,E/) is the number of knock-on atoms that slow down through E 1 for one PKA at T and dEVdx is the energy loss per unit path length for knock-on atoms with energy E*. Thompson argues that dEVdx can be taken to be approximately equal to e V d where D is the nearest neighbor distance. The form of v(T,E/) is based on the work of several people and takes the form / 79 T]T/(E ). The constant T] is of order unity where for example Sanders shows for an inverse square potential between colliding atoms T] = 0.52. Substitution of the above expressions for v and dEVdx into Equation (33) gives Equation (12). Thompson now makes the assumption that the infinite solid is cut in half and the flux of atoms crossing the surface with energies in dE at E are observed. This assumption will lead to an overestimate of ejection particularly at low energies. The surface effect on the flux of sputtered atoms is taken into account by assuming that a binding force acts normal to the sur face. The surface therefore has a refractive effect where a sputtered atoms velocity component normal to the surface will be reduced by subtracting the binding energy E^ from that part of its kinetic energy. When this surface effect is taken into account the flux of sputtered atoms in the energy interval dE at E and traveling into a solid angle dQ is given by Equation (13). The integral in Equation (13) over the primary knock-on spectrum is approximated in this dissertation by 79 M. W. Thompson, Phil. Mag., p. 386. 79 replacing the actual spectrum with a set of monoenergetic sources. This was done since there is no simple analytical function which will fit the PKA energy spectrum over its entire energy range. A piecemeal approximate fit can be made with exponential functions and in fact these functions are used to obtain the monoenergetic source energies. The total flux of sputtered atoms emitted from the surface in the energy interval dE at E is cp(E)dE = H £ Z q T EdE 3 . (34) 4 1. 1 1 (e + Ebr In the integration over E to obtain the total emitted flux, the inte gration limits are taken from zero to the PKA source energy. Because of the high PKA source energies which are of interest in these studies little error is introduced by setting the upper limit equal to infin ity. Integration of Equation (34) is straightforward and yields * - 1 si; ? Ordered Model The type of collision sequence considered here occurs along the closest packed rows in the f.c.c. lattice. This is called "simple" focusing and occurs along the <110> crystal direction. At sufficiently low energies a knock-on atom traveling along this crystal direction has a tendency to focus momentum into the closely packed atom row. This arises from a geometrical property of a line of elastic spheres. In 80 this manner momentum can be focused over rather large distances in the solid and if the end of a chain of atoms involved in a focusing colli sion sequence happens to interact the solid surface an atom can be sputtered. Consider a knock-on atom produced by a PKA at energy T which has energy E 7 and initiates a focusing sequence. The kinetic energy transferred to the focusing sequence is given approximately by c = E 7 - D - V(e) (36) where D is the nearest neighbor spacing in gold, dE/dx is the kinetic energy lost per unit path length to atoms not in the focusing row, and V(e) is the stored potential energy which propagates with the sequence. If the focusing sequence travels a distance r to the target surface and arrives with kinetic energy e 7 and potential energy V(e7) then where r becomes the range of the focusing event when e = E^. In determining the flux of sputtered atoms Thompson neglects 80 the refractive effect of the surface but does correct for the energy loss due to the surface binding energy E^. 80 This should not significantly affect the number of sputtered atoms. 81 In the calculation of the flux of sputtered atoms it is assumed that the potential energy term can be neglected and dE/dx equals a E for E ^ E^ and dE/dx -» 03 for E > E^ with o' a constant. Both approximations tend to underestimate the energy loss in the focusing sequence. Now the number of focused collision sequences produced by primary recoils in dT at T with starting energies in the range dE' at E /, in a slab of thickness dr cos Y at depth r cos Y from the surface, and traveling in a particular direction which makes an angle Y to the surface normal is J q(T) X (T,E') dE' dr cos Y dT (38) T where q(T)dT is the PKA density and X(T,E') dE' is the number of col lision sequences generated with energy in the interval dE' at e ' by a PKA of energy T and traveling along a particular close packed crystal direction. The integration is over the PKA spectrum. The total flux crossing the surface into dE at E and directed along a particular close packed crystal direction is A r f q(T) J* X(T,E') dE' dr cos Y dT (39) T o where the integral over r accounts for slabs down to ?, the maximum range for ejection with energy E. Equation (39) is identical to Equation (17). 82 An expression for X(T,E7) has been derived by Sanders and 81 Thompson where interatomic collisions in a collision cascade are based on collisions with an interatomic potential depending on the inverse square of the interatomic potential and focused collisions -r /b are treated with a Born-Mayer potential Ae . The expression for X(T,e ') is E 8 Tl/2,„,'3/2 In ( A £or E ' < Ef X(T,e') ■[ 2D E f 1 2 (e')3 2 E j. f (40 ) = 0 for E' ^ E f In order to integrate Equation (39) over r it is necessary to express X(T,E;) and dE* in terms of r. From Equation (36) with V(e) ^ 0 and dE/dx ~ O' E ' e ~ e ' (1 - Do-) . (41) According to Thompson fty is on the order of 0.1 therefore e ^ E* and from Equation (37) it follows that E / ~ e /eQ?r. Since&' is related to E by E = e / - E ^ j E 7 = (E + E^) and d E 7 = dE effr. Also from Equa tion (37) it follows that E * = a ln ( r r i r ) • (42) Tjb Equation (40) becomes: -3/2 o-r - B T (L - or) e for E ^ E, - E, X(T,E') { 2D E f1/2 (E + Eb )3/2 f b (43) = 0 for E > E f 81 J. B. Sanders, and M. W. Thompson, Phil. Mag., 12* 83 where L = In • b Substitution of Equations (42), (43), and the expression for d E / into Equation (39) gives T L lot . 2£ cp(E,Y)dE=J q(T)T B y°| Y-— — 3/^ J (L - or) e 2 dr (44) g 2D E^ (E + E^) which is Equation (18). After integrating Equation (44) over r, the flux in dE at E emitted from the surface along a particular close 82 packed crystal direction is T T? 3 / 2 TT . j X.W ^YP.T (_L) + __ 13 01 b > D D E f f /E + EL v 1/2 . 2 ( - j - i ) - 2 } dE . (45) If the PKA energy spectrum is approximated by a set of mono energetic sources Equation (45) is identical to Equation (19). The total flux emitted from the target surface is found from Equation (45) by integrating over dE from zero to E^ - E^ and summing over all close packed crystal directions which lead out of the target surface. Performing these operations and assuming a set of monoener getic sources given for the total flux of sputtered atoms 82 This differs from an expression given at this point by Thompson. It appears that Thompson neglected the factor ea v when d E 7 (Thompson's dE//7) was replaced by dE ea r . M. W. Thompson, Phil. Mag., 18, p. 397. 84 78B S1 1 COS *3 1 rrr r / , Wf\ / 2' ,i 4f4E,1/2 < P " ---- ^ ------I qi T i { L1 + V J • ln(Ef/Eb) \- T T i- rb£l} • <4« \ E f In this equation a has been replaced by (1/39D) ln(E^/E^). This rela tion is determined from Equation (37) where the maximum range of simple focusing sequences able to cause ejection is R o 83 Theoretical estimates by Thompson gave R(E^) at 340 K as 39D. 83 The Interaction of Radiation With Solids, edited by R. Strumane, J. Nihoul, R. Gevers, and S. Amelinckx (John Wiley and Sons, New York, 1964), p. 108. APPENDIX B. LEAST SQUARE MATRIX METHOD FOR ANALYZING NEUTRON SPECTRA Basically the determination of neutron spectra requires the solution of the* following set of integral equations for cp(E). E max (48) o where N. = number of atoms of material i 9 (E) = neutron flux per unit energy a.(E) = energy dependent neutron cross section for the 1 .th - ., i foxl E neutron energy til saturation activity of the i foil.A. 1 Because one is limited to a discrete number of equations determined by the number of foils (n), it is only possible to deter mine the function 9 (E) to some approximation. At least six different basic methods have been used to solve Equation (48) as shown in Table 9. The degree of success attainable with the various methods 84 is discussed in some detail elsewhere and will, therefore, not be repeated here. However, all of the differential flux methods have one 84 J. C. Ringle, "A Technique for Measuring Neutron Spectra in the Range 2.5 to 30 MeV Using Threshold Detectors", UCRL-10732 (1963). 85 86 difficulty in common. Instabilities or oscillations arise if a full til n order approximation is used. These instabilities show up as poor error propagation properties when the response or coefficient matrix is inverted. This difficulty can be minimized by an extremely careful selection of threshold detectors. However, in doing so, good experi mental detectors which could serve to improve the spectral resolution must be discarded. TABLE 9 METHODS FOR FINDING FAST NEUTRON SPECTRA FROM ACTIVATION EXPERIMENTS 1. Flux Integral Method 2. Step Function Approximation 3. Polygonal Method 4. Cross-Section Expansion 5. Legendre Polynomial Expansion 6 . Fourier Expansions A more satisfactory approach to solving Equation (48) is to overdetermine the response matrix. For the sectionally continuous methods, i.e., step function and polygonal, this corresponds to requiring more detectors than energy groups. The use of more foils than energy groups, of course, results in a rectangular response matrix. Fortunately, a simple matrix method can be used to obtain the best least-square.minimization of the error residuals. This procedure consists of multiplying the matrix by its transpose. 87 The majority of spectra of interest in reactor and shielding applications fall off so rapidly that polygonal and unweighted poly nomial expressions give poor results. Dierckx investigated several types of spectra and found they 85 could best be fit by discrete exponential functions. Assume the expression for the flux connecting E^ and Ek+^ has the form -CkE q)(E) = cpke and from Equation (48) E £A - Z m \I k+1 • -C kF - Z m V* 1 k-i Ek k-i where m equals the number of energy groups. In matrix form the set of equations represented by Equation (49) becomes [A] = [R] [tp] . (50) Now [r ] can be a rectangular matrix with the number of energy groups ■J- less than the number of foils. Multiplying Equation (50) by R , the transpose of R, permits the least square solutions [cpl = { [ R l V ]}"1 [R]+[A] . (51) Neutron Dosimetry,Proceedings on the Symposium on Neutron Detection, Dosimetry, and Standardization (International Atomic Energy Agency, Vienna, 1963), Vol. I, pp. 325-335. 88 Equation (49) can be solved by an iterative technique in which the n *"*1 value of is calculated using the flux averaged center of til the interval from the (n-1) iteration. In practice no more than two iterations are required when the fission spectrum is used for the first iteration. One advantage of this technique, at least, for shielding experiments is that all energy intervals can be normalized to give the same relative error. Thus, a spectrum measurement cover ing several orders of magnitude can be adequately analyzed. Negative values of flux are prohibited in the iteration. However with suffi cient over determination this prohibition becomes unnecessary. A Space Fortran G-20 program has been written for the expo nential method. In the sputtering experiment nine foils and six energy groups were used. The foils that were used are given on page 25. BIBLIOGRAPHY Beeler, J. R., Jr., "Displacement Spikes in Cubic Metals. I. Brinkman, J. A., "Production of Atomic Displacements by High-Energy Particles," American Journal of Physics, 24, 246-267 (1956). Carter, G., and Colligon, J. S. Ion Bombardment of Solids. American Elsevier Publishing Co., New York, 1968. Coltman, R. R . , Jr., Klabunde, C. E., McDonald, D. L . , Redman, J. K. "Reactor Damage in Pure Metals," Journal of Applied Physics, 33, 3509-3519 (1962). Cranberg, L., Frye, G., Nereson, N., Rosen, L., "Fission Neutron Spectrum of u235}" Physical Review, 103, 662-670 (1956). Ehret, G. "The Determination of Epithermal Neutron Spectra by Means of Resonance Probes (Sandwich Method,” Atompraxis, 7_, 393-400 (1961). Epstein, H. M., Fairand, B. P., and Schrock, B. L. "Least Square Matrix Method for Analyzing Neutron Spectra," American Nuclear Society Transactions, ]_, 371-372 (1964). Fairand, B. P., and Epstein, H. M. "A Suggested Standard Method to Evaluate Effective Threshold Foil Parameters," American Nuclear Society Transactions, (>, 33 (1963). Garber, R. I., Dolya, G. P., Kolyada, V. M . , Modlin, A. A., Fedorenko, A. I. "Radiation Sputtering of a Single Crystal of Gold by Fast Neutrons," Journal of Experimental and Theoretical Physics (letters), 7, 296-297 (1968). Gibson, J. B., Goland, A. N., Milgram, M., and Vineyard, G. H. "Dynamics of Radiation Damage," Physical Review, 120, 1229- 1253 (1960). Goldberg, Murrey D., May, Victoria M., and Stehn, John R. Angular Distributions in Neutron Induced Reactions. Prepared by Sigma Center Brookhaven National Laboratory. BNL 400, Vol. II, 2d ed., October, 1962. 89 90 Goldberg, Murrey D., Mughabghab, Said F., Purohit, Surendra N., ' _« Magurno, Benjamin A., and May, Victoria M., Neutron Cross y. Sections. Prepared by Sigma Center Brookhaven National Laboratory, BNL-325, Vol. IIC, 2d ed., Supp. 2, August, 1966. Goldman, David T., and Simon, Albert. "Theory of Sputtering by High- Speed Ions," Physical Review, 14, 383-386 (1958). Holmes, D. K., and Leibfried, G. "Range of Radiation Induced Primary Knock-Ons in the Hard Core Approximation," Journal of Applied Physics, 31, 1046-1056 (1960). Jan, R. v. "Defektverteilung in Verlagerungskaskaden, I. Kaskaden- theorie," Physica Status Solidi, 6, 925-938 (1964). Jan, R. v. "Defektverteilung in Verlagerungskaskaden, II. Berilck- sichtigung von Gittereffekten," Physica Status Solidi, 1_, 299-305 (1964). Jan, R. v. "Defektverteilung in Verlagerungskaskaden, III. Edel- metalle," Physica Status Solidi, £, 331-344 (1965). Keller, K. "Search for Sputtered Atoms by H^(d,n)He^ Neutrons That May Contaminate a Thermonuclear Plasma," Plasma Physics, 10, 195-199 (1968). Keller, Keaton, and Lee, R. V., Jr. "Recoil Gold Atoms From Fast- Neutron Bombardment," Journal of Applied Physics, 37., 1890- 1892 (1966). Makin, M. J. (ed.) The Nature of Small Defect Clusters. Report of a Consultants Symposium, Harwell, July 4 to July 6 , 1966. Pre pared by the Atomic Energy Research Establishment. Harwell, 1966. Vol. I, pp. 8-37. Merkle, K. L. "Energy Dependence of Fission-Fragment Damage in Gold Films," Journal of Applied Physics, 38, 301-309 (1967). Nelson, R. S. The Observation of Atomic Collisions In Crystalline Solids. John Wiley and Sons, Inc., New York, 1968. Neutron Dosimetry. Proceedings on the Symposium on Neutron Detection, Dosimetry, and Standardization. Prepared by International Atomic Energy Agency. Vienna, 1963. Vol. I, pp. 325-335. Norcross, D. W., Fairand, B. P., and Anno, J. N. "Sputtering of Polycrystalline Gold by Fast Neutrons," Journal of Applied Physics, 37, 621-623 (1966). Nuclear Data Sheets: 1959-1965, Academic Press, New York, London. 91 Pashley, D. W. "The Study of Epitaxy in Thin Surface Films," Advances in Physics, 5, 173-240 (1956). Ringle, J. C. "A Technique for Measuring Neutron Spectra in the Range 25 to 30 MeV Using Threshold Detectors," UCRL-10732, October 11, 1963. Sanders, J. B., and Thompson, M. W. "The Generation of Focused Colli sion Sequences in Irradiated Crystals: a Calculation Based on the Inverse Square Potential," The Philosophical Magazine, 17, 211-214 (1968). Seitz, Frederick, and Turnbull, David (ed.). Solid State Physics. Academic Press, New York, 1966. Sheely, W. F. (ed.). Radiation Effects. Gordon and Breach Science Publishers, Inc., New York, 1967. Sigmund, Peter, "Theory of Sputtering. I. Sputtering Yield of Amorphous and Polycrystalline Targets," Physical Review, 184, 383-415 (1969). Silsbee, R. H. "Focusing in Collision Problems in Solids," Journal of Applied Physics, 28, 1246-1250 (1957). Strumane, R . , et al. (ed.). The Interaction of Radiation With Solids. John Wiley and Sons, New York, 1964. Stull, D. R., and Sinke, G. C. Thermodynamic Properties of the Elements. Special Publications Department American Chemical Society, Washington, 1956. Taimuty, S. I., "Proposed Reactor Radiation Damage Monitor," Nuclear Science and Engineering, ]J3, 403-404 (1961). Thompson, M. W. "The Energy Spectrum of Ejected Atoms During the High Energy Sputtering of Gold," The Philosophical Magazine, 18, 377-414 (1968). Thompson, M. W. Defects and Radiation Damage in Metals. Cambridge University Press, London, 1969. Thomson, David B. "Nuclear Level Densities and Reaction Mechanisms from Inelastic Neutron Scattering," Physical Review, 129, 1649-1667 (1963). Verghese, K., and Piascilc, R. S. "Ejection of Uranium by Fission Fragments--Evidence of Clusters and Knoclc-Ons," Journal of Applied Physics, 40, 1976-1977 (1969).