Volume 32A. number t P H Y S I C S L E T T E R S 27 July 1970

P O S I T R O N A N N I H I L A T I O N I N D I L U T E S O L I D

I. Ya. D E K H T J A R Institute of Metal Physics, AS UkrSSR. I~iev

Received 27 May 1970

S O L U T I O N S

The impurity effect on the form changing of the angular correlat ion curve for annihilation radiation is investigated. The annihilation mechanism in dilute solid solutions containing localized magnetic moments is related to positron capture by the perturbation centers.

A n a l y s i s of the i n t e r a c t i o n b e t w e e n p o s i t r o n s and d i s l o c a t i o n c o r e s [1] m a y be u s e d fo r the s tudy of the i n t e r a c t i o n b e t w e e n p o s i t r o n s and i m - p u r i t i e s in the m e t a l l a t t i ce . In th is a s p e c t i t i s i n t e r e s t i n g to c o n s i d e r the r e s u l t s of an i n v e s t i g a - t ion of p o s i t r o n ann ih i l a t i on in d i lu te so l i d s o l u - t ions of p a l l a d i u m in i r o n [2], w h e r e it w a s shown that the f o r m chang ing of the a n g u l a r c o r r e l a t i o n c u r v e is a c c o m p a n i e d by an i n c r e a s e in the a r e a unde r the p a r a b o l a (S o) and by a d e c r e a s e in tha t unde r the G a u s s i a n (gg)o It should be no ted that the ann ih i l a t ion p r o b a b i l i t y of p o s i t r o n s wi th conduc - t ion e l e c t r o n s i s i n c r e a s e d by 17% whi l e the an - n ih i l a t i on p r o b a b i l i t y wi th i n n e r she l l e l e c t r o n s i s d e c r e a s e d by 7% ( see t ab le 1).

The m e n t i o n e d v a r i a t i o n of the p o s i t r o n an - n ih i l a t ion p r o b a b i l i t y was e x p l a i n e d [3] by the fac t that p o s i t r o n s w e r e t r a p p e d by e x c e s s c h a r g e s which a p p e a r e d in the ne ighbou rhood of F e a toms°

It may be s u p p o s e d that the p o s i t r o n a n n i h i l a - t ion m e c h a n i s m in a g iven so l i d so lu t ion is due to the p r e s e n c e of l o c a l m a g n e t i c m o m e n t s which l e a d s to the p o l a r i z a t i o n of e l e c t r o n s in the c o n - duc t ion band°

Tak ing into accoun t the s i z e of a l oca l p o l a r i z a - t ion r e g i o n it m a y be shown that in the c r y s t a l of P d wi th 1at. % Fe t h e s e r e g i o n s a r e o v e r l a p p i n g and thus it i s not n e c e s s a r y fo r p o s i t r o n s to m i - g r a t e th rough l a r g e d i s t a n c e s to p e r t u r b a t i o n c e n t e r s ° T h e s e d i s t a n c e s a r e , fo r e x a m p l e , of the o r d e r 14 Ao

The t r a p p i n g of a p o s i t r o n in a r e g i o n wi th

] 'able 1

Metal S Sp Sg A Sp/Sp AS g/ Sg

Pd 1.0 0.288 0.712 Pd + lat. (;'~Fe 1.0 0.337 0.663 ~ 0.17 - 0.07

l oca l p o l a r i z a t i o n r e s u l t s in an i n c r e a s e in i t s l i f e t i m e . By a s i m i l a r me thod to [1] it i s p o s - s i b l e to d e r i v e e x p r e s s i o n s fo r the f r a c t i o n of t r a p p e d p o s i t r o n s (~m) and for t h e i r a v e r a g e l i f e t i m e ( rm) :

~pC m ~X 1-x2)exp(x l -x 2- UpCm)¥ m - •

+ UpC mYm (1)

+ ~PC mT I~] (2)

w h e r e C m i s the c o n c e n t r a t i o n of r e g i o n s wi th l o c a l i z e d m o m e n t s ; r 1 the l i f e t i m e of p o s i t r o n s in t h e s e r e g i o n s ; r 2 t h e i r l i f e t i m e in a p u r e s o l - vent ; X 1 = r i l , X 2 ; r~ 1 the c o r r e s p o n d i n g v e l o c - i t i e s of p o s i t r o n ann ih i l a t ion ; VpC m the v e l o c i t y of t h e i r t r app ing ; Vp the p a r a m e t e r of the so l id solut ion°

In p r i n c i p l e the m e n t i o n e d p a r a m e t e r shou ld be d e t e r m i n e d by the i n t e r a c t i o n b e t w e e n the t h e r m a l i z e d p o s i t r o n and l o c a l i z e d m o m e n t s . In the f i r s t a p p r o x i m a t i o n th i s i n t e r a c t i o n may be t r e a t e d with the he lp of a s c r e e n e d Cou lomb p o - t e n t i a l due to the g e n e r a l p r o p e r t i e s of the p l a s - ma . Quan t i t a t i ve a n a l y s i s at p r e s e n t i s , h o w e v e r , d i f f icul t .

Wi th ~ m = 0.17, if we put ¥ / r 2 > 1, we find that r l / ' r 2 > 1 and Xl/X 2 < 1 showing that the an - n ih i l a t ion e n h a n c e m e n t f a c t o r of p o s i t r o n p o l a r i - za t ion of e l e c t r o n s in the r e g i o n s wi th l o c a l i z e d m o m e n t s should be l o w e r than in a p u r e m a t r i x (Pd). In th is e a s e the bond b e t w e e n v a l e n c e e l e c - t r o n s and a t o m s in the d i lu te so l id so lu t ion m u s t be s t r o n g e r than in the p u r e m a t r i x .

246

Volume 32A, number 4

R e f e r e n c e s [1] I.J.Dekhtjar. Phys. Letters 31 (1970) 10.

P H Y S I C S L E T T E R S 27 July 1970

121 I . J . D e k h t j a r . R . G . F e d e h e n k o . F iz . Met . M e t a l - loved 21 (1966~ 833.

[3] I . J . D e k h t j a r . C z e c h o s l o v . J o u r n . P h y s . 12B (1968) 1503.

E P R I D E N T I F I C A T I O N O F V 1 C E N T E R S IN I R R A D I A T E D B e O

A. HERVE and B. M A FFE O * Laborato ire de R~sonance MagnOtique, Centre d 'Etudes NuclOaires de Grenoble

Cedex 85. 38 Grenoble-Gate . France

Received 16 June 1970

Electron irradiated (single crystal) BeO studied by EPR at liquid helium Lemperatures shows spectra attributed to holes trapped at cation vacancies. V 1 centers. Room temperature studies and comparison with similar impurity associated defects obtained by ?/-irradiation support the model.

We have obtained 35 GHz EPR spec t r a at l iquid hel ium t e m p e r a t u r e s (1.5 - 4.2°K) of a BeO c ry s t a l which had been i r r ad ia ted , at room t e m p e r a t u r e , with 3 MeV e l ec t rons at a c u r r e n t densi ty of 30 # A / c m 2 for 6 hours . When the ex te rna l magnet ic f ie ld/- /o is pa r a l l e l to the c rys t a l l i ne c axis , the re a re two EPR l ines , at g = 2.0026 labe l led A and a t g = 2.0149 labe l led B, both showing pa r t i a l ly r e s o l v e d super - hyperf ine (shf) s t ruc ture° A is m o r e intense than B and does not spl i t for an a r b i t r a r y d i r e c - tion of / - /o while B spl i ts into six equally intense l ines. If we neglec t the shf s t ruc tu re , whose study has not yet been completed, the angular dependence of both spec t r a is des r ibed by the spin Hamil tonian ~ = fl /-/o" g ° S with S = ½. g is an axial ly s y m m e t r i c tensor . F o r the A spec t rum its p r inc ipa l axis is the c axis with g , = 2°0026 ± 0.0005 a n d g ~ = 2o0155 ± 0.0005. F o r B the p r inc ipa l axis is one of the three equivalent basal t e t r ahed ra l bonding d i rec t ions , at 109 ° to c , w i t h g H = 2.0026 ± 0.0005 and g~_ = 2.0164 ± 0.0005 (the six magnet ica l ly ineq- u ivalent s i t e s being provided by the two di f ferent t e t r ahed ra of the BeO wur tz i t e s t ruc tu re , ro ta ted 60 ° around c with r e s p e c t to each other). The main f ea tu re s of the shf s t ruc tu re on l ines A and B indicate an i so t rop ic in te rac t ion with th ree Be ÷+ nuclei (I = 3/2).

* Fellowship of the "Capes/Ford Foundation Project" of Brazil.

We suggest that the i so la ted cation vacancy having t rapped one hole on one of the four n e a r e s t neighbour oxygen ions (V 1 center) is respons ib le for these spec t ra . Because of the po la r axial c rys t a l l i ne e l e c t r i c f ield of the wur tz i te s t r u c - ture we expect to find two sl ight ly d i f ferent ty- pes of V 1 center . The f i r s t , a s soc ia t ed with spec t rum A, has the hole t rapped on the oxygen ion lying along the c axis , the second, a s soc ia t ed with B, has the hole t rapped on one of the three nonaxial oxygen ions° The axial defect (C3v sym- met ry) and the nonaxial one (C s symmet ry ) have, r e spec t ive ly , two magnet ica l ly equivalent and six magnet ica l ly inequivalent s i tes . In these p r e - l imina ry m e a s u r e m e n t s , no depar tu re f rom axial s y m m e t r y was de tec ted for the g tensor a s so - c ia ted with the non-axia l defect° Since A and B do not show 1 : 3 intensi ty ra t io when H o is pa r a l l e l to c , the hole apparent ly occupies p r e f e r en t i a l l y the axial oxygen site. All other above-ment ioned fea tu res of the spec t ra , in pa r t i cu l a r the pos i t ive g - sh i f t s , a re en t i re ly compat ible with the p r o - posed model.

At higher t e m p e r a t u r e s we might expect t h e r - mal ly act ivated hopping of the hole among the four oxygen s i tes . For high enough hopping f r e - quency one single absorpt ion line must be ob- s e rved at g, the mean value of g taken over the four s i tes . Fo r smal l anisot ropy of the g t ensor ( ( g ± - g ~ ) / g ± <~: 1). ~ is independent

I of the d i rec t ion of /-/o and given by ~ =

(g , +2g±), providing that the t e t r ahedron

247