A NEW METHOD FOR MEASURING THE DEPTHS OF EMBEDDED RADIOTRACER ATOMS USING A PRECISION

@-RAY SPECTROMETER'"

R. L. GRAHAM, F. BROWN, J. A. DAVIES, AND J. P. S. PRINGLE Ge?ieral Pliysics a?id Research Ckenzistry Brancltes, Atotiiic Eiiergy of Canada Liirzited,

Clialk Riuer, Ontario

Received July 11, 1963

ABSTRACT

A quantitative method has been developed for measuring the tliean depth within a solid of those radioactive atoms which decay with the emission of mono- energetic conversion electrons. By acceleration to kev encrgies in a mass separator 16.8-hour SeE5atorns were injected into metal foils, and the intense K 54.96 and K 188.4 conversion lines were then scanned in the Chalk River ~ 4 2 &ray spectrometer. The manner in which these conversion line shapes varied with Xel?j depth was calibrated by covering the foil surfaces with known thicknesses of A1 or Au; it was fo~111d that the peak heights decreased in an approximately exponential manner with increasing );el?j depths. With this calibration, mean depths can be determined ~ ~ n d e r unl;nown conditions; the lnaxirnum sensitivity is about 6 atotn layers (15 A) ullder the most favorable conditions. Examples are given of the application of the method to rnetal oxidation studies and to );e12j range measurements.

1. INTRODUCTION

A 6-spectroscopic method has been developed for ~lleasuring quantitatively the depth a t which certain foreign atolns are located beneath the surface of any solid. This method can be used for studying the range of accelerated atoms in solids as a function of incident energy, and also for following the movement of such atoms, relative to the surface, during subsequent diffusion or solid-state chemical reactions. An example of the latter is the study by Davies, Pringle, Graham, and Brown (1962) of the anodic oxidation process in aluminum and tantalum in which the changes in depth of the foreign atoms (Xe12" were measured wit11 the aid of a 6-ray spectrometer. The principle underlying this 6-spectroscopic method of measurement is that changes in the spectral line shape of conversion electrons emitted by the foreign atoms can be related quantitatively to the depth of the foreign atoms themselves. This novel application of a 6-ray spectrolneter has been described in preliminary fashion by Graham, Davies, and Brown (1962); the present article describes the method in more detail.

Several techniques had previously been developed for locating the position of foreign atoins close to the surface of a solid. Chemical methods such as etching (Bredov and Oltuneva 1957; Davies, iMcIntyre, and Siins 1962) or, better, electrochemical peeling of thin layers (Davies, Friesen, and iVIcIntyre 1960; McCargo, Davies, and Brown 1963) are extremely sensitive, and enable the depth distribution of embedded radioactive atoms to be studied in some detail. Such methods, however, are restricted to those few materials with

*Issued as A.E.C.L. No. 1825.

Canadian Journal of Physics. Volume 41 (1963)

1686

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GRAII.4Bf ET .\L.: DEPTII OF EMBEDDliD ATOMS 1687

appropriate chemical properties; also, they can oilly be used once on a parti- cular specimen, and so cannot be used to follow changes in distribution.

Nuclear spectroscopic techniques are based on measurement of the energy lost by charged particles in traversing the distance between the surface and the embedded foreign atoms, and can be classified according to the direction in which this distance is traveled. Protons traverse it in the forward direction in Amsel and Sanluel's (1962) work, where the apparent increase in the proton resonance energy for the nuclear reaction 018(fi, a:)N1%vas related to the depth of the 018 layer within a growing oxide film. In the proton scattering method of Powers and Whaling (1962) and Nielsen (1936), incident monoenergetic protons are backscattered by the foreign atoms, and so travel the required distance in both directions; energy analysis of the scattered protons then gives a measure of the depth distribution of the foreign atoms. This method is, however, restricted to foreign atoms considerably heavier than those of the host lattice.

Finally, the charged particle can originate within the nucleus of the foreign atom itself, and then traverse the distance to the surface. If the charged particles are initially monoenergetic, the energy spectrum of those escaping from the surface can be related to the thickness traversed, and hence to the depth of the source atoms. This principle has been followed by Domeij et al. (1963) using 5.486-NIev a: particles from embedded Rn3"; the present paper describes the use of monoenergetic conversion electrons from Xe12j for the same purpose.

The energy spectrunl of the escaping conversion electrons is measured with the Challi. River ~ 4 2 P-ray spectrometer, using XeE5 sources prepared in an electromagnetic isotope separator. The latter is, in effect, an ion gun which can be used to inject radioactive ions a t kev energies into suitable collector foils. Other experiments with XelZ5 (Bergstrom et al. 1963) had shown that the shape of the conversion electron lines depends markedly on the injection energy used, with higher injection energies leading to broader pealcs and more pronounced low-energy tails (Figs. 1 and 2). The sensitivity of the shape to small variations of incident ion energy, and hence to the depth of the embedded atom, suggested the possibility of using the conversion line spectrum as a depth gauge for measuring the location of embedded Xel" atonls in any unknown sample.

2. ESPERIMESTAL PROCEDURE AND RESULTS

( a ) Preparation of Sor~rces Xel5 was produced by neutron irradiation of natural xenon in the NRU

reactor; the irradiated gas was then fed to the ion source of the electromagnetic isotope separator. The use of the separator in preparing sources for nuclear spectroscopy has been described by Bergstro~n et al. (1963). With appropriate choice of accelerating and retarding voltages, and using either singly, doubly, or triply charged ions, the energy of the focused XeE5 beam striking the collector foil (Fig. 3) could be adjusted over the range 0.1-240 Icev. The XeE5 sources so prepared were embedded in nletal foils 3.5 X l.0X0.02 cm in the form of lines 3.5 cm long and 0.1 cm wide.

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CAN;IDIAN JOURN;\L 01; PHYSICS. VOL. -11, 1983

I K 54.96 LINE I NATURAL PEAK POSlTiON

0 W N 7 kev a I 4 0 ke v [L 2 0 0 z

20

t \40 I I I

21.6 I

21.7 21.8 21.9 ELECTRON ENERGY IN kev

FIG. 1. K 54.96 conversion line spectra fro111 S e E s injected a t dillerent energies into -11 foil.

7,' NATURAL \\\\

I I I 21.6 21.7 21.8 21.9 '

ELECTRON ENERGY IN kev

FIG. 2. IC 54.96 con\:ersioti line spectra from injectecl a t different energies into \\i foil.

( b ) JJeeasurement o j C o ~ z v e r s ~ o n Lsine Spectra Accurate colnparison of the conversion line spectra froin one sample to the

next requires that the size and position of the effective source area in the ~ d 2 P-ray spectrometer be highly reproducible. T o achieve this, each XeE5 source prepared in the isotope separator was inounted behind an accurately machined slit, 3.0x0.073 cm, in a copper disk, which in turn could be inounted

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GRAHAM E T AL.: DEPTH O F EMBEDDED ..\TOMS

PREPARATION OF xelP5 SOURCES IN MASS SEPARATOR

MOUNTING OF SOURCES IN j3 SPECTROMETER

FOUR TARGETS ON ROTATABLE

HOLDER

INE' IMAGE ON TARGET

i 3 5 k v TARGET

DEFLECTOR 2 5 EFT^[ f mm -

SCREEN

SHUTTER

FOCUSED I '

ION BEAMS I I OF MASS A 4''

I l l FROM ION SOURCE

AT + 3 5 k v

SLOT 0.75 mm WIDE

BY - 3 0 m m LONG MACHINED IN SOURCE

TARGET FROM

MASS SEPARATOR

SOURCE POSITION

- ELECTRON ORBITS.

SOURCE MOUNTING P L A T E

I;Ic;. 3. Schcmntic illustration of the way in which the S e l ? j sources are prepared and mounted.

on pins in the source plate of the spectronleter (see Fig. 3). Only those con- version electrons which escape from the XeE"ource and pass through the defining slit are analyzed in the magnetic field of the spectrometer. For all the experime~lts described here the spectrometer lvas set for an instrumental focusing aberration corresponding to 0.05% in momentum. The detector was a proportional counter having a defining aperture 3 mm wide, and the line width to be expected for monoenergetic conversion electrons mas -0.05% in momentum. A detailed discussion of the design and operation of this instrumcnt has been given by Graham, Ewan, and Geiger (1960).

The most intense Xel?" conversion lines have electron energies of 21.79 1;ev and 153.2 kev, and arise from K coilversioil of the 54.96-lcev and 155.4-1;ev ll~~clenr transitio~ls, respectively; these lines are therefore designated I< 54.96 and I< 188.4. Each line was scanned stepwise using an ailtonlatic programming and print-out unit; the steps or channels werc indexed in momentum units of gauss-cm. For convenience, we shall label our plots with the equivalent energ)- units for tlle purposes of this study. The Inomenturn and energy scales used arc illustrated in Fig. 4 for the I< 54.96 line, and in Fig. G for the I< 155.4 line. Each momentum cl~annel had a width of S ev for the I< 54.96 line and 37 ev for the I< 155.4 line.

( c ) D e d ~ ~ c t i o n of N e t Conversion Electron L i n e S h a p e s I11 this worli it was i~nportant to establish a routine net hod for treatment

of the experimental data wllicll yielded the net collversion electron spectrull~

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1690 CANADIAN JOURNAL OF PHYSICS. VOL. 81. 1963

corresponding to unit effective source strength (i.e. the strength of the source material in the 3.OX0.075 cin area which was "visible" to the spectrometer). This required that the raw data be corrected in three ways.

(i) Background mte . In addition to the constant cosmic-ray rate of about 25 counts per ininute there was always some additional rate due to other effects-such as Ar41 gamma rays (Graham, Ewan, and Geiger 1960) and an apparent continuurn for the K 54.96 line due to the tails of the I<-LL Auger lines (Graham, Bergstrom, and Brown 1962) which varied from sample to sample. In each case, the rate to be subtracted was talcen as the average of the rates observed in a series of channels a t energies greater than that of the conversion line. This correction rarely exceeded 1-2y0 of the pealc height for either line.

3 k e v ~ e " ' IN A l

I I I I . * .

5 0 0 501 5 0 2 503 ELECTRON MOMENTUM Ih

--- I GAUSS I cm

ELECTRON ENERGY IN k e v

I . 4. El-fect of increasing thicliness of A1 absorber on K 54.96 conversion line shape.

(ii) Effective source strength. In order to correct for the differences in effective source strength froin sample to sample, an empirical method was sought which gave appropriate norinalizing factors. The integrated counting rate of one of the conversion lines was found to be the most accurate norinalizing factor; the I< 188.4 line was used for this purpose.

(iii) Radioactive decay. Since the I< 54.96 and I< 188.4 lines could not be scanned si~nultaneously, a correction for radioactive decay had to be applied. Exainination of the literature showed a rather large spread in the reported values for the half-life of Xel?j. The value was therefore redetermined, using an isotopically separated Xe1z5 source and a ;'\;a1 y counter with the discri- nlinator set a t 100 kev to exclude X rays froin the decay of the 60-day IIz5 daughter. The resulting half-life was 16.Sf 0.2 hours, rather less than the earlier values of 20 hours (Anderson and Pool 1950) and 1s hours (Bergstrom

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1952) but in good agreement with Moore's (1960) value of 17 hours. As the decay periods involved in the present work were typically less than one hour, uncertainty in the value of the half-life produces a negligible error in the decay correction factors.

( d ) l i eprod~~cib i l i ty of Conversion Line Shapes The success of the method described in this paper is contingent on the

conversion line shape being independent of all factors except the depth distribution of the tracer atoms and the nature of the material in which they are embedded. The iron-free ~ 4 2 &ray spectrometer used here (Graham, Ewan, and Geiger 1960) is capable of very high stability (-1 part in 105) provided tha t the spectrometer settings and source position are not disturbed. In this work, i t was important that there be a high degree of reproducibility in the instrumental contribution to line shape and position when examining in succession a variety of bombarded target areas, no two of which had identical source dimensions. The source mounting technique described above was adopted a t an early stage in these experiments and many of the subse- quent experiments have been aimed a t testing the reproducibility of conversion- line shape and position.

Representative examples of conversion line shapes are shown in Figs. 4 and 6. In some cases, the experiinental data points with error bars (standard deviations) have been shown as well as the smoothed spectral lines drawn through them. In most figures only the spectral line shapes are shown.

Short-term reproducibility of the spectral line shape and position has been checked experimentally in several ways. In one test the K 54.96 line was scanned four times in succession using the same Xel?j source. The resulting line shapes were found to be consistent within the statistical counting errors and the peal; "position" was reproducible to about a quarter of a channel (2 ev 011 the energy scale or 3 parts in lo5 011 the inonlenturn scale). As a further checl;, a similar source was removed from its copper mask, remounted, and rescanned five times during a 30-hour period. Again the same degree of reproducibility was observed, thus showing that the inevitable small variations in locating the Xel?j source behind the 111as1i have a negligible effect. I t might be noted that a lateral shift of 0.2 mm in the centroid of the source activity visible through the 0.75-~nm-wide mask slot (see Fig. 3) would give rise to an apparent shift in line position of one-quarter of a channel. Finally, four different sources, all 3-lcev Xel?j ions in Al, were prepared, and again the spectra were reproducible within the statistical counting errors.

Long-term reproducibility also has been checked by conlparing the line positions of sources in the various series of runs which would be expected to give identical results (same target material and incident ion energy). In some cases the peak position appeared to have shifted as much as one channel. This indicates the difficulty in reproducing the same spectronleter settings (baffle aperture, counter slit widths, etc.) a t intervals several nlonths apart, during which interval the instrument was used for other experiments. To correct for this small uncertainty in reproducibility the peal; position a t the beginning

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1692 ChSr\ l ) I . \S JOI;RN.-\I, OF PHYSICS. \'OL. -11. 1963

and end of each series, lasting one or two days, was determined by scanning a standard source of 3-lcev Xel?j in Al; this procedure also verified that there were no drifts within a series.

The reproducibility of the R 188.4 line was similar in all respects to that of the Ii 54.96 line, except that a quarter of a channel corresponds to a soine- what larger energy, i.e., about 9 ev. The peal; height ratio (R 54.96/K 188.4) for all these standard (3-liev XeE5 in Al) sources was found to remain constant within a standard deviation of 2%.

3. CALIBRATIOS

The energy losses suffered by fast electrolls during passage through solids is little understood, and no quantitative relation betlveen such losses and the changes in conversion line shape is available. Consequently, the manner in which line shape depends on atorn depth must be calibrated. To do this i t is convenient to select one parameter measured from the relatively broad line shape. The obvious choice is the nornlalized peal; height; this proved con- venient for the R 188.4 line, where the line remains ' reas~nabl~ narrow (Fig. G), but was not so appropriate for the I< 34.96 line, particularly for Au ab- sorbers (Fig. 3). 111 analyzing the behavior of the R 34.96 line we have chosen the normalized counting rate in the channel having the maximun~ counting rate for the thinnest sources. This setting has been labeled as the "natural peak position" and corresponds to an electron energy of 21.7SG 1;ev. These parameters (normalized counting rates) were measured as a function of known

depths by successivelji subli~ning weighed amou~lts of absorber over a thin Xe12j source, i.e., one prepared a t low (3 lcev) injection energy.

21.6 21.7 21.8 21.9 ELECTRON ENERGY IN k e v

I . 5 . ETIect of increasing thicliness of Au absorber on IC 54.96 conversion lilie shapc.

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GRAI-IAM ET .4L.: DEPTH OF EMBEDDED ATOMS 1693

I . . Elfcct ol increasing ..\I atid -$LI thicknesses OII I< ISS.1 conversion line shape.

( a ) C(~/iBratio~a o f I< Z4.96 Lifze T\vo sources \irere prepared by bo~nbardlng electropolished A1 foils with

3-kev Xe1j5 ions, and their conversion spectra measured. The sources were then renloved from t h e ~ r copper ~nount ing dislis, placed in a vacuum subli- niatioil chamber together with four alu~niilulll disks of lano\\rn area, and a thin layer of A1 sublimed onto each. To ensure uniforn~ deposition of Al, each sample was lnounted in a comparable geometric position 20 cm from the hot Al-coated t~lngsten filament. The thicl~ness of the sublimed layer was deter- ~nined by weighing each of the four aluminum dislis on a microbalance before and after the subl i~nat io~l step; in any one step, the ~naxi rnu~n variation il-L weight gain between these four disks was 10%. The coated sotrrces were remounted in the (3-ray spectrometer, and the conversion spectra again measured. This sublimation process was repeated several times in order to build LIP successively thiclcer layers of A1 on t he two sources. A si~nildr cali- bration was carried out with two 3-1;ev Xel?j sources in a foil of high atomic number, namely tungsten, using gold as the sublin~ing metal since i ts electron scattering properties are expected to be similar t o those of tungsten.

The IC 54.96 conversion line spectra from each series of calibrations are illustrated in Figs. 4 and 5 . Figure 7 is a plot of iV, the normalized counting rate a t the setting of 21.786 liev which we have chosen as "the natural peal; position", against 2 , the mean depth of the Xe12j atorus. .The value of n: was obtained by adding the mean ranges for 3-1;ev Xe12" in aluminurn and tung- sten, 2.Sf 0.3 pg/cm2 and 9 f 2 pg/cnl? respectively, as determined by the electrolytic peeling neth hod (1IcCargo ct al. 1963), to the thickness of the

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l(i04 C.-\N:IDIAN JOURN:\L O F PIIYSICS. VOL. 41, 1 9 1 3

FIG. 7. Calibration of iV, the nor~llalized counting rate a t the n a t ~ ~ r a l peal; position of the I.= 54.96 line, against the mean "exponential" depth, 3, of the Se1?5 atoms.

added layer of absorber sublimed onto the surface. The reproducibility for duplicate spectra was within the experimental errors stated earlier.

As can be seen froin Fig. 7, N follows an exponential relati011 very closely for Au, the extra thickness, tllz, required to reduce the counting rate by a factor of two being 25 .5f 2 pg/cm2. The agreement with an exponential relation is not so good for A1 absorbers, where the experimental points indicate some curvature on this semilogarithmic plot. The slope gives an approximate relation t l I 2 = 8 pg/cm2. As a check on the validity of our calibration, we note that both the Al and Au curves should extrapolate bacl; to the sarne point, No, on the ordinate a t 2 = 0; the agreement is poor unless the curvature of the A1 calibration is talcen into account.

Using the calibration curves in Fig. 7, we see that XelZ5 depths can usefully be studied over a range in inean depth of 0-30 pg/cm2 in A1 and 0-100 pg/cm2 in Au, with a precision of &1070 of the total depth. The illaximuin sensitivity, obtainable a t very small depths, is about 1 pg/cm2 (37 A or 15 a t a n layers) for Al, and about 3 pg/cin2 (15 A or 6 atom layers) for Au.

(b) Calibration of K 188./, Line The peak height of the K 188.4 line as a function of Xei2j depth was cali-

brated in a similar fashion, except that A1 and Au foils of ltnown thicltness were used to provide the largest absorber thic1;nesses. The resulting spectra are shown in Fig. 6, and the peal; height calibrations in Fig. 8. There is con- siderable scatter among the experimental points, particularly for gold, but both lines follow an exponential relation quite closely. The useful range of calibration is extended to approximately 300 pg/cm2 for Al, and to 1 mg/cm2 for Au, but with a considerable decrease in sensitivity. The inaximu~n sensi- tivity obtainable a t small depths is about 10 pg/cn~Vor All and 20 pg/cin2 for Au. At large depths, the precision is f 2 0 y 0 of the total depth.

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GRAHAM ET AL.: DEPTI-I O F EMBEDDED ATOMS

Al ABSORBER \ > \

FIG. 8. CalibraAion of the normalized peak counting rate of the K 188.4 conversion line against the meail exponential" depth, %, of the XeIz5 atoms.

(6) Interpretation of Changes in the Line Shapes The effect of XelZ6 depth on the shape of the K 54.96 line is shown in Figs.

4 and 5, and on the K 185.4 line in Fig. 6. As the absorber thickness increases, the peak height decreases, the line

width becomes greater, and the magnitude of the low-energy tail increases. With the exception of the I< 54.96 line in Au absorbers, the peak position also shifts somewhat to lower energies. For a given XelZ5 depth the effects are much less pronounced in the K 188.4 spectrum than in the K 54.96 spectrum.

The changes produced in such charged-particle spectra depend on the nature of the energy-loss process for the particle concerned. If the energy loss per interaction is very much smaller than the line width, and the mean free path between losses is also short, each particle will suffer a large number of small energy losses on its way to the surface. On the average, then, each particle originating a t a particular depth within the solid will lose the same total amount of energy, and so the effect of increased absorber thickness will be to shift the spectral line to lower energies without altering its shape appreci- ably. Such an effect was observed in the a-spectroscopy study of Domeij et al. (1963).

As the magnitude of the energy loss per interaction increases, the line shape tends to broaden, the peak height decreases, and the peak position shifts less and less to lower energy. When the energy loss per interaction is appreciably larger than the line width, satellite peaks, corresponding to one, two, etc. interactions, appear on the low-energy side of the original peak. In the con- version spectra observed here, no satellite peaks were ever observed; this, and the small shift of the original peak to lower energy, suggest that the energy loss per interaction suffered by the conversion electrons is comparable to or slightly smaller than the line width.

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1696 CANADIAX JOURNAL OF PHYSICS. VOL. 41, 1963

A quantitative description of the methods by which fast electrons lose energy in solids is not available. More than one process is involved, but the most important for this study is inelastic scattering, which is also the one with the smallest interactional energy loss. Marton, Arol Simpson, Fowler, and Swanson (1962) have shown that this energy loss (which they define as the "characteristic energy loss") is 14 ev for 20-kev electrons inelastically scattered in Al; other work-ers (see summary by Marton, Leder, and Mend- lowitz 1955) have found that the values for 4 u and W are somewhat greater -about 23 ev. Since the initial Ii 54.96 spectrum of 21.79-lrev conversion electrons, typified by that of 1-kev Xe125 in Al (Fig. l ) , has a line width of about 40 ev, these characteristic energy losses are, in fact, rather less than the line width.

The smaller characteristic energy loss in A1 as compared to Au is reflected by the K 54.96 spectra (Figs. 4 and 5) in that the line broadening is less for A1 absorbers, while the peal- shift to lower energies is greater. The low- energy tails observed in both spectral lines arise from energy-loss processes with larger energy losses per interaction.

To a first approximation, the normalized couilting rate, N, of the Ii 54.96 line a t its "natural peak position" will be determined by the number of con- version electrons tha t have not lost any energy in passing from the Xe12j atoms to the surface of the specimen. Provided that the interactions are independent events, this number will be a simple function of the absorber thickness 3, accordiilg to the relation

where No is the counting rate a t 3 = 0 and A , the mean free path between interactions, is given by t1,2X 1/0.693. As can be seen from Fig. 7, this equation describes the observed behavior very well, with A,,, = 3 7 f 8 pg/cm" and AAl = 11 pg/cm2.

The counting rate, N, corresponds to the number of zero-energy-loss elec- trons only if the energy lost per interaction is large compared to half the K 54.96 line width. For smaller energy losses, N will include contributions from electrons, originally on the high-energy side of the peak, that have suffered one or more interactions and so been scattered into the peak channel. I t can be shown that the effect of such contributions is to make a plot of log N versus 3 concave towards the origin, as is observed for A1 absorbers, and that, under these circumstances, the true mean free path is less than tha t calculated from equation (1).

The value of A,, reported here is much sinaller than the value of 22 pg/cm2 obtained by Marton, Arol Simpson, Fowler, and Swansoil (1962) for 20-kev electrons passing through A1 foils. iVIarton, however, used a highly collimated, monoenergetic beam from an electron gun, and his value refers only to the characteristic energy loss produced by inelastic scattering. The mean free path obtained in our work refers to the probability that an electron will lose suffi- cient energy to be displaced from the natural peak channel; i t therefore represents the mean free path for all scattering processes. Obviously, the

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GRAHAM ET AL.: DEPTH OF EMBEDDED ATOMS 1697

overall meail free path must be less than that for one constitueilt process, such as inelastic scattering.

The energy losses suffered by the 155.2-kev electrons of the K 188.4 line are more difficult to interpret qualitatively than those of the 21.79-ltev elec- trons corresponding to the K 54.96 line. The characteristic energy loss for 155.2-kev electrons, if of the same magnitude as for 21.79-kev electroils (i.e. about 20 ev), will be much smaller than the width of the Ii 188.4 line, which with the resolution used was 160 ev. The behavior of the K 188.4 spectra, shown in Fig. 6, suggests that the energy loss per interaction is in fact con- siderably less than the line width. In such a case, the counting rate a t the "natural peak position" has little physical significance and the observed peak height (i.e. the maximuin counting rate) proved a more convenient measure of the Xel" depth. The approximately exponential relationship between peak height and absorber thickness (Fig. 8) has no simple theoretical significance.

( d ) Comparison with Previous Range Measurements The conversion spectra of Figs. 1 and 2 can be ailalyzed using the calibration

curves of Fig. 6 to provide a measure of the average depths to which Xe12j atoms have penetrated in A1 and W targets. The depth distribution for XelZ6 ions injected a t kev energies in these metals is known from the electrolytic peeling studies of Davies, Brown, and McCargo (1963) and hIcCargo, Davies, and Brown (1963) and so the usefulness of the P-ray-spectrometer method for range measurements can be tested.

I t should be noted that the mean depth measured by the P-ray-spectrometer method is not the arithmetic mean depth R. Instead, for absorbers consistent with equation (I), an "exponential mean depth" f is measured, defined by the expression :

where p(x) is the XelZ5 population a t a depth x, and P is the total number of XelZ5 atoms present.

If the Xel?%toms are all a t the same depth, the measured values of R and 2 should be identical; but as the depth distribution broadens Z will become smaller than R. The difference (R-f) is not great provided that the width of the XePz distribution is less than the X value for the material concerned. In these calibration experiments, with the sharp Xe125 distributions obtainable a t low injection energies, 5 has therefore been taken equal to R.

In Table I , the mean penetration depths f , obtained from the spectra of Figs. 1 and 2 using the calibrations of Fig. 6, are compared with the mean values found froin the electrolytic peeling method. In the electrolytic peeling method, the actual distribution of the embedded Xe atoms is obtained. This distri- bution is found to consist of an asymmetric peak followed by a penetrating "tail" (as illustrated in Fig. 3 of Davies, Brown, and McCargo 1963). The width of the distribution increases with increasing injection energy and is considerably greater in W targets than in Al (see Fig. 4, McCargo et al.

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1698 CANADIAN JOURN-\L OF PHYSICS. VOL. 41. 1063

TABLE I

Mean range of accelerated X e y ' ions in metals

Measured XelZ5 injection energy (in kev) : range* -

Metal (in pg/cm2) 1 a 20 40

*k is the true mean range deduced from the electrolytic peeling method (Davies. Brown, and McCargo 1963; McCargo. Davies, and Brown 1963). ;is the mean "exponential" range deduced using the 8-spectroscopic method described in this paper.

1963). Consequently, as illustrated in Table I , the difference between 3 and R is greatest for W a t high energy.

Using equation (2), it is possible to calculate 3 (instead of R) from the observed distribution obtained by the electrolytic peeling method-provided Xw is known. The 3's calculated in this manner for 20-kev and 40-kev Xe in W (assuming Xw = A,, = 37 pg/cm2) are 23 pg/cm2 and 33 pg/cm2, re- spectively. These are in extremely good agreement with the values (Table I) obtained from the K 54.96 conversion line spectra.

4. DISCUSSION

The 0-ray-spectrometer technique makes it possible to measure the depth of tracer XelZ5 atoms beneath the surface of a solid without in any way alter- ing the nature of the specimen. Using the K 54.96 conversion lines, and the calibration curves of Fig. 7, depths of less than 30 pg/cm2 of Al, or 100 pg/cm2 of Au, can be measured with a precision of flOyo. The ranges of measurable depths can be extended by a factor of 10 using the K 188.4 line. The maxi- mum sensitivity (using the K 54.96 line) is 1 pg/cm2 of Al, and 3 pg/cm2 of Au.

For solids other than Al or Au, a separate calibration is needed to obtain quantitative results. However, semiquantitative information can be obtained by comparisons with the Al and Au calibrations, and changes in mean depth can be detected in any solid without calibration. The same considerations apply in extending the technique to tracers other than Xe125.

Two examples of the application of this method can be given. (a) The "mean exponential" range, 3, of XelZ5 can be measured as a function

of energy in various solids. In Table I , 3 values for 1, 5, 20, and 40 kev Xe125 ions in Au have been deduced from the K 54.96 conversion line spectra. The values are considerably smaller than the corresponding ranges in W. An even more marked difference between values in Au and W has been observed by Domeij et al. (1963) using Rna2, and has been attributed to the difference in crystal structure of these two metals. This effect is illustrated in Fig. 9.

( b ) By measuring the location of the embedded Xe125 tracer atoms a t various stages during the anodic oxidation of a metal surface, i t is possible

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GRAHAM ET AL.: DEPTII OF EMBEDDED ATOMS 1699

~ e " ' ENERGY IN kev

FIG. 9. Exponential mean range (3) of XeIZ5 in tungsten (a) and it1 gold (X) as a function of energy.

to study the nature of the mobile atomic species contributing to the oxida- tion process. In the first step, anodization to low voltage converts only the surface layers of metal to oxide, so that the XelZ5 is now located within the oxide layer. If oxygen is the mobile species, then, on continued anodizing to higher voltages, fresh oxide layers will be formed a t the metal-oxide interface, and so the XelZ5 will remain close to the outer surface of the oxide. If, on the other hand, the inetal ions migrate, fresh oxide will be laid down outside the XeE5 layer, and so the XelZ5 will become buried. In Al, anodized a t a current density of 0.1 ma/cm2, the Xe'?5 was found to remain on the surface, whereas in T a a t 2 ma/cin2, it became deeply buried (Fig. 10).

Thermal oxidation can also be investigated in the same way. A preliminary study of the oxidation of Zr by steam a t 400° C has shown that the XelZ5 relnains close to the oxide surface, indicating that oxygen is the mobile species.

In summary, we see that the P-spectroscopic technique of depth ineasure- ment as described here will be a useful tool for studying the location and migration of subsurface tracer atoms. I t should become applicable for a wide variety of medium- and high-Z tracer species which emit intense conversion electron lines of appropriate energy. In this respect i t will have wider applica- tion than the a-spectroscopic technique of Domeij et al. (1963), which is restricted to high-Z tracer species. However, it should be noted that our n~ethod has a fundamental limitation in that, unlike the a-spectroscopic technique of Domeij, i t does not provide quantitative infor~~lation on the depth distribz~tion of the embedded tracer atoms.

I t is a pleasure to acknowledge the contribution of Dr. I. Bergstrom, who collaborated with us during the initial stages, and of Drs. G. Ewan and J. Geiger for many fruitful discussions during the development of the technique.

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CANADIAN JOURNAL O F PI-IYSICS. VOL. 41. 1963

/ I , l l l l , l l l l l l l l l , l 1 1 1 , 1 1 1 1

DISTRIBUTION OF xeI2' ATOMS

5 k e v xe Iz5 IONS

ANODIZED TO 200 v

0 20 4 0 60 60 1 0 0 .\ DEF'TH IN pq /cmz 1 -

200 7 -

56

0

\ 0 20 4 0 6 0 8 0 100 - DEPTH IN pq lcmZ -

7 1 / 1 1 % 1 1 1 1 / 1 1 1 , 1 1 , , , , 1 , , , ,

21.6 21.7 21.8

ELECTRON ENERGY IN kev

FIG. 10. Effect of anodic oxidation on the K 54.96 line shape of Se12& injected a t 5 kev into Al and Ta targets: Al anodized a t 0.1 ma/cm2, ?'a a t 2.0 ma/cm2.

We are particularly grateful to Dr. M. AlIcCargo, W. L. Perry, G. Sims, and R. \Vall<er for their assistance in operating the spectrometer, and to J. Tole and R. L. Cushing for preparing the sources in the isotope separator.

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MARTON, L., LEDER, L. B., and MESDLOWITZ, H. 1955. Advances in Electron. 7, 183. MCCARGO, M., DAVIES, J. A., and BROWS, F. 1963. Can. J. Phys. 41, 1231. MOORE, R. B. 1960. Bull. Am. Phys. Soc. 5 (5), 335, A4. NIELSES, I<. 0. 1962. I n Electromagnetically enriched isotopes and mass spectrometry

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