Post on 21-Jan-2021
AE-502
DEPTH DISTRIBUTION STUDIES OF CARBON, OXYGEN AND NITROGENIN METAL SURFACES BY MEANS OF NEUTRON SPECTROMETRY
by
J. Lorenzen
SUMMARY
A method has been developed to reveal the depth distributionsof the light elements carbon, nitrogen and oxygen in heavy matrices.For this purpose steel and zircaloy samples have been irradiated withdeuterons and the neutron groups emitted in (d, n)-reactions with thedifferent light nuclei have been measured using time-of-flight technique.The method has been applied to the study of steel samples that feature in-homog* neous carbon and nitrogen distributions and also to the measure-ment r.f diffusion profiles of oxygen in zirconium.
With the present technique depth ranges of 1 0 to 1 5 pm can beanalysed if the deuteron energy is chosen between 2. 5 MeV and 3. 5 MeV.The depth resolution improves with penetration from being of the orderof I - 2 um at the surface to 0. 5 u m at greater depths under optimumconditions. The detection limit of the light element increases with theatomic number of the matrix and the analysed depth. For oxygen in zir-conium and carbon in steel the limit of detection is of the order of 100 ppmat a depth of 10 im Limitations in the analysable range of fhe differentprofiles due to interfering neutron groups are discussed.
The method is particularly useful for the study of oxygen pro-files. It is less adequate for reactions with positive Q-values above5 MeV.
Printed and distributed in March, 1975
LIST OF CONTENTS
INTRODUCTION
THE METHOD OF PROFILE MEASUREMENTS
EXPERIMENTAL
The time-of-flight spectrometer
The target chamber
SAMPLES
C i rbon
Nitrogen
Oxygen
ANALYSIS OF THE MEASURED NEUTRON GROUPS
Analysis I: Integration over sectioned layers
Analysis II: Comparison with a homogeneous standard
ENERGY CALIBRATION AND DEPTH SCALES
Calibration
Transformation of flight time into a depth scale
RESOLUTION
OPTIMIZATION OF THE EXPERIMENTAL CONDITIONS
The optimal choice of initial deuteron energy
The optimal choice of angle for neutron detection
ERROR CALCULATION
LIMITATIONS OF THE METHOD
The finite deuteron range
Interfering neutron groups
Interference due to the presence of different elements
Interference due to neighbouring neutron states
RESULTS AND DISCUSSIONS
Carbon profiles
Nitrogen profiles
Oxygen profiles
Page
H
H
8
8
9
10
10
1 i
I I
14
14
1 S
1 5
16
17
18
I 8
18
- I l l -
AC KNO W LE DG E ME NT
REFERENCES
TABLES
FIGURE CAPTIONS
FIGURES
APPENDIX I
Calculation of the true concentration profile
APPENDIX II
Calculation of the depth resolution
1
INTRODUCTION
In recent years many methods have been developed to reveal
concentration profiles of different elements in various matrices. As
regards light elements in heavy matrices it 's not possible to apply
neutron activation due to the low reaction cross-sections, nor back-
scattering techniques due to the dominating yield from the matrix. On
the other hand charged particle induced nuclear reactions constitute a
promising tool since the Coulomb barrier is lower for the light elements
studied than for the heavier matrix nuclei thus providing a good signal-
to-background ratio. The energy loss of the bombarding charged par-
ticle is such that only the surface region of the sample is analysed
and the associated energy-range relationship can be used to establish
a depth scale for any kind of material.
Proton induced nuclear reactions have been used to make profile
measurements of carbon [?] , oxygen fc, 3] and fluorine [4] present in
metal surfaces. These studies demonstrate the possibility for obtaining
depth distributions by measuring the alpha particles or y-rays emitted
at certain resonance energies.
He-particles [5, 6] and tritons [7] have been used to detect
oxygen in metal surfaces at depths of up to 5 um. However, while the
application of He-ions necessitates the use of O-enriched targets,
only few laboratories are prepared to accelerate tritons since the use
of this active isotope may involve health hazards and contamination
of the facility.
Deuteron induced nuclear reactions have been applied to oxygen16 17 18 19
diffusion profiles making use of the reactions O(d, p) O, O(d, p) Oto t /
and O(d,er) N [8, 9] . In these experiments determination of the
distribution of the oxygen isotopes depends upon measurement of the
energy spectra of the emitted charged particles. For this reason it is
necessary to take into account the energy loss of both the bombarding
and of the emitted particles with the result that only surface layers of
less than 5 tint thickness can be investigated.
An interesting alternative is afforded by the use of (d, n)-reac-
tions. Since the neutrons emitted in this instance do not suffer from
energy losses when penetrating the target or the target chamber, they
-1 -
can be detected outside the vacuum system. Under these conditions the
time-of-flight technique constitutes the best method of measuring neutron
energies in the MeV-region and has previously been used for the micro-
analysis of light elements in metal surfaces [lOJ and in gases [1 ij .
The aim of the present work has been to demonstrate ho* (d, n)-
reactions can be used to study concentration profiles of the light elements
carbon, nitrogen and oxygen in metal surfaces.
THE METHOD OF PROFILE MEASUREMENTS
When a thick target is irradiated with monoenergetic deuterons
the neutrons emitted within a given solid angle have different energies.
The energy spectrum is due to the production of neutrons at various
depths below the surface. The energy of the emitted neutron is dependent
on the energy of the deuteron at the instant of reaction. The deuteron
energy, however, is a decreasing function of the penetration depth x due
to the stopping power of the matrix. The energy available for the emitted
neutron in the C. M. system is thus given by
= E d - | j ' (dE/dx)dx |+Q (1)
where E , is the initial deuteron energy, dE/dx the stopping power of the
matrix and Q the energy released in the (d, n)-reaction concerned (Table I).
According to eq. 1 neutrons are emitted in groups. For a given
reaction, i . e . for a certain Q-value, also the neutron energy is a decreas-
ing function of the depth x. The spectrum of such a neutron group has a
well defined high energy edge (x = 0) and a smooth broadening towards the
low energy side (x > 0) (Fig 1). The distribution of intensity as a function
of the neutron energy in this broadened peak provides all the information
necessary to determine the concentration profile of a given light element.
The number of nuclei of this element per depth intervall is measured by
the neutron yield in the corresponding energy intervall.
The yield Y of the neutrons with energies between E and E + dE7 * n n nis determined by
YdEn . ld e(En , r)NA(x)a(Ed> ö)dx (2)
- 3 -
where
I , = deuteron currento
c(E . r) s detector efficiency for neutrons with ene rev F. at an n
distance r from the target
N.(x) = density of the nucleus A at a depth xA
.,9) =r differential cross section for the reaction A(d, n) at
a deuteron energy E . emitting neutrons at an angle ö
dx = thickness of the layer from which the neutrons with
energies between E and E + dF are emitted.n n n
In the following it will be shown how the measured neutron yield
as a function of the neutron energy can be used to describe the concen-
tration profile of the light elements carbon, nitrogen and oxygen.
EXPERIMENTAL
The time-of-flight spectrometer
The measurement* were performed with the 5. 5 MV Van de
Graaff accelerator at Studsvik. This machine is equipped with a
klystron bunching system that provides pulses with a repetition fre-
quency of 1 MHz and a FWHM of about 1.5 .is [12]. Under these condi-
tions it is possible to obtain an ion beam mean current of about 8 nA.
Fig. 2 shows a block diagram of the time-of-flight spectro-
meter with conventional ORTEC electronics. The scintillation detector
consists of a fast liquid scintillator NE 21 3 with dimensions <$ 5" x 2"
coupled to a photomultiplier of type RCA 8830 via a light guide (length
5 cm) all surfaces not viewed by the photomultiplier being covered with
reflector paint.
The scintilla tor has pulse shape discrimination properties which
makes it possible to appreciably reduce continuous Y-radiation from the
activated target. Fig. 3 show* the effect of n-Y-discrimination on the
time-of-flight spectrum of an oxygen sample. The signal-to-background
ratio is increased by about one magnitude, while the y-peak is reduced
by two magnitudes.
- 4 -
The neutron detector is positioned inside a massive container
constructed of shielding materials iron, lead and paraffin mixed with
lithium carbonate. This unit is mounted on an arm which moves in an arc
along a horizontal track v.ith the target positioned at the axis of rotation.
The target chamber
The target holder is shown in Fig- 4. A steel clamp at the to?
of the cylindrical target chamber supports the sample, which may hav
either cylindrical or plane geometry. An insulated shield of brass in
front of the sample is maintained at -1 J5 V to suppress secondary elec-
tron tmission. The final size of the beam is determined by an insulated
tantalum diaphragm of 6 mm in diameter. The use of such a small bea.n
is made necessary when irradiating cylindrical targets in order to
reduce the deviation from the mean range to less than 2 %.
The whole target chamber serves as a Faraday cup. Thus, when
steel targets were used the chamber was connected to a current inte-
grator and the accumulated charge, for the time of irradiation, was
measured via the target. For targets of zirconium, which is a good
insulator, current measurements were carried out separately during
the course of irradiation. For this purpose a small tantalum plate,
rotatable on an axis, was periodically inserted into the beam to monitor
the current.
SAMPLES
Carbon
Carbon distributions were studied in flat steel samples of 1 to
2 cm in diameter and 1 to 2 mm thickness. The gradient samples were
prepared by evaporation and baking in a carbon containing atmosphere
or by the surface decarburization of carbon steel. Other backing mate-
rials have also been used (Al, Cu, Ta and Au).
Homogeneous reference steel samples with a carbon content
ranging from 0. 047 % to 4. 6 % were prepared by careful, high tempera-
ture homogenization. Iron with a carbon content of 0. 03 % was used for
making background measurements. For resolution determinations and
to establish depth scales measurements were performed on tantalum
samples carrying evaporated carbon layers 500 A and 800 A thick,
- 5 -
Nitrogen
For nitrogen distribution measurements the same backing ma-terial was used as for carbon. In this instance, however, no refer-ence sample with a known nitrogen content was available and only qual-itative shape determinations could be performed.
Oxygen
Oxygen profiles were studied in flat zirconium samples with di-mensions identical to those mentioned above. Another group of samplesconsisted of small zirconium tubes with an outer diameter of 16 mm, awall thickness of 1 mm and a height of 50 mm. These samp.'es had beenheated systematically at temperatures between 700 C and 1 200 C fordifferent numbers of cycles. In this context a cycle is defined as anautoclave treatment during which the sample is first heated from ambienttemperature, then kept at constant temperature for 10 sec and finallycooled to the ambient temperature again. The cycle time was 10 min.After completing the specified number-of cycles the sample was keptin the autoclave for 21 days at 350°C in a steam atmosphere under apressure of 100 atm,
ANALYSIS OF THE MEASURED NEUTRON GROUPS
Analysis I; Integration over sectioned layers
Since eq. 2 describes the neutron spectrum as a function of thedepth distribution N.(x) of the atoms A, the distribution can be analysedby the following procedure.
During the experiment the geometry is unchanged and the de-crease in the deuteron flux due to the reactions within the range x isnegligible {ål/l <10~ ) . Accordingly, the neutron flux is essentiallyproportional to four parameters: t(F , r), <y(Ed# *), N
A(x) and dx.
The function* «(En,«r) and or(Ed,9) are known and can be ex-pressed as functions of the depth variable x. For each layer of thick-ness dx the density N. (x) is proportional to
«lEn (x). r]<y[Ed(x), 9]
where E (x) and Ed(x) are the neutron and deuteron energy, respectively,at the depth x in the target. This type of analysis has been carried out
- 6 -
for a homogeneous carbon distribution. Thus, tho neutron spectrum
was sectioned into intervals corresponding to layers of ! um thickness
at successive depths below the specimen surface. The integrated m-utro..
yield for each interval was then divided bv the corresponding effrctiw
cross-section ~(E,, 6)e(E , r) for each layer. The result elvmld provide
a linear plot of the concentration distribution (Fig. 5). However, th«-
accuracy to which ^(E ,, ö) is known is as low as 20 - 50 % so that for
purposes of revealing concentration profiles the result of the di-con-
volution is unsatisfactory. Furthermore, the determination of the eiti-
ciency fuction e(E , r) is a tedious task. The above problems an-
circumvented by performing the following type of analysis.
Analysis II: Comparison with a homogeneous standard
Instead of comparing the measured neutron yield from a studied
profile with the effective cross-section the neutron spectrum is compared
with the equivalent spectrum from a homogeneous distribution, obtained
under the same experimental conditions. Let N.(x) be the true concrn-
trction profile of the element A in the sample to be studied while N_
represents the content of the same element in the homogeneous standard
sample. A ratio function R(x) can now be generated by performing a
channel-by-channel division of spectrum A by spectrum 3 (Appendix I).
The profile to be studied is then given by
NA(x) = K NB R(x) (3)
where K is the ratio of the stopping powers of the two matrices A and B.
The principle of the analysis is demonstrated in Fig, 6 for
carbon in steel. The measured carbon spectrum is corrected for the
neutron contribution from the iron matrix (Fig. 6a), A standard
sample with a homogeneous carbon content of 0, 85 % is measured
under the tame experimental conditions (Fig. 6b). A channel-by-
channel division of both spectra yields the ratio function R(x), i .e.
the true carbon distribution as a function of depth. This sample con-
tains a decarburiated surface zone which extends to a depth of 4 ^m
(Fig. 6c).
The carbon content of 0. 03 % in the background sample is ac-
counted for in establishing the quantitative scale for carbon graded
in per cent.
- 7 -
The detector efficiency e(E , r) and the cross-section e(E.,9)do not enter eq. 3 numerically so that the ratio function R(x) is inde-pendent of the initial deuteron energy. However, the statistical errorof R(x) is sensitive to the magnitudes of c(E , r) and a (E., 9) and thereaccordingly exists an optimal choice of er-rgy in such an experiment.The choice of optimal conditions will be discussed in a later section.In accordance with the conditions set out in eq. 3 the result N.(x) isgiven directly in terms of the standard matrix, which includes a cali-bration of the content of the element A in the sample to be studied. Theneutron energy spectra given by different homogeneous standard samplesare identical in shape, although the matrices differ in stopping power(Fig. 7), Accordingly, the use of different standards in eq. 3 impliesonly a change of K, while the depth scale, i. e. the parameter x, is tobe evalutated according to the range data of the matrix A alone.
The atomic stopping power of the light elements is greaterthan that for the high-Z matrix atoms. Thus, in a steel matrix, whichcontains various components, the stopping power does not change app-reciably with the composition unless the amount of carbon and nitrogenexceeds the order of some ten per cent. Accordingly, steel has beentreated in this work as if it were constituted of a pure iron matrix.For oxygen profiles in zirconium the case is different since the amountof oxygen in sirconia (ZrO2) is 66 atomic per cent compared to theamount of interstitial oxygen in the diffusion region which is below29 atomic per cent. For this reason the different parameters sucha* range, straggling, d-»pth resolution etc are calculated for both Zrand ZrO~.
ENERGY CALIBRATION AND DEPTH SCALES
Calibration
According to eq. 1 the highest neutron energy in each neutrongroup is given by neutrons emitted from the uppermost surface of the•ample (x * 0). The sero point of the depth scale for each element isthus given by the high energy edge of the corresponding neutron group.The identification of the different neutron groups is performed accordingto the known Q-values of the reactions concerned. An accurate calibra-tion was subsequently performed by irradiating samples which featuredthin surface layer* of the light element* studied. Layer* of the orderof 500 - 800 A are belcw the resolution for the method and they there-fore provide sharp symmetrical peak* which were used for the energycalibration as well a* to define the zero point of the depth scales.
- 8 -
Transformation of flight time into a depth scale
The measured time -ot'-flight spectra can be transtorm.-d into ch-u-
teron energy spoctra by applying classical nuclear reaction kinematics
[l l] . The corresponding deuteron ranges were taken from tables o'
range and stopping power [t 4] to provide the necessary depth scales
for the relevant matrix. For this purpose an off-line program was
written which calculates the depth scale for a given light element in
a defined matrix on the basis of the dorived calibration points. It will
be evident that the evaluation of A new depth scale is necessary for
each set of element (neutron group), matrix and initial deuteron enerey
since the energy spectra are a non-linear function of the channel num-
ber.
RESOLUTION
The total resolution afforded by th» technique is mainly depend-
ent on the time resolution of the spectrometer which, in combination
with the stopping power of the matrix, provides an instrumental reso-
lution dx. This contribution can be described as
dx = (A. + BEd) (C + DEJ; +
where A, B, C, D and F are matrix-dependent constants and E, and E
are the initial deuteron and neutron energy, respectively (Appendix II).
According to eq. 1 the neutron energy E can be expressed in
terms of the deuteron energy E - and the Q-value of the reaction con-
cerned, so that the depth resolution depends on the element studied.
Furthermore, for a given element and initial deuteron energy the neutron
energy decreases with increasing reaction depth in the matrix and the
resolution accordingly varies strongly along the depth of the profile. In
Fig. 8, eq. 4 is applied to obtain resolution curves for the elements
carbon, nitrogen and oxygen, studied at deuteron energies between 1 and
4 MeV. At the detector cut-off (E = 0. 5 MeV) each element affords a
maximum depth resolution of better than 0, 5 pm.
At greater depth» the uncertainty in the rang», of the deuterons,
the so called straggling parameter 0, contributes appreciably to the
depth resolution. Thus the thickness of the resolved layer D is given by
- 9 -
D =Vdx2 + n 2
where 0 can be written as
0= kVx (pdE/dx)'1
(5)
(6)
and k is a matrix-dependent constant.In Figs. 9 - '2 the depth resolution D is shown as a function of
depth for each of the three elements studied and at several initial deu-teron energies. These diagrams are constructed from calculations thatuse the exact relations, derived in Appendix II, in which stragglingis included. The formulae derived demonstrate that the resolvablelayer dx only varies within ' 0 % for a 50 % change in the duration ofthe deuteron pulse or in the thickness of the detector.
For a given deuteron energy the reaction with the lowest Q-value provides the best resolution. This accounts for the fact thatelements with Q-values above 5 MeV are unsuitable as regards depthprofile investigations since they afford depth resolutions of severalmicrometers.
OPTIMIZATION OF THE EXPERIMENTAL CONDITIONS
The optimal choice of initial deuteron energy
The spectrum obtained in a profile measurement of a given ele-ment i is the convolution of the true distribution N.(x) with the effectivecross-section c(E >r)<7(E.,9)* A high effective cross-section thus pro-vides better statistics for a given time of measurement and the (d,n)-cross-section <j(E., 6) is in general an increasing function of the deuteronenergy in the MeV-region [15] .
The depth resolution, however, generally deteriorates with in-creasing energy as was shown in the previous section. Accordingly,there is an optimal choice of initial deuteron energy for each elementto be studied. This optimisation is illustrated in Fig. 13 for a givencarbon distribution. The effective cross-section is weighted by the in-
strumental resolution dx and the value ofcr<Ed,e)e(En,r)
is shown as afunction of the deuteron energy. From this diagram it is clear that2. 5 MeV is an optimal choice for the initial deuteron energy, sincethe plateau between 1. 2 MeV and 4 MeV provides both a low yield anda poor resolution.
- 10 -
Fie. '4 illustrates the corresponding conditions for oxygen inzir. omum. In this instance optimum energies appear to He between3. 5 MrV and 4 MeV. Unfortunately, where sirconium is concerned itis necessary for the deuterons to penetrate a thin film of stoichiometrirdioxide before reaching the region of oxygen diffusion. This oxide layerhas i xtTi-mc resistivity and hardness and it cannot be ground or etchedon' without affecting the diffusion region. Accordingly, the film thicknessof between Z and 10 am that occur must to be taken into account wht-noptimizing the d.uteron energy (Fig. 12).
The optimal choice of angle for neutron detection
In peneral the differential (d, n)-cross-sections are forwardpeaked. The author, however, observed differences of some ten de-crees in the maxima of the angular distributions for the neutronsemitted from nuclei at the levels concerned. Thus, while carbon andnitrogen yield a maximum neutron emission at 20 the maxima dueto oxygen were found to occur at 50 for the ground state reaction,'(nn). and at 0° for the first excited state in F, c(n.). At 0° theratio of T(n )/r(nn) varies between 30 and 5 for the deuteron energiesbetween 2. 6 MeV and 3. 5 MeV.
The fact that <j(n ) mainly exceeds °(n0) by more than one orderof magnitude, together with the already mentioned increase of depth re-solution for the neutron group n. , encourages the use of these ratherthan ground state neutrons for studying oxygen profiles. In fact oxygendepth distributions have been measured at 0° in order to optimize theyield ratio Y(n. )/Y(nn) which reduces the intrinsic interference of thesetwo groups.
The effective differential cross-sections of both reactions havebeen used for a theoretical derivation of the 0°-yield from a homoge-neous sample. This has been compared with an experimentally meas-ured spectrum. The result is shown in Fig. 18 and the agreementbetween the two curves demonstrates that after a correction of theno-neutrons the effect of interference ir negligible and that there isno measurable background from the Zr-matrix.
ERROR CALCULATION
The depth profile is described by two parameters namely theyield Y and the depth x. The errors that correspond to each parameterare given by two independent groups of uncertainties (Table II). The
- 11 -
main sources of error relating to the yield Y are due to the statistical
errors in the neutron spectra for both the gradient sample and for
the reference sample, to the uncertainty in the current recording
and to the background in each measurement. The main sources of
error relating to the depth parameter x are the range data used for
the depth calculation and the energy calibration, including the accuracy
to which the initial deuteron energy in the beam can be determined.
A separate error is produced by the curvature of the zirconium tubes.
The oxygen distribution in the cylindrical walls is radial and the radi-
al projection of the deuteron range accordingly varies as a result of
the finite size of the beam. This uncertainty increases with the width
of the beam, but is non-existent for flat targets. Since each profile
is determined by a comparative measurement, all the variables that
are identical for the sample and for the standard contribute no error
to the final result. Such variables include flight path, detector effi-
ciency, cross-section etc.
Owing to the shape of the neutron groups the statistical errors,
ranging from 0. 5 % to 2 % are far less in the surface region than at
greater depths. For a homogeneous sample, however, the statistical
error can be kept below i % even at greater depths (10 to ? 5 \im).
Error* produced by the background are very low. The random
Y-radiation is decreased appreciably by the application of n-V-discrimi-
nation. As far as profiles in steel arc concerned the neutron yield from
the matrix can be subtracted from the spectrum by performing a mea-
surement on a pure iron sample. For oxygen profile measurements
the immediate oxidation of the fresh metal surface (Al, Zr) prevents
application of the same procedure. For high-Z matrices such as zir-
conium, however, the background neutron contribution is negligible,
especially at initial deuteron energies less than 4 MeV.
LIMITATIONS OF THE METHOD
The finite deuteron range
The profile to be studied may occur in a narrow layer. As long
as this layer doe* not exceed tha effective deuteron range the entire
profile can be studied. (The effective deuteron range is defined as that
part of the penetration depth within which neutrons are produced with
energies exceeding the detector cut-off). Although it is possible to
extend the profile depth by 4 nm/MeV by increasing the initial deuter-
on energv, straggling causes a deterioration of the resolution while
the background is enhanced at deuteron energies above 4 MeV.
With regard to carbon and nitrogen in steel matrices the ana-
Ivsable depth can also be extended by etching off the uppermost 5 or
10 um of material. This approach has also been tested »nd the result
is shown in Fig 16. Unfortunately, it is evident from the plot that the
overlapping of the corresponding depth regions does not result in a
satisfactory match. The discontinuities may be due to uneven etching
over the area of the target. However, this technique provides, at le-tst
qualitatively, a systematic study of concentration distributions beyond
the depth given by the effective deuteron range.
Interfering neutron groups
Alternatively, a limit may be imposed by the presence of an
interfering neutron group. This is explained as follows.
If the Q-values of two neutron groups differ by dQ then the max-
imum analysable depth of the neutron group with the greater Q-value is
yiven approximately by
x r dQ (dÉ/dx) " ^
where dfc/dx is the mean stopping power of the matrix over the range
x under consideration. Interference may now arise by two different
mechanisms. Thus a second neutron group with a lower Q-value may
be produced either by atoms of another element present in the surface
of the target; or by the existence of an excited level close to that being
measured in the nucleus of the element under review»
Interference due to the presence of different elements
An example of this type of interference is provided by the pre-
sence of nitrogen in carbon steel. When deuterons of 3.0 MeV energy
are used nitrogen "cuts" the carbon profile at a depth of 15 urn. At-
tempts have been made to eliminate this disturbance by subtracting
the spectrum due to pure nitrogen from the measured spectra. Ground
state neutrons emitted in the N(d, n) reaction (Q * 5, 066 MeV) do not
interfere with the carbon spectrum and can thus be used for normali-
zation purposes. This procedure i s , in principle, applicable to homo-
- 13 -
geneous nitrogen distributions. Difficulties may arise, however, be-
cause of slight deviations in the energy spectra measured at different
instances and because of errors produced in the correction for a small
effect by subtiaction of nearly equal numbers. For inhomogeneous nitro-
gen distributions on the other hand correction of the disturbing peak is
altogether impossible. Since nitrogen i» commonly present in carbon
steel carbon spectra can thus only be studied quantitatively up to a
depth of 15 tim without interference.
In accordance with the Q-value sequence the measurement of
nitrogen profiles are subject to interference when oxygen is present
in the target. In general, however, the amount of oxygen in steel is
so low that no interference arises. Nitrogen profiles can then be stud-
ied over the same range as carbon distributions. However, if oxygen
is present in amounts exceeding 5 % of the nitrogen content the re-
sulting interference reduces the analysable depth to 5 ^m. In Fig. 17
the analysable depths for carbon and nitrogen are shown as functions
of the initial deuteron energy with and without interference. Oxygen,
which features the lowest Q-value of the three elements discussed,
is accordingly unaffected by this type of interference.
Interference due to neighbouring neutron states
An example of the interference due to the neutron emission
from neighbouring nuclear states is provided by oxygen. As a result
of the (d, n)-rcdCtion with O the residual nucleus F can remain
in the ground state (n ; Q = -1.627 MeV) or in the first excited state
(n1 :Q= -2.1 27 MeV). The difference dQ between these two neutron
groups is 500 keV which corresponds to an interference free ZrO?-
layer of 10 n,m in the nQ-group at a deuteron energy of 3. 5 MeV. Ground
state neutrons that are produced beyond 10 (im accordingly interfere
with those n1 -neutrons that are produced in the surface of the target.
The surface region of oxygen profiles that exceeds 1 0 ^m can thus be
studied analysing ground state neutrons, whereas greater depths can
be studied by analysing n. -neutrons.
However, it has been found out that in almost all cases only
n1 -neutrons need to be analysed. The exponentially decreasing tails
in the diffusion region of the n--spectra cause negligible interference
with the n1 -group. Here use is made of the strong angular dependence
14 -
ot the cross-stction ratio c(n^)/7(nA. Thus only a low no-yield, pro-
duced by the lower i(n.)-cross -section in the low concentration diffu-
sion region, interferes with the higher n. -yield, produced by a 5 to
}0 times larger r(n1 )-cross -section in the oxide layer at 0 . This
effect causes un uncertainty of about 1 to 5 % which after correction
for the n_-yield contribution reduces to less than 2 %.
As regards the production of neutrons in the n. -group the res-
idual nucleus F* decays to the ground state by the emission of prompt
gamma radiation with an energy of 500 keV. The n. -neutrons can be
measured in coincidence with the 500 keV \-rays and the signals due
to the n_-neutrons are rejected [l6j. The same technique can be usod
for the elimination of "nitrogen neutrons" in carbon profiles. Here
use is made of anti-coincidence measurements of the 6. 73 MeV v-
rays from the residual nucleus O. Preliminary studies of this type
indicate, however, that the time of measurement is increased by at
least two magnitudes, and the rapidity of the profile measurements
is thereby lost.
RESULTS AND DISCUSSIONS
The technique which has been developed permits the depth dis-
tribution of the light elements carbon, nitrogen and oxygen to be mea-
sured quantitatively in metal surfaces over a range of 10 to 15 ^m,
The technique is both rapid and non-destructive. A profile with a
concentration level of about 1 % can be measured in 1 0 min for an
overall resolution lying between 1 and 0. 5 ^m and a total error of
about 9 %, on irradiating the samples with deuteron» of an initial energy
of "$. 5 MeV at a current of 0. \ to 1 nA. Use of a low beam current is
necessary to keep the dead time below 20 % and to prevent the target
from being overheated. It should be mentioned that destructive thermal
effects have: been observed at higher currents.
The determination of a profile necessitates the irradiation of
a) the sample containing the element whose distribution is to be mea-
sured, b) a standard sample containing a homogeneous distribution
of the same element in the same matrix, and finally c) a sample pro-
viding data for background subtraction.
Carbon profiles
A representative example of the determination of carbon pro-
files in steel surfaces is shown in Fig. 6. The reproducibility of the
method has been demonstrated by repeating the measurement at dif-
ferent energies (2.5 and 3.0 MeV; Fig. 18). The total errors are in-
dicated in the diagram as vertical bars and the depth resolution as
horizontal bars. The agreement between the two sets of measurements
is considered to be satisfactory since the observed deviations coincide
within the total error for each set. The result obtained has been veri-
fied by microscopical measurements and the (p, v)-resonance method
as described i n [ l ] .
The detection limit of carbon in a steel matrix is a function
of the initial energy and the depth, (Fig. 19). From this diagram it
is evident that the detection limit can be approved by using higher
deuteron energies. However, for E . > 4 MeV this is no longer true
owing to the increased background contribution.
Nitrogen profiles
As mentioned before nitrogen gives rise to a neutron group which
interferes with those from carbon that corresponds to a depth of 1 5 ^m.
This fact makes possible simultaneous measurement of carbon and ni-
trogen profiles in samples where the carbon distribution is less than
15 um (carburized surfaces). In such cases , the neutron groups from
nitrogen and from carbon are separated in the energy spectra md, with
the aid of a carbon and a nitrogen standard, both concentration profiles
can be determined in the same sample in a single measurement.
Oxygen profiles
As regards the determination of oxygen distributions there is
no interference from other light elements as long as the contamination
occurs only at the surface. Owing to the low Q-value of the O(d,n.)-
reaction, the depth resolution of the oxygen profiles is the best of the
three light elements studied.
In view of the use of ssirconium tubes in reactor technology the
oxide thickness and the shape of the diffusion profile are important
parameters in corrosion studies.
The (d, n)-method has therefore been used to measure the con-
centration profiles within and beyond the ox'Je layer in a number of
- !o -
zirconium samples oxidized under various conditions. Some of the re-
sults obtained are shown in Figs. 20 - 23, where the concentration
profiles of three sets of samples have been plotted. The difference in
the measured depths of the profiles is the result of different treat-
ments of each sample in the autoclave. The profiles are labelled with
numbers that are listed in Tables III - V together with the maximum
temperature and the numb'-r of cycles for the three sets.
The first set oi samples was pr -pared for the purpose of com-
paring the results of the (d, n)-rnethod with those obtained frj.n mi-
croscopical studies. The phase junction between th«* ZrO->-layer and
the meta] fliftision zone) is visible under the microscope. It Fig. 20
th • position of this phase junction is compared with the profile as ITHM-
sured by the 3. 5 MeV deuteron irradia.i >n.
The horizontal bars in the diagram represent the resolution
ct the microscopical measurements while the bars below the range
scale show the resolution afforded by the (d, n)-method. Both results
are in satisfactory agreement with each other, since the half maximum
of the oxygen concentration and the position of the phase junctions co-
incide within the resolution of both techniques.
The second and third set of samples differ as regards the com-
position of their zirconium matrix (Table VI) but are essentially simi-
lar with respect to the thermal treatment (Tables IV and V).
Fig. 21 clearly demonstrates the increase in the thickness of
the oxide layer as a function of the number of cycles (1, 5 and 10) at
900°C.
The long tails of the profiles that are formed at higher tempera-
tures were measured at 5 MeV (Fig. 22) and are well resolved.
A comparison between sample No 3 (1 x t 200°, dark) and No 4
(5 x 900 ) where the oxide layer is of the same thickness indicates in
this diagram that the extent of the diffusion profile beyond the oxide
layer is relatively shorter after a number of cycles than after a single
cycle. The change in the gradient might be interpreted as a progressive
growth of the oxide layer into the diffusion region with increasing number
of cycles.
An equivalent sequence of profiles has been measured for the
third set of samples (Fig. 23). The shapes of the profiles of both series
- 17 -
1 orri-spond to each other at the same number of cycles and temp-er.t-
turi-s, with the exception of those following the treatment at 5 x (idO"C'..
In this instance the extrapolated dtpth of the diffused zone in the tw •
ser ies is h um (No 7 in Fig. 2^) and 15 m (No 6 in Fig. 2i) . respec-
tively. The difference in the thickness of the oxide layer is in excell. r.t
agreement with a sharp increase ,! the t ransvers ductility ratio (i. ••,
plastic deformation) which occurs precisely at 1 000 C. [ '7j .
\t the phase junction between the stoichiometrical dioxide and
the diffusion zone the oxygen content a l ters from 66 to 29 atomic p>-r
c<nt. But this cannot be detected as a sharp edge in the neutron energy
spectra . The "smoothing out of the true concentration distribution",
which is due to the finite resolution, is a basic feature of th» method.
In order to relate this inadequacy to the experimental e r r o r s a numerical
convolution of a constructed oxygen profile with a resolution function
has h'-en performed on a PDP-15 computer. The "true concentration
distribution" was simulated by a step function for the oxide at the sur -
face and by a funct'on tha' decreases exponentially with depth in the
diffusion region. The shape of the profile and the width of the Gaussian
resolution function were chosen to correspond to the experimental con-
ditions.
The convoluted "spect rum" was found to fit the construced pro-
file for both the oxide layer and for the diffusion zone by better than
2 %. At the surface of the target and at the phase junction the profiles
were smoothed out as expected. (Compare Fig. 1 5).
According to the resul ts given by the mathematical procedure,
the rapid determination of oxygen diffusion profiles in zirconium using
this technique seems to provide a complement to hitherto used tech-
niques.
It is therefore intended to apply this method to other oxidation
problems, in particular to the growth of oxide layers as a function of
time under stable thermal conditions.
Further, it is planned to incorporate the analysis programs
that have been developed in the available on-line program?. The aim
is to facilitate study of the ratio function R(x) by displaying it on the
computer screen during the course of the measurement , This increases
the rapidity of the present technique, since the resul t , i . e . the normalized
concentration distribution with depth would be immediately available at
the end of a 1 0 min irradiation.
18 -
ACKNOWLEDGEMENT
The author is deeply indebted to Dr S. Malmskog for invaluable
help and fruitful discussions, for his participation i" the experiments
and in the computer programming. For the preparation of the zirconium
samples thanks are extended to Dipt Ing A. Sietnieks and Ing F. Blaha.
- 19 -
1 .
2 .
3.
4 .
5.
6.
9.
10.
REFERENCES
LORENZEN, J. ,Depth distribution studies of carbon in steel surfaces by meansof the nuclear reaction ^ c f p . y ) 1 3j^.Nucl Instrum. Methods 121 (1974) p. 467.
AMSEL, G. and SAMUEL, D. ,The mechanifrn of anodic oxidation.J. Phys. Chem. Solids 23_ (1962) p. 1707.
PALMER, D. W. ,Oxygen diffusion in quartz studied by proton bombardement.Nucl. Instrum. Methods 3_8 (1 965) p. 187.
MÖLLER, E. and STARFELT, N. ,Microanalysis of fluorine in zircaloy by the u6e of the1 9 F ( p , -Vv) i 6 O reaction.NucL Instrum. Methods 50 (1 967) p. 225.
OLLERHEAD, R. W. . ALMQVIST, E. and KUEHNER, J. A. ,A method of utilizing nuclear reactions in the study of oxidelayers.J. Appl. Phys. £7(1966) p. 2440.
COX, B. and ROY, C.Transport oi oxygen in oxiby the nuclear reaction 1 7O(3He,a)1 6O.Electrochem. Technol. 4 (1966) 3 - 4 p.
ide films on zirconium determined
121
BARRANDON, J. N. and ALBERT, Ph . ,Determination of oxygen present at the surface of metals byirradiation with 2 MeV tritons.In Modern Trends in Activation Analysis.Ed. by J. R. DeVoe and Ph. D. LaFleur, vol 2 p. 794.Pvoc. 1968 Int. Conf. held at NBS Gaithersburg, Md,Oct. 7 - 11 , 1968.(NBSSpec. Publ. 312).
AMSEL, G. , BÉRANGER, G , , DE GELAS, B. and LACOMBE, P.Use of the nuclear reaction '°O (d.p) 1 7O to study oxygendiffusion in solids and its application to zirconium.J. Appl. Phys. 39 (1968) p. 2246.
AMSEL, G. and SAMUEL, D . ,Microanalysis of the stable isotopes of oxygen by means of nuclearreactions.Anal. Chem. 39(1967) p. 1689.
MÖLLER, E. , NILSSON, L. and STARFELT, N. .Microanalysis of light elements by means of (d,n)-reactions,Nucl. Instrum. Methods 50 (1967) p. 270.
11. NAUDE, W. J. , PEISACH, M., PRETORIUS, R. andSTREBEL, P. J. ,Determination of carbon, nitrogen and oxygen in gases byneutron time-of-flight spectrometry.J. Radional Chem. 1_ (1968) p. 231.
T 2. TYKESSON, P. and WIEDLING, T. ,A klystron bunching system for a 6 MV van de Graaff accelerator.Nucl. Instrum. Methods 77_ (1 970) p. 277.
13. MARION, J. B. and YOUNG, F. C ,Nuclear reaction analysis.North Holland Publ. Concp., Amsterdam 1968.
14. WILLIAMSON, C. F . , BOUJOT, J. P. and PICARD, J. ,Tables of range and stopping power of chemical elementsfor charged particles of energy 0 . 5 - 500 MeV.1966.(CEA-R-3042).
15. LORENZEN, J. and B RUNE, D . ,Excitation functions for charged particle induced reactions inlight elements at low projectile energies.1973.(AE-476).
16. BECKER, J. A. and WILKINSON, D. H. ,Electric quadrupole transitions near A s 16:The life times of the first excited states of i 7 Oand 1 'F .Phy». rev. 134B (i964) p. 1200.
17. SIETNIEKS, A. ,Atomic Energy Company, Studsvik, Sweden. Private Communi-cation.
18. BOHP, N. .The penetration of atomic particles through matter.K. Danske Vidensk. Selsk. Mat. Fys. Medd. J_8 (1948) 8.
- 21 -
TABLE I
Reaction characteristics for the three light elements studied
Peacti.on
12 13
14N(d.n4)^O*
l6O(d.n0)17O
'6o(d,n,)l7o*
Q-value
(MeV)
- 0.281
- 1.724
- 1.627
- 2.127
Optimaldeuteron energy
E d(MeV)
2.5 - 3.5
3.5 - 4.5
3.0 - 4.5
3.5 - 5.0
Optimalangle
e
20°
20°
50°
0°
TABLE II
Error contributions of the various parameters for profile evaluation
(* The table is valid for concentrations in the per cent range
at deuteron energy E . = 3.5 MeV, current I , = 0.1 - \ yiA and irradi-
ation time of 10 min).
Source oferror
Statisticalerror
Currentrecording
Background
Interference
Range data
Energycalibration
Error*in %
0,5
2
3
5
1
2
5102
0,12
Comment
Surface regionAt depth of 1 0 to 15 u-m
Conducting targetInsulator
Negligible for Zr matrix;can be subtracted for Fe matrix
Regarding oxygen profiles
Pure matrix (Fe)Composite matrix (ZrO->)Curved surface; beam radius 3 mm
Initial beam energyTime spectra
TABLE HI
Treatment of zirconium samples (Set I, Fig. 20)
No
1
2
3
4
Number ofcycles
5
5
5
Max Temp(°C)700
800
900
1 000
Remarks
no auto-clave
treat-ment
TABLE IV
Treatment of zirconium samples (Set II, Pigs. 21 and 22)
No
01
2
3
4
5
6
7
8
9
Number ofcycles
_
1
1
51
10
5
5
55
Max Temp(°C)
-900
1 000900
1 200900
1 0001 0001 0001 200
Remarks
blank
dark surface
dark surfacewhite surfacegrey sirface
TABLE V
Treatment of zirconium samples (Set III, Fig. 23)
No
0
1
2
3
4
5
6
7
8
Number ofcycles
1
1
10
10
1
1
55
Max Temp(°c)
700
800
700
800
1 0001 0001 0001 100
Remarks
blank
grey surfaceblank surface
- 23 -
TABLE VI
Composition of samples and reference standard
S e t
II
III
N b
-
(1.0 + 0 .15)%
Sn
-
* 200 ppm
F e
0. 07 %
* 0.05 %
C r
1. 35 %
* 1 00 ppm
Z r
Balance
Balance
Reference
s ta nda rd
SiO-,
1.4%
CaO
6 . 7 %
HfO-,
2.1
ZrO.
Balanct
FLGURE CAPTIONS
Fig. ? A neutron time-of-flight spectrum obtained by irradiating
an iron sample with deuterons of 4 MeV. Neutron groups
produced by (d, n)-reactions with the light elements carbon,
nitrogen and oxygen are identified. Note the broadening of
the neutron group due to nitrogen.
Fig. 2 Block diagram of the electronics used in the time-of-flight
measurement.
Fig 3 Time-of-flight spectra from the (d, n)-reaction in a target
containing oxygen and carbon. The diagram shows the effect
of n-V discrimination (lower curve), which reduces the back*
ground caused by time uncorrelated Y-radiation by about one
magnitude.
Fig. 4 Sample holder. The steel clamp on the left hand side is de-
signed to hold samples with both plane and cylindrical geo-
metry. Next follows the sample holder housing with an ex-
ternal connection for secondary electron suppression. The
small cube-shaped box that follows to the right contains a
tantalum plate which is used as a current monitor when
insulating targets are irradiated.
Fig. 5 Result due to analysis 1, which represents a homogeneous
carbon distribution (circles) in an iron matrix. The neutron
group emitted in the C (d, n)-reaction (dots) is integrated
over intervals of 1 nm and divided by the effective cross -
section Aa (crosses) of the corresponding layer Ax. The
scatter of the circles is * 9 % from the mean value.
Fig. 6 Principle of analysis II
1 7 a represents the neutron spectrum obtained by the irra-
diation of a steel sample containing a non-homogeneous car-
bon distribution. After correction for background neutrons
from the steel matrix ( ) the total neutron yield ( . . . . ) is
reduced to the yield of neutrons emitted in the C(d, n)-
reaction (solid line).
- 25 -
Fig. 7
Fig, 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
17 b represents the background corrected neutron yield dm-
to a homogeneous carbon distribution.
The plot in 1 7 c represents the function R(x) which is the re-
sult of the channel-by-channel dh.lsion of the spectrum in
1 7 a by that in I 7 b (left hand scale). P(x) can be transformed
to the depth distribution function N , (x) which is indicatedr carbon* 'by the right hand scale, graded in per cent.
Neutron groups emitted in the O(d, n)-reaction at E , »
= }. 5 MeV in three different matrices (A1,O,, SiO,, ZrO,).
The spectra due to SiO, and ZrO^ have been displaced by '0
and 20 channels, respectively. Note the decrease of back-
ground with the atomic number (right hand side).
The three curves represent the instrumental resolution dx
for carbon (upper curve) and nitrogen (middle) in an iron
matrix and oxygen (bottom) in a zirconium matrix. The
detector cut-off at E = 0. 5 MeV is indicated for each curve.n
At this energy the resolution is better than 0. 3
three elements.
for all
Overall depth resolution D for carbon in a steel matrix as
a function of the penetration depth x. The upper curve for
each pair of curves includes the straggling parameter 0.
Overall resolution D for nitrogen in a steel matrix as a func-
tion of the penetration deoth x. The upper curve for each
pair of curves includes the straggling parameter 0.
Overall resolution D for oxygen in a pure zirconium ( )
and a pure zirconium oxide matrix (----) as a function of
the penetration depth x. The upper curve for each pair
of curves includes the straggling parameter 0.
Overall resolution D for a composite matrix consisting of a
ZrO? layer on bulk zirconium. The oxide layer is assumed
to have a thickness of 2 ^m and 10 j. m, respectively. The
curve» are plotted for a deuteron energy of 4 MeV (upper set)
and of 3. 5 MeV (lower set). It is evident from the diagram
that the resolution within the oxide layer deteriorates by
about 50 %.
to
L
Fig ' ^ The diagram illustrates; tho optimization of the deuteron
energy when carbon profiles are to be studied. Tho ofti-
ciency curve £( ) and the cross-section "(. . . . ) arc
folded and the result is divided by the instrumental resolu-
tion dx(— . — . —) for the corresponding deuteron energies.
Large values of C and c and low values of dx evidently im-
prove the profile determination; accordingly the peak value
of the ratio ee/dx indicates an optimum energy of E , -
= 2. 0 MeV. In the experiments energies of 2. 5 and \ MeV
were chosen in order to increase the effective range.
Fig. 14 The diagram illustrates the optimization of the deuteron
energy when oxygen profiles are to be studied. The proce-
dure is described in the captiur. r'f Fig. 1 3.
Fig 15 The experimentally measured neutron groups nn and n. due
O(d, n)-reactions are compared with the calculated neutron
yield ( ) for a deuteron energy of 3. 5 MeV. The theoretical
curve is based on the cross-sections <?(n ) and c(n.) and on
tho efficiency of the neutron detector. Resolution is not taken
into account (note the difference of the high energy edge of the
n. -neutrons for both curves).
Fig. 16 Result from repeated profile measurements on the same sample
before (o) and after (0 , v) surface treatment. Layers of 5 .m
and 10 |im have been etched off, respectively. The statistical
errors are indicated at 5 points.
Fig. 17 Effective deuteron ranges without (a and b) and with inter-
ference {c and d) for carbon (a and c) and nitrogen (b and d)
as a function of the deuteron energy.
Fig. 18 The diagram is obtained from profile measurements of a
4 nm carbon concentration gradient in the surface of a steel
sample. Identical results are obtained with the (d, n)-method
at a deuteron energy of 2. 5 MeV (Q) and 3. 0 MeV (o). The
same profile has been obtained by the (p, Y)-method (•) and
by a microscopical study (arrow) as described in ref 1. Over-
all errors and depth resolution are indicated for the (d,n)-
method below the depth scale and for the (p, Y)-method in the
plot.
- 27 -
Fig. 19 The diagram shows the detection limit of carbon at various
depths for two different energies. The sharp deterioration
in the detection limit with penetration depth is mainly due
to the decrease of the C(d, n)-cross-section towards lower
deuteron energies. The detection limit at a given depth x in
a layer dx is defined as the amount of carbon that is equal
to 3 VB, where B is the background in the corresponding layer.
Fig. 20 Oxygen profiles for 4 different diffusion temperatures (TOO,
800, 900 and 1 0OO°C). The same samples have been studied
under the microscope and the location of the phase junctions
ZrO,/Zr have been indicated in the plot together with their
depth uncertainties. The corresponding depth resolution
afforded by the (d.n)-method is shown b^low the depth scale.
Fig. 21 Oxygen profiles for 3 different numbers of cycles (1 , 5 and
10) at 900°C.
Fig. 22 Oxygen profiles for a number of treatments as described in
Table IV. The samples were irradiated with 5 MeV deuterons
in order to extend the effective range that can be analysed.
Fig. 23 Plot of oxygen diffusion profiles in the third set of Zr-samples.
Note the difference in the extrapolated range for sample No 7
compared to sample No 6 in Fig. 22 which have been treated
identically. (5 x 1 000°C).
z
o
"el
zoo
'C
•fSP
Accelerator drift tube
Be»t
Power
bias
Flight path
Target
Pick-up tube
Tis»pick-offORTEC 260
Currentintegrator
Tia» pick-off controlORTEC 4O3A
neg.
output
DelaygeneratorORTEC 416A
»top. tis«-to-pulse-icight conver-ter ORTEC 437*
I.start
Constant frac-tion timit.g.M. base
ORTEC 270
lin. output
neg,
output
Tisw pick-offcontrol
ORTEC 403A
•OrJX.
Delay aa^li-fier
ORTEC 427
Linear gateORTEC 426
Ienab lc
Multichannel
analyser
disc,output
Delay lineaaplificrORTEC 460
unipolaroutput»3 Q
Pulse shapeanalyser
OtTEC 45»
Lfindow
Sealer
Fig. I
n-YIELD/W min
I t *
3.5M«V
10*5-103
103
5-1O2
10050
10
6D(d.no) 12C(d.n)
discrimination
CHANNEL
Fig. 3
en
CROSS SECTION rC(d.n) in mb/sr
»lOMtV
SOAS4035302520IS105
• 065 %C YIELD»CROSS SECTION•YIELD I am COUNTS
15000
10000
5000
4*0 500 520 540 560 500 600 620 640 660. 6M CHANNEL
17 16 O 12 10 • 6 4 2 0 R A N O C Mm
12 13 U 15 1.6 16 2,0 2 A .6 M 10
Fig. 5
COUNTSK)3 A1211
toS
6
7
6
5
32t
EOO-2
ORlG SPECTRUMFt» BACKGROUND
. CORR SPECTRUM
COUNTS
* 1 0 3 /
24222018
1614121006
4
2
0
R(x) *
2.0181.6141.21.00.00.60.40.2
13
1300 1350 UOO U50 1500 t
Fig. 6 a
1600 1650
0fl5V. HOMOG CARBON(CORf» FOR Ft BACKGR0UN0)
1300 1350 UOO 1450 1500 1550 1600 165?
Fig. 6 b
CHANNEL
ABS CARBON CONT
homog.
v••*•
14
12
8
6
.4
.2
1300 1350 UOO 1450 1500 1550 1600
12 10x.
2 f 0
CHANNEL
OEPTH-rtpm
F i g . 6 c
n - YIELD
O(d.n,]
- Z r CHANNEL
Fig. 7
A IUT
4- en
«N
C
X
M
D(yum)
Dtyum)Carbon in
Fe-matrix
10 15 20 25 30(yum)
1.5
1.0
05
•
VE *4 0Mtf
\v 35MeV N
V
N\. • . . 1 • .
Nitrogen inFe-matrix
V
\ \ \• < > • • • • > ' • • • > • • —
10 15 20X (yum)
Fip. 9 Fig 10
£3
(NO
v_M£3.
Q q
U
a>.. Oro
>a»i nCO
, OCN
.. o
st
BO
•oHi
1-6*»ii
cOJ
O
x•o
N
\ \
p
—» 1—T—
1 1 r—
1 T I 1 r -
—
—r—i ( . T-
—i . t i 1 1——.i n
—p—i—> . . - • — i —oo oo oo
UJ
I-S w I»
Ioo
»v-
I \ I • I I Itet
in
O
oi
en c* —> i i • i > i i i » » i i t
§ § §
cÉ
3oO
I ^
£ 10
. 00E
Carbon
0.8
o original sampleO surface - 5 /amv surface - 10
Q6
0.4
0.2
•^6£°.ft
O• a
o o o o o o oD O °
24 22 20 18 16 14 12 10 8 0
Fig. 16
oet.
• • * •
f a * . 1
o o O
V
]OO 00
9Oooo
o ^Ci CM
0 00
oo ooo o
— , - o* " C C o
3 2 3 i« o O —•
IO 1 1
MI
o a -* c*I1Q O
ot-
00
K2 -»
DETECTION LIMITin (weight)-'/.CARBON
0.1
1 2 3 U 5 6 7 8 9 10 11 12 13 U 15 DEPTHinpm
Fig. 19
Oxygenin % MeV
70 H
60
Fig.
Otpth(/jm)Depth resolution
i?
roII
UJ
-- o
- CM
• CO
. CD
- O
x *4O •
8 OUD
oen o
CM
Oxygen
70
60-
50-
40-
30-
20-
10-
V.
8
_ • • < •
— 5 =
E.=3.5MeVd
//I/ //IIIAI
i i | i — » — i — i — I
8 2 o Depth (yum)Depth resolution
Fig. 23
APPKNMX I
i a l c u l a t i o n of the t r u e . o n t en t r a t i o n p r o f n e
i hr f r i c t i o n s e(F , r ) and c(F: ,-*') a r e i n d e p e n d e n t of the d i s -
t r i b u t i o n \ ' , ( \ ; Ac» - - d i n g l y , t h r .- .t 11. >
dF.( l .D
of the t w.i snfi ;r,i in a c:hannel-bv- c hannel division is civpn bv
C o n s t
Const dx B
(1:2)
The distribution function NL,(xi of a homogeneous sample is a
constant over the range x (N_(x) = N_), The unknown distribution of
A can thus be written as
N,(x) r R(x) NndxR/dxA B B' A
The depth intervalls dx and dx are related to each other by the corre-A x3
spondinp stopping powers (dE/dx), and (dE/dx)_ of the two matrices,
A and B, respectively. A systematic study of the variation of stopping
power with deuteron energy ha6 shown that dE/dx changes almost identi
cally in different matrices. Consequently, the ratio of stopping powers
is a constant over the whole energy range relevant in this work, i .e.
(dE/dxA/(dE/dx)_ = K. In the neutron energy spectra dE is identical
for both spectra and from eq. 1 it is evident that dE = dE . (the actualn a
difference is less than 0. 1 %). Thus the following relation is validdxB/dxA = (dE/dx) A/(dE/dx)B = K (1:4)
Inserting (1:4) into (1:3) the desired distribution function for the
element A is given by
NA(x) = K NB R(x) (1:5)
APPENDIX II
Calculation of the depth resolution
The total depth resolution D is compounded ot the layer dx,
resolved by the spectrometer , and of the straggling parameter il,
which is the uncertainty in the range of the penetrating deuterons.
since both contributions are supposed to be Gaussian in character and
inde pendent of each other the depth resolution can be defined a?
D = (dx' (11:1)
The resolved layer dx is related to thp resolvable deuteron m e r c y
dE . by the stoppir
to the expression
dE . by the stopping power dE/dx of the matrix (density o) according
dx = (p dE/dx)"1 dE d
From eq 1 it is evident that dE = dE, and the resolution dE inn n d n
the neutron energy can be calculated from the known relationship
dE / E = 2 dt / tn' n n n
which leads to
(11:2)
2(p dE/dx) E dt / t* ' n n' n
{11:1)
The time resolution of the spectrometer dt comprises three com-
ponents
dt = rdt2 . + dt2 , t + dt2 , ) 1 / / 2
n pulse electr detector '
where
dt . is the duration of the deuteron pulse striking the target.
Under the experimental conditions it is generally about 2 ns.
dt - is the empirically established overall time uncertainty
of the electronic circui try and is about 1 ns .
dt , is the time resolution due to the thickness of thedetector
detector (5 cm), and depends on the neutron energy Eand on the flight path (3 m). It is given by dt =
« /- *" ueiccior: 3,6 f
A contribution due to the finite solid angle of the detector is
negligible. The overall time resolution of the spectrometer is thus
given by
dt r (=, + n E "V^ 2 (H:4)n n
The flicht time t over a flicht path of ' m is 216 E " ' . Re--• n n
placing t and dt in eq. II:? the resolved layer is evaluated by theexpression
dx = 9. ? 10"3 (D dE/dx)"'(5 F ^ + I3E V ' 2 (11:5)n n
Straggling can be evaluated according to the relationship
d « 2wg(c dE/dx)"1 (II;6)
where 0. is the uncertainty in the energy loss over the range x accor-
ding to Bohr ft 8 ] ,
Both Qg and (o dE/dx)" are matrix-dependent and for the ma -
trices steel, zirconium and ZrO2 given numerically as
^ e ( F e ) = 7 . 6 5 « TO"3 Vx Mev (11:7)
Q£(Zr) = S.40 . 10*3Vx MeV (11:8)
ng(ZrO2) = 6. 50 • iO" \x~MeV (11:9)
(p dE/dx)" (Fe) = 5 + 2.46 Efl nm/MeV (II:!0)
(p dE/dx)" ' (Zr) • 10. 2 + 3. 2 E d nm/MeV < I I : ' f )
(p dE/dx)" ' (ZrO,) = 4 + 2. 75 E . nm/MeV (11:12)
Combining eqs. 11:5 - 11:12 with eq, 11:1 the following threeequations ran be uaed to evaluate the depth resolution in the threedifferent matrices, »teel, zirconium and ZrO.,
D(Fe) ( 1 1 : 1 •
D(Zr) r (10. 2 + }. 2 F.d)(8*. » x)'^ 10 " -m (TI:M,
D(ZrO2) = (4 + 2. 7 5 F.d)(8^. 10 (11:1
LIST OF PUBLISHED AE-RCPORTS
1-499 iSee beck cover earlier reports.»
451.
432.
4)1.
•M.
4M.
4M
417.
O*.
O».
44*.
441.
441.
444.
444.
441.
44».
447.
44*.
44*.
4Sf.
451.
4M.
4».4S4.
4*4.
Theoretical studies ol aqueous system» ebove « C I Pial l f l l far equilibrium diaarams and lomt generel features of the watersystem. By Derek Lewis 1171. 27 p. So cr IS:-.Thaoiailial studies el oqueeua systems ebove » C I TK» inn - »alarsystem. By Data* Lewis 1*71. 41 p. So. er. IS -* detector far <n. I era» section measurements By J Hellström and SM a i . tt71. V p. Sw c 15 -Influoaci «f e'attic eni»otrepy on attended ditlacaliari node» » I •Pettenaea. 1171. 17 p. Sw. cr IS.-.Lattica dynemic» af CsBr By S. Rolendson and O. Reunio. 1*71 J4 p Swcr. U : -The hydrelyeit of iron (III) and iron III) ion» between 25 C and J7J C ByDank Lewi*. 1*71. 1* p. Sw. cr 15 -Studiet af I t» tendency af intergrenuler corrosion cracking of eustenifieFe-C?-Mi alley» in high purity - . tar al N T C. By W. Hubner. I . Johanssonand M. da Peurbeii. 1*71 N p. Sw. cr. IS -
recovery boiler*. Sy OS cr. IS -leest squi-o lit of eatcu-
II. Numerical result» By H
4S7.
45»,
m.
Stadia* cswcaining weter-surfece depeaits in rotStrandberg. J. Arvesen end L Oehl. i n . 1J3 p. SwAdjustment of neutron cross section date byleted quantities to eiperimentol result.. PartKtggbtem. 1*71. 7* p. Sw, cr 15:-.Sail poweiad neutron and samme detects» for in-con meosuroments. ByO. Strindaheg. 1*71. I t p. Sw cr. 15—Neutron capture gamma ray cross sections for Ta, Ag. In and Ay betweenI t eat) ITS keV. By J. Hellström and S. Beshei 1*71. N p. Sw. cr. 15 -Tbaimadynemical properties of the solidified rare goto* By I. Ebtttia 1*714* p. Sw. cr. 15:-.Peat neutiaa radiative cextun cross section for some important standard»from W keV to 1.1 MeV. By J. Hellström 1(71. 11 p. Sw cr 15 -A Oe (Li) bar* hole probe for in »itu gamma ray spoctrometry By A. Lao-bar and 0 . Lendstrem. 1*71. M p. Sw cr. 15 -Nautian melest.e Mattering study el liquid argon By K Skild. J. M. Rewe.0 . Ostrewski end P. 0. Randolph. 1*71. »1 p. Sw. cr 15 -Personnel dasimetry at Studsvik during 1*7*. By L. Hedlin and C O Wid.ll1(71. * p. Sw. cr. IS:-.On the action el a reteting magnetic field on a conducting liquid. By IDahlberg. 1(71. M p. Sw. cr. IS;-.Low grade heat from thermal electricity production. Quantity, worth andpatstwa utilisation in Sweden By J. Chrislensen 1*72. 102 p Sw. cr. IS -Personnel deaimetry at Studtvik during 1*71. By L. Hedlin and C O Widell1*71. I p. Sw. cr. IS:-.Deposition of aerosol particles in electricelly cherged membrane filter*. ByL. Stram. 1*71. M p. Sw. cr. IS:-.Depth attribution studies ef carbon in steel surfaces by means of chereedparticle activation analysis with an account of heat and diffusion effects inthe temple By D. Bruno. J. Lorenton end E. Witelit. 1(71. 4* p. Sw.cr. 15 -Fast neutron elastic scattering eteeriments. By M. Salarna. 1*71. t* p. Sw.cr. IS : -Progress newt 1*71. Nuclear chemistry. 1*T1. 21 p. Sw. cr. IS:-.Measurement of bane mineral content using redietion sources. An annotatedbibliography. By P. Sehmeling. 1*71. U p. Sw. cr. IS:-.
, Mtnuiamanl of bone mineral content uting redietion source». An ennelafedbibliography. Suppl. 1. By P. Schmeling. 1*74. 2» p. Sw. er 20:-Longterm lest of telf-powered detectars in HBWR. By M. Brakas. O, Slrin-dohag and B. Söderland. 14 p. 1(71. Sw. cr. 15 -
. Maatunmanl ef the effective delayed neutron (faction in three differentFR*-coret. By L. Moberg and J. Kockum. 1*71. Sw. cr. I I : - .Application) af majnetohydrodynemic* in the metal industry. By T. Robin,son. J. Bmm and S. Linder. 1*72. 41 p. Sw cr. IS:-.Accuracy and precision studies of e
analysis in the field of life sciences. By K. Samsahl. 1*71.far estivationI t p. Sw. er. IS:-.'Temperature increments from depesitt on heal transfer turfecet: the thermalresistivity anal Mental conductivity of deposit» af magnetite, calcium hydro-ay apatite, hwrnus end copper o»ides. By T. Kolen and J. Arvesen 1(71. Mp. Sw. er. 1 * : - .
4M. leniieten af a high-prassur» gas flaw in a longitudinal discharge. By S.Polmaren. 1171. 20 p. Sw. cr. IS:-.
441. The esuttlt ttres» corrosion cracking ef allayed ttee.s - an electrochemi-cal study, ty L. Dahl, T. Oehlgren and N. Lsgmyr. I t » . 41 p, Sw. cr. IS:-.
411, Electrodepttilion af "saint" Cu"<l roentgan taurcet. By P. Bereniut, B.Jehemton *nd R. Soremar». 1*71. 11 p. Sw. cr. IS:-.
4*1. A twin large-ana proportional flaw counter for the a»say of plutonium Inhuman lung». By R. C. Sherma, I. Nilsson and L. Lindgran. I t » . M p. Sw.er. I I : - .
444. Maatuiamant» and analytit ef gamma heating in the Rl core. By R. Carls-can and L. 0). Larsson, 1*71. M p. Sw. er. 1 * : - .
4M, Determination af eiyaen in ilrcaloy eurfeee* by meant ef charged particleecllvelien analytit. By J. Lorenten anal D. »nu*. 1(71. I I p. Sw. er. IS:-.
4M. Neutron aetlvetlon af liquid sample* at law temperature in nectar* withraiereaea ta nuclear chemistry, f^ 0. Bruno. 1(71. I p. Sw. er. 11.—.Irredlatian fecllltitt far coated partiala fuel letting in the Studtvik Rl re-actor. By S. Sandklef. I t » . M p. Sw. er. l t ; - ,
. Neutron abtarber technique» developed in Ike Studtvik Rl reeclor, By R.Badh and I . Sandklef. I t » . I I p. Sw" er. »:-.
. A radleehemleel mechlne far the enelytlt ef Cd, Cr, Ca, Ma end In. By K.Semtehl, P. 0 . Wetter, O. BlemepM. I t » . 11 p. Sw. cr. ».-.
. redtelytlt. By H, C. dtrittaman. 0 . Nilsson. T. RaHbargerThaiaiml. I t » , M p. Sw, er, fa:- .
4*7,
47»,
471.4».
4».
474.
Prof nparl 1*71, Nuclear chemistry. »71. a p. Sw. cr. ».-.An autantatla aampllng sletlon far ll'.slen gat enelvsls, By S, Sandklef amiP. Svanttan, 1*71. IT p. Sw. cr. 1 * : - ,Seleethra Map Manning: a simple meant ef eutometlng the Philips aUffrM-tomater far studiet af lina preflles mté ratiduel ttnst. By A. Brawn endt . A. Urn*, t i n , I t p. Sw. er. If:- .Redletla* damage I* CaF, end BaF. Invetligaled by the ahenwlinf la**.nh*M. By », hélrearg and a. Meg. 1(71. M p. Sw.tr, » : - .
47»
47».
471
47*
4*1
4M
A survey af applied tnetrument »y»tem» far see with light waaar fs t t tv -costaimsant». By H. Tuien-Meyer. 1*71. IB p. Sw cr. I t : - .Eicitetten ttmctiost tor charged particle induced reectioM w light »Isrnant»at low prafectite energies. By J. Lerenaea and D. Biuna. 1(71. 1S4 p Sw.c». I * . - .Studio* of n d e i equilibria at elevated lamaantun* 1. OiieWealde ana)oiide metal couples of iron, nickel, copper, silver, mercury end antimony inaqueou» tystoms up to lef"C. By Karin Johaaaeen. Keratin Johnsaen andDerek Lewi*. 1*71 U p. Sw. cr. 3 * - .Imdiation fae l i t . . . for LWP. fuel totting in me Studtvik Rl reacter. By S.SeneVef end H Temeni. 1*7) W p Sw cr 2* -Sy»tomet:c» in the Ip.ml end (p.panl reactien crot» sections By L. Jeki1*7). 14 p. Sw. cr. 2» - .Aiiel end tnmvene memanlum balan» In aubchannel a-ialyele. By S. Z.*euheni. 1*71. H p. Sw cr » -Neutron ineleatic scattering cress sectione In me eneren renew 1 ta 4.SMeV meaturem.nl. end calculation». By M. A. Itemed. 1*71. (Fp . Sw. cr.
Neutron *!a»tic »cattering meeturament» at 7.1 MaV By M A.1*71 M p. Sw cr. 2* -Zooplenkten in Tvären 1 Hi -1*41 By E. Akwquiet. 1*7) M p. Sw.
radiograph, at the Studavtk M - * nectar. By I. Outlets»** end E.ski. 1*74. V "Sekelo S4 p Sw
Bibliography an bone morahemetry end dansltaiwelrymin and M. Simpson. K74. I l l p. Sw. cr. M r - .
ITS
4sV Optical model calculatieas of last neutron elastic scattering areas section*lor some reector mcterio!». By M. A. Ettmed. 1*74 IP) a, Sw cr 2*:- .
44* High cycle fettau* crock BMW*» ef two urc.nium alloy*. By V, S. Ha*.1*74 J* p. Sw cr I t . . .
4(7. Studio* ef turkul.nl flow parallel le a rad bundle ef Inangulor array. By B.Ki.ll.trtm. 1*74. I N p. Sw. cr. 20 -
4*1. A criticet easlyaia af the ring etpaneian la*t en tirceley cteddtejg tube*. ByK. Petlerseea. t*74. • p. Sw. cr. 7» -
4N. Bone mineral determination» PitcaatSngs af the aimpttlaai en bane mine-ral determinstiem held In Stockholm-Studtvlk. Swldan. 1 7 U moy 1*74
Vol 1. Presented paper» 1*74. 17* p. Sw. er. I t — .Vol 1. Pi a senled poser* (cent.) and grawp diacuatiea*. 1(74. I N a. Sw.c It—Vol. 1. Dibit*A. Her*m»i
•a*. The i . . . . . . _ .- need el »ystemetic, nlevent and eccunte imdietien iaveetigclieii*. -Program proposel. By H. Mogerd. 1*74. Sw. cr. It:—.
4*1. PHonon enharmonicity of germanium in the lempeiature nnga t t—t t t P*.By O Nelin end 0 Nil**an. 1*74. 2» p. Sw. cr. I t : - .
4*2. Harmonic lattice dynamics cf germanium. By G. Nolin. 1t74. 11 p.Sw. cr. » -
4*1. Diffusion of hydrogen in the -shate al Po-H studied by *mell anaraiIr.n. ' .r neutron »cettering. By O. Nelin and K. Skald. 1*74. M p. Sw.cr. 20 -
4*4. High tamsaratun themscouale application» in the M-naete». Studsvik. ByB. Rehne. 1*74. 2t p. Sw. cr. 2» -
4*5. Estimation of the rate ef sen*ititett**j in nickel ba*e alley*. By J. Wiberg.1*74. 14 p. Sw. cr. I t : - .
4M. A hortol-comple» in Sweden. By J. Chri»ten»en. 1*74. U p. Sw. cr. I t : - .4*7. Effect af well friction and vårtet generation an radial veM distrnVutien - Mw
well-vortai affect. By Z. Rauhaai. 1*74. 1* p. Sw. cr. J* : - .4M. The deposition kinetic» ef calcium hydrety apatite en heat transfer surface*
at boiling. By T. Kelan end R. Gustafsson 1t74. M p. Sw. cr. 2» -4M. Observations af phases and volume changes during precipitation at Kvdrid*
in lireenium alley*. By O Östberg. N. Borgqvltt, K. Pettersson, R. "K. Norrgsrd, L-O Jansson and K. Melon. 1174. 1* p. Sw. cr. * • : - .
Stt. X-ny elastic constants for cubic materiel». By K. Melon. 1*74. K p. Sw. er.S01. Electromagnetic *cr*oning and »kin-cumnt dfttrlbutlea with magnetic and
non-magnetic conductor» By E. Dahlberg. 1*74. 44 p. Sw. cr. M r - .5*3. Depth distribution studies el carbon, onsen anal nitrogen in motel sur-
faces by mean* af neutren seectremetr) By. J. Lertmtea, 1*TS. S4 p.Sw. cr. M:—.
List ef published AES-nports (In Swedish)
I. Analysis by meant ef gemma tpectrematry. By 0. Bruna. 1(41. 1* p. Bw.cr. I : - .
1. Irrediatlen changes end nevtran atmaeahen in nectar arettare veesafe-same point* af view. By M. Oraunet. 1M1. n p. Sw. er. %:-.
1. Study ef the elongation limit in mild »teal. By 0 , Oitberg anal R. Altar.ma. 1MJ. IT p, Sw. er. ».-,
4. Technical purehating In the natter field. By Erik Jontan. 1(41. 14 p.Sw. cr. I : - .
I , Ageste nuclear power tletlon, Summerv »I technical data, aatcHptiee»,etc. (ar the reecter. By B. Lillleheak, MM. H I p. Sw. ar. I I : - .
I . Atom Day 1*N. Summery ef leeturet and dltaustlant, By S. tandtaiaw)I N * . » 1 p. Sw. «r. I I : - .
7. Building malarial* containing radium aentlaWree1 fram the rediation pra-tectlen point ef viaw. By Stig O. W. Bergttrem end Tar Wahlberg. iStT.M p. Sw. cr. I t ; - .
I . Uranium market. 1(71. M p. Sw. er. I I : - .I . Radlagrephv day at Studsvik. Tuesday tt spril 1tT1. Arranged by AS Alam-
enargy, tVA» Cemmltlee far nonaottnwtive letting emfTRC AB. 1t71.i n p. Sw, «r. I I : - .
I t . The supply af enriched uranium. By M. Merterttsee. 1(71. U p. Sw. ar, 1 * : - .11. Fire studio* ef pletllt-inwteiee' aleetrie asMe*, »aaflm laad-l* wire* mé
switch saw eueielet and flaart. I t » . 117 p. iw. ar. JeT-,11. Sovtat-Swasiph tympa*liMi a» nertar safety pntlesi». SkjwavHl, ware* s-T,
It».Pani.SwedHh *. t t» . l i t p. Sw. »r, » : -Part 1. Serlet papers. I t» . 1» p. Bw. ar. Mr-,
* * *" •" • ' 4apJaam)laWa »ram ma Library al AB Alamanarai, Peak, M i l t iI'ff^veB^B^'g.Bw^ P ^ aeT B^B t rWeva
Pego Print, Stockholm 1t7S