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

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9

10

10

1 i

I I

14

14

1 S

1 5

16

17

18

I 8

18

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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,

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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

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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

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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

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24222018

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R(x) *

2.0181.6141.21.00.00.60.40.2

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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

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v_M£3.

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24 22 20 18 16 14 12 10 8 0

Fig. 16

oet.

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f a * . 1

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9Oooo

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oo ooo o

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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

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x *4O •

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70

60-

50-

40-

30-

20-

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V.

8

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— 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