Nuclear Reactions

4 Nuclear Reactions J.R. BIRD ANSTO

4.1

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Lucas Heights

Research Laboratories Menai, Australia

PRINCIPLES 153 4.1.1 K i n e m a t i c s 154 a. T h r e s h o l d s 154 4.1.2 R e a c t i o n Y i e l d s 156 4.1.3 D e p t h Profiling 159 ION-ION REACTIONS 159 4.2.1 E q u i p m e n t 159 a. C h o i c e o f D e t e c t o r 160 b. Alternative Detectors 161 4.2.2 C h o i c e o f E x p e r i m e n t a l C o n d i t i o n s 162 a. R e a c t i o n Angle 162 b . S a m p l e Angle 164 c. Special G e o m e t r i e s 164 d. I o n S e p a r a t i o n 164 e. I o n I d e n t i f i c a t i o n 165 f. D u a l I o n C o i n c i d e n c e D e t e c t i o n 166 4.2.3 T h i n Sample Analysis 168 a. N a r r o w R e s o n a n c e R e a c t i o n s 168 b. Layer Thickness Determination 169 4.2.4 Bulk A n a l y s i s 169 4.2.5 D e p t h Profiling 170 4.2.6 N o n - E l a s t i c R e c o i l 770 4.2.7 P e r f o r m a n c e 174 ION-GAMMA REACTIONS 175 4.3.1 I s o t o p i c A n a l y s i s M e t h o d s 175 a. E x p e r i m e n t a l A r r a n g e m e n t 7 75 b. Spectrum Analysis 7 79 181 c. D e t e r m i n a t i o n o f C o n c e n t r a t i o n d. I s o t o p e R a t i o s 183 4.3.2 D e p t h Profiling 183 a. M u l t i p l e R e s o n a n c e s 187 b. Yield Curve Unfolding 187 4.3.3 P e r f o r m a n c e 755 a. D e t e c t i o n L i m i t s 188

149 ION BEAMS FOR MATERIALS ANALYSIS

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J.R. Bird b. P r o t o n - G a m m a Analysis 188 c. D e u t e r o n - G a3m m a R e a c t i o n s 189 190 d. T r i t o n a n d H e R e a c t i o n s e. A l p h a - I n d u c e d G a m m a E m i s s i o n 190 f. H e a v y I o n - G a m m a A n a l y s i s 191 ION-NEUTRON REACTIONS 191 4.4.1 M e t h o d s 192 a. N e u t r o n Y i e l d 192 b. N e u t r o n Energy 193 c. D e p t h Profiling 195 4.4.2 P e r f o r m a n c e 197 a. (p,n) R e a c t i o n s 197 b . (d,n) R e a c t i o n s 197 c. (t,n) R e a c t i o n s 198 d. (α,η) R e a c t i o n s 198 e. H e a v y I o n R e a c t i o n s 198 ION ACTIVATION ANALYSIS 198 4.5.1 M e t h o d s 199 a. Analysis 799 b. Measurements 799 4.5.2 P e r f o r m a n c e 201 4.5.3 T h i n L a y e r A c t i v a t i o n 202 CHOICE OF REACTION 204 REFERENCES 206

T h e study of nuclear reactions, w h i c h began in t h e 1930s, quickly brought a realisation t h a t very p u r e s a m p l e materials, a n d even s e p a r a t e d isotopes, were n e e d e d to a v o i d t h e effects of interfering nuclear reactions. O n m a n y occasions, nuclear physicists were t h u s engaged in t h e analysis of their own target m a t e r i a l s b u t it was n o t until 1957 t h a t R u b i n et al (1957) published a p a p e r o n " C h e m i c a l Analysis of Surfaces by N u c l e a r M e t h o d s " which p a v e d t h e way for t h e use of accelerated ion b e a m s for P r o m p t N u c l e a r Analysis ( P N A ) of samples. F r o m 1960 o n w a r d s , t h e use of nuclear reactions in p r o m p t analysis began t o grow rapidly. H o w e v e r , this is o n e of t h e m o s t c o m p l e x of t h e ion b e a m m e t h o d s . Every isotope can u n d e r g o a variety of nuclear reactions, each h a v i n g u n i q u e character­ istics such as energy release, excited state energies, cross-sections a n d angular distributions. A p p l i c a t i o n s to specific analytical p r o b l e m s require assessment of all these factors for t h e isotope of interest a n d for possible c o m p e t i n g reactions in o t h e r isotopes p r e s e n t in a s a m p l e . It is c o n v e n i e n t to c o n s i d e r reactions according to t h e type of p r o d u c t r a d i a t i o n since this d e t e r m i n e s t h e m e t h o d s a n d e q u i p m e n t r e q u i r e d . F o u r major categories are o u t l i n e d in Highlight 4 . 1 , viz. i o n - i o n ,

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i o n - g a m m a , i o n - n e u t r o n a n d a c t i v a t i o n analysis. T h e i m p o r t a n t fea­ tures of N u c l e a r R e a c t i o n Analysis are: • • • •

high selectivity in t h e d e t e r m i n a t i o n of specific light nuclides; good sensitivity for m a n y nuclides w h i c h are difficult t o deter­ m i n e by o t h e r t e c h n i q u e s ; u n i q u e capabilities for n o n - d e s t r u c t i v e d e p t h profiling of specific light nuclides, a n d accurate absolute d e t e r m i n a t i o n of m a n y nuclides.

M u c h is k n o w n a b o u t t h e nuclear physics of useful r e a c t i o n s b u t t h e knowledge of available reactions is still e x p a n d i n g — particularly in t h e field of heavy ion i n d u c e d reactions. A p p l i c a t i o n s of P N A h a v e b e e n recently reviewed b y Peisach (1981), D e c o n n i n c k (1978), D e c o n n i n c k et al ( 1981 ) a n d Borderie ( 1980). A bibliography of a p p l i c a t i o n s r e p o r t e d u p t o 1976 h a s b e e n p u b l i s h e d (Bird et al.9 1978) a n d m u c h i n f o r m a t i o n is c o n t a i n e d in t h e proceedings of I n t e r n a t i o n a l Conferences o n I o n B e a m Analysis (see t h e table in t h e i n t r o d u c t i o n to this b o o k ) .

H I G H L I G H T 4.1 ENERGY RELATIONS IN NUCLEAR REACTIONS Energy level d i a g r a m s are used to illustrate t h e energy relations in nuclear reactions. Typical e x a m p l e s involving p r o t o n or d e u t e r o n i r r a d i a t i o n of a 1 s9 are s h o w n in Fig. 4 . 1 . If a 2 p0r o t o n s a m p l e c o n t a i n i n g fluorine a t o m merges with t h e nucleus of a F a t o m , a c o m p o u n d nucleus ( N e ) is 2 0 T h i s is illustrated b y formed a n d 1a n9 energy of 12.485 M e V is released. placing t h e F energy level d i a g r a m a b o v e t h e 2N0e d i a g r a m by a d i s t a n c e p r o p o r t i o n a l t o t h e energy release (Q). T h e N e nucleus is f o r m e d in a highly excited state a n d m a y decay in a n u m b e r of ways. Full details of possible reactions can b e o b t a i n e d from t h e references in T a b l e 4 . 1 . T h e following e x a m p l e s illustrate the use of energy level d i a g r a m s t o display the energy relations i n v o l v e d in v a r i o u s types of nuclear reaction.

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2 0 a. I o n - G a m m a Reactions, e.g. F ( p , y ) N e ; Q = 12.845 M e V . Suppose t h a t t h e i n c i d e n t p r o t o n h a d a n energy of 0.872 M e V . T h e N e nucleus is t h e n f o r m e d with a n excitation energy of 13.717 M e V ( = E! + Q) (arrow (1) in Fig. 4.1). A n excited nucleus m a y e m i t o n e or m o r e g a m m a - r a y s as s h o w n by 2w 0a v y lines linking t h e initial state a n d low 2 0 excitation lying excited states w i t h i n t h e N e level d i a g r a m . After t h e full energy has b e e n e m i t t e d as g a m m a - r a y s , a stable nucleus of N e r e m a i n s ,

152 J.R. Bird

Fig. 4.1 Energy levels a n d cross-sections in n u c l e a r r e a c t i o n s .

i.e. F has b e e n t r a n s m u t e d t o N e . T h e g a m m a - r a y energy s p e c t r u m has peaks at energies w h i c h are characteristic of t h e energy levels i n v o l v e d in this reaction a n d the p e a k intensities can be used to d e t e r m i n e t h e c o n c e n t r a t i o n of fluorine in t h e s a m p l e . G a m m a - r a y e m i s s i o n m a1y 6 also a c c o m p a n y o t h e r reaction types. F o r e x a m p l e in (p, a) reactions, 0 can 6 be formed in a n excited state w h i c h decays by g a m m a - r a 1 y emission to the g r o u n d state as s h o w n by t h e wavy lines w i t h i n t h e 0 level d i a g r a m . G a m m a - r a y s at 6 to 7 M e V characterise this reaction a n d can also b e used for F d e t e r m i n a t i o n . N o t e t h a t t h e cross-section curve in Fig. 4 . 1 . is for the (p, ay) reaction a n d n o t t h e (p, y) reaction although t h e 872 keV resonance occurs in b o t h reactions. l 9 1 9 1 9 of C o u l o m b Excitation, e.g. F ( p , p ' γ) F , is a n i m p o r t a n t source g a m m a - r a y s . F o r e x a m p l e , t h e first a n d second excited state of F at 110 a n d 198 keV are readily excited by a passing p r o t o n a n d they decay by emission of g a m m a - r a y s of these energies. O n c e again these are a clear signature for t h e presence of fluorine in t h e s a m p l e .

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2 0Reactions, e.g. F ( p , a ) 0 Q = 8.115 M e V . b . Ion-Ion 6 If the N e c o m p o u n d1 nucleus decays by t h e e m i s s i o n of a n alphaparticle, a nucleus of 0 is f o r m e d (arrow (2) in Fig. 4.1). T h e energy of the e m i t t e d alpha-particle d e p e n d s o n t h e difference in energy of t h e

2 0

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6 states in N e a n d 0 (see section 14.1.1). In Fig. 4.1 a r r o w (2) shows t h e f o r m a t i o n of t h e g r o u n d state of 0 a n d a r r o w (3) shows t h e f o r m a t i o n of a n excited state. E a c h state c o n t r i b u t e s a s e p a r a t e energy g r o u p to t h e al­ pha-particle s p e c t r u1 m9 a n d any o n e of these can b e u s e d for t h e d e t e r m i n a t i o n of F in t h i n layers at t h e surface of t h e s a m p l e . Each g r o u p is designated by t h e sequence n u m b e r of t h e excited state formed. T h u s a r r o w (2) is t h e (p,a0) reaction a n d a r r o w (3) is t h e ( p , a 2) reaction. 19

1 9

Resonant Scattering, e.g. F ( p , p ) F Q = 0. 1 9 by the c o m p o u n d nucleus can also o c c u r a n d this leads P r o t o n emission back t o t h e F nucleus. T h i s process is indistinguishable from R u t h e r f o r d scattering except t h a t t h e cross-section will n o w show features such as resonances which are typical of n u c l e a r reactions. R e s o n a n t scattering is d o m i n a n t for i n c i d e n t energies n e a r a n d a b o v e t h e C o u l o m b b a r r i e r ( E q u a t i o n (1.9), T a b l e 1.1) a n d can b e significant at even lower energies. 6 F o r e x a m p l e , t h e r e is a1well-known r e s o n a n c e at 3.045 M e V in alpha-par­ ticle scattering from 0 a n d this is c o m m o n l y o b s e r v e d in b a c k s c a t t e r i n g e x p e r i m e n t s . R e s o n a n c e scattering is discussed further in C h a p t e r 3.

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c. Ion-Neutron Reactions, e.g. F ( p , n ) N e Q = -4.020 M e V T h e Q-value for this reaction is negative a n d high energy p r o t o n s m u s t b e 1 9 used before t h e r e a c t i o n b e c o m e s energetically possible (see Section 4.1.2a). T h e p o s i t i o n of the energy level d i a g r a m for N e is s h o w n in Fig. 4.1 a n d a r r o w (4) shows t h e relative energy i n v o l v e d in t h e (p, n) reaction.

19 1 9 1 9 d. Particle Induced Activation Analysis (PAA), e.g. F ( p , n ) N e

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C F. T h e nuclei f o r m e d in a a n d b a b o v e are stable b u t N e is r a d i o a c t i v e with a half-life of 17.2 s. After s a m p l e i r r a d i a t i o n h a s b e e n c o m p l e t e d , t h e b e t a radioactivity or any associated g a m m a - r a y e m i s s i o n can b e o b s e r v e d in t h e s a m p l e a n d can b e used for s a m p l e analysis in t h e s a m e m a n n e r as for t h e well k n o w n t e c h n i q u e of N e u t r o n A c t i v a t i o n Analysis (NAA). R a d i o a c t i v e g a m m a - r a y s are s o m e t i m e s o b s e r v e d d u r i n g P N A m e a s u r e ­ m e n t s b u t usually with relatively low intensities.

4.1 PRINCIPLES N u c l e a r reactions are g o v e r n e d by t h e general e q u a t i o n s for energy k i n e m a t i c s a n d yields are given in C h a p t e r s 1 a n d 12. H o w e v e r , t h e application of these e q u a t i o n s d e p e n d s o n i n f o r m a t i o n o n energy levels, observed particle a n d g a m m a - r a y g r o u p s a n d cross-sections w h i c h is given in nuclear physics p u b l i c a t i o n s (Table 4.1). A catalog of n u c l e a r

154 J.R. Bird T A B L E 4.1 References t o n u c l e a r r e a c t i o n d a t a Reaction Q-Values G o v e , N . B . a n d W a p s t r a , A . H . ( 1 9 7 2 ) . N u c l . D a t a T a b l e s 11, 127. Energy Levels A = 3 Nucl. A = 4 Nucl. A = 5-10 Nucl. A = 11-12 Nucl. A = 13-15 Nucl. A = 16-17 Nucl. A = 18-20 Nucl. A = 21 - 4 4 Nucl.

Phys. Phys. Phys. Phys. Phys. Phys. Phys. Phys.

A251 A206 A413 A433 A360 A375 A392 A310

(1975) (1973) ( 1984) (1985) (1981) (1982) (1983) ( 1978)

Other Elements Nuclear D a t a Sheets (Academic Press, San Diego) N u c l e a r Level S c h e m e s ( 1 9 7 3 ) , Ed., N u c l e a r D a t a G r o u p , O R N L , Academic Press, N e w York. Cross-sections Bird, J . R . (1980). Nucl. Instrum. Methods 168, 8 5 . F e l d m a n , L.C. a n d P i c r a u x , S.T. ( 1 9 7 7 ) . ' I o n B e a m H a n d b o o k ' , e d s , M a y e r , J . W . a n d R i m i n i , E., A c a d e m i c P r e s s , N e w Y o r k , 112. Jarjis, R.A. ( 1 9 7 9 ) . N u c l e a r C r o s s - s e c t i o n D a t a for Surface Analysis, D e p t . P h y s . , U. Manchester.

reactions a n d e x p e r i m e n t a l p a r a m e t e r s w h i c h are useful in analytical applications is given in C h a p t e r 14.4.1.

4.1.1 Kinematics T h e k i n e m a t i c s of nuclear reactions are d o m i n a t e d b y t h e m a g n i t u d e of the energy b a l a n c e Q ( E q u a t i o n (1.21), T a b l e 1.3). M o s t useful reactions h a v e large positive values of Q (Table 4.2) a n d this results in relatively high energy p r o d u c t r a d i a t i o n . T h o s e reactions w h i c h h a v e t h e highest Qvalues give p r o d u c t s which are easy to observe as h a v i n g the highest energies. L o w <2-value reactions m a y well b e m a s k e d by c o m p e t i n g reactions. M o r e extensive lists of β - v a l u e s can b e f o u n d in G o v e a n d W a p s t r a ( 1972). If t h e final nucleus is f o rfm e d in a n excited state of energy E\ t h e n a modified energy b a l a n c e (Q = Q — E') m u s t b e u s e d in kinematics calculations. a.

Thresholds

If Q is negative, this energy m u s t b e p r o v i d e d b y t h e i n c i d e n t i o n before a reaction is possible. In o r d e r to m e e t t h e a d d i t i o n a l r e q u i r e m e n t s of

T A B L E 4.2 β - V a l u e s of n u c l e a r r e a c t i o n s (keV) Nuclide

2Ή 3H 4H e 6H e 7L i Li 'Be io

B "l B2 , C3 l C4 l N5 N

,7 o 21 9 F0 2N1e 2N2e 2N3e 2N4a 2M5g 2M6g 2M7g 2A81 2S 9i 3S 0i Si

33 1 p2 s

d,p

4021 17347 2125 1146 8590 -7551 -4063 -2922 4966 -5218 1193 3980 8115 -4129 -1738 -1675 2377 -6884 -3144 -1820 1600 -7715 -4820 -2372 1916 -4200

4033 18353 -3115 5026 -192 4587 9231 1145 2722 5952 8609 265 1918 5822 1732 4377 4536 8141 2972 4735 5107 8869 4218 5501 6249 8385 4364 5712 6419

3 d,a

He,p

3

3 He,a

α,ρ

ρ,η

23848 18354 22374 14230 7151 17822 8031 -1341 5169 13575 7688 3111 9802 4245 10033 2797 6466 2702 6913 1963 7049 2915 6708 1429 6013 3129 8165 4901

10323 19695 13185 4779 10666 15243 8552 2033 8321 6876 11888 5784 11440 8034 11305 5920 11646 8278 12341 6355 10189 7515 9789 6067

18913 12143 9123 1857 15632 10025 9745 4909 16436 12532 10148 3713 13817 10213 8161 4048 13247 9485 7521 3401 12105 9969 3370 5490

-6886 4063 784 -4966 -7423 -1193 -3980 -8115 -5656 -5601 1675 -2377 -2179 -3533 1820 -1601 -1207 -2865 2372 -1916 -2453 -2959 625 -1866

-5070 -1644 -1850 -4433 -2765 -3003 -5927 -3542 -3542 -2438 -4020 -4331 -3625 -4839 -5062 -4787 -5592 -5726 -5010 -6224

d,n

t,n

He,n

α,η

3269 -5153 -4185 3384 15028 4361 6467 13733 -281 5326 5067 9903 -1624 3384 5768 10620 206 4516 6568 9467 46 4082 6046 9361 523 3375 5073 6639 53

9559 18930 12421 4015 9902 14479 7788 1269 7557 6112 11124 5020 10677 7270 10541 5156 10882 7514 11577 5592 9425 6752 9025 5303

7558 1569 10182 -1149 7124 -969 5010 -3196 4301 13119 7557 202 6601 12766 6243 76 6054 12138 6615 -566 3965 8443 3423 -759

5702 1060 157 -8508 2215 -4735 -6418 588 -698 -1950 -7216 2553 -480 -2967 -7193 2653 33 -2638 -8140 -1526 -3492 -5648 -8612

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conservation of m o m e n t u m , t h e t h r e s h o l d ion energy r e q u i r e d to m a k e a nuclear reaction possible is given b y E q u a t i o n (1.27). E x a m p l e s of useful threshold reactions include C o u l o m b excitation a n d (p, n) reactions.

4.1.2 Reaction Yields T h e yield of nuclear reaction p r o d u c t s is d e p e n d e n t o n t h e r e a c t i o n crosssection ( C h a p t e r s 1.1.Id a n d 12.1). Each r e a c t i o n cross-section h a s its own characteristic d e p e n d e n c e o n energy a n d angle of o b s e r v a t i o n (see Highlight 4.2). N u c l e a r physics m o d e l s can b e u s e d t o calculate m a n y cross-sections b u t for analytical work, m e a s u r e d values are used. T a b u ­ lations are available in t h e references of T a b l e 4.1 a n d cross-sections for the m o s t useful reactions are p r e s e n t e d in C h a p t e r 14.4.

H I G H L I G H T 4.2 NUCLEAR REACTION CROSS-SECTIONS a. Resonance Reactions R e s o n a n c e s in nuclear r e a c t i o n cross-sections arise from t h e effects of excited states in t h e c o m p o u n d nucleus. T h i s is illustrated in Fig. 4.1 for p r o t o n i r r a d i a t i o n of fluorine. A cross-section curve for t h e (p, ay) 1 9(plotted 2 0 vertically), is reaction, as a function of i n c i d e n t p r o t o n energy shown b e t w e e n t h e energy level d i a g r a m s for F a n d N e . A n u m b e r of peaks (resonances) are o b s e r v e d in t h e cross-section a n2d 0each occurs at a n energy w h i c h c o r r e s p o n d s t o a n excited state of t h e N e nucleus. T h e cross-section at a specific energy m a y involve t h e s u m of a n u m b e r of resonance t e r m s , a s m o o t h c o m p o n e n t a n d , if necessary, interference terms. A n isolated r e s o n a n c e can b e exploited for t h e analysis of a very t h i n layer of a s a m p l e a n d for d e p t h profiling by t h e r e s o n a n c e scanning m1e 9 t h o d ( C h a p t e r 12.2). A typical e x a m p l e is t h e 0.872 M e V r e s o n a n c e in ( F + p) reactions w h i c h p r o d u c e s a high yield of alpha-particles a n d g a m m a - r a y s from a t h i n layer in t h e s a m p l e for which t h e i n c i d e n t ion energy is close to t h e p e a k of t h e r e s o n a n c e . W h e n t h e i n c i d e n t energy is high, m a n y resonances will c o n t r i b u t e to t h e yield from a thick s a m p l e a n d a n averaged c o m p o s i t i o n of t h e s a m p l e can t h e n b e derived. However, each r e s o n a n c e h a s a different p e a k cross-section a n d h e n c e sensitivity. T h e m e a s u r e d total yield is t h e s u m of u n e q u a l c o n t r i b u t i o n s from a set of isolated layers at w h i c h t h e i n c i d e n t ions reach t h e energy of each r e s o n a n c e in t u r n .

4. Nuclear Reactions R e s o n a n c e s offer a n u m b e r of special a d v a n t a g e s in analysis, for e x a m p l e : • •

•

•

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materials

simpler spectra m a y b e o b s e r v e d t h a n for a thick s a m p l e ; for a t h i n layer, t h e p r o b a b i l i t y for t h e d e s i r e d r e a c t i o n t o o c c u r can b e m a x i m i s e d by choosing t h e i n c i d e n t energy t o c o i n c i d e w i t h a cross-section peak; m o s t of t h e o t h e r p o t e n t i a l c o m p e t i n g r e a c t i o n s will t h e n h a v e low p r o b a b i l i t i e s unless they c h a n c e t o h a v e a r e s o n a n c e at t h e s a m e energy — or at a n y lower energy if a thick s a m p l e is used; it is possible t o m i n i m i s e c o n t r i b u t i o n s from surface c o n t a m i ­ n a t i o n by using a n i n c i d e n t energy a b o v e t h e r e s o n a n c e energy w h i c h w o u l d t h e n only give high yield from a layer w i t h i n t h e s a m p l e (see C h a p t e r 12.2); a n d in d e p t h profiling, a very n a r r o w r e s o n a n c e will give excellent d e p t h resolution (e.g. 10 n m or better).

b . Direct Reactions I 7 as A different k i n d of cross-section c u r v e is o b s e r v e d for r e a c t i o n s such (d,p) (d,a) a n d (d,n) r e a c t i o n s (see c u r v e t o t h e left of t h e 1 90 level1 7 d i a g r a m in Fig. 4.1). T h i s shows t h a t t h e cross-section for t h e F ( d , a ) 0 reaction, w h i c h h a s a β - v a l u e of 10.033 M e V , changes s m o o t h l y as t h e incident d e u t e r o n energy increases. Such cases are useful in thick s a m p l e analysis a n d for d e p t h profiling by t h e energy s p e c t r u m m e t h o d ( C h a p t e r 12.2). c. Coulomb Excitation A n o t h e r type of reaction with a s m o o t h d e p e n d e n c e of cross-section o n incident ion energy is C o u l o m b excitation. T h e cross-section h a s a separate t h r e s h o l d for each excited state a n d increases rapidly a b o v e t h a t energy. F o r i n c i d e n t energies well a b o v e t h r e s h o l d , t h e cross-section is related t o t h e R u t h e r f o r d scattering cross-section (daR) by: da = PdaR

(4.1)

where Ρ is t h e p r o b a b i l i t y for excitation of a low-lying level in t h e target nucleus. T h2e differential cross-section t e r m i n t r o d u c e s a d e p e n d e n c e o n ( Ζ 1Ζ 2/ 4 £ ' 1) . C o u l o m b excitation cross-sections are larger t h a n o t h e r reaction cross-sections for i n c i d e n t energies b e l o w t h e C o u l o m b b a r r i e r b u t at higher energies this is n o longer t r u e . T h e m o s t c o m m o n analytical a p p l i c a t i o n of C o u l o m b excitation involves t h e o b s e r v a t i o n of deexcitation g a m m a - r a y s .

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T h e differential cross-section {άσΙάθ) is usually given as m b / s r for a specific angle (Θ) relative to t h e i n c i d e n t ion direction. Cross-sections at other angles are related by t h e angular d i s t r i b u t i o n function:

dalde=f{Eue)a{E{)

(4.2)

where σ(Εχ) is t h e total cross-section for t h e reaction. R e a c t i o n s involving c o m p o u n d nucleus f o r m a t i o n usually h a v e angular distribu­ tions which are s y m m e t r i c a b o u t 90° b u t w h i c h change from r e s o n a n c e t o resonance. Direct reactions are strongly forward p e a k e d . If the d e t e c t o r solid angle is large c o m p a r e d with t h e rate of change of differential cross-section with angle, t h e o b s e r v e d yield involves a n integral over angle. In t h e i r r a d i a t i o n of thick samples, all energies from the incident energy d o w n t o zero are i n v o l v e d leading to averaging of angular d i s t r i b u t i o n s w h i c h usually change w i t h i n c i d e n t energy. T h e r e is often a lack of p u b l i s h e d i n f o r m a t i o n for t h e specific energies a n d geometries chosen for analytical a p p l i c a t i o n s a n d a calibration using a s t a n d a r d s a m p l e is necessary. R e a c t i o n yields are related t o s a m p l e c o m p o s i t i o n as described in C h a p t e r 12.1. In the case of t h i n samples for w h i c h energy loss by t h e incident ion is n o t sufficient t o change t h e cross-section or stopping p o w e r significantly, t h e relation is very simple ( E q u a t i o n s (12.7) a n d (12.8)). T h i s has similar a d v a n t a g e s to t h e use of a n a r r o w r e s o n a n c e (see Highlight 4.2) b u t t h e r e are also significant d i s a d v a n t a g e s . T h e yield of p r o d u c t r a d i a t i o n is usually very low a n d s a m p l e p r e p a r a t i o n requires great care, a n accurate d e t e r m i n a t i o n of s a m p l e thickness a n d , possibly, the use of a p u r e backing m a t e r i a l which does n o t give c o m p e t i n g reactions. Because of these d i s a d v a n t a g e s , t h i n s a m p l e m e a s u r e m e n t s h a v e only b e e n used w h e n the original m a t e r i a l is a t h i n layer o n a t h i n or inert backing (e.g. air filters, surface layers, corrosion p r o d u c t s ) or w h e n the effort r e q u i r e d to p r e p a r e t h i n s a m p l e s a n d m e a s u r e their thickness is worthwhile. F o r thick u n i f o r m samples, t h e n e e d to use integral yield e q u a t i o n s ( C h a p t e r 12.1) is a significant c o m p l i c a t i o n , since t h e m a j o r e l e m e n t c o m p o s i t i o n m u s t b e k n o w n in o r d e r t o calculate t h e s t o p p i n g p o w e r as a function of energy. T h i s p r e s e n t s n o difficulty for t h e d e t e r m i n a t i o n of m i n o r or trace e l e m e n t s in a k n o w n m a t r i x b u t m u s t b e t a k e n i n t o a c c o u n t for m o r e general analytical p r o b l e m s . A p p r o x i m a t i o n s which can usually b e used t o o b t a i n results w i t h sufficient accuracy are discussed in C h a p t e r 12.1. In nuclear reaction analysis, it is c u s t o m a r y to use s t a n d a r d samples t o establish t h e cross-section or reaction yield for specific e x p e r i m e n t a l c o n d i t i o n s a n d t h e n to use s t o p p i n g p o w e r correc­ tions to m e a s u r e m e n t s with u n k n o w n samples (e.g. E q u a t i o n 12.18). If

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t h e samples are similar in c o m p o s i t i o n , t h e c o r r e c t i o n s are small a n d nuclear reaction m e t h o d s are t h e n suitable for a b s o l u t e m e a s u r e m e n t s requiring only t h e d e t e r m i n a t i o n of yield a n d i n c i d e n t b e a m dose. N o a t t e n u a t i o n correction is r e q u i r e d .

4.1.3 Depth Profiling T h e variety of o p t i o n s available for n o n - d e s t r u c t i v e d e p t h profiling is o n e of t h e m o s t i m p o r t a n t features of p r o m p t n u c l e a r analysis. T h e principles used are d e s c r i b e d in C h a p t e r 12.2. T h e i r use in c o n j u n c t i o n with nuclear reactions exploits t h e following features: i. t h e high p e a k cross-section of a r e s o n a n c e gives high sensitivity; ii. energy loss by t h e i n c i d e n t ion can b e u s e d t o d e t e r m i n e d e p t h profiles by r e s o n a n c e s c a n n i n g or yield c u r v e unfolding b u t t h e m a x i m u m d e p t h is l i m i t e d by r e s o n a n c e spacing in t h e f o r m e r case; iii. energy loss by b o t h i n c i d e n t a n d p r o d u c t ions can b e used with i o n - i o n reactions for energy s p e c t r u m profiling; in this case t h e m a x i m u m d e p t h is l i m i t e d by t h e spacing of different p r o d u c t energy groups; iv. t h r e s h o l d s in (p,n) reactions also p r o v i d e a m e t h o d for d e p t h profiling w i t h g o o d resolution; a n d v. glancing angle t e c h n i q u e s a n d t h e effects of t o p o g r a p h y are i m p o r t a n t ( C h a p t e r 12.2).

4.2 ION-ION REACTIONS I o n - i n d u c e d n u c l e a r reactions are i n h i b i t e d b y t h e C o u l o m b b a r r i e r which, a c c o r d i n g t o E q u a t i o n (1.9), increases w i t h t h e a t o m i c n u m b e r of b o t h t h e i n c i d e n t ion a n d target nuclide. I o n e m i s s i o n from a n excited nucleus is further i n h i b i t e d (relative to g a m m a - r a y o r n e u t r o n e m i s s i o n ) because of t h e C o u l o m b barrier. At energies u p t o a few M e V , i o n - i o n reactions are c o n s e q u e n t l y m o s t p r o b a b l e for light ion i r r a d i a t i o n of light nuclides. R e a c t i o n s u s e d for analysis a n d d e p t h profiling are listed in C h a p t e r 14.4.1. F e a t u r e s such as n o n - R u t h e r f o r d ( r e s o n a n t ) scattering a n d p r o d u c t n u c l e u s recoil a d d t o t h e choice of i o n - i o n m e t h o d s of analysis.

4.2.1 Equipment T h e e q u i p m e n t r e q u i r e d for i o n - i o n analysis is similar t o t h a t for backscattering a n d is s h o w n schematically in Fig. 4.2. If t w o d e t e c t o r s are used, b o t h R B S a n d i o n - i o n reactions can b e s t u d i e d w i t h t h e s a m e equipment.

160 J.R. Bird

F i g . 4.2 S c h e m a t i c l a y o u t of i o n - i o n a n a l y s i s e q u i p m e n t .

a. Choice of

Detector

A solid state d e t e c t o r is c u s t o m a r i l y used — or m u l t i p l e detectors if higher c o u n t rates are r e q u i r e d . H o w e v e r , a high c o u n t rate from scattered ions is o b s e r v e d at low energies unless a foil is placed in front of the detector. T h e thickness of t h e foil should b e equal t o t h e range of t h e scattered ions so t h a t these are a b s o r b e d while t h e higher energy reaction p r o d u c t s pass t h r o u g h . Mylar, w h i c h h a s a c o m p o s i t i o n H 1 C080 4, a n d t h i n metal foils, are c o m m o n l y used for this p u r p o s e (see C h a p t e r 14.4.1). It is i m p o r t a n t to m e a s u r e t h e thicknesses a n d n o t j u s t use t h e r a t e d thickness. T h e major d i s a d v a n t a g e of t h e a b s o r b e r foil t e c h n i q u e , is t h a t energy loss straggling occurs in t h e foil resulting in p o o r energy resolution in t h e m e a s u r e d s p e c t r u m . F o r e x a m p l e , a d e t e c t o r resolution w h i c h is typically 10 to 15 keV for a Si detector, m a y b e d e g r a d e d t o 50 to 100 keV. T h i s is not i m p o r t a n t if t h e r e is sufficient energy difference b e t w e e n ion groups from different reactions or different target nuclides b u t is a m a j o r limitation if d e p t h profiles are t o b e m e a s u r e d . T h e p r o b l e m of p o o r energy resolution is e x a c e r b a t e d by any i n h o m o g e n e i t i e s in thickness of the absorber foil. V a r i a t i o n s of at least a few p e r c e n t in a b s o r b e r thickness m u s t be expected a n d i n c l u d e d in q u a d r a t u r e with o t h e r c o n t r i b u t i o n s to energy resolution. If a n a b s o r b e r foil is m o u n t e d o n a m o v a b l e support, it can b e r e m o v e d w h e n r e q u i r e d so t h a t backscattering m e a s u r e m e n t s can b e m a d e with t h e s a m e detector. T h i s is a c o n v e n i e n t way t o calibrate t h e de­ tection efficiency a n d solid angle using t h e absolute value of the backscattering cross-section. Angle a d j u s t m e n t of t h e s a m p l e a n d de­ tectors from outside t h e c h a m b e r is n e e d e d for versatile o p e r a t i o n . High detection efficiency can b e achieved by placing o n e or m o r e

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161

T A B L E 4.3 P e r f o r m a n c e of i o n d e t e c t i o n m e t h o d s Detector

Reject Scattering

Sensitivity

Energy Resolution (keV)

Depth Resolution

no yes no partial yes yes yes no yes yes

good good good good medium good excellent excellent poor poor

1% 1% 10 10 10 >25 200 20 <10 <10

very poor very poor medium medium medium poor poor medium excellent excellent

G a s ionisation I o n identification Surface b a r r i e r Low detector bias P o s i t i o n sensitive A b s o r b e r foil G r a d e d foil Convergent beam Magnetic analyser Electrostatic analyser

large surface b a r r i e r detectors close t o t h e s a m p l e or b y t h e use of a n a n n u l a r d e t e c t o r (see Fig. 4.2). A solid angle of 1 sr is possible b u t 10 to 100 m s r a n d e v e n lower values m a y b e necessary to a c h i e v e t h e best energy resolution. S o m e typical c o u n t rates from c o m m o n l y u s e d reactions are i n c l u d e d in C h a p t e r 14.4.1. b. Alternative

Detectors

A c o m p a r i s o n of v a r i o u s a l t e r n a t i v e d e t e c t i o n t e c h n i q u e s is given in T a b l e 4 . 3 . Solid state d e t e c t o r s suffer d e t e r i o r a t i o n in resolution d u e t o r a d i a t i o n d a m a g e especially w h e n they are u s e d to detect h e a v y ions. T h i s can b e a v o i d e d by t h e use of gas i o n i s a t i o n d e t e c t o r s (England, 1974) b u t they a r e larger a n d m o r e c o m p l e x t h a n Si d e t e c t o r s . E i t h e r t y p e can b e used in d e t e c t o r 'telescopes' w h i c h use t h e rate of energy loss t o d e t e r m i n e t h e a t o m i c n u m b e r of each d e t e c t e d ion. M a g n e t i c analysers (see C h a p t e r 2) c a n b e used b o t h t o separate reaction p r o d u c t s from scattered ions a n d t o achieve b e t t e r energy resolution t h a n c a n b e o b t a i n e d with a solid state detector. H o w e v e r , solid angle a n d d e t e c t i o n efficiency are low a n d t h e good energy res­ olution is only useful for reactions occurring n e a r t h e s a m p l e surface. At d e p t h s b e y o n d 10 t o 20 n m , t h e d e p t h resolution w o r s e n s b e c a u s e of the effects of energy loss straggling a n d a m a g n e t i c analyser n o longer h a s any a d v a n t a g e . It is also possible t o use a n electrostatic analyser for t h e analysis of p r o d u c t ion energies b u t similar p r o b l e m s arise. T h e s e p a r a t i o n of scattered a n d p r o d u c t i o n s is discussed further in Section 4.2.2d. Time-of-fight t e c h n i q u e s h a v e b e e n used in R u t h e r f o r d Backscattering a n d s h o u l d also b e useful for i o n - i o n r e a c t i o n s . E x a m p l e s of

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J.R. Bird

ENERGY (MeV)

F i g . 4.3 S c h e m a t i c energy s p e c t r u m f r o m 9 7 2 k e V d e u t e r o n i r r a d i a t i o n of t h i n (full c u r v e ) a n d t h i c k e r ( d a s h e d c u r v e ) layers of C, Ν a n d O . P e a k s labelled w i t h t h e target n u c l e u s a n d p r o d u c t p a r t i c l e (see text).

the use of different d e t e c t i o n t e c h n i q u e s t o solve specific p r o b l e m s are discussed in t h e next section. A typical s p e c t r u m o b s e r v e d in ion-ion reaction studies is s h o w n schematically in Fig. 4.3 for t h e case of a very t h i n layer c o n t a i n i n g C, Ν a n d Ο which is i r r a d i a t e d with 972 keV d e u t e r o n s . T h i s energy is r e c o m m e n d e d for s i m u l t a n e o u s analysis of these e l e m e n t s using (d,p) a n d (d,a) reactions ( D a v i e s et al, 1983). H i g h e r energies are preferable for greater sensitivity in Ν d e t e r m i n a t i o n if this is t h e m a i n interest. Each energy g r o u p in Fig. 4.3 is labelled with the nuclide a n d p r o d u c t particle involved. If a s a m p l e is used for which t h e p r o d u c t ion energy loss is greater t h a n t h e d e t e c t o r resolution, each p e a k in Fig. 4.3 will b e e x t e n d e d to lower energies as illustrated by t h e d a s h e d curves. If t h e sample is t o o thick, p e a k s from reactions in different isotopes m a y overlap a n d analysis t h e n b e c o m e s difficult.

4.2.2 Choice of Experimental Conditions Analysis using ion-ion r e a c t i o n s involves t h e choice of reaction, suitable values of i n c i d e n t energy, r e a c t i o n angle, d e t e c t o r angle a n d resolution, sample angle a n d thickness a n d v a r i o u s special geometries. a. Reaction

Angle

T h e change of p r o d u c t particle energy w i t h r e a c t i o n angle (Θ) d e p e n d s o n the Q-value a n d a t o m i c m a s s e s i n v o l v e d a n d is different for different reactions a n d for different excited state groups. T h i s is illustrated in Fig. 4.4 for the reactions s h o w n in Fig. 4 . 3 . T h e d a s h e d curves i n d i c a t e t h e

4. Nuclear Reactions

163

72

> ω

>- 10

h

LU LU

8 40

80

120

160

40

80

120

160

REACTION ANGLE

F i g . 4.4 T h e d e p e n d e n c e of p r o d u c t p a r t i c l e energy o n r e a c t i o n angle for t h e r e a c t i o n s s h o w n i n Fig. 4 . 3 . T h e d a s h e d c u r v e s s h o w t h e effects o f a n a b s o r b e r u s e d t o r e m o v e scattered ions.

effect of a n a b s o r b e r foil o n t h e energy of t h e high energy groups. T h e r e are t h r e e i m m e d i a t e c o n s e q u e n c e s : i. t h e d e t e c t o r angle can often b e selected so as to a c h i e v e o p t i m u m s e p a r a t i o n of a n energy g r o u p from a r e q u i r e d isotope from groups arising from c o m p e t i n g reactions; ii. t h e change in energy o v e r t h e solid angle s u b t e n d e d b y t h e d e t e c t o r m a y b e sufficient to d e g r a d e t h e o b s e r v e d energy resolution; a n d iii. v a r i a t i o n s in t h e ion p a t h length o c c u r w i t h i n t h e s a m p l e a n d a b s o r b e r i n t r o d u c i n g a n a d d i t i o n a l energy spread. A n a n n u l a r Si d e t e c t o r c a n b e used (Fig. 4.5a) to give a larger solid angle a n d h e n c e sensitivity (without increasing t h e energy s p r e a d ) b y detecting all ions e m i t t e d in a c o n e h a v i n g t h e r e q u i r e d r e a c t i o n angle. However, it can only b e used for reaction angles close t o 180°. F u r t h e r increases in solid angle can b e a c h i e v e d if t h e thickness of t h e a b s o r b e r foil is g r a d e d a c c o r d i n g to r a d i u s t o c o m p e n s a t e for t h e changes in 5 energy (Fig. 4.5b). T h e use of such a system w i t h t h e p1r δ o d u c t 1ion Ο ( ρ , α ) Ν r e a c t i o n is s h o w n in Fig. 4.5c. In t h i s case, t h e alpha-particle peak w i d t h for a solid angle of 0.42 sr w a s i m p r o v e d from 2 5 0 t o 2 0 0 k e V (Lightowlers et al, 1973). T h i s is still i n a d e q u a t e for g o o d d e p t h profiling b u t w a s f o u n d useful for o b t a i n i n g c o n c e n t r a t i o n s of surface o r s u b ­ surface Ο a n d Β in s e m i c o n d u c t o r s .

164 J.R. Bird

© Incidenj Beam || Defining " Aperture

τ Sample

[p

7

sI o n

Product Graded 1 J) Absorber Al Absorber -Γ Foil C—

(c)

Graded

Y I DE 1L 0(8ρ) αι · /\Absorber S a m pml e 2:T052a. 9 n - ( 4O 0) % _ E p =V6 8 5 k e Uniform E = 3 .V3 M e jfcda f 2 e r0s . 4 lAbsorber F lo i Ι ό μ Γπ B ιΜ |emγa= Ι1Cα2 μ -1 " Aluminiumf (MeV)

1 8 Fig. 4.5a. A n n u l a r d e t e c t o r a r r a n g e m e n t ; measurements with a graded absorber.

b. Sample

b . special

purpose

graded

absorber;

c.

0

Angle

A very i m p o r t a n t aspect of e x p e r i m e n t a l configuration is t h e use of glancing angle t e c h n i q u e s to e n h a n c e d e p t h resolution. In reaction studies, the d e p t h resolution is d e p e n d e n t o n t h e rate of energy loss by b o t h incident a n d p r o d1u c66t ions a n d is d o m i n a t e d by w h i c h e v e r h a s t h e higher Z . T h u s , in t h e 0 ( L i , p ) r e a c t i o n t h e i n c i d e n t ion h a s t h e highest stopping p o w e r a n d t h e best d e p t h resolution is a c h i e v e d by placing t h e sample so as to h a v eΙ 8a glancing angle of i n c i d e n c e (Fig. 4.6a). O n t h e o t h e r h a n d , in t h e 0 ( ρ , α ) reaction, t h e s t o p p i n g p o w e r of t h e p r o d u c t ion is greatest a n d a glancing e m e r g e n c e angle is preferable (Fig. 4.6b). This is discussed further in Section 4.2.5. T h e o p p o s i t e choice s h o u l d b e m a d e to m i n i m i s e d e p t h effects in s a m p l e analysis. c. Special

Geometries

If the b e a m is convergent w h e n it strikes t h e sample, it is possible t o arrange t h e s a m p l e a n d d e t e c t o r so t h a t different i o n p a t h s involve t h e s a m e reaction angle (Fig. 4.6c). Falk et al. (1976) s h o w e d t h a t a n 12 9 i m p r o v e m e n t in energy resolution by a factor of three could b e achieved using this m e t h o d for t h e d e t e r m i n a t i o n of C with t h e C ( p , a ) B reaction. A position sensitive d e t e c t o r was used to allow corrections t o b e applied for changes in energy with reaction angle across the d i a m e t e r of the detector. In this case, t h e s a m p l e m u s t b e t h i n e n o u g h to t r a n s m i t t h e p r o d u c t ions with little energy loss. d. Ion

Separation

O n e m e t h o d for r e m o v i n g scattered i o n s is to use a small m a g n e t i c analyser (Fig. 4.7a). A m a g n e t i c field of a few h u n d r e d m T a p p l i e d over a

4. Nuclear Reactions

G L A N C I N G INCIDENCE

GLANCING EMERGENCE

CONVERGING BEAM

Detector

Detector

/Thin Sample Incident Beam 18

Incident Beam 1 66

0(p,CC)

0( Li,p) (b)

(a)

165

Sample Detector

F i g . 4.6a. G l a n c i n g i n c i d e n c e g e o m e t r y for h e a v y i o n i r r a d i a t i o n ; b . g l a n c i n g e m e r g e n c e for h e a v y p r o d u c t i o n s ; c. special g e o m e t r y t o i m p r o v e e n e r g y r e s o l u t i o n w i t h a large s a m p l e .

distance of 5 t o 10 c m will cause e n o u g h spatial s e p a r a t i o ln l ble tsw e e n 1 9 scattered p r o t o n s a n d alpha-particles from (ρ,α) r e a c t i o n s in B , O a n d F . An a p e r t u r e in front of t h e m a g n e t limits t h e a c c e p t a n c e solid angle a n d a carefully placed a p e r t u r e after t h e m a g n e t will t r a n s m i t only reaction p r o d u c t s a n d a few multiple-scattered i n c i d e n t ions. Giles et al. (1977) used a p o s i t i o n sensitive d e t e c t o r t o h e l p distinguish p r o d u c t ions from scattered ions. T h i s g e o m e t r y involves a r e d u c t i o n in a c c e p t a n c e solid angle by t h e o r d e r of a factor of t w o w h i c h can often b e offset b y a n increased b e a m c u r r e n t . A small electrostatic analyser can also b e used. F o r e x a m p l e , plates 174 m m long, placed as s h o w n in Fig. 4.7b w i t h a p o t e n t i a l difference of 10 kV, will separate scattered ions from r e a c t i o n p r o d u c t s from light isotopes in t h e s a m p l e (Moller et al., 1977). S o m e results o b t a i n e d with this t e c h n i q u e are discussed in Section 4.2.5e. e. Ion

Identification

Ions of different m a s s a n d energy can b e identified by r a t e of energy loss, or range ( G o u l d i n g a n d H a r v e y , 1975). F o r e x a m p l e , alpha-particles can b e detected in t h e presence of scattered p r o t o n s b y r e d u c i n g t h e bias o n a Si detector until t h e d e p l e t i o n d e p t h is 100 μτη or less. Scattered p r o t o n s pass right t h r o u g h such a t h i n sensitive layer a n d give pulses c o r r e s p o n d ­ ing to t h e fraction of t h e i r energy w h i c h is lost in t h e layer. Alphaparticles of similar energy h a v e a range less t h a n t h e layer thickness a n d 31 28 h e n c e give full energy pulses. Ligeon et al. (1973) u s e d this m e t h o d with t h e P ( p , a ) S i r e a c t i o n to profile Ρ in Si. T h e β - v a l u e of this reaction is only 1.917 M e V a n d 3 M e V alpha-particles are p r o d u c e d for a n i n c i d e n t energy of 1.892 M e V . T h e range of these a l p h a s is m u c h t o o low t o b e able t o use a n a b s o r b e r foil to r e m o v e scattered p r o t o n s . Pulse-height spectra from a 10 μτη thick detector gives a n isolated a l p h a p e a k (Fig. 4.8a) w h i c h is suitable for Ρ

166

J.R. Bird

)

( Q

MAGNETIC SEPARATION

ELECTROSTATIC SEPARATION

Incident Beam

1 Ji 1 S\> ^^S/bample \ Collimators ' J \

\

Sample Incident 1 Beam |

N V ' Electrostatic

E

\

SAMagnetic

D L

/ W

XollimatorsC^^^J^T

Field

\jff

)

Detector Defector

^5>\

F i g . 4.7 S c h e m a t i c a r r a n g e m e n t for: scattered and reaction product ions.

a. m a g n e t i c ,

and

b. electrostatic

14

separation

of

- 2

d e t e r m i n a t i o n in Si at levels d o w n t o t h e o r d e r of 1 0 a t o m s c m . W i t h a 300 μτη detector, pulses from scattered p r o t o n s interfere with t h e alphaparticle peak. A m o r e sophisticated particle identification system consists of t w o detectors which can b e either i o n i s a t i o n c h a m b e r s o r Si detectors (Fig. 4.8b). T h e first d e t e c t o r is m a d e t h i n e n o u g h t o give a signal for each ion which is p r o p o r t i o n a l t o energy loss (ΔΕ) a n d t o completely a b s o r b short range particles while t r a n s m i t t i n g long range particles t o t h e second detector. F o r e x a m p l e , T h o m a s et al. (1975) used a 50 μτη Si d e t e c t o r fol­ lowed by a " t h i c k " Si d e t e c t o r t o detect C at t h e surface of a b o r o n layer. T h e first d e t e c t o r is j u s t thick e n o u g h t o a b s o r b p r o d u c t s of (d,p)1 a2n d (d,a) reactions in Β while t r a n s m i t t i n g t h e p r o t o n s from t h e C ( d , p ) reaction. T h e full energy of t h e latter is o b t a i n e d by s u m m i n g t h e signals from b o t h detectors a n d this allows n o r m a l resolution to b e a c h i e v e d (in this case 40 keV) r a t h e r t h a n h a v e t h e resolution d e g r a d e d by at least a factor of t w o which w o u l d occur if a passive a b s o r b e r foil was used. /

Dual Ion Coincidence

Detection

In suitable cases, it is possible t o detect recoil a t o m s s i m u l t a n e o u s l y with t h e detection of t h e light p r o d u c t ions. F o r reactions in light nuclides, 6 from 3 4an there is n o clear d i s t i n c t i o n b e t w e e n t h e t w o particles emerging i o n - i o n reaction. As a n e x a m p l e , let us c o n s i d e r t h e L i ( p3, H e ) H e 4 e V a n d if t h e H e ion is reaction at Ex = 1.9 M e V . T h e β - v a l u e is 4.021 M observed at 110° ( £ 3 = 2.709 M e V ) , t h e n t h e H e ion m u s t recoil at a n angle of 48. \°(E4 = 3.212 M e V ) in o r d e r t o satisfy t h e k i n e m a t i c relation ( E q u a t i o n (1.21), T a b l e 1.3). T w o d e t e c t o r s can b e placed as s h o w n in Fig. 4.9a a n d typical spectra (from t h e forward detector) a r e s h o w n in

4. Nuclear Reactions

31 DETECTOR THICKNESS

167

Ί Ζ

P(p c)

DETECTOR TELESCOPE

jC

Counts

Πα,ρ)

Sample Incident] Beam 5 0 π η ^ Detector

μ

ENERGY (b)

(Q)

Thick Ε Detector

3 1 F i g . 4.8a. S c h e m a t i c energy s p e c t r a f r o m t h i n a n d t h i c k solid s t a t e d e t e c t o r s for P ( p , « ) s t u d i e s ; b . S c h e m a t i c l a y o u t o f t h i n a n d t h i c k d e t e c t o r t e l e s c o p e for p r o d u c t i o n identification.

Fig. 4.9b. T h e t o p c u r v e is t h e s p e c t r u m w i t h n o c o i n c i d e n c e r e q u i r e m e n t a n d t h e b o t t o m c u r v e shows t h e d r a m a t i c simplification a c h i e v e d by d e m a n d i n g t h a t a particle is also o b s e r v e d in c o i n c i d e n c e in t h e s e c o n d detector ( P r e t o r i u s a n d Peisach, 1978). T h e m a i n l i m i t a t i o n t o such m e a s u r e m e n t s is t h a t t h e s a m p l e m u s t b e t h i n e n o u g h t o t r a n s m i t b o t h p r o d u c t particles. N u c l i d e s for w h i c h suitable r e a c t i o n s a r e available are listed in T a b l e 4.4 (Coetzee et α/., 1975). T h e coincidence circuit m u s t use a t i m e delay a n d r e s o l u t i o n w h i c h take i n t o a c c o u n t t h e difference in velocities of t h e t w o particles b e i n g sought. Energy w i n d o w s can b e u s e d t o further restrict t h e t y p e of e v e n t which can give a coincidence. T h e s u m of t h e pulses in b o t h d e t e c t o r s will give a single p e a k (Fig. 4.9c) w h i c h is q u i t e n a r r o w , even if t h e a c c e p t a n c e

YIELD

Incident Beam

I

Detector 2(110' ENERGY (MeV)

6

34

F i g . 4.9 C o i n c i d e n c e d e t e c t i o n of c h a r g e d p a r t i c l e s f r o m t h e L i ( p , H e ) H e r e a c t i o n i n a t h i n s a m p l e , a. D e t e c t o r g e o m e t r y ; b . p u l s e h e i g h t s p e c t r a w i t h c o i n c i d e n c e off ( t o p ) o r o n ( b o t t o m ) ; c. s u m s p e c t r u m .

168

J.R. Bird

T A B L E 4.4 Light e l e m e n t r e a c t i o n s for c o i n c i d e n c e Reaction N2u c l i d e 3D 6H e 7L i 9L i Be

d,p

3

3m e a s u r e m e n3t s He,p

He,d

He,a

α,ρ

α,ά

X X X

X

X

X

X

X

X X

"B

d,«

X

X

X

X

X

X

X

X

X

X X

χ X

X

solid angle of the detectors is sufficiently large for k i n e m a t i c b r o a d e n i n g to be significant. T h i s follows from t h e fact that: Ex + Q = E3 + E4 - AE

(4.3)

where AE is a c o n s t a n t s u m of energy losses by t h e t w o particles in t h e sample material, irrespective of t h e d e p t h at w h i c h t h e reaction occurs. T h e coincidence t e c h n i q u e c a n n o t b e used if o n e of t h e p r o d u c t s has8 a short half-life a n d decays before reaching t h e detector. F o r e x a m p l e , B e , which is p r o d u c e d in a n u m-b eI r 6of light e l e m e n t reactions, has a half-life of a p p r o x i m a t e l y 3 X 1 0 s a n d b r e a k s u p i n t o t w o alpha-particles. T h e s e ions are responsible for t h e c o n t i n u u m c o u n t - r a t e at low energies shown in Fig. 4.9b b u t they d o n o t satisfy t h e coincidence r e q u i r e m e n t a n d d o n o t c o n t r i b u t e to t h e final spectra.

4.2.3 Thin Sample Analysis a. Narrow Resonance

Reactions

As an e x a m p l e of t h e use of a n 1a r9r o w r e s o n a n c e to analyse t h i n samples, _1 (see C h a p t e r consider the r e s o n a n c e in t h e F ( p , a ) reaction at 1348 keV 14.4.2). T h e m a x i m u m cross-section at 150° is 3.2 m b s r a n d this gives 2.4 counts//zC 15using a d e t-2 e c t o r solid angle of 0.12 sr a n d a s a m p l e of F ( D i e u m e g a r d et ai, 1980). O f o t h e r containing 1 0 a t o m s c m elemental constituents, only Li can give rise to alpha-particles of the s a m e or higher energy a n d F d e t e r m i n a t i o n is t h u s a l m o s t interference free. T h e F c o n t e n t of d e n t a l e n a m e l , a n o d i c oxide layers a n d o t h e1r3 - 2 be m e a s u r e d in this way with a sensitivity b e t t e r t h a n 1 0 materials can atoms c m .

4. Nuclear Reactions b. Layer

Thickness

169

Determination

6 t h1a t4 a b r o a d p e a k with a n a l m o s t flat t o p is It was s h o w n in Fig. 14.3 observed from t h e 0 ( d , a ) N reaction in a thick oxide layer. F o r a n incident d e u t e r o n energy of 9 0 0 keV, 2.63 M e V alpha-particles are p r o d u c e d at 145° a n d t h e i r energy (E3"), after emerging from t h e s a m p l e is related to t h e d e p t h (t n m ) at w h i c h t h e reaction o c c u r r e d b y E q u a t i o n (12.35). T u r o s et al. (1973a) s h o w e d t h a t t h e relation is a p p r o x i m a t e l y linear to d e p t h s of 1 μπι a n d , for reactions in S i 0 2: ί = 2.91 (2.63 - £ 3" )

(4.4)

Results for S i 0 2 layers o n Si were f o u n d to agree w i t h m e a s u r e m e n t s b y ellipsometry to w i t h i n 2 % using this a p p r o a c h . G l a n c i n g angle g e o m e t r y can b e used to i m p r o v e t h e precision of thickness d e t e r m i n a t i o n s b u t it is limited b y the relatively p o o r energy resolution available in m o s t i o n - i o n reaction studies. If t h e energy loss in t h e layer is m u c h less t h a n t h e w i d t h of t h e resol­ u t i o n function, t h e p e a k will n o t b e flat t o p p e d a n d d e p t h i n f o r m24 a t i o n is - 2 resolution limited. In this case a n e s t i m a t e of thickness (t . 1 0 ~ a t o m s c m ) can b e o b t a i n e d from t h e p e a k area (A3): t = A3/dadQ

(4.5)

If a n a r r o w r e s o n a n c e is used, t h e differential cross-section can b e replaced by t h e r e s o n a n c e a r e a (Ar) w h i c h is given in n u c l e a r physics tables as p r o p o r t i o n a l to (2J + 1) Γα Tb/T w h e r e J is t h e angular m o m e n t u m q u a n t u m n u m b e r , Γα a n d are partial w i d t h s describing scattering a n d reactions respectively a n d Γ is t h e w i d t h of t h e r e s o n a n c e . Relative values of r e s o n a n c e areas are listed in C h a p t e r 14.4.2. O b s e r v e d cross-sections are n o t zero b e t w e e n r e s o n a n c e s so t h a t small c o r r e c t i o n s are n e e d e d w h e n using r e s o n a n c e areas from nuclear physics tables (which are integrated from — oo t o + oo) with e x p e r i m e n t a l p e a k areas t a k e n over a finite energy range. T h e simplest a p p r o a c h is t o o b t a i n a value of t h e p r o d u c t of effective r e s o n a n c e a r e a a n d d e t e c t o r solid angle by calibration with a s t a n d a r d s a m p l e .

4.2.4 Bulk Analysis Bulk c o m p o s i t i o n c a n b e d e r i v e d from i o n - i o n m e a s u r e m e n t s o n t h e a s s u m p t i o n t h a t t h e s a m p l e is h o m o g e n e o u s . T h i s can b e illustrated by the d e t e r m i n a t i o n of nitrogen in steels using t h e c o m b i n e d c o u n t s from

170 J.R. Bird the (d,p 0) a n d ( d , a 0) reactions (see Fig. 4.3). T h e cross-sections for these reactions increase rapidly with energy b u t this is also t r u e for o t h e r c o m p e-1 t i n g reactions. U s i n g 1.9 M e V d e u t e r o n s , Ν can b e d e t e r m i n e d at mg g levels by c o u n t i n g p r o t o n s a n d a l p h a s a b o v e 8 M e V from s t a n d a r d a n d u n k n o w n samples (Olivier et al, 1975). G r e a t e r sensitivity can b e achieved by exploiting t h e higher c o u n t rate from these reactions 1 d e u t e r o n s of only 1.2 M e V , Ν c a n at forward angles (e.g. 45°). E v e n with t h e n be d e t e r m i n e d below 100 μ% g " p r o v i d e d t h a t b o r o n is n o t p r e s e n t at m u c h higher levels (Olivier et al, 1976).

4.2.5 Depth Profiling T h e principles used in d e p t h profiling with i o n - i o n reactions are described in C h a p t e r 12.2. R e a c t i o n s used, typical e x p e r i m e n t a l par­ a m e t e r s a n d p e r f o r m a n c e figures are s u m m a r i s e d in C h a p t e r 14.4. Examples are given in this Section t o illustrate t h e m o s t i m p o r t a n t features of i o n - i o n profiling. T h e r e s o n a n c e s c a n n i n g m e t h o d w h i c h is illustrated in Section 4.3.2 is of only l i m i t e d use with i o n - i o n reactions because n a r r o w1 rδe s o n1a5n c e s are u n u s u a l in t h e i r cross-sections. E x a m p l e s include t h e 3Ο ( ρ , α4 ) Ν reaction w i t h a n a r r o w r e s o n a n c e at 629 keV a n d the H e ( d , p ) H e reaction w i t h a b r o a d a s y m m e t r i c r e s o n a n c e at 430 keV. In t h e latter case, the r e s o n a n c e s h a p e m u s t b e t a k e n i n t o account w h e n deriving the d e p t h profile ( P r o n k o a n d P r o n k o , 1974) — something t h a t is n o t usually necessary with r e s o n a n c e scanning. T h e energy s p e c t r u m m e t h o d is t h e m a i n profiling t e c h n i q u e used with ion-ion reactions a n d is described in Highlight 4 . 3 . It is a relatively quick m e t h o d since t h e necessary d a t a are o b t a i n e d d u r i n g o n e ir­ r a d i a t i o n with a fixed i n c i d e n t energy, in a very similar way to the use of R u t h e r f o r d backscattering ( C h a p t e r 3). H o w e v e r , t h e p r o d u c t ion is usually different to t h e i n c i d e n t ion a n d higher in energy w h i c h h a s a n i m p o r t a n t influence o n t h e choice of e x p e r i m e n t a l c o n d i t i o n s a n d t h e p e r f o r m a n c e achieved. T h e o p t i m i s a t i o n of d e p t h resolution following t h e principles described in C h1a p9t e r 12.2, is illustrated in Highlight 4.4. M o s t isotopes from *H to F can b e profiled with this m e t h o d , t h e 'surface' resolution being typically in t h e range 10 t o 100 n m . T h i s is n o t as good as often a c h i e v e d by r e s o n a n c e scanning with i o n - g a m m a 1 2 w h e n1 several 6 reactions b u t is nevertheless useful, especially isotopes can be profiled s i m u l t a n e o u s l y (for e x a m p l e C a n d 0 ) .

4.2.6 Non-Elastic Recoil It was p o i n t e d o u t in Section 4.2.2f t h a t t h e recoiling nucleus can s o m e t i m e s b e d e t e c t e d after a nuclear reaction in a very t h i n sample. T h i s can also b e d o n e if the b e a m is i n c i d e n t at a glancing angle t o t h e surface

4. Nuclear Reactions

171

H I G H L I G H T 4.3 PROFILING WITH REACTION ENERGY SPECTRA T h e simplest m e t h o d for deriving d e p t h d i s t r i b u t i o n s from t h e o b s e r v e d peaks in reaction energy spectra is to use reference s a m p l e s a n d a

ALPHA ENERGY

1 6 F i g . 4.10 S c h e m a t i c i l l u s t r a t i o n of a (full c u r v e ) .

0 ( d , a ) spectrum (points) a n d a calculated

spectrum

channel-by-channel ratio (Nu/Ns) of c o u n t s from u n k n o w n (u) a n d s t a n d a r d (s), E q u a t i o n (12.43). T h i s is a good a p p r o x i m a t i o n p r o v i d e d t h a t t h e s t o p p i n g p o w e r curves for s t a n d a r d a n d u n k n o w n are a p p r o x i m a t e l y parallel (Gossett, 1980). T h e d e p t h scale can b e calculated with E q u a t i o n (12.35). a. Spectrum Simulation S p e c t r u m s i m u l a t i o n is straightforward if t h e cross-section a n d concen­ 1 p4l e , t h e r e is only a small t r a t i o n functions h a v e a simple form. F o1r 6e x a m linear increase in cross-section of t h e 0 ( d , a ) N r e a c t i o n b e t w e e n 800 a n d 900 keV. T h e calculated yield (Y3) for a l p h a particle energy E3 is given by (see C h a p t e r 12.2): Y3dE3 = Nxed&

c(x) σ(Εχ)

dx/m2S(Ex)

(4.6)

It is necessary to calculate t h e d e p t h change (dx) for each i n c r e m e n t in p r o d u c t particle energy (dE3) using E q u a t i o n (12.33) or (12.34). T o include t h e effects of energy spread, E q u a t i o n (12.41) s h o u l d b e used. T h e i n c i d e n t ion energy (E{) at t h e b e g i n n i n g o r c e n t r e of t h e d e p t h interval is also n e e d e d ( E q u a t i o n 12.31) t o e v a l u a t e t h e cross-section a n d stopping power. T h e calculation can b e r e p e a t e d with different forms of c(x) until a satisfactory fit is o b t a i n e d to t h e o b s e r v e d s p e c t r u m . Fig. 4.10 shows t h e s h a p e of calculated a n d m e a s u r e d yields for a n 800 n m thick S i 0 2 layer o n Si ( T u r o s et al, 1973b). T h e c o n c e n t r a t i o n profile was a s s u m e d t o b e u n i f o r m w i t h d e p t h a n d t h e e x p e r i m e n t a l

172 J.R. Bird

4

8 12 PROTON ENERGY (MeV)

16

20

F i g . 4.11 S c h e m a t i c i l l u s t r a t i o n of:2a. t h e p3r o t o n e n e r2g y s p e c t3r u m f r o m 0.4 M e V d e u t e r o n i r r a d i a t i o n of N i w i t h i m p l a n t e d D a n d H e ; a n d b . D a n d H e d e p t h profiles o b t a i n e d by d e c o n v o l u t i o n of t h e s p e c t r u m p e a k s .

resolution, as well as effects of straggling, were i n c l u d e d t o o b t a i n t h e fit at low energies. It is desirable to include m u l t i p l e scattering effects in s p e c t r u m s i m u l a t i o n a n d suitable c o m p u t e r p r o g r a m s h a v e b e e n re­ p o r t e d by M a r c u s o et al. (1983) a n d S i m p s o n a n d E a r w a k e r (1986). Simulations can also b e b a s e d o n a n expected shape for t h e c o n c e n t r a t i o n profile such as t h o s e i n v1o l6v e d in simple diffusion m o d e l s . T h e first excited state g r o u p from t h e 0 ( d , p ) reaction is useful for d e p t h profiling because of its high yield a n d slowly varying cross-section between 800 a n d 920 keV. Calculated energy spectra for c o n c e n t r a t i o n profiles based on diffusion t h e o r y define t h e diffusion coefficient from a best fit to t h e m e a s u r e d s p e c t r u m (Amsel et al., 1968). b. Spectrum Deconvolution As a n alternative to simulation, t h e c o n c e n t r a t i o n profile c(x) can be derived from a n observed energy s p e c t r u m , Y(E3), by inverting E q u a t i o n (4.6) a n d including a resolution function:

x

c(x) = kY(E3)

(Sx (Ex) dE3ldEx) R(E3) [do(Ex)Y

(4.7)

W h e r e k = m2INxe dQ,. T h e d e c o n v o l u t i o n of cross section, σ(Εχ) energy loss, S(x) a n d resolution function, R(E), can be carried out by using a p p r o p r i a t e a p p r o x i m a t i o n s or with n u m e r i c a l t e c h n i q u e s (see C h a p t e r 12.2). Examples are s h o w n in Fig. 4 . 1 1 . T h e lower curve shows 2 s p e c t r3u m from 0.4 M e V d e u t e r o n irradia­ schematically t h e ion energy tion of N i i m p l a n t e d with D a n d H e . P e a k s from (d,p) reactions in t h e 2 i m p l a n t e d species a n d surface C 3are observed. T h e u p p e r curves illustrate the d e p t h profiles of D a n d H e o b t a i n e d by d e c o n v o l u t i o n after re­ m o v a l of the surface C p e a k (Moller et al., 1977).

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H I G H L I G H T 4.4 OPTIMISATION OF DEPTH RESOLUTION T h e c o n d i t i o n s for o p t i m u m d e p t h resolution are: • • • • •

a reaction w i t h high Ζ i n c i d e n t o r p r o d u c t ions o r b o t h ; a glancing angle t o t h e surface for t h e high Ζ ion; a low b e a m d i a m e t e r , divergence a n d energy spread; a high resolution d e t e c t o r w i t h small solid angle a n d n o a b s o r b e r foil; a n d a low r e a c t i o n angle if this is consistent w i t h good s e p a r a t i o n of p r o d u c t energy groups.

2 ANGLE β

DEPTH IN Ni (mg/cm )

3i g . 4.12a. Energy a n d d e p t h r e s o l u t i o n s as a f u n c t i o n of e m e r g e n c e a n g l e (β) for t h e F H e ( d , a ) r e a c t i o n w i t h E = 42 5 0 K3e V , θ = 90° a n d t = 2 3 0 n m ; b . D e p t h r e s o l u t i o n as a { f u n c t i o n of d e p t h for t h e D ( d , p ) T r e a c t i o n w i t h E, = 2 M e V , θ = 40°, φ = 25°, a n d ψ = 65°. 1 = D e t e c t o r r e s o l u t i o n ; 2 = g e o m e t r i c a l effects; 3 = m u l t i p l e s c a t t e r i n g of p r o d u c t i o n s ; 4 = e n e r g y straggling of p r o d u c t i o n s ; 5 = m u l t i p l e s c a t t e r i n g of i n c i d e n t ions; 6 = lateral s p r e a d of i n c i d e n t i o n s ; 7 = lateral s p r e a d of i n c i d e n t i o n s ; 8 = e n e r g y straggling of i n c i d e n t i o n s . H a v i n g chosen values of these p a r a m e t e r s a p p r o p r i a t e t o t h e r e a c t i o n being used, it r e m a i n s t o assess h o w small a glancing angle can b e u s e d 3 angle 1until o t h e r since t h e d e p t h resolution i m p r o v e s as t h e sine of this factors i n t e r v e n e . T h i s is s h o w n in Fig. 4.12a for t h e H e ( d , a ) H reaction w h e r e t h e p r o d u c t energy resolution (AE3) a n d t h e e q u i v a l e n t d e p t h resolution (Δ/) are p l o t t e d as a function of angle of e m e r g e n c e (β) of t h e p r o d u c t a l p h a particles (Bottiger, 1978). T h e c o m p o n e n t s of t h e energy resolution are also shown, t h e m o s t i m p o r t a n t being energy straggling a n d m u l t i p l e scattering. H o w e v e r , at small angles, t h e c o n t r i b u t i o n from geometrical effects a n d t h e lateral s p r e a d of t h e a l p h a particles rise rapidly a n d t h e d e p t h resolution d e t e r i o r a t e s below 8°. T h i s is a typical result, b u t t h e o p t i m u m angle m a y v a r y from < 5° t o > 10° d e p e n d i n g o n

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the reaction a n d e x p e r i m e n t a l p a r a m e t e r s involved. O f course, t h e m a x i m u m d e p t h t h a t can b e analysed also decreases with sin β. 3 F o r fixed geometry, t h e d e p t h resolution d e t e r i o r a 2t e s rapidly as t h e d e p t h increases. T h i s is s h o w n in Fig. 4 . 1 2 b for t h e D ( d , p ) T r e a c t i o n (Môller et al, 1977). M u l i t p l e scattering of t h e i n c i d e n t ions is m o s t i m p o r t a n t close to t h e surface, a n d t h e i r lateral s p r e a d is d o m i n a n t at large d e p t h s . T h e d e p t h resolution w h i c h is usually q u o t e d ( C h a p t e r 14.4) is the 'surface' resolution with c o n t r i b u t i o n s from i n c i d e n t b e a m energy spread a n d g e o m e t r y a s s u m e d to b e small c o m p a r e d t o t h e d e t e c t o r resolution. Energy straggling in a n a b s o r b e r foil is also ignored w h e r e a s this is likely to b e t h e d o m i n a n t factor if a foil is used.

of a thick sample. T h i s is analogous to E R A ( C h a p t e r 3) b u t t h e energy gain available in m a n y nuclear r e a c t i o n s gives t h e recoil nucleus greater energy. C o n s e r v a t i o n of m o m e n t u m restricts recoil nuclei to travel within a c o n e in t h e forward d i r e c t i o n a n d this can b e exploited to o b t a i n an e n h a n c e d yield close to t h e m a x i m u m angle defined by k i n e m a t i c relations, E q u a t i o n (1.30), T a b l e 1.3. H i g h m a s s i n c i d e n t ions increase the k i n e m a t i c collimation a n d a variety of h e a v y ion reactions h a v e b e e n p r o p o s e d for non-elastic recoil profiling of isotopes from H t o F ( C o n l o n a n d Parker, 1980).

4.2.7 Performance I o n - i o n reaction m e t h o d s h a v3e b2e e n d e m o n s t r a t e d for t h e d e t e r m i n a t i o n 3 of m o s t isotopes from *H t o S . T h e m o s t used reactions are (ρ,α), (d,p) a n d (d,a) with H e reactions 1 6 alternatives for t h e d e t e r m i n a t i o n of isotopes such 6as p2 r o v i1d i 2 n g useful D , C a n d 0 . A l p h a i n d u c e d reactions h a vne h a d l i m i t e d use. S o m e L i i n d u c e d reactions h a v e b e e n tested a n d t h e ( B , a ) reaction h a s b e e n used for hydrogen d e t e r m i n a t i o n a n d profiling. I n c i d e n t ion energies from 0.5 to 2 M e V are m o s t useful for m i n i m i s i n g interference from reactions in h e a v y isotopes. I n contrast, energies a b o v e 3 M e V m a k e (d,p) reactions useful for t h e study of m e t a l s . High b e a m c u r r e n t densities can b e used in this case so t h a t m i c r o p r o b e scans are also practicable for b e a m d i a m e t e r s of t h e o r d e r of 10 μτη a n d reactions which h a v e b e e n used in this way are_1listed in T a b l e 10.5. R e a c t i o n cross-sections of 10 t o 100 m b s r are o b s e r v e d for p r o t o n -1 isotopes such as D , Li, Be a n d B. a n d d e u t e r o n i n d u c e d reactions in light Sensitivities of t h e o r d e r of 10 μ% g or even less are t h e n possible w i t h m e a s u r i n g t i m e s of t h e o r d e r of t e n s of m i n u t e s . T h r e e d i m e n7s i o n a l analysis ( s i m u l t a n e o u s d e p t h profiling a n d m i c r o p r o b e scans) of L i h a s

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b e e n described by H e c k (1988). F o r t h e i m p o r t a n t case of isotopes of C, Ν a n d O, similar sensitivities are possible. Cross-sections are smaller for higher Ζ isotopes a n d h e n c e c o u n t rates are lower. Level densities also increase with Ζ a n d t h e choice of i n c i d e n t energy a n d r e a c t i o n angle is crucial for m i n i m i s i n g interference from u n w a n t e d g r o u p s in t h e observed s p e c t r u m . F o r t u n a t e l y , light e l e m e n t s such as Li, Be a n d Β 3 2 usually occur at low c o n c e n t r a t i o n s a n d , if this is t h e-1case, isotopes u p to S can b e d e t e r m i n e d in h e a v i e r m a t r i c e s at m g g or p e r cent levels d e p e n d i n g o n t h e c u r r e n t t h a t t h e s a m p l e will w i t h s t a n d . D e p t h i n f o r m a t i o n is always available from t h e p r o d u c t ion spec­ t r u m if t h e d e p t h exceeds t h a t c o r r e s p o n d i n g to t h e energy resolution. T h e energy interval t o t h e next lower g r o u p in t h e s p e c t r u m sets t h e m a x i m u m d e p t h t h a t can b e profiled. T h e s e p a r a m e t e r s are u n i q u e for each reaction a n d are catalogued in C h a p t e r 14.4. T h e m a x i m u m d e p t h is usually l i m i t e d to t h e o r d e r of 1 μτη. U n f o l d i n g t e c h n i q u e s can increase this range s o m e w h a t . T h e use of glancing i n c i d e n c e or e m e r g e n c e for heavy incident or p r o d u c t ions respectively can give typical d e p t h resolutions at t h e surface of 10 to 100 n m . At d e p t h s greater t h a n a p p r o x i m a t e l y 100 n m , t h e effects of m u l t i p l e scattering a n d energy loss straggling o n b o t h i n c i d e n t a n d p r o d u c t i o n s so degrade t h e resolution t h a t t h e r e is n o p o i n t in using low efficiency, high resolution d e t e c t i o n systems. M o s t i o n - i o n r e a c t i o n m e a s u r e m e n t s are therefore m a d e with a very simple e x p e r i m e n t a l a r r a n g e m e n t . Surface r e m o v a l a n d wedge s c a n n i n g h a v e b e e n u s e d t o e x t e n d i o n - i o n d e p2t h 3 n to1a 2n8y 3d e p t h2 with 2 profiling c o3n s1t a n t resolution for t h e profiling of *H, D , H e , B , 0 , N a , A1 a n d P b u t t h e surface resolution is only of t h e o r d e r of 10 n m .

4.3 ION-GAMMA REACTIONS Particle I n d u c e d G a m m a ray E m i s s i o n ( P I G M E or P I G E ) is a versatile t e c h n i q u e which c o m p l e m e n t s o t h e r ion b e a m t e c h n i q u e s for s a m p l e analysis a n d n o n - d e s t r u c t i v e d e p t h profiling. It is t h e m o s t c o m m o n application of nuclear reaction analysis a n d h a s recently b e e n reviewed by Borderie (1980), D e c o n n i n c k et al (1981) a n d P e i s a c h (1981). R e a c t i o n s used for analysis are i n c l u d e d in C h a p t e r 14.4.1.

4.3.1. Isotopic Analysis Methods a. Experimental

Arrangement

G a m m a - r a y detectors, with associated shielding, are usually t o o large to be fitted w i t h i n a typical v a c u u m c h a m b e r for analysis w o r k a n d this is

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F i g . 4.13a. C o m p a c t c h a m b e r l a y o u t for m u l t i p l e d e t e c t o r s ; b . large solid angle a r r a n g e ­ m e n t for g a m m a - r a y d e t e c t i o n ; a n d c. e x t e r n a l b e a m s y s t e m for P I G M E a n a l y s i s .

not necessary since g a m m a - r a y a t t e n u a t i o n in a suitable w i n d o w m a t e r i a l (e.g. 1 m m Al) is negligible for g a m m a - r a y energies a b o v e 100 keV. However, d e t e c t o r efficiencies are relatively low a n d it is a d v a n t a g e o u s to use a small v a c u u m c h a m b e r so t h a t t h e d e t e c t o r d i s t a n c e can b e m i n i m i s e d . A c o m p a c t a r r a n g e m e n t for t h e use of u p t o five detectors can be seen in Fig. 4.13a (Giles a n d Peisach, 1976). A typical d e t e c t o r solid angle is 0.1 to 0.5 sr b u t this can b e increased to at least 2 sr (sample to detector distance 1 c m or even less) w i t h a n a r r a n g e m e n t such as t h a t shown in Fig. 4.13b. In this case, corrections m a y b e necessary for g a m m a - r a y a t t e n u a t i o n in t h e s a m p l e . A similar layout is also possible w h e n using a n external b e a m w h i c h is well suited t o P I G M E m e a s u r e ­ m e n t s (Fig. 4.13c). G a m m a - r a y s p r o d u c e d in t h e w i n d o w m a t e r i a l ( R a i t h et al, 1980) can b e m i n i m i s e d by choice of m a t e r i a l , nickel being particularly suitable. T h e choice of d e t e c t o r is discussed in Highlight 4.5. T h e d e t e c t o r angle is n o t critical p r o v i d e d t h a t differential cross-sections or g a m m a ray yields a p p r o p r i a t e to t h e specific e x p e r i m e n t a l g e o m e t r y are used in c o n c e n t r a t i o n calculations. A u n i f o r m angular d i s t r i b u t i o n of g a m m a rays is usually o b s e r v e d with a thick s a m p l e b u t d e v i a t i o n s can arise if t h e 4 i n a t e d by o n e r e s o n a n c e . Such a case is t h e large g a m m a - r a y yield is d2o m resonance in t h e M g ( p , p ' ) r e a c t i o n at 2.330 M e V . T h i s r e s o n a n c e i n t r o d u c e s a strong a s y m m e t r y i n t o t h e angular d i s t r i b u t i o n of t h e 1.368 M e V g a m m a - r a y for ion energies of 2.4 t o 2.5 M e V ( K e n n y et al, 1980). T h e lower t h e i n c i d e n t ion energy t h e fewer r e s o n a n c e s are i n v o l v e d in

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i o n - g a m m a reactions a n d n o n - u n i f o r m a n g u l a r d i s t r i b u t i o n s are m o r e likely to b e observed. T h e choice of s a m p l e angle affects t h e d e p t h of ion p e n e t r a t i o n a n d h e n c e t h e thickness of t h e layer w h i c h c a n b e analysed. Low detector efficiency a n d h e n c e low c o u n t rates can b e offset t o s o m e extent by a n increase in b e a m c u r r e n t p r o v i d e d t h a t s a m p l e d a m a g e d o e s n o t occur. F o r m e t a l s a n d o t h e r good t h e r m a l c o n d u c t o r s it is possible to use a b e a m c u r r e n t of t h e o r d e r of 1 μΑ w i t h o u t special cooling a r r a n g e m e n t s . By m o u n t i n g t h e s a m p l e o n a cooled backing, at least 10 μΑ of b e a m can b e used. Such high b e a m c u r r e n t s allow high sensitivities to b e achieved. F o r p o o r t h e r m a l c o n d u c t o r s , s a m p l e d a m a g e can b e m i n i m i s e d by m o u n t i n g a t h i n s a m p l e o n a cooled backing. E v e n so, P I G M E studies of biological m a t e r i a l s are necessarily l i m i t e d by t h e n e e d t o a v o i d s a m p l e d a m a g e — particularly w h e n using a m i c r o b e a m . O t h e r w i s e , t h e r e a r e few special r e q u i r e m e n t s for s a m p l e p r e p a r a t i o n a n d satisfactory analyses can usually b e m a d e of u n t r e a t e d a n d u n p o l i s h e d s p e c i m e n s as well as pressed p o w d e r s .

H I G H L I G H T 4.5 CHOICE OF DETECTOR T h e probability of g a m m a - r a y i n t e r a c t i o n s d e p e n d s o n v a r i o u s p o w e r s of t h e a t o m i c n u m b e r of t h e d e t e c t o r m a t e r i a l a n d t h e d e t e c t o r efficiency also d e p e n d s o n its size (see C h a p t e r 2). F o u r types of d e t e c t o r h a v e b e e n used in analytical applications, viz. • • • •

B i s m u t h G e r m a n a t e ( B G O ) — highest efficiency; p o o r e s t resol­ ution; S o d i u m I o d i d e ( N a l ) — high efficiency; p o o r resolution; L i t h i u m Drifted G e r m a n i u m (Ge(Li)) — low efficiency; good resolution; a n d Intrinsic G e r m a n i u m (IG) — lowest efficiency; best resolution.

C o m p a r i s o n s of pulse height spectra from N a l a n d G e ( L i ) d e t e c t o r s are p r e s e n t e d in Figure 2.16 a n d t h e reasons for choosing o n e for analytical work are illustrated by t h e following e x a m p l e s . F o r high sensitivity, a N a l d e t e c t o r (or B G O if available) c a n b e used p r o v i d e d t h a t t h e p o o r energy resolution d o e s n o t lead t o interference between peaks from g a m m a - r a y s e m i t t e d in different n u c l e a r reactions. T h e best k n o w n e x a m p l e is t h e use of a large v o l u m e N a l d e t e c t o r (at 19 l9 t h e 6.13, 6.92 a n d 7.12 least 10 to 15 c m d i a m e t e r a n d length) t o detect M e V g a m m a - r a y s from t h e F ( p , a y ) or *H( F,ay) reactions. T h e s e reactions h a v e a high cross-section a n d t h e c o m b i n e d c o u n t rate from all

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F i g . 4.14 G a m m a - r a y s p e c t r u m 3f r o m 2.5 M e V p r o t o n i r r a d i a t i o n of oil shale ( U S G S s t a n d a r d S G R 1 ) u s i n g a 120 c m G e ( L i ) at 135° a n d 155 m m f r o m t h e s a m p l e .

7

-2

t h r e e g a m m a - r a y s allows a fluorine d e t e c t i o n limit of 1 0 ~ g c m t o b e achieved ( M a l m q v i s t et al, 1982). B a c k g r o u n d r e d u c t i o n by using a plastic a n t i c o i n c i d e n c e d e t e c t o r is useful for large d e t e c t1o r5s a n d h a s b e e n applied for i m p r o v i n g t h e p e r f o r m a n c e w i t h t h e N ( p , a y ) reactions ( D a m j a n t s c h i t s c h et al, 1983). It can also b e a d v a n t a g e o u s t o use a t h i n filter (2 t o 5 m m P b ) t o preferentially r e d u c e t h e c o u n t r a t e from low energy g a m m a - r a y s so t h a t t h e b e a m c u r r e n t can b e increased t o give a greater c o u n t rate for t h e high energy g a m m a - r a y s of interest. A similar a p p r o a c h can b e a d o p t e d with a Ge(Li) d e t e c t o r by s u m m i n g all c o u n t s from, say, 5 M e V t o 7 M e V . T h i s h a s t h e a d v a n t a g e t h a t t h e high resolution s p e c t r u m can b e i n s p e c t e d t o verify t h a t n o a d d i t i o n a l interfering g a m m a - r a y s are present. H o w e v e r , Ge(Li) detec­ tors are m u c h smaller t h a n can b e readily o b t a i n e d using N a l o r B G O a n d they are p r e d o m i n a n t l y u s e d for detecting low energy g a m m a - r a y s ( u p t o the o r d e r of 1.5 M e V ) w h i c h are m o s t used for P I G M E analysis. A typical s p e c t r u m is s h o w n in Fig. 4.14 for 2.5 M e V p r o t o n i r r a d i a t i o n of oil shale ( U S G S s t a n d a r d S G R 1 ) . T h e p e a k s are labelled a c c o r d i n g t o t h e responsible target nuclide a n d t h1e9p e a k s a n d c o n t i n u u m at high energies are almost entirely from t h e F ( p , a y ) reaction. A c c u r a t e energy deter-

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m i n a t i o n a n d good s e p a r a t i o n of p e a k s for g a m m a - r a y s from different nuclear reactions are i m p o r t a n t — especially if i n c i d e n t energies a b o v e 3 M e V are used to increase g a m m a - r a y yields. Intrinsic G e ( I G ) d e t e c t o r s h a v e b e t t e r resolution t h a n Ge(Li) b u t they are only available with small v o l u m e s a n d so can only b e used to ad­ vantage for g a m m a - r a y energies u p t o a few h u n d r e d keV. H e a v y elements usually h a v e low-lying states w h i c h are readily excited by C o u l o m b excitation a n d it is s o m e t i m e s a d v a n t a g e o u s t o use a n I G detector for t h e i r d e t e r m i n a t i o n . F o r e x a m p l e , P I G M E yields from F e are relatively low a n d g a m m a - r a y s from m i n o r or trace e l e m e n t s in steels can readily b e o b s e r v e d using p r o t o n or alpha-particle i n d u c e d reactions. T h e i m p r o v e d resolution a n d lower c o n t i n u u m o b s e r v e d w i t h a small I G r a t h e r t h a n a Ge(Li) d e t e c t o r allows greater sensitivity a n d precision for the d e t e r m i n a t i o n of Cr, M n , M o , a n d W in steels (Peisach a n d G i h w a l a , 1981; G i h w a l a a n d Peisach, 1982).

b. Spectrum

Analysis

M a n y analytical p r o b l e m s involve simple g a m m a - r a y spectra w i t h a few well-separated peaks. T h e effects of m u l t i p l e scattering cause t h e c o n t i n u u m to b e higher at t h e low energy side of a p e a k t h a n j u s t a b o v e the peak, a n d this step function in c o n t i n u u m is difficult t o fit with a u t o m a t e d peak search p r o c e d u r e s . Since t h e step is c a u s e d by t h e s a m e g a m m a - r a y s as c o n t r i b u t e to t h e peak, t h e difference in c o u n t s s u m m e d over the c h a n n e l s c o n t a i n i n g t h e p e a k a n d in a suitable b a c k g r o u n d region j u s t a b o v e t h e p e a k is a g o o d m e t h o d of b a c k g r o u n d s u b t r a c t i o n . Sophisticated p e a k search a n d fitting r o u t i n e s are widely used for c o m p u t e r analysis of c o m p l e x pulse height spectra (see C h a p t e r 2). O v e r l a p p i n g p e a k s r e q u i r e a fit of G a u s s i a n o r a s y m m e t r i c p e a k functions a n d a suitable c o n t i n u u m function. P e a k p o s i t i o n s can b e d e t e r m i n e d t o a n accuracy of t h e o r d e r of 0.1 keV a n d p e a k areas o b t a i n e d which are r e p r o d u c i b l e t o b e t t e r t h a n 1%. H o w e v e r , different peak fitting m e t h o d s m a k e different a s s u m p t i o n s a b o u t t h e s h a p e of t h e c o n t i n u u m u n d e r a p e a k a n d h e n c e can give significantly different values of peak areas. It is m o s t i m p o r t a n t therefore to use t h e s a m e a l g o r i t h m for d e t e r m i n i n g p e a k areas d u r i n g d e t e c t o r calibration as in m e a s u r e m e n t s on u n k n o w n samples. T h e energy scale, i n c l u d i n g a n y non-linearity, can be d e t e r m i n e d using r a d i o a c t i v e sources such as those listed in T a b l e 2.9 or reaction g a m m a - r a y s (see C h a p t e r 14.4.3). Sources with calibrated emission rates are available for t h e d e t e r m i n a t i o n of d e t e c t o r efficiency as a function of g a m m a - r a y energy (see T a b l e 2.9).

180 J.R. Bird T A B L E 4.5a Commonly observed background radioactivity E

7

(keV) 129 186 239 227 285 296 328 339 352 463 478 511 583 609 666 727 769 795 861 911 935 969

Nuclide(s)

2 2 8 2 A2c 6 2 , R2 a 2 1 4 P2b , 2 8 Pb 2 A1c 4 Bi

22 1 42p b8 2 A2c 8 Ac

22 1 42p b8 7A c Be Annihilation

22 0 81j j 2 B1i 2 B1i 2 B1i 2 B2i

4 4 2 4 8

Ac

2 2 8 208JJ 2 A, c 4 2 B2i 8

E, (keV) 1120 1155 1238 1378 1408 1461 1509 1588 1592 1621 1630 1661 1693 1732 1764 1850 2103 2210 2448 2614

Nuclide(s)

2 1 2 B1i 2 B1i 2 B1i 2 B1i

4 4 4 4 4

Bi

24 01K4 2 B2i 8 Ac

208

B220 8i1T1 2 ) 2 B2i 8 2 A1c 4 2 B1i 4 2 B1i 4(se) 2 B1i 4 2 BIi 4

γ y

d

e

Bi

208

Β220 ί8 1Τ1?4 ) 2 B1i 4 Bi

2 0 8 g ^ 208-pj

Ac

d e = d o u b l e e s c a p e p e a k (Ε

(

— 1.022)

se = single e s c a p e p e a k ( E — 0.511)

Possible sources of interfering b a c k g r o u n d g a m m a - r a y s include n a t u r a l radioactivity in s u r r o u n d i n g m a t e r i a l s , r e a c t i o n s in collimators a n d o t h e r b e a m - l i n e e q u i p m e n t w h i c h m a y b e i r r a d i a t e d by t h e b e a m , re­ actions caused by n e u t r o n s p r o d u c e d d u r i n g i r r a d i a t i o n of t h e s a m p l e a n d collimator materials, a n d reactions p r o d u c e d by scattered ions. T h e first t w o c o n t r i b u t i o n s c a n b e r e d u c e d b y carefully p o s i t i o n e d lead shielding a n d t h e last o n e by using low yield m a t e r i a l s in c h a m b e r construction. If n e u t r o n s are p r o d u c e d d u r i n g s a m p l e i r r a d i a t i o n they n o t only constitute a r a d i a t i o n h a z a r d b u t they also create a high b a c k g r o u n d in N a l detectors because of N a a c t i v a t i o n a n d n e u t r o n c a p t u r e in i o d i n e . N e u t r o n s also cause increased b a c k g r o u n d in Ge(Li) detectors a n d 8 of resolution. 10 -2 r a d i a t i o n d a m a g e w h i c h causes a loss T h e onset of d a m a g e occurs for doses of t h e o r d e r of 1 0 t o 1 0 n e u t r o n s c m for small a n d large detectors respectively a n d can b e assessed by o b s e r v a t i o n of t h e

(

s

e

4. Nuclear Reactions

181

T A B L E 4.5b Neutron induced background gamma-rays E

Reaction

(keV)

7 3 m 7 G3e m 2 7G e 1Α1(η,α) 9 7F (5n , nm ') 6 G5 e 1C9u ( n j ) 7F (1n , nm ') 2 7G e 7Al(n,<*) 6 2 G0e (7n , n ' ) 7P b4( n , n ' ) 7G4e ( n , n ' ) 7G2e ( n , n ' ) 2G7e ( n , n ' ) 7A2l ( n , y ) 5G4e ( n , n ' ) 2F 7e ( n , p ) 7A4l ( n , n ' ) 7G3e ( n , n ' ) 7G2e ( n , a )

y

53 67 91 110 140 186 197 198 472 563(b) 570 596(b) 608(b) 690(b) 757(de) 834(b) 839 844 867(b) 885 894(b)

Origin

Ε

γ

(keV) Detector Detector System System Detector System System Detector System Detector Shield Detector Detector Detector System Detector System System Detector Detector Detector

Ge(n,n')

962 985 989 992 1014 1039(b) 1039 1115 1201 (de) 1238 1268(se) 1369 1464(b) 1698 1712(se) 1732 1779 1809 1811 2223 2243 2754

Reaction

6 3 2C7u ( n , n ' ) 2A7l ( n , p ) 6A4l ( n , n ' ) 2Z7n ( n , n ' ) 7A0l ( n , n ' ) 6G6e ( n , n ' ) 6Z 5n ( n , n ' ) !C u ( n , n ' ) 5H6( n , y ) 2F7e ( n , n ' ) 2A7l ( n , y ) 7Α1(η,α) 2 2G7e ( n , n ' ) !A l ( n , p ) 2Η7( η , 7 ) 2Α1(η,α) 7 2A7l ( n , y ) 5A6l ( n , d ) !F e ( n , n ' ) 2H7( n , y ) 2Α1(η,α) 7 Α1(η,α)

Origin System System System System System Detector System System Shield System System System Detector System Shield System System System System Shield System System

b — b r o a d high e n e r g y tail f r o m recoil a b s o r p t i o n d e — d o u b l e e s c a p e p e a k ( E — 1.022) y se — single e s c a p e p e a k (Ε — 0 . 5 1 1 )

γ

c u m u l a t i v e intensity of g a m m a - r a y s at 6 9 3 k e V w h i c h arise from inelastic scattering of n e u t r o n s (Wilenzick, 1972). Because of these p r o b l e m s , m o s t P I G M E analysis is d o n e w i t h ions a n d energies chosen to involve negligible n e u t r o n p r o d u c t i o n . Lists of b a c k g r o u n d g a m m a - r a y s a n d n e u t r o n i n d u c e d g a m m a - r a y s are given in T a b l e 4 . 5 . c. Determination

of

Concentration

P e a k areas from thick s a m p l e s w i t h k n o w n a m o u n t s of a p a r t i c u l a r nuclide can b e used t o d e r i v e e s t i m a t e s of c o n c e n t r a t i o n in a n u n k n o w n s a m p l e using E q u a t i o n ( 12.18) or t h e o t h e r m e t h o d s d e s c r i b e d in C h a p t e r 12.1. T h e s t o p p i n g p o w e r correction (Ss/S) r e q u i r e s t h e e v a l u a t i o n of a n integral of t h e cross-section as a function of i n c i d e n t energy ( E q u a t i o n s (12.11) a n d (12.12)) (or a s u m w h e n t h e cross-section involves a set of

182

J.R. Bird

ATOMIC NUMBER OF MATRIX

Fig. 4.15 Comparison of yield estimates using the surface energy (E^ approximation and the E,/2 rule as a percentage difference from the result of full integration.

well-separated resonances). Since t h e correction factor is close to u n i t y unless the s t a n d a r d a n d u n k n o w n s a m p l e s h a v e m a j o r e l e m e n t s w i t h very different Z, sufficient accuracy can b e a c h i e v e d with simple a p p r o x i ­ m a t i o n s . T h e s t o p p i n g p o w e r r a t i o calculated at t h e i n c i d e n t ion energy (surface a p p r o x i m a t i o n ) can lead to errors greater t h a n 1% whereas t h a t calculated at an energy for w h i c h t h e g a m m a - r a y yield is one-half t h a t at the incident energy is usually a c c u r a t e to m u c h b e t t e r t h a n 1% (Fig. 4.15). A reliable knowledge of t h e thick target yield curve is r e q u i r e d to d e t e r m i n e the half-yield energy a n d an iterative a p p r o a c h m u s t b e u s e d to allow for t h e effect of t h e sought e l e m e n t s o n s t o p p i n g power. T h i s m e t h o d is a d e q u a t e for m o s t w o r k b u t t h e 'effective m e a n energy' m e t h o d (Ishii et al, 1978a,b) involves negligible error w h a t e v e r t h e m a t r i x c o m p o s i t i o n , a l t h o u g h it requires detailed i n f o r m a t i o n o n t h e relevant yield curves a n d reliable s t o p p i n g p o w e r d a t a . It s h o u l d b e n o t e d t h a t the a p p r o x i m a t i o n s i n t r o d u c e systematic errors r a t h e r t h a n r a n d o m errors. A possible i m p o r t a n t source of systematic errors is s a m p l e i n h o m ogeneity. M o s t of t h e yield c o m e s from t h e first p a r t of t h e ion range where t h e ion energy is highest. T h e v o l u m e analysed is typically of t h e

3 2

3

4. Nuclear Reactions

183

o r d e r of 1 0 d c m (d = b e a m d i a m e t e r in c m ) for 2 to 3 M e V p r o t o n s a n d less for h e a v i e r ions. I n h o m o g e n e i t i e s w i t h d i m e n s i o n s of t h e o r d e r of (100 d) μτη will h a v e a significant effect o n o b s e r v e d c o n c e n t r a t i o n s . Lateral i n h o m o g e n e i t i e s can b e easily checked by changing t h e b e a m p o s i t i o n a n d observing t h e effect o n scatter of results (Giles a n d Peisach, 1979). T h e presence of d e p t h i n h o m o g e n e i t i e s can b e c h e c k e d by changing t h e ion type or energy or by using several g a m m a - r a y s from t h e s a m e target nuclide w h i c h h a v e different yield curves. d. Isotope

Ratios

Isotopes of o n e e l e m e n t h a v e very different nuclear p r o p e r t i e s w h i c h can 13 2 b e exploited for t h e m e a s u r e m1 e n0nt of isotope ratios. E x a m p l e s of 1such 5e n4t of B / B (Olivier a n d Peisach, 1985), C / C w o r k are t h e m e a s u r e1m1 (Ricci, 1971) a n d N / N ( X e n o u l i s a n d D o u k a , 1979). T h e low a b u n ­ d a n c e isotopes c a n b e d e t e c t e d at o r a b o v e n a t u r a l levels b y t h e choice of high yield nuclear reactions b u t , even so, t h e statistical accuracy in ion b e a m analysis is s e l d o m b e t t e r t h a n 1% a n d n o a t t e m p t h a s b e e n m a d e t o observe t h e small changes of a b u n d a n c e which are of m a j o r i m p o r t a n c e in e n v i r o n m e n t a l a n d o t h e r studies.

4.3.2 Depth Profiling It is useful to distinguish t w o types of g a m m a - r a y t r a n s i t i o n i n v o l v e d in nuclear reactions. P r i m a r y g a m m a - r a y s are those w h i c h are e m i t t e d as a t r a n s i t i o n from a highly excited state in w h i c h a c o m p o u n d nucleus is 2 0 state. A n e x a m p l e is t h e g a m m a - r a y originating f o r m e d to a low lying n e a r t h e t o p of t h e N e level d i a g r a m in Fig. 4 . 1 . T h e energy of p r i m a r y g a m m a - r a y s changes as t h e i n c i d e n t ion energy is c h a n g e d a n d this can b e exploited for d e p t h profiling by t h e energy s p e c t r u m m e t h o d ( C h a p t e r 1 6 states such 12.2). Secondary g a m m a - r a2y s0 are e m i t t e d by low lying excited as the 1.632 M e V level in N e or t h e 6.14 M e V level in 0 (see Fig. 4.1). T h e energy of s e c o n d a r y g a m m a - r a y s d o e s n o t change with t h e i n c i d e n t ion energy a n d they c a n n o t b e used for energy s p e c t r u m profiling. 1 e2n t s of1 t h6e energy of p r i m a r y g a m m a - r a y s h a v e b e e n1 2used Measurem 6 A b r o a d r e s o n a n c e in C(p,y) in profiling C a n d 0 via (p,y) 1reactions. occurs n e a r 0.45 M e V a n d 0 h a s a s m o o t h l y v a r y i n g cross-section a b o v e 1 M e V . T h e o b s e r v e d g a m m a - r a y p e a k s h a p e can b e c o n v e r t e d to a d e p t h profile using t h e m e t h o d s d e s c r i b e d in Highlight 4 . 3 . H o w e v e r , yields from these reactions are relatively low a n d little use h a s b e e n m a d e of this t e c h n i q u e . N a r r o w r e s o n a n c e s a r e a c o m m o n feature of m a n y g a m m a - r a y p r o d u c i n g reactions a n d either p r i m a r y or s e c o n d a r y g a m m a -

184

J.R.

Bird

rays can be used in r e s o n a n c e s c a n n i n g or yield curve unfolding ( C h a p t e r 12.2). Profiling by r e s o n a n c e s c a n n i n g is described in Highlight 4.6 a n d s o m e u n u s u a l effects w h i c h m u s t b e k e p t in m i n d are discussed in Highlight 4.7.

H I G H L I G H T 4.6 P R O F I L I N G BY R E S O N A N C E S C A N N I N G A list of resonances used for d e p t h profiling is given in C h a p t e r 14.4.2. T h e e q u i p m e n t r e q u i r e d for r e s o n a n c e s c a n n i n g is t h e s a m e as described in Section 4.3.1a plus a suitable system for frequent changes in t h e incident ion energy. In o r d e r to take a d v a n t a g e of n a r r o w r e s o n a n c e s to achieve good d e p t h resolution, it is necessary to use a n i n c i d e n t b e a m with a small energy s p r e a d — p r e f e r a b l y of t h e o r d e r of 100 eV b u t usually n o greater t h a n 1 t o 3 keV. Stabilisation a n d a u t o m a t e d b e a m energy scanning are described in C h a p t e r 2. T h e use of a large N a l d e t e c t o r is a d v a n t a g e o u s if t h e g a m m a - r a y resolution is a d e q u a t e , in o r d e r to speed u p d a t a taking a n d r e d u c e t h e total t i m e to c o m p l e t e a profile (e.g. Lenz etal., 1987). T h e p r o c e d u r e for profiling by energy s c a n n i n g is to c o m m e n c e i r r a d i a t i o n of the s a m p l e with a b e a m energy w h i c h is j u s t below t h a t of a resonance with a large p e a k cross-section. T h e yield of g a m m a - r a y s , which are k n o w n to b e strongly excited at t h e r e s o n a n c e , is c o u n t e d for a fixed dose (e.g. 1 //C or m o r e ) . T h e b e a m energy is t h e n raised step by step a n d the yield m e a s u r e d at each interval to o b t a i n a yield curve as a function of incident energy. T w o e x a m p l e s are s h o w n in Fig. 4.16 w h e r e Τ

1

1

1

1

r

DEPTH (μπι)

9 D e p t h 1profile

Fig. 4.16a. for F diffusion i n t o d e n t a l e n a m e l m e a s u r e d u s i n g t h e 8 7 2 6K e V H( Li,ay) r e s o n a n c e in F ( p , a y ) ; b . H profiles in h y d r a t e d glass m e a s u r e d u s i n g t h e r e a c t i o n at 6.400 M e V .

l

4. Nuclear Reactions

0

1

0

0.4

0.8

1.2

185

1.6

DEPTH (μπη)

Fig. 4.17 T h e c h a n g e in s h a p e of t h e d e p t h r e s o l u t i o n f u n c t i o n as a f u n c t i o n of d e p t h c a u s e d b y energy straggling of t h e i n c i d e n t i o n s .

t h e i n c i d e n t energy scale h a s b e e n c o n v e r t e d t o a d e p t h scale w i t h t h e res­ o n a n c e energy c o r r e s p o n d i1n g9 to zero d e p t h . Fig. 4.16a shows t h e use of t h e 872 keV r e s o n a n c e in F (p,ay) t o d e t e r m i n e t h e d e p t h d i s t r i b u t i o n of F in d e n t a l e n a m e l (Bodart a n d G h o o s , 1980). T h e d e p t h scale is o b t a i n e d from t h e change in b e a m energy w i t h d e p t h , E q u a t i o n (12.30), which requires a knowledge of t h e m a j o r e l e m e n t c o m p o s i t i o n of t h e s a m p l e in o r d e r to calculate t h e s t o p p i n g power. A n a p p r o x i m a t e F d e p t h d i s t r i b u t i o n is o b t a i n e d from c(x) = KY 3(El)Sï

(4.8 )

where Y 3(EX) i s t h e m e a s u r e d yiel d curv e a n d Κ c a n b e o b t a i n e d by calibration with s t a n d a r d s a m p l e s such as t h i n layers of p u r e e l e m e n t s , c o m p o u n d or i m p l a n t e d ions of k n o w n energy a n d dose. T h e s e c o n d e! x a 1m p5l e is of1Η2 profiles, m e a s u r e d with t h e 6.400 M e V r e s o n a n c e in t h e H ( N , a y ) C r e a c t i o n (Lanford, 1978). Fig. 4.16b shows a n u m b e r of profiles w h i c h define t h e thickness of t h e h y d r a t i o n layer in o b s i d i a n for increasing h y d r a t i o n t i m e s . In o r d e r to o b t a i n a c c u r a t e d e p t h i n f o r m a t i o n it is necessary to take into a c c o u n t t h e change in s t o p p i n g p o w e r with ion energy a n d t h e effects of energy straggling o n d e p t h resolution a n d profile s h a p e . T h e effects of straggling are s h o w n b y t h e change in s h a p e of profiles calculated for t h e 340 keV r e s o n a n c e in F at v a r i o u s d e p t h s (Fig. 4.17, M a u r e l et al, 1982). F o r d e p t h s u p to t h e o r d e r of 10 t o 20 n m , V a v i l o v d i s t r i b u t i o n s m u s t b e used b u t at greater d e p t h s t h e straggling d i s t r i b u t i o n can b e a s s u m e d to b e G a u s s i a n ( C h a p t e r 14.2).

186 J.R. Bird H I G H L I G H T 4.7 UNUSUAL EFFECTS IN DEPTH PROFILING

High resolution (i.e. near-surface) profiling can b e subject to a n u m b e r of processes which i n t r o d u c e u n e x p e c t e d s t r u c t u r e i n t o t h e d e p t h profile. A 'surface' peak is often o b s e r v e d b e c a u s e of t h e presence of a t o m s a d s o r b e d at the s a m p l e surface, especially for such c o m m o n e l e m e n t s as H , C a n d O. A n a d d i t i o n a l c o n t r i b u t i o n to a p e a k at zero d e p t h c o m e s from the Lewis effect (Fig. 4.18). T h i s arises b e c a u s e t h e i n c i d e n t ion loses energy in finite a m o u n t s ( d e p e n d i n g o n t h e angle of small-angle scattering events) so t h a t , even for a m o n o e n e r g e t i c b e a m , less t h a n 100% of t h e ions h a v e p a r t i c u l a r value of energy o n c e s o m e energy loss h a s t a k e n place. T h e Lewis effect is only o b s e r v e d if t h e r e s o n a n c e w i d t h a n d e x p e r i m e n t a l resolution are of t h e o r d e r of 100 eV or less. T h e z e r o - d e p t h peak can b e r e p r o d u c e d by calculations b a s e d o n stochastic theories of energy loss (Maurel et al, 1982) b u t it m a y b e ignored in t h e m e a s u r e ­ m e n t of d e p t h profiles below t h e surface. C h a n n e l i n g (see C h a p t e r s 1 a n d 6) can also modify the rate of energy loss if the s a m p l e is crystalline. It is c o m m o n , especially in s e m i c o n d u c ­ tor studies, to p r e p a r e a s a m p l e with a crystal axis colinear with t h e surface n o r m a l a n d to m o u n t s a m p l e s n e a r p e r p e n d i c u l a r to t h e i n c i d e n t b e a m for nuclear reaction analysis. C h a n n e l i n g is likely to affect observed d e p t h profiles in these c i r c u m s t a n c e s a n d can b e exploited in a t o m location studies (see C h a p t e r 6). A rule-of-thumb, w h i c h is useful b u t n o t guaranteed, is t o incline such s a m p l e s at 7° to t h e direction of t h e incident b e a m in o r d e r to o b t a i n results which a p p r o x i m a t e t h e case of a r a n d o m direction of incidence. F o r a b e t t e r u n d e r s t a n d i n g of t h e effects of crystallinity it is necessary to carry o u t a series of m e a s u r e m e n t s with different angles of incidence. If a n insulating s a m p l e b e c o m e s positively charged d u r i n g irradi­ ation, it will cause deceleration of t h e i n c i d e n t ions with a r e d u c t i o n in their effective energy. T h i s will lead to a n a p p a r e n t shift in t h e r e s o n a n c e energy a n d a n incorrect d e p t h scale. T h e m o s t serious effect of this k i n d is p r o d u c e d by sparking w h i c h will change t h e effective energy r a n d o m l y . Since surface p o t e n t i a l s of t h o u s a n d s of volts can easily occur, a n y a t t e m p t to carry o u t d e p t h profiling with good resolution can b e completely destroyed by sparking. V a r i o u s m e t h o d s for p r e v e n t i n g surface charging are discussed in C h a p t e r s 2 a n d 3. Finally, a n y d e p a r t u r e from a s m o o t h flat surface can effect d e p t h profiling. If ions are i n c i d e n t n o r m a l t o t h e s a m p l e surface, a profile will

4. Nuclear Reactions

187

1170 1180 INCIDENT ENERGY(keV)

1 8 D e p t h profiles of t h i n T a o x i d e r a t i o s m e a s u r e d u s i n g t h e 1167 k e V r e s o n a n c e in F i g . 4.18 t h e 0 ( p , y ) r e a c t i o n . T h e p e a k at low e n e r g i e s is e v i d e n c e for t h e Lewis effect. b e o b t a i n e d w h i c h describes successive layers parallel t o t h e surface even if this is n o t flat. F o r o t h e r angles of i n c i d e n c e , surface r o u g h n e s s or t o p o g r a p h y will cause a w o r s e n i n g of d e p t h resolution ( C h a p t e r 12.2).

a. Multiple

Resonances

If t h e i n c i d e n t ion energy is s c a n n e d o v e r a range c o n t a i n i n g m o r e t h a n o n e resonance, t h e n o r m a l m e t h o d for calculating a d e p t h profile is subject t o error. T h e c o n t r i b u t i o n from successively higher energy resonances can b e e s t i m a t e d from a knowledge of t h e d e p t h d i s t r i b u t i o n o b t a i n e d at lower energies a n d suitable corrections can b e m a d e t o e x t e n d the d e p t h profile to greater d e p t h s , E q u a t i o n (12.44). V a r i o u s n u m e r i c a l m e t h o d s h a v e b e e n d e v e l o p e d for this p u r p o s e b u t , in practice, profiling is generally n o t c o n t i n u e d far b e y o n d t h e energy difference b e t w e e n adjacent resonances. H o w e v e r , profiles of F in teeth h a v e b e e n m e a s u r e d o n 10 pm layers by applying corrections to t h e yield c u r v e for p r o t o n en­ ergies from 0.8 t o 1.5 M e V ( K r e g a r etal., 1979). G r e a t e r thicknesses were studied by t h e r e m o v a l of successive 10 pm layers a n d r e p e a t e d profile determination. b. Yield Curve

Unfolding

If t h e r e are m a n y r e s o n a n c e s in t h e r e a c t i o n cross-section, t h e o b s e r v e d P I G M E yield as a function of i n c i d e n t ion energy is a series of steps. If t h e cross-section is a s m o o t h function of energy, t h e n t h e yield c u r v e is also s m o o t h . T h e d e c o n v o l u t i o n of energy spectra a n d yield curves is discussed in C h a p t e r 12.2 b u t a large c o m p u t e r is r e q u i r e d a n d , to d a t e , t h e r e h a s b e e n little use of this a p p r o a c h for d e p t h profiling — s p e c t r u m s i m u l a t i o n being t h e preferred a p p r o a c h .

188

J.R. Bird

4.3.3 Performance a. Detection

Limits

S o m e typical values of d e t e c t i o n limits for P I G M E analysis are p l o t t e d in Fig. 4.19 showing t h e favourable p e r f o r m a n c e for m a n y isotopes with A < 30, Ζ < 15 a n d useful p e r f o r m a n c e for higher Z. Such d e t e c t i o n limits are illustrative only since, in practice, they d e p e n d o n d e t e c t o r g e o m e t r y a n d efficiency a n d o t h e r e x p e r i m e n t a l factors including t h e possible effects of interfering reactions. S o m e of t h e factors t h a t distinguish t h e P I G M E m e t h o d are: • • •

•

• •

s i m u l t a n e o u s m e a s u r e m e n t s can be m a d e of g a m m a - r a y s from a n u m b e r of nuclides; cross-sections are highest for light isotopes (A < -1 30) so t h a t these can be d e t e r m i n e d with g o o d sensitivity (1 μ% g or less) t h e yield from C o u l o m b excitation of m a n y h e a v y e l e m e n t s are sufficiently high t h a t these can b e d e t e r m i n e d if light e l e m e n t s are not present in high c o n c e n t r a t i o n s ; low yield m a t e r i a l s such as C, C o , N i a n d P b can b e used in t h e target c h a m b e r to m i n i m i s e g a m m a - r a y s p r o d u c e d by scattered ions; m a n y reactions h a v e n a r r o w r e s o n a n c e s w h i c h are suitable for d e p t h profiling with a resolution of 1 t o 10 n m ; a n d T h e observed yield is n o t strongly affected by v a r i a t i o n in surface angle or surface roughness w h i c h are i m p o r t a n t for low energy X rays.

b. Proton-Gamma

Analysis

P r o t o n b e a m s h a v e b e e n widely used for t h e d e t e r m i n a t i o n of o n e or m o r e isotopes of e l e m e n t s from Li to CI (although n o t all simultaneously) a n d m a n y heavier e l e m e n t s . F o r p r o t o n energies below 1 M e V , C o u l o m b excitation cross-sections are low a n d only light nuclides with low energy resonances give reasonable g a m m a - r a y yields. In this region, t h e p r o t o n energy can often b e chosen to o p t i m i s e m e a s u r e m e n t s o n a Ip a2r t i c u l a rI 6 nuclide. F o r e x a m p l e 500 k e V p r o t o n s give a good yield from C a n d 0 a n d this is suitable for t h e i r d e t e r m i n a t i o n in biological m a t e r i a l s ( D e m o r t i e r , 1974). S o m e w h a t higher energies (e.g. 1.8 M e V ) are n e e d e d for Ν d e t e r m i n a t i o n . F o r p r o t o n s with energies from 1 t o 3 M e V , t h e highest yields are from Li, B, F , N a a n d Al a n d these e l e m e n t s can b e d e t e r m i n e d simultaneously in m a n y cases. F o r e x a m p l e , a precision of b e t t e r t h a n 1%

4. Nuclear Reactions

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Fig. 4.19 E s t i m a t e d d e t e c t i o n l i m i t s in P I G M E a n a l y s i s u s i n g 2.5 M e V p r o t o n s ( D e c o n ­ n i n c k et al, 1981), 4.5 M e V p r o t o n s ( G i h w a l a et al, 1982), 3.5 M e V t r i t o n s ( B o r 3 der5 ie and B a r r a n d o n , 1978), 3.5 M e V a l p h a s ( B o r d e r i e a n d B a r r a n d o n , 1978) a n d 55 M e V C l i o n s ( B o r d e r i e et al, 1979).

can be o b t a i n e d in F a n d N a d e t e r m i n a t i o n w i t h a m e a s u r i n g t i m e of a few m i n u tle s . F l u o r i n e is of p a r t i c u l a r interest, w i t h very high sensitivity (0.1 pg g ~ ) being available for a n e l e m e n t w h i c h is difficult t o d e t e r m i n e by n o n ion b e a m t e c h n i q u e s . T h e s i m u l t a n e o u s use of P I X E d a t a a d d s a n o t h e r 20 or m o r e e l e m e n t s in m a n y a p p l i c a t i o n s b u t , e v e n so, t h e P I G M E d a t a r e m a i n valuable for t h e light e l e m e n t s a n d b e c a u s e of t h e i r precision. At energies a b o v e 3 M e V , t h e g a m m a - r a y yield from m e d i u m a n d heavy e l e m e n t s begin to c o m p e t e w i t h t h e light e l e m e n t s . F o r e x a m p l e , B, F, N a , Mg, Al, Si a n d C u h a v e b e e n d e t e r m i n e d in p o t s h e r d s at 4 M e V (Peisach et al, 1982). c. Deuteron-Gamma

Reactions

G a m m a - r a y s are p r o d u c e d by d e u t e r o n i r r a d i a t i o n of m o s t nuclides although light nuclides h a v e t h e highest cross-sections. T h i c k s a m p l e

190 J.R. Bird

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F i g . 4.20 I o n - n e u t r o n a n a l y s i s e q u i p m e n t , a. s i m p l e c o n f i g u r a t i o n for n e u t r o n c o u n t i n g ; b . large solid angle n e u t r o n c o u n t i n g s y s t e m ; c. time-of-flight m e a s u r e m e n t of n e u t r o n energies.

yields increase rapidly w i t h d e u t e r o n energy, slowing d o w n s o m e w h a t for light nuclides a n d energies a b o v e 3 M e V . In principle, therefore, d e u t e r o n i n d u c e d g a m m a - r a y e m i s s i o n could p r o v i d e a versatile m u l t i ­ element capability if it was n o t for t h e associated n e u t r o n flux from (d,n) reactions.

3 d. Triton and He

Reactions

T h e highest g a m m a - r a y yields from t r i t o n i r r a d i a t i o n are from Li, C, Ο a n d F . E s t i m a t e d d e t e c t i o n limits for these a n d o t h e r e l e m e n t s are included in Fig. 4.19. O n l y Ο h a s b e e n analysed with a t r i t o n b e a m — taking a d v a n t a g e of t h e high yield of 937, 10422a n d 1982 keV g a m m a rays to achieve a d e t e c t i o n limit of 0.13 pg c m " of oxygen for 1.9 M e V 3 triton i r r a d i a t i o n of steel (Peisach, 1972). G a m m a rays from H e i r r a d i a t i o n of Li, Be, B, C a n d Ο h a v e b e e n assessed ( D e c o n n i n c k a n d D e m o r t i e r , 1973) b u t t h e i r usefulness for analysis of a range of s a m p l e materials has n o t b e e n investigated. e. Alpha-Induced

Gamma

Emission

T h e g a m m a - r a y yields listed in C h a p t e r 14.4 show t h a t t h e sensitivity of a l p h a - i n d u c e d g a m m a - r a y e m i s s i o n is particularly good for Li, Be, Β, N , F a n d N a . A n u m b e r of m e d i u m a n d h e a v y e l e m e n t s also give r e a s o n a b l e

4. Nuclear Reactions

191

sensitivity, including M n , T a , Br, As, R e , R h , V, Ir, W , Ag, G e a n d T i in t h a t order. O n t h e o t h e r h a n d , essentially n o g a m m a - r a y s are o b s e r v e d form C, S, Ca, C o , N i , G a , Sr, Y, N b , In, Sn, Ba, La, Ce, Pr, N d , P b a n d Bi a n d these are favourable m a t r i x m a t e r i a l s in w h i c h o t h e r e l e m e n t s can readily b e detected. F o r e x a m p l e , successful m e a s u r e m e n t s h a v e b e e n m a d e of a n u m b e r of m i n o r e l e m e n t s in steels ( G i h w a l a a n d Peisach, 1980). A n a d d i t i o n a l a d v a n t a g e of a l p h a s is t h a t few high energy g a m m a rays are p r o d u c e d w h i c h increase t h e C o m p t o n c o n t i n u u m in t h e lower energy regions of t h e g a m m a - r a y spectra. A n i m p o r t a n t feature of t h e P I G M E m e t h o d is t h e d e p t h to w h i c h t h e i n c i d e n t ions p e n e t r a t e before the g a m m a - r a y yield b e c o m e s insignificant. In gold this d e p t h is 20 μτη for 3 M e V p r o t o n s a n d only 3 μτη for 3 M e V alpha-particles. T h i s h a s b e e n exploited by Basutcu (1980) to investigate surface e n r i c h m e n t in coins a n d o t h e r objects c o n t a i n i n g Au, Ag a n d C u . C o p p e r is preferen­ tially r e m o v e d from t h e surface region of A u a n d Ag alloys a n d Ag is also preferentially r e m o v e d from A u alloys. T h e yield of silver g a m m a - r a y s from t w o i r r a d i a t i o n s w i t h different ions allows t h e d e t e r m i n a t i o n of t h e degree of surface e n r i c h m e n t or d e p l e t i o n . /

Heavy Ion-Gamma

Analysis

T h e m o s t n o t a b l e a p p l i c a t i o n of h e a v y ion i n d u c e d g a m m a 7 - r a y1 e m i1s s5i o n 1 9 has b e e n in t h e d e p t h profiling of h y d r o g e n using b e a m s of L i , *B, N or F ions (see Fig. 4.16b). Analysis of h e a v i e r isotopes c a n b e carried o u t with heavy ions by exploiting C o u l o m b excitation (Borderie et al, 1979).

4.4 ION-NEUTRON REACTIONS N e u t r o n s are p r o d u c e d in m a n y n u c l e a r r e a c t i o n s b u t are usually ignored r a t h e r t h a n exploited. Like g a m m a - r a y s , n e u t r o n s emerge from s a m p l e a n d s a m p l e c h a m b e r w i t h o u t energy loss a n d usually w i t h only very m i n o r loss in intensity. S a m p l e analysis can b e carried o u t b y t w o methods: i. by c o u n t i n g t h e n u m b e r of n e u t r o n s p r o d u c e d — a m e t h o d w h i c h is useful if it is k n o w n t h a t only o n e , n u c l i d e is c o n t r i b u t i n g t o t h e n e u t r o n yield; a n d ii. by m e a s u r i n g n e u t r o n energy spectra w h i c h c a n reveal t h e existence of different energy g r o u p s from o n e or m o r e reactions. Energy spectra also define d e p t h profiles since t h e n e u t r o n energy is d e p e n d e n t o n t h e energy of t h e i n c i d e n t ion at t h e d e p t h at w h i c h t h e r e a c t i o n occurs, t h r o u g h t h e usual k i n e m a t i c e q u a t i o n s (see C h a p t e r 1). A list of i o n - n e u t r o n r e a c t i o n s u s e d for s a m p l e

192

J.R. Bird analysis a n d d e p t h profiling a n d relevant d a t a are i n c l u d e d in C h a p t e r 14.4.

4,4.1 Methods a. Neutron

Yield

T h e yield of n e u t r o n s from a n i o n - i n d u c e d nuclear r e a c t i o n can be m e a s u r e d by placing a h y d r o g e n o u s scintillator(plastic, l i q u i d o r a crystal scintillator such as stilbene) n e a r t h e s a m p l e c h a m b e r (Fig. 4.20a). A suitable range of pulse heights is selected for c o u n t i n g , d e p e n d i n g o n t h e Q-value of t h e r e a c t i o n of interest a n d t h e k i n e m a t i c s . A pulse s h a p e d i s c r i m i n a t o r m a y b e used t o h e l p reject b a c k g r o u n d pulses c a u s e d by g a m m a - r a y i n t e r a c t i o n s in t h e scintillator. F o r a t h i n s a m p l e , t h e c o n c e n t r a t i o n of t h e i s o t o p e responsible for n e u t r o n p r o d u c t i o n is given by E q u a t i o n s (12.7) a n d (12.8). F o r a t h i c k s a m p l e E q u a t i o n s (12.11) a n d (12.12) m u s t b e used. 7 F o r e x a m p l e , t h e high cross-section of t h e L i ( p , n ) r e a c t i o n (20 t o 80 m b / s r a b o v e 2.14 M e V ) can b e u s_1 ed to determine the lithium content of a s a m p l e at levels d o w n t o 1 //g g p r o v i d e d t h a t o t h e r n u c l i d e s w i t h thresholds below 2 M e V are n o t p r e s e n t in large q u a n t i t-1 i e s . T h e Li c o n t e n t of d i a m o n d h a s b e e n s h o w n t o b e less t h a n 2 μ% g (Sellschop et al, 1978) a n d t h e d e p t h d i s t r i b u t i o n of Li in glass h a s b e e n d e t e r m i n e d by t h e wedge s c a n n i n g m e t h o d (see C h a p t e r 1.7) w i t h 2 M e V p r o t o n s ( P o m o r s k i et al, 1976). T h e efficiency of n e u t r o n d e t e c t o r s d e p e n d s o n t h e size a n d type of scintillator u s e d a n d is generally in t h e range from 5 t o 20%. H o w e v e r , if placed o u t s i d e t h e s a m p l e c h a m b e r , t h e solid angle m a y b e q u i t e small. H i g h e r c o u n t i n g rates can b e a c h i e v e d b y s u r r o u n d3i n g t h e c h a m b e r w i t h a large d e t e c t o r assembly such as a set of B F 3 o r H e c o u n t e r s in a large paraffin m o d e r a t o r (Fig. 4.20b). T h e d e t e c t i o n efficiency, i n c l u d i n g solid angle, for such a system can b e at least 10% a n d this gives g o o d sensitivity for t h e d e t e r m i n a t i o n of n u c l i d e s w i t h high r e a c t i o n cross-sections. I n this case E q u a t i o n (12.1), i n v o l v i n g t h e total cross-section r a t h e r t h a n t h e 9 differential cross-section for a specific d e t e c t o r angle, is used. 1 3 Th1 0 1 7nuclides n e only w2i t6h p o s i t i v e (Rvalues for (α,η) r e a c t i o n s are B e , C , B , 0 , B a n d M g in d e s c e n d i n g o r d e r . T h e p r o d u c t n e u t r o n energies follow t h e s a m e s e q u e n c e a n d this can b e exploited for essentially interference-free d e t e r m i n a t i o n of Be. F o r a n i n c i d e n t alphaparticle energy of 2.69M e V , chosen t o use a local m a x i m u m of 30 m b / s r in t h e cross-section of B e ( a , n ) r e a c t i o n at 0°, n e u t r o n s from o t h e r nuclides can be e l i m i n a t e d w i t h a d i s c r i m i n a t o r setting of 4.75 M e V . C o n c e n -

-1

4. Nuclear Reactions

193

t r a t i o n s of Be d o w n t o 2 0 0 /zg g can b e readily d e t e r m i n e d by n e u t r o n c o u n t i n g a n d diffusion profiles can b e d e t e r m i n e d by m i c r o9b e a m scanning ( M c M i l l a n et al, 1978). At t h i s b e a m energy, t h e B e ( d , p ) reaction is m o r e sensitive b u t subject t o interference from n u m e r o u s light nuclides. T h e selectivity of t h e (α,η) r e a c t i o n is of c o n s i d e r a b l e v a l u e in a v o i d i n g p r o b l e m s from interference b1y 3C a n d o t h e r e l e m e n t s . A lower d i s c r i m i n a t o r setting w o u l d p e r m i t C d e t e r m i n a t i o n a n d profiling in the s a m e way p r o v i d i n g t h a t Be was k n o w n t o b e a b s e n t or d e m o n s t r a t e d to b e absent with higher d i s c r i m i n a t o r l r3u n s . A s o m e w h a t higher alphaparticle energy i m p r o v e s t h e yield in C m e a s u r e m e n t s . A n i m p o r t a n t feature of n e u t r o n c o u n t i n g is t h e o b s e r v a t i o n of accurately defined t h r e s h o l d s . R e a c t i o n s w i t h negative Q-values c a n only take place w h e n t h e i n c i d e n t ion energy is greater t h a n t h e t h r e s h o l d value given by E q u a t i o n (1.27), T a b l e 1.3. If t h e p r o d u c t n u c l i d e is f o r m e d in a n excited state t h e β - v a l u e is correspondingly m o r e negative a n d t h e t h r e s h o l d energy is even higher. F o r b e a m energies j u s t a b o v e threshold, c o n s e r v a t i o n of m o m e n t u m r e q u i r e s t h a t n e u t r o n s c a n only b e emitted within a narrow cone about the incident b e a m direction, where t h e cone angle is given b y E q u a t i o n ( 1.29), T a b l e 1.3. As t h e b e a m energy is increased, t h e c o n e angle increases until, at energy Emax (given by E q u a t i o n (1.28), T a b l e 1.3) all angles of e m i s s i o n are possible. T h e 0° n e u t r o n yield increases d r a m a t i c a l l y a b o v e t h e t h r e s h o l d energy a n d this can b e exploited to identify t h e nuclide responsible for n e u t r o n emission, the c o n c e n t r a t i o n of t h a t nuclide a n d , in suitable cases, its d e p t h d i s t r i b u t i o n (from t h e n e u t r o n energy d i s t r i b u t i o n ) . T h e k i n e m a t i c c o l l i m a t i o n effect is stronger for h e a v y ion i n d u c e d reactions w h i c h can b e exploited for light e l e m e n t d e t e r m i n a t i o n . A list of t h r e s h o l d energies a n d n e u t r o n energies is given in T a b l e 4.6 for all p r o t o n a n d a l p h a i n d u c e d reactions w i t h Ζ < 3 3 , Q < 3 M e V . O n l y s o m e of these reactions h a v e b e e n used in analysis b u t t h e i n f o r m a t i o n c a n b e used in considering possible c o m p e t i n g reactions a n d r a d i a t i o n h a z a r d s . b. Neutron

Energy

A n e u t r o n energy s p e c t r u m c a n b e o b t a i n e d b y unfolding t h e pulse height response function of a h y d r o g e n o u s scintillator from t h e o b s e r v e d pulse height s p e c t r u m . H o w e v e r , t h e m o s t c o m m o n a p p r o a c h is t o m e a s u r e the time-of-flight of each n e u t r o n . A n e u t r o n d e t e c t o r is placed at a suitable distance a n d angle relative to t h e d i r e c t i o n of t h e ion b e a m (Fig. 4.20c). N e u t r o n a n d g a m m a - r a y shielding is placed so as to m i n i m i s e t h e detector b a c k g r o u n d . A pulsed ion b e a m is u s e d w h i c h h a s t h e smallest possible pulse w i d t h (e.g. 1 ns or less) a n d a r e p e t i t i o n r a t e selected t o suit

194 J.R. Bird T A B L E 4.6 T h r e s h o l d energies for i o n - n e u t r o n r e a c t i o n s (Q < 3 M e V , Ζ < 31) (ρ,η) R e a c t i o n s Nuclide Abundance Threshold (MeV) 3

7H 9L i UB e 1B 3 C

318Q7 C1

44 1 K 5 Sc 49

TI 5s i y3 5C 5r 5M7n 5F e9 6C4o 6N5i 6C 7u 7Z 0n Zn

-

92.4 100 80.4 1.1 0.2 24.2 6.9 100 5.5 99.8 9.5 100 2.2 100 1.1 30.8 4.1 0.6

1.019 1.880 2.057 3.017 3.236 2.574 1.640 1.233 2.909 1.413 1.564 1.405 1.032 1.648 1.888 2.495 2.168 1.810 1.458

(α,η) R e a c t i o n s Neutron Energy (keV) 64 30 21 21 17 7 1.2 0.7 1.4 0.6 0.6 0.5 0.3 0.5 0.5 0.6 0.5 0.4 0.3

Nuclide Abundance Threshold (MeV) 7

9L i

Be ni o

1BB3 1C7 o

18Q

21 9 F5 2M7g 2A91 3S3i 4s 3 4C5a Sc 47

TI 459 3 TI 5C 7r 6F e7 Zn

92.4 100 19.6 80.4 1.1 0.04 0.2 100 10.1 100 4.7 0.8 0.2 100 7.3 5.5 9.5 2.2 4.1

0 0 0 0 0 0 0.851 2.360 0 3.027 1.736 2.244 0 2.440 0.347 0 0.351 1.451 3.142

Neutron Energy (keV)

7 18 13 6 7 4 0.5 0.4 1.6 2.5

(d,n) r e a c t i o n s p r o d u c e n e u t r o n s for all d e u t e r o n energies

the flight p a t h a n d t h e lowest n e u t r o n energy t h a t is t o b e m e a s u r e d . O v e r l a p n e u t r o n s , w h i c h h a v e a flight t i m e greater t h a n t h e t i m e b e t w e e n b e a m pulses, c o n t r i b u t e t o t h e b a c k g r o u n d a n d r e q u i r e careful a t t e n t i o n . D e t e c t o r pulses in a suitable range of pulse heights start a t i m e to a m p l i t u d e c o n v e r t e r w h i c h is s t o p p e d by a signal from t h e next b e a m pulse. T h e shortest t i m e s t h e n c o r r e s p o n d to t h e greatest flight t i m e s a n d hence to t h e lowest n e u t r o n energies. A typical time-of-flight s p e c t r u m from an F e s a m p l e i r r a d i a t e d with 3 M e V d e u t e r o n s is s h o w n in Fig. 4.21a. T h e n e u t r o n d e t e c t o r was placed 1at2 16°4 t o t h1e 6i n c i d e n t b e a m direction. P e a k s d u e t o (d,n) reactions in C , N a n d 0 were o b s e r v e d (Lorenzen, 1976). T h e r a t i o of b a c k g r o u n d corrected areas of specific peaks in spectra from s t a n d a r d a n d u n k n o w n m a t e r i a l s c a n b e u s e d to estimate t h e c o n c e n t r a t i o n of t h e relevant n u c l i d e in t h e u n k n o w n sample p r o v i d e d t h a t t h e s t o p p i n g p o w e r s of t h e t w o s a m p l e s are t h e s a m e . Otherwise t h e m e t h o d s of C h a p t e r 12.2 m u s t b e u s e d t o calculate t h e c o n c e n t r a t i o n of each n u c l i d e .

4. Nuclear Reactions

I

TIME OF FLIGHT

Ζ Λ

I

ι

ι

195

l T _

TIME OF FLIGHT

F i g . 4.21a. N e u t r o n time-of-flight s p e c t r u m f r o m 4 M e V d e u t e r o n i r r a d i a t i o n of steel; b . n e u t r o n time-of-flight s p e c t r u m f r o m 2 M e V p r o t o n i r r a d i a t i o n of a t r i t i a t e d T i layer o n C u ; a b o v e t h e h i g h energy p e a k a d e p t h profile of Τ d e r i v e d f r o m t h e m e a s u r e d s p e c t r u m is shown.

T h e relative positions a n d m a g n i t u d e s of t h e p e a k s vary with t h e angle of o b s e r v a t i o n w h i c h can therefore b e chosen to suit p a r t i c u l a r p r o b l e m s . T h e possible c o n t r i b u t i o n from h e a v i e r e l e m e n t s m u s t also b e kept in m i n d . F o r e x a m p l e , Cr, F e a n d N i as m a j o r e l e m e n t s m a y c o n t r i b u t e a significant n u m b e r of n e u t r o n s . Small d i p s c a n a p p e a r in time-of-flight spectra because of r e s o n a n c e a b s o r p t i o n of n e u t r o n s in nitrogen a n d oxygen in t h e flight p a t h b e t w e e n s a m p l e a n d detector. If necessary, this can b e a v o i d e d by using a v a c u u m or H e filled c o n t a i n e r r a t h e r t h a n a n air gap. c. Depth

Profiling

A d e p t h d i s t r i b u t i o n can b e o b t a i n e d from t h e s h a p e of t h e time-of-flight s p e c t r u m of a specific energy g r o u p . T h e simplest m e t h o d is t o calculate a c h a n n e l by c h a n n e l r a t i o of c o u n t s from s t a n d a r d a n d u n k n o w n s a m p l e s . If these h a v e e q u i v a l e n t s t o p p i n g powers, t h e result will b e a d e p t h profile b u t with a n o n - l i n e a r scale because of t h e s q u a r e r o o t relation b e t w e e n t i m e of flight a n d n e u t r o n energy. T h e yield scale is also d i s t o r t e d b e c a u s e d o n e c h a n n e l c o r r e s p o n d s t o different d e p t h intervals at different n e u t r o n energies. T h e calculation of t h e t r u e d e p t h d i s t r i b u t i o n of t h e n u c l i d e of interest in a different m a t r i x (m) to t h a t of t h e s t a n d a r d (s) requires a different a p p r o a c h (Lefevre et al, 1976; L o r e n z e n , 1976; Overley a n d Lefevre, 1976). T h e k i n e m a t i c E q u a t i o n (1.21), T a b l e 1.3, a n d t h e t i m e of-flight E q u a t i o n (1.7), T a b l e 1.1, are used t o calculate n e u t r o n energies, a n d h e n c e time-of-flight intervals (Atm , Ats) c o r r r e s p o n d i n g t o e q u a l depth intervals. T h e results are different for spectra from the standard a n d

196

J.R. Bird

DEUTERON ENERGY (MeV)

DEPTH (μπ>)

Fig. 4.22 D e p t h r e s o l u t i o n in n e u t r o n time-of-flight profiling of C, Ν a n d O . a. D e p e n d e n c e o n i n c i d e n t d e u t e r o n energy; b . d e p e n d e n c e o n i n t e r a c t i o n d e p t h (full c u r v e s ) ; t h e influence of energy straggling is i n c l u d e d in t h e d a s h e d c u r v e s .

u n k n o w n samples unless these h a v e t h e s a m e s t o p p i n g p o w e r (ε). T h e ratio of yields in t h e calculated t i m e intervals gives t h e r e q u i r e d c o n c e n t r a t i o n at d e p t h x: fm(x)

= fs(x) lYm (Atm )/Ys(Ats)]

[es/ej

(4.9)

If the nuclide being d e t e r m i n e d is present in sufficient q u a n t i t y to modify t h e stopping cross-sections, E q u a t i o n s (1.7), T a b l e 1.1, a n d (4.10) m u s t b e integrated to o b t a i n self-consistent values of t h e c o n c e n t r a t i o n 3 profile a n d rate of energy loss. A typical s p e c t r u m a n d c o r r e s p o n d i n g d e p t h profile of H i n a 8 tritiated T i layer o n C u is s h o w n in Fig. 4.21b (Lefevre et al, 3 1976).4 In this case, n e u t r o n s are o b s e r3v e d from (p,n) reactions in b o t h H a n d T i . If the total thickness of t h e H c o n t a i n i n g layer was m u c h greater, t h e two regions w o u l d overlap a n d analysis w o u l d b e c o m e m o r e complex. T h e d e p t h resolution (Αχ μτη), from time-of-flight m e a s u r e m e n t s , d e p e n d s o n c o n t r i b u t i o n s from i n c i d e n t b e a m energy s p r e a d (ΑΕΊ), straggling (AEls ) a n d t h e t i m e resolution (Δ/). A l t h o u g h these are n o t all necessarily characterised by G a u s s i a n d i s t r i b u t i o n s , it is c o n v e n i e n t to c o m b i n e t h e m in q u a d r a t u r e , E q u a t i o n s (12.37) a n d (12.38). l t h5e time-of-flight m e t h o d is t h a t t h e d e p t h A n u n u s u a l feature of resolution d e p e n d s o n E ( C h a p t e r 12.2) a n d h e n c e it i m p r o v e s with d e p t h because of t h e r e d u c e d n e u t r o n e n e r g y — i n spite of t h e effects of b e a m energy straggling. T h i s is illustrated in Fig. 4.22a for (d,n) profiling of C, Ν a n d Ο (Lorenzen, 1976). It also i m p r o v e s at low i n c i d e n t b e a m

4. Nuclear Reactions

197

energies or w h e n using low Q-vakxt groups, b e c a u s e lower energy n e u t r o n s are t h e n p r o d u c e d . T h i s is illustrated in Fig. 4.22b for t h e s a m e reactions. Because t h e d e p t h resolution is also d e p e n d e n t o n t h e s t o p p i n g cross-section of t h e s a m p l e , o p t i m i s a t i o n m u s t b e c o n s i d e r e d for each analytical p r o b l e m using t h e m e t h o d s d e s c r i b e d in detail by L o r e n z e n (1975). M e a s u r e m e n t s can b e m a d e of a d e p t h profile at C, Ν a n d Ο levels of 1% in a p e r i o d of 5 t o 30 m using d e u t e r o n c u r r e n t s of 0.1 to 1 μΑ, d e p e n d i n_1 g o n t h e c o n c e n t r a t i o n s . D e t e c t i o n limits are of t h e o r d e r of 100/ig g a n d are best w h e n using a h e a v y e l e m e n t m a t r i x .

4,4.2 Performance a. (p,n)

Reactions

9 Nucl3 i d e s7 with relatively low t h r e s h o l d energiesn a n d high cross-sections -1 T a b l e 4.6). T h e s e a n d B can b e d e t e r m i n e d at are H , L i a n d B e (see levels of of 10 μg g or less a n d h a v e also b e e n s t u d i e d in a n u m b e r of d e p t h profiling a p p l i c a t i o n s . Typical d e p t h resolutions are 0.3 t o 3 μχη d e p e n d i n g o n t h e length of flight p a t h a n d o7t h e r p a r a m e t e r s . T h e m a x i m u m d e p t h is 10 t o 100 μτη a l t h o u g h in t h e L i r e a c t i o n c o r r e c t i o n s m u s t b e m a d e for a n excited state g r o u p w i t h a t h r e s h o l d at 2.38 M e V . 1 3 re­ 1 5 At p r o t o n energies a b o v e 3 M e V , m o s t nuclides will u n d e r g o (p,n) 1 7 actions a nld scross-sections increase rapidly. T h e m i n o r isotopes C , N , 0 a n d O h a v e lower (p,n) t h r e s h o l d s t h a n t h e m a j o r isotopes of these elements. A d v a n t a g e can b e t a k e n of this fact t o detect t h e p r e s4e n3c e of 4m i8n o r isotopes in t h i n layers (Peisach, 1968). T h e C a isotopes, C a a n d C a , h a v e also b e e n d e t e c t e d in this way. b. (d,n)

Reactions

Stripping reactions h a v e mostly positive β - v a l u e s a n d relatively high a n d s m o o t h cross-sections — particularly in light nuclides. R e a c t i o n yields generally increase with d e u t e r o n energy a n d b r o a d m a x i m a m a y b e observed at v a r i o u s energies. T h e cross-sections usually h a v e a n angular d i s t r i b u t i o n which is p e a k e d at a n angle n e a r t h e i n c i d e n t b e a m 2 1 2 1N4u c l i d e s1 w6h i c h h a v e b e e n s t u d i e d with (d,n) r e a c t i o n s i n c l u d e direction. D , C , N a n d 0 . N e u t r o n s are p r o d u c e d in v a r i o u s energy groups, which are b r o a d e n e d o n t h e low energy side if a thick s a m p l e is u s e d a n d so profiling is possible with a d e p t h resolution of t h e o r d e r of 0.5 μτη. T h e limiting thickness t h a t c a n b e profiled is set b y t h e spacing b e t w e e n adjacent energy groups a n d is at least 10 μχη (Lorenzen, 1976). M e a s u r e m e n t s can b e m a d e of a d e p t h profile at levels of 1% in a

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J.R. Bird

period of 5 to 30 m i n using b e a m c u r r e n t s of t h e o r d e r of 0.1 to 1 μΑ, de­ p e-1n d i n g o n the c o n c e n t r a t i o n s . D e t e c t i o n limits are of t h e o r d e r of 100 μ% 2 e n t m a t r i x . All m e a s u r e m e n t s2 g a n d are best w h e n using a h e a v y e l e m are a c c o m p a n i e d by n e u t r o n s from t h e D ( d , n ) reaction arising from D self-implanted i n t o t h e s a m p l e d u r i n g i r r a d i a t i o n . At high d e u t e r o n energies, n e u t r o n b a c k g r o u n d s b e c o m e q u i t e high, being p r o d u c e d by heavy m a j o r isotopes in t h e s a m p l e as well as m i n o r isotopes. c. (t,n)

Reactions

O n e such reaction h a s b e e n used in t h e analysis of hydrogen, viz. *H(t,n). This has a high cross-section a n d can b e used with similar d e p t h resolution to t h a t of (p,n) reactions. T h e m a i n d r a w b a c k is t h a t n e u t r o n p r o d u c t i o n can occur with m o s t c o m m o n m a t e r i a l s used in t h e b e a m line a n d with h y d r o g e n w h i c h is a c o m m o n c o n t a m i n a n t . Tests using a high Ζ target such as Au, h a v e s h o w n t h a t b a c k g r o u n d n e u t r o n levels can b e equivalent to 3 % H in t h e s a m p l e . H a z a r d s arise in t h e use of 3t r i t o n b e a m s from n e u t r o n p r o d u c t i o n a n d from i m p l a n t a t i o n of t h e T i n t o b e a m line c o m p o n e n t s . O t h e r m e t h o d s of h y d r o g e n profiling are t h u s generally preferred. d. (a,n)

Reactions

π

Overley et al. (1979) h a v e p o i n t e d o u t t h a t t h e Β ( α , η ) reaction has a favourable cross-section a n d s h o u l d give considerably b e t t e r d e p t hn res­ olution in time-of-flight profiling t h a n can b e a c h i e v e d with t h e B ( p , n ) reaction. e. Heavy Ion

Reactions

O n e use of a heavy ion4 i n1d u0c e d n e u t r o n reaction h a s b e e n r e p o r t e d for H e profiling with t h e H e ( B , n ) reaction. A liquid scintillator was used (Bottiger et al, 1976) to d e t e r m i n e t h e profile of i m p l a n t e d H e with a resolution of 60 n m to a d e p t h of 1 μπι a n d a sensitivity of 1 % of H e .

4.5 ION ACTIVATION ANALYSIS Activation analysis using a n accelerated d e u t e r o n b e a m was d e m o n ­ strated in t h e early stages of t h e d e v e l o p m e n t of nuclear t e c h n i q u e s (Seaborg a n d Livingood, 1938). M a n y types of ions h a v e since b e e n used for activation analysis a n d t h e choice of type a n d energy of ion as well as the variety of reactions available m a k e this a c o m p l e x field of appli-

4. Nuclear Reactions

199

cations. H o w e v e r , b e c a u s e of t h e w i d e s p r e a d availability of n e u t r o n activation analysis, ion a c t i v a t i o n is n o r m a l l y only c o n s i d e r e d if it offers special a d v a n t a g e s for p a r t i c u l a r p r o b l e m s . H o s t e a n d Vandecasteele (1987) a n d E n g e l m a n n (1981) h a v e re­ viewed ion a c t i v a t i o n analysis m e t h o d s a n d a p p l i c a t i o n s a n d systematic studies for light ions include: p r o t o n s — B a3r r a n d4o n et al (1976), D e b r u n et al (1976), Borderie et al (1977); H e , H e — B o r d e r i e (1982), E n g e l m a n n (1981); a n d , h e a v y i o n s — S c h w e i k e r t ( 1 9 7 8 , 1981). In a d d i t i o n , t h e r e are m a n y b o o k s a n d reviews w h i c h p r e s e n t t h e theory a n d practice of n e u t r o n a c t i v a t i o n analysis a n d m u c h of this m a t e r i a l is applicable t o ion a c t i v a t i o n . T h e following sections therefore only give a brief d e s c r i p t i o n of ion a c t i v a t i o n .

4.5.1 Methods a.

Analysis

T h e acitivity (A) resulting from a specific n u c l e a r reaction, w h i c h is present at t h e e n d of a n i r r a d i a t i o n , is o b t a i n e d from E q u a t i o n ( 12.11 ) for the reaction yield, with a n a d d i t i o n a l t e r m t o a c c o u n t for t h e decay t h a t takes place d u r i n g i r r a d i a t i o n : A, = Nx(c2NQ IMx)

A 4(l - e x p [ - A 4r ] )

[a(Ex)ISm (Ex)\

dE (4.10)

w h e re λ4 is t h e decay c o n s t a n t of t h e p r o d u c t nuclide; a n d τ is t h e d u r a t i o n of t h e i r r a d i a t i o n . T h e s a t u r a t i o n activity r e a c h e d w h e n τ is m u c h greater t h a n t h e half life of t h e p r o d u c t is: A4(SAT)

= Nx{c2NJMx)

λ4

[a(Ex)/Sm (Ex)]

dE

(4.11)

If a d e q u a t e cross-section d a t a is n o t available, especially for irradi­ ation at relatively high energies (10 t o 50 M e V ) , absolute d e t e r m i n a t i o n s are n o t possible a n d t h e activity of k n o w n a n d u n k n o w n s a m p l e s m u s t be c o m p a r e d using t h e a p p r o x i m a t i o n s discussed in C h a p t e r 1 2 . 1 . b.

Measurements

Although m e a s u r e m e n t s are possible o n r o u g h surfaces, s a m p l e s s h o u l d preferably b e s m o o t h a n d flat. T h e y m a y also n e e d t o b e m o u n t e d o n a

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cooled backing to p r e v e n t o v e r h e a t i n g d u r i n g i r r a d i a t i o n . Even t h e n , t h e t e m p e r a t u r e of t h e s a m p l e surface m a y rise by m a n y h u n d r e d s of degrees with b e a m c u r r e n t s of t h e o r d e r of 10 μΑ. T h i s m a y b e acceptable for s o m e materials b u t it is desirable t h a t they b e b a k e d before use t o a v o i d excessive outgassing d u r i n g i r r a d i a t i o n . A c o n d u c t i n g surface layer or foil m a y b e n e e d e d w h e n i r r a d i a t i n g insulating m a t e r i a l s to p r e v e n t sparking a n d c o n s e q u e n t s a m p l e d a m a g e . T h e b e a m dose can b e d e t e r m i n e d by current integration or by placing a t h i n s t a n d a r d foil in front of t h e sample a n d m e a s u r i n g t h e foil a c t i v a t i o n i n d e p e n d e n t l y . A n i m p o r t a n t c o n s i d e r a t i o n is t h e b e a m u n i f o r m i t y since m e a s u r e ­ m e n t s of decay p r o d u c t s are m a d e with a different g e o m e t r y to t h a t involved in i r r a d i a t i o n . A n y changes in b e a m p o s i t i o n or t h e d i s t r i b u t i o n of current w i t h i n t h e b e a m spot change t h e c o u n t i n g efficiency. It is therefore desirable to use such t e c h n i q u e s as defocussing or oscillation to spread the b e a m a n d t h e n collimate it to a n accurately k n o w2n d i a m e t e r to ensure u n i f o r m i r r a d i a t i o n of a n area of t h e o r d e r of 1 c m . If t h e b e a m energy is higher t h a n t h a t r e q u i r e d for s a m p l e activation, t h e energy can be r e d u c e d by energy loss in a filter foil of carefully chosen thickness. Samples are r e m o v e d from t h e i r r a d i a t i o n c h a m b e r a n d activities c o u n t e d at successive intervals chosen to suit t h e half lives for t h e decay of specific radioisotopes. A light etch m a y b e necessary to r e m o v e any activated surface c o n t a m i n a t i o n , including b e a m d e p o s i t e d c a r b o n , if the best sensitivity is to b e achieved. Surface r e m o v a l t e c h n i q u e s can b e used to o b t a i n d e p t h profiles, for e x a m p l e in t h e study of t h e o x i d a t i o n of metals (Perkins, 1977). It is also possible to r e m o v e a considerable thickness a n d only m e a s u r e activities at d e p t h s below w h i c h a c o m p e t i n g reaction is n o t energetically allowed (if t h e b e a m energy c a n n o t b e lowered). R a d i o i s o t o p e s with short half-lives can b e o b s e r v e d d u r i n g irradi­ ation a n d the b a c k g r o u n d can b e m i n i m i s e d by pulsing t h e b e a m or deflecting it so t h a t m e a s u r e m e n t s can b e m a d e while t h e b e a m is off t h e sample. It is also possible to use chemical s e p a r a t i o n to isolate specific radioisotopes before m e a s u r i n g t h e i r activities by g a m m a ray spec­ trometry. Charged particle b o m b a r d m e n t often leads to t h e creation of positron e m i t t e r s which can b e d e t e c t e d by b e t a c o u n t i n g or t h e m e a s u r e m e n t of a n n i h i l a t i o n r a d i a t i o n (511 keV). T h e identification of a specific p r o d u c t r a d i o n u c l i d e is t h e n only possible by t h e m e a s u r e m e n t of decay curves a n d t h e extraction of specific half life c o m p o n e n t s . Internal conversion a n d electron c a p t u r e are also c o m m o n so t h a t delayed X-ray emission can be used to e x t e n d t h e scope of ion a c t i v a t i o n m e t h o d s ( M c G i n l e y a n d Schweikert, 1976).

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201

4.5.2 Performance T h e a d v a n t a g e s of ion a c t i v a t i o n include:

_1

• • •

• •

sensitivities d o w n t o 1 ng g for a different suite of isotopes t o those for w h i c h n e u t r o n a c t i v a t i o n is m o s t sensitive; t h e choice of ion type a n d energy p r o v i d e a versatility for o p t i m i s i n g sensitivity a n d selectivity t o suit p a r t i c u l a r p r o b l e m s ; radioactivity is only p r o d u c e d in a surface layer, t h e thickness of which d e p e n d s o n t h e ion energy a n d t h e v a r i a t i o n of r e a c t i o n cross-section with energy — t h e total activity p r o d u c e d is 13 therefore low; i n c i d e-n t1 particle fluxes can b e very high (10 μΑ = 6.24 Χ 1 0 ions s ) w h i c h offsets relatively low cross-sections; a n d accelerators are available in m a n y l a b o r a t o r i e s w h i c h d o n o t h a v e facilities for n e u t r o n a c t i v a t i o n analysis.

T h e r e m a y also b e d i s a d v a n t a g e s such as: • • •

•

s a m p l e h e a t i n g w h e n a high b e a m c u r r e n t is used m a y lead t o changes or d a m a g e t o t h e s a m p l e ; cross-sections are generally lower t h a n those for n e u t r o n acti­ v a t i o n analysis; c o u n t i n g t i m e s of 10 t o 120 h are necessary t o achieve high sensitivity a n d this reduces t h e n u m b e r of samples t h a t can b e analysed; a n d ionisation energy loss p r e v e n t s t h e i r r a d i a t i o n of large v o l u m e s a n d so t h e activity p r o d u c e d is l i m i t e d by t h e ion range.

H i g h e r b e a m energies are generally u s e d for a c t i v a t i o n analysis t h a n for p r o m p t nuclear analysis except for a few cases of light isotope activation. F o r e x a m p l e , p r o t o n energies from 5 t o 20 M e V are n e e d e d t o o b t a i n a high e n o u g h cross-section for good sensitivity in P A A . H o w e v e r , the higher t h e energy t h e m o r e likely it is t h a t interfering r e a c t i o n s will create difficulties a n d t h e best choice of ion type a n d energy d e p e n d s o n the p r o b l e m in h a n d . A catalog of s o m e of t h e r e a c t i o n s available at energies u p to 10 M e V is given in C h a p t e r 14.4.5 a n d typical values of es­ t i m a t e d d e t e c t i o n limits are p l o t t e d in Fig. 4.23 for 3 6 0 0 μΟ i r r a d i a t i o n s a n d u p to 60 h c o u n t i n g t i m e s . P A A h a s excellent sensitivity for such light elements as B, C, Ν a n d Ο a n d is u n i q u e a m o n g s t a c t i v a t i o n t e c h n i q u e s for the use of h e a v y ion b1e a m s for t h e d e t e r m i n a t i o n of Η a n d H e w i t h sensitivities below 1 μ%%~ . E l e m e n t s such as T i , Sr, M o a n d P b are also of special interest b e c a u s e they are difficult t o d e t e r m i n e b y N A A b u t c a n b e d e t e r m i n e d at similar levels by P A A . T h e fact t h a t at least 70 e l e m e n t s

202

J.R. Bird -ζχ

1

1

1

1

Γ

1

10"

Δ Δ ο ο

Ο Δ 10

h-

Ο

°

°0ο

Ο

Δ

DETECTION LIMITS PAA ANALYSIS ο 10 MeV Protons Δ 3.5 MeV T r i t o n s

0 οο

ο ο ο

-AJ

L 20

40 ATOMIC NUMBER

60

80

Fig. 4.23 E s t i m a t e d d e t e c t i o n l i m i t s in P A A u s i n g 10 M e V p r o t o n s ( B a r r a n d o n et al, D e b r u n et al, 1976) a n d 3.5 M e V t r i t o n s ( B o r d e r i e et al, 1977).

1976;

can be d e t e r m i n e d at these levels m a k e s P A A a powerful t e c h n i q u e w h e n a sufficiently large accelerator is available.

4.5.3 Thin Layer Activation Ion i n d u c e d radioactivity occurs at d e p t h s less t h a n t h e range of t h e incident ions so t h a t only a t h i n layer is a c t i v a t e d r a t h e r t h a n t h e whole sample. F u r t h e r m o r e , a small b e a m area can b e used to activate only t h a t part of t h e surface of a large object w h i c h is of interest. T h e s e are m a j o r advantages in t h e study of surface r e m o v a l processes since, a l t h o u g h t h e activity in t h e region of interest m a y b e reasonably high, t h e total activity can b e so low t h a t n o r5m6a l h a n5d 6 l i n g of t h e s p e c i m e n is possible. F o r e x a m p l e t h e F e ( p , n ) C o r e a c t i o n h a s a t h r e s h o l d at 5.35 M e V a n d a b r o a d cross-section m a x i m u m in t h e region of 10 M e V . I r r a d i a t i o5n 6 of the surface of a n iron o r steel object will therefore p r o d u c e C o activity in a layer of a p p r o x i m a t e l y 0.25 m m thickness at d e p t h s from 0

4. Nuclear Reactions

Collimator Incident Beam

I Window^

Sample

Sample

Detector PM •Preamp

Activated Region

203

activated Region

|Scaler|

Layer Removed by Wear F i g . 4.24a. T h i n L a y e r A c t i v a t i o n b y 15 M e V p r o t o n b e a m ; b . m e a s u r e m e n t of a c t i v i t y after surface w e a r .

t o 1 m m or m o r e , d e p e n d i n g o n t h e p r o t o n energy u s e d (Fig. 4.24a). T h e size a n d s h a p e of t h e a c t i v a t e d a r e a c a n b e controlled b y changes in b e a m focussing a n d / o r s c a n n i n g a n d t h i s a r e a c a n b e p o s i t i o n e d as r e q u i r e d o n t h e object by suitable s a m p l e m o u n t i n g systems. A g a m m a - r a y d e t e c t o r placed close t o o p e r a t i n g m a c h i n e r y will m o n i t o r t h e d r o p in r a d i o a c t i v i t y as w e a r takes place (Fig. 4.24b). A sensitivity of t h e o r d e r of 0.2 μπι can b e a c h i e v e d in this way. Alternatively, m a t e r i a l r e m o v e d from t h e surface can b e t r a p p e d in a filter (for e x a m p l e in oil o r 7 c o o l a3n t s t r e a m ) a n d a very high sensitivity can t h e n b e o b t a i n e d , e.g. 1 0 ~ c m . T h i n layer a c t i v a t i o n h a s b e e n s h o w n t o b e a versatile t e c h n i q u e for t h e study of wear, corrosion a n d o t h e r surface d e g r a d a t i o n p r o b l e m s in engines, m a c h i n e tools a n d m a n y k i n d s of i n d u s t r i a l c o m p o n e n t s (Conlon, 1982; J e a n n e a u , 1983). E l e m e n t s w h i c h h a v e b e e n listed as suitable for t h i n layer a c t i v a t i o n are s h o w n in T a b l e 4.7 a l t h o u g h further d e v e l o p m e n t will u n d o u b t e d l y increase this list.

T A B L E 4.7 S o m e n u c l e a r r e a c t i o n s u s e d for t h i n layer a c t i v a t i o n Matrix

5 T2i 5C 6r 5F e6 5F e8 9F e2

48

Zr

Reaction

(P,n)

(P,n) (P,n) 6( d , n ) ( Li,«) (P,n)

Product

5 2 5M6n 5C 7o 5C 8o 9C 2o

E, (MeV)

48y

Nb

13 9.2 24

Useful Depth

Material

(μπι) 25

Ti

300 150 25

steel cast i r o n steel

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J.R. Bird

4.6 CHOICE OF REACTION T h e catalog of n u c l e a r r e a c t i o n s w h i c h h a v e b e e n u s e d for s a m p l e analysis a n d d e p t h profiling ( C h a p t e r 14.4.1) is far from a c o m p l e t e list of all possibilities b u t it shows t h a t t h e r e is a considerable choice available for t h e study of a n y o n e isotope ( Z < 17). T h e selection of a preferred re­ action d e p e n d s o n t h e p r o b l e m , t h e m a t e r i a l a n d t h e e q u i p m e n t available b u t experience p o i n t s t o o b v i o u s a d v a n t a g e s in t h e use of specific reactions in m a n y cases.

15

•

•

• • • •

•

• • •

• •

*H — t h e ( N , a y ) r e a c t i o n gives t h e best d e p t h resolution a n d 7 yield for profiling at a m o d e r a t e b e a m energy ( > 6.385 M e V ) ; t h e ( Li j ) reaction r e q u i r e s1 a9 lower energy a n d h a s a greater m a x i ­ m u m d e p t h while t h e ( F , a y ) reaction at either 6.418 o r 16.586 M e V2is often3 used for H d e t e r m i n a t i o n o r profiling. 3 — t h e ( H e , a ) r e a c t i o n gives t h e best d e p t h resolution; t h e D ( H e ,1p )5 a n d (d,p) reactions are useful for D d e t e r m i n a t i o n while the ( 3N , n y ) r e a c t i o n h a s b e e n s h o w n t o h a v e b e t t e r sensitivity. T — t h e ( d , a ) r e a c t i o n gives excellent sensitivity a n d m o d e r a t e d e p t h4 resolution. H e — t w o reactions h a v e b e e n s h o w n t o h a v e reasonable d e p t h 6 resolution b u t p o o r sensitivity. L i —7 t h e (d,a) reaction gives r e a s o n a b l e p e r f o r m a n c e . L i — b o t h t h e (p,p'y) a n d (α,α'γ) reactions give good sensitivity for Li d e t e r m i n a t i o n a n d t h e (p,y) reaction is useful for d e p t h 9 profiling. B e — t h e (α,ηγ) reaction h a s excellent sensitivity (even being used with a l p h a sources for p o r t a b l e Be m o n i t o r s ) ; t h e (ρ,α) 1 0 is useful for d e p t h profiling. reaction B —n t h e (ρ,αγ) reaction gives good sensitivity. B — t h e (ρ,α) a n d (p,y) reactions are useful for profiling a n d Β 3 deter1 m i2n a t i o n . C — t h e ( d , p 0) reaction is m o s t used b u t t h e ( H e , p ) reaction h a s b e t t e r d e p t h resolution; b o t h c a n b e used in s i m u l t a n e o u s C, Ν a n d Ο d e t e r m i n a t i o n in t h i n layers; t h e (d,py) reaction c a n b e used 1 3 samples o r (p,p'y) reactions 3 for thick at energies a b o v e 6 M e V . C — t h e (p,y), (d,p) a n d ( H e , p ) reactions c a n b e u s e d for deter1 m i4n i n g a n d profiling a n d C isotope ratios. N — t h e ( d , p 0) a n d (d, aQ ) reactions c a n b e used together for nitrogen d e t e r m i n a t i o n b u t t h e (d,a) reaction is t h e best t o use for s i m u l t a n e o u s C, Ν a n d Ο d e t e r m i n a t i o n in t h i n layers a n d for Ν profiling; o t h e r (d,p) energy groups in these reactions are also useful as is t h e (d,py) reaction for thick samples.

1 5 • •

• •

• • •

• • • •

• • •

•

4. Nuclear Reactions

1 5

205

N — t h e (ρ,α) o r (p,ay) r e a c t i o n s are useful for N d e t e r m i ­ n a t i o nI . 6 0 — t h e (d,p) r e a c t i o n is m o s t u s e d for profiling a n3d simul­ t a n e o u s C , N a n d Ο d e t e r m i n a t i o n in t h i n layers b u t t h e ( H e , a ) re­ a c t i o n is also useful, t h e (d,py) r e a c t i o n can b e u s e d for t h i c k s a m p l e s o r (p,p'y) r e a c t i o n s a b o v e 6 M e V ; t h e (t,n) r e a c t i o n can b e 1 7a c t i v a t i o n analysis a n d a u t o r a d i o g r a p h y . used for 0 —1 is8 little s t u d i e d b e c a u s e of its low a b u n d a n c e . 0 — t h e (ρ,α) r e a c t i o n at t h e n a r r o w 629 k e V r e s o n a n c e o r b r o a d 846 keV r e s o n a n c e is widely u s e d in stable t r a c e r studies a n d profiling; t h e (d,p) o r ( d , a ) r e a c t i o n s c a n also b e used; a c t i v a t i o n analysis w i t h t h e (p,n) r e a c t i o n gives g o o d sensitivity 1 9 resolution by a u t o r a d i o g r a p h y . a n d spatial F — t h e (p,p'y) gives t h e best sensitivity for F d e t e r m i n a t i o n a n d 2 0 r e a c t i o n can b e u s e d for profiling o r analysis. t h e (ρ,αγ) 2 1 w i t h t h e (p,y) r e a c t i o n a n d d e t e r m i n e d N e — can b e profiled 2 3 from t h e resulting N a activity. N a — excellent sensitivity is a c h i e v e d w i t h t h e (p,p'y) o r (α,α'γ) reactions a n d t h e (ρ,α) o r (ρ,αγ) r e a c t i o n s h a v e n a r r o w r e s o n a n c e s for d e2p 4 t h profiling. M g — h a s relatively low r e a c t i o n yields a n d h e n c e p o o r sensi­ tivity.2 5 M g — t h e (p,p'y) r e a c t i o n gives r e a s o n a b l e sensitivity for M g d e t e r2m i6n a t i o n . M g — c a n b e d e t e r m i n e d w i t h t h e (p,y) r e a c t i o n b u t t h e r e is 2 7interference from Al. serious A l — can b e d e t e r m i n e d w i t h g o o d sensitivity by t h e (p,p'y) r e a c t i o n a n d profiled w i t h a n a r r o w r e s o n a n c e in t h e (p,y) 28 reaction. S i — can b e d e t e r m i n e d w i t h r e a s o n a b l e sensitivity using t h e (d,p) 3o r0 (p,p'y) reactions. S i — h a s a n a r r o w r e s o n a n c e in t h e (ρ,γ) r e a c t i o n suitable for 3 1 profiling. P — t h e (ρ,α) r e a c t i o n gives t h e best sensitivity, t h e (p,p'y) reaction is useful a b o v e 3 M e V ; b o t h (ρ,α) a n d (p,y) can b e u s e d 3 2 for profiling. S — t h e (d,p) a n d (p,p'y) r e a c t i o n s h a v e b e e n u s e d for S d e t e r m i n a t i o n a n d profiling.

H e a v i e r e l e m e n t s h a v e m o s t l y b e e n analysed using P I G M E t e c h n i q u e s o r by a c t i v a t i o n analysis w i t h relatively high energy ions. T h e sensitivities for these t e c h n i q u e s are illustrated in Figs. 4.19 a n d 4 . 2 3 .

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