van der Woude f, K.H.J

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Journal of Non-Crystalline Solids 61 & 62 (1984) 421-426 421 North-Holland. Amsterdam

MOSSBAUER ISOMER-SHIFTS AND QUADRUPOLE SPLITTINGS IN THE AMORPHOUS IRON- BORON SYSTEM

W. Hoving r , F. van der Woude f, K.H.J. Buschow and I. Vincze #

i Solid State Physics Laboratory, University of Groningen, 1Melkweg, 9718 EP Groningen, The Netherlands.

~Philips Research Laboratories, Eindhoven, The Netherlands.

~Central Research I n s t i t u t e f o r Physics, H-1525 Budapest 114, P.O.B. 49, Hungary.

The isomer s h i f t s and quadrupole s p l i t t i n g s of amorphous FexB 1 v a l l o y s (10 a/o < x < 90 a/o) were studied by 57Fe M~ssbauer spectroscopy.-~he isomer shif~ vs~ composition can be described by the &#~- and Anws-terms of Miede- ma's c e l l u l a r model to p r e d i c t the heat of formation of b~nary alloys and an a d d i t i o n a l volume mismatch term. This term is necessary f o r boron-rich a l - loys (x < 50 a/o). We conclude that these samples have a strained atomic structure. The values of the quadrupole s p l i t t i n g s at the boron-rich side i n - crease s t r o n g l y , i n d i c a t i n g t h a t the Fe-atoms are squeezed i n t o asymmetric atomic surroundings. Implanted iron i n t o c r y s t a l l i n e boron has a comparable isomer s h i f t and quadrupole s p l i t t i n g as the boron-rich a l l o y s .

1. INTRODUCTION

Amorphous FexBl_x-alloys can be prepared by several experimental techniques.

Melt quenching with an e f f e c t i v e cooling rate of 106 K/s is l i m i t e d to compositions near the deep e u t e c t i c at 17 a/o B in the Fe-B phase diagram (72 a/o < x

< 88 a / o l ) . Vapour quenching techniques o f f e r a much wider composition range extending from I0 a/o to 90 a/o B, due to the much higher cooling rate of about 1016 K/s. Another technique to make amorphous FexBl_ x could be implantation of Fe-atoms i n t o boron 2 where the cooling rate is 1014 K/s.

57Fe M~ssbauer Effect Spectroscopy (MES) provides information about the e l e c t r o n i c and magnetic s t r u c t u r e of these a l l o y s . In t h i s paper we concentrate on the isomer s h i f t and quadrupole s p l i t t i n g . The isomer s h i f t r e f l e c t s the charge on the iron atoms, whereas the quadrupole s p l i t t i n g is determined by the charge d i s t r i b u t i o n on neighbouring atoms.

2. EXPERIMENTAL

2.1. Sample preparation

Amorphous FexBl_ x samples have been prepared by s p u t t e r i n g on boron n i t r i d e substrates kept at room temperature (RT) or l i q u i d nitrogen temperature.

Targets of the appropriate compositions were DC-sputtered in an argon-gas atmos- phere of 0.1-0.5 Torr (V =1.5 kV,l =2mA). Base pressure before sputtering wasbe- low 2 × 10 -6 Torr. A presputtering cycle of about 30 minutes with a molybdenum

0022-3093/84/$03.00 © Elsevier Science Publishers B.V.

(North-Holland Physics Publishing Division)

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422 W. Hoving et al. / M~ssbauer isomer-shifts and quadrupole splittings

shutter between the sputter target and the substrate was performed in order to s t a b i l i z e the sputtering conditions and to activate the gettersputtering-ac- tion 3,4, resulting in a very low partial pressure (10 -10 Torr of lower 4) of con- taminating gases near the substrate. The thickness of the sputtered samples was a few micrometers.

Amorphous iron-boron films on quartz and aluminium substrates were prepared by two-source coevaporation of the elements 13'14. The base pressure of the va- cuum system was about 5 × 10 -8 Torr. The thickness of the samples was about 5000 R. A f t e r deposition the thin films were examined by X-ray d i f f r a c t i o n (CuK) confirming n o n - c r y s t a l l i n i t y . Accuracy of composition of the evaporated samples is better than 2 a/o. Until now the composition of the sputtered samples is not known exactly, we assumed that these are equal to the target compositions.

2.2. M~ssbauer measurements

Transmission M~ssbauer e f f e c t spectra of the sputtered samples were recorded in s i t u . In this work we report only RT measurements. Evaporated samples were measured with MES and CEMS (Conversion Electron M~ssbauer Spectroscopy) at RT.

3. RESULTS AND DISCUSSION

3.1. IS and AEQ from M~ssbauer e f f e c t measurements

Amorphous FexBl_ x with x ~ 50 a/o showed paramagnetic spectra 5. These were f i t - ted by two Lorentzian lines. The mean i s o m e r s h i f t T ~ r e l a t i v e to ~-Fe and quadrupole s p l i t t i n g AEQ were determined from the peak positions. The ferromagnetic spectra were f i t t e d by a sextuplet of Lorentzians from which only the mean isomer s h i f t is taken in this study. Values o f T S-and A--~are shown in figures 1 and 2, respectively. The value of AE---Q of amorphous Fe82.5BI7.5 was obtained from the paramagnetic state. This measurement had to be performed very quickly and c a r e f u l l y to avoid c r y s t a l l i z a t i o n I. AEQ was 0.43 mm/sec at 610 K. The corresponding value at room temperature was extrapolated from temperature de- pendent AEQ measurements to be about 0.52 mm/sec. Values o f T Sand A--~ f o r 57Fe implanted into c r y s t a l l i n e boron 2 are also indicated in f i g u r e I and 2.

3.2. I n t e r p r e t a t i o n o f T ~ w i t h Miedema-Van der Woude model

The Miedema model was o r i g i n a l l y developed as an empirical model to predict the heat of formation of binary alloys 6. I t was shown by Miedema and Van der Woude 7'8 that the 197Au isomer s h i f t in Au alloys and compounds could also be analyzed in terms of the so-called Miedema parameters and an additional volume mismatch term. According to this Miedema-Van der Woude model the isomer-shift

( r e l a t i v e to ~-Fe) IS(x) of amorphous FexAI_ x alloys is given by:

IS(x) = Cs(X ) 6(IS)max • (1)

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W. Hoving et al. / MOssbauer isomer-shifts and quadrupole splittings 423

04 ~ 1~

o] ! ~l]p

i i

.s.. oz "° ° ° ~ "I ~ o,i

! I i

01 o o ~ O.6i ~ o x o

o o ~ 20 4o 60 e0 ~oo o 4! zo ~o 60 eo loo

Fe el % B B Fe (It % B B

FIGURE 1 FIGURE 2

Mean isomer s h i f t ~ r e l a t i v e to ~-Fe ( f i g . I) and quadrupole s p l i t t i n g ( f i g . 2) a t room temperature versus boron content in amorphous i r o n - b o r o n , "

o sputtered on b o r o n - n i t r i d e at RT;

• sputtered on b o r o n - n i t r i d e at LN2-temp.;

? evaporated on q u a r t z ; A evaporated on alumin~um;

a data of C~ien et a l . J, s p u t t e r e d ; implanted L Fe i n t o c r y s t . B;

+ c r y s t a l I i ne compounds ; :~ melt-quenched ribbon.

Cs(X ) is the contact surface c o n c e n t r a t i o n of A-atoms around Fe-atoms defined by:

( I - x) V~/3-

Cs(X) = .~2/3 (1 - x) V 2/3 " (2)

XVFe + A

Here V is the atomic volume per mole. ~(IS)max is the isomer s h i f t ( r e l a t i v e t o

~-Fe) in a d i l u t e unstrained system in which each Fe atom i s surrounded by A atoms only. I t i s represented as:

, A F e , , Fe

~(IS)max = P ' ( ~ - ~ e ) + Q (nws - nWSJ/nws . (3) The f i r s t term in eq. (3) r e f l e c t s the i n t e r a t o m i c charge t r a n s f e r between atomic c e l l s of atom A and the Fe-atoms, thereby changing the s - e l e c t r o n density a t the Fe nucleus. A l i n e a r r e l a t i o n s h i p between the change o f the number of e l e c - trons (s and d t o g e t h e r ) per i r o n atom and the increase in the s - e l e c t r o n densi- t y a t the Fe-nucleus is assumed. This term i s determined by the d i f f e r e n c e in e l e c t r o n e g a t i v i t y or chemical p o t e n t i a l between the c e l l s . Instead o f t a k i n g the chemical p o t e n t i a l the macroscopic w o r k f u n c t i o n @* is used 9. The second term of eq. (3) takes i n t o account the i n t r a - a t o m i c charge r e d i s t r i b u t i o n on a l l o y i n g , when there i s a d i f f e r e n c e in e l e c t r o n d e n s i t y nWS o f the d i s s i m i l a r atomic c e l l s (WS is the Wigner-Seitz c e l l ) . This e l e c t r o n - d e n s i t y mismatch a t the c e l l boundaries i s removed by means of s + d e l e c t r o n t r a n s i t i o n . Since s - e l e c t r o n s

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424 W. Hoving et al. / Mbssbauer isomer-shifts and quadrupole splittings

r e s i d e more a t the o u t s i d e regions o f the atomic c e l l s than d - e l e c t r o n s , conversion o f s - t y p e e l e c t r o n s i n t o d - t y p e e l e c t r o n s r e s u l t s in a decrease o f nWS. P' and Q' are o f o p p o s i t e sign and w i t h i n a given class o f m a t e r i a l s (Fe-base a l - l o y s ) they can be regarded as c o n s t a n t s .

For s t r a i n e d systems an a d d i t i o n a l term is necessary t o take i n t o account the change i n isomer s h i f t when the volumes o f the i r o n c e l l s change i n a m a t r i x of A atoms o f d i f f e r e n t s i z e . This volume mismatch c o n t r i b u t i o n can be d e r i v e d from e l a s t i c continuum c o n s i d e r a t i o n s 7 ' 8 ' 1 0 "

0.615 K A VA - VFe ~ IS

ISvol = 0.615 K A + K F e F - - - V - ~ e ~ " (4)

K is the bulk modulus I I

Values o f ~ , nWS, V and K f o r i r o n and boron are given i n Table 1 6'11 TABLE

~*(v)

Fe 4.93

B 4.75

nWS 5.55 3.72

Vm(cm3) 7.1 4.7

K(IO I I N/m 2) 1.683 1.78

3.3. A n a l y s i s o f IS and AEQ of amorphous i r o n - b o r o n .

The isomer s h i f t T ~ a s a f u n c t i o n o f boron surface c o n c e n t r a t i o n C s i s given i n f i g u r e 3.

°4

03 -"

o ~ o

LSQ -tit #

I~ o]..:.>oj.S ~x ° :

0 0 ~ ' ~'(] ' z' 0 ' g'O ' 9'0 ' 100

FIGURE 3

Mean isomer s h i f t T ~ a t room temperature ( r e l a t i v e t o ~-Fe) as a f u n c t i o n o f surface c o n c e n t r a t i o n o f boron atoms C s i n amorphous i r o n - b o r o n . For legend see f i g . 1 and 2.

A l e a s t squares f i t t o a s t r a i g h t l i n e on the i r o n - r i c h side and e x t r a p o l a t i o n to C s = i gives 6 ( I S ) ~ _{m Q A} = 0.50 mm/sec.

Fe C s (%~ B

From the Miedema-Van der Woude model w i t h o u t volume c o r r e c t i o n term we f i n d ( w i t h P' = 0.66, Q' = - i . 5 0 as determined from a f i t o f 6(IS)max o f 57Fe d i l u - ted i n several c r y s t a l l i n e t r a n s i t i o n metal h o s t s , analogous to r e f e r e n c e 8, 13 and 14) ~(IS) c a l c = 0 38 mm/sec The volume mismatch c o n t r i b u t i o n c a l c u l a t e d

, , , m ~ ~IS" I ~ ] 12 • , , l ~ , C a l c

from eq. tq) wl~n ~ = .JJ mm/sec ms ~ m)vol = - 0 . 1 8 mm/sec. With volume IS~ c a l c = (0.38 - 0.18) mismatch term we then f i n d f o r s t r a i n e d systems 6( ' m a x , s t r a i n e d

mm/sec = 0.20 mm/sec.

With the Miedema-Van der Woude model i n mind we draw the f o l l o w i n g conclu-

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W. Hoving et al. / M~ssbauer isomer-shifts and quadrupole splittings 425

sions from f i g u r e 3:

on the i r o n - r i c h side the amorphous F e x B l _ x - a l l o y s are dense s t r a i n f r e e pack- ed;

- f o r x < 50 a/o the volume mismatch c o r r e c t i o n term is necessary, i n d i c a t i n g _% t h a t the i r o n atoms OCCUpy s t r a i n e d p o s i t i o n s in the heap of boron atoms;

implanted i r o n i n t o boron also has a s t r a i n e d s t r u c t u r e .

I t can also be seen from f i g u r e 3 t h a t our data of the isomer s h i f t are in good agreement with Chien's data 5 f o r sputtered samples; a t x ~ 50 a/o small d e v i a - t i o n s occur. This could be caused by u n c e r t a i n t i e s in the compositions of the sputtered samples. Also the substrate temperature of the sputtered samples seems to i n f l u e n c e the value o f ~ . As noted before, the composition of the evaporated samples is b e t t e r c o n t r o l l e d .

The c o n t r i b u t i o n s to the e l e c t r i c f i e l d g r a d i e n t (which is p r o p o r t i o n a l to the quadrupole s p l i t t i n g ^~EQ) at the 57Fe nuclei can be d i v i d e d in an i n t e r a t o - mic and i n t r a - a t o m i c c o n t r i b u t i o n . But since the i n t r a - a t o m i c r e d i s t r i b u t i o n is u s u a l l y assumed to r e f l e c t the nearest neighbour charge asymmetry, the i n t e r a t o - mic c o n t r i b u t i o n is considered as an a m p l i f i c a t i o n term so t h a t only the neighbour c o n t r i b u t i o n has to be c a l c u l a t e d f o r the r e l a t i v e shape o f the AE n vs.

composition dependence. The e l e c t r i c f i e l d g r a d i e n t has been c a l c u l a t e d ~5 ~ as- suming p o i n t charges in computer simulations of quasi c r y s t a l l i n e packings and dense random packings of hard spheres (DRPHS). We f i n d t h a t not only in the case of DRPHS models, as suggested by Czjek et a l . 16 , but also in t h a t of quasi c r y s t a l l i n e models the p r o b a b i l i t y f o r ~EQ = 0 and the asymmetry parameter n = 0 is very small. Furthermore we compute t h a t the shape o f the ~ vs. com- p o s i t i o n is convex, in disagreement with the experiments. With the isomer s h i f t s in mind t h i s suggests the f o l l o w i n g conclusion from f i g u r e 2: in the i r o n - r i c h region AEQ f o l l o w s the " i d e a l " s l i g h t l y convex curve. The s i g n i f i c a n t increase a t the b o r o n - r i c h side probably i n d i c a t e s t h a t the Fe atoms are squeezed i n t o more asymmetric atomic surroundings.

3.5. Concluding remarks

I t must be noted t h a t in Miedema's model f o r the d e s c r i p t i o n of the heat of f o r - mation of Fe with s,p-elements an a d d i t i o n a l term was necessary associated with the h y b r i d i z a t i o n of the Fe 3d band with the s,p-bands o f the nonmagnetic com- ponent (the s o - c a l l e d R-term6'7). I t is not c l e a r what the e f f e c t o f h y b r i d i z a - t i o n of the i r o n 3d band is on the isomer s h i f t . In cases analyzed u n t i l now the Miedema-Van der Woude model can describe the general f e a t u r e s (e.g. the sign and trend) o f the isomer s h i f t versus composition in the amorphous i r o n - b o r o n system s a t i s f a c t o r y , although u n c e r t a i n t i e s about possible ordering e f f e c t s (chemical s h o r t range order) which a f f e c t the surface concentrations s t i l l remain. To re- move these u n c e r t a i n t i e s and prove the v a l i d i t y of the Miedema-Van der Woude

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426 W. Hoving et aL / MOssbauer isomer-shifts and quadrupole splittings

model a s i m i l a r examination of other amorphous systems combined with d i f f r a c - t i o n experiments, such as (energy-dispersive) X-ray d i f f r a c t i o n , neutron d i f - f r a c t i o n and EXAFS is necessary. Photo-electron spectroscopy combined w i t h band s t r u c t u r e c a l c u l a t i o n could be very useful in checking the v a l i d i t y of the Miedema-terms.

ACKNOWLEDGEMENT

We l i k e to thank Mr. C. Bos, Mr. E.A.G. Weits and Drs. P.M.L.O. Scholte f o r t h e i r help at performing the measurements and the helpful communications.

This i n v e s t i g a t i o n forms part of the research program of the " S t i c h t i n g voor Fundamenteel Onderzoek der Materie" (Foundation f o r Fundamental Research on Matter - FOM) and was made possible by f i n a n c i a l support from the "Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek" (Netherlands Organization f o r the Advancement of Pure Research - ZWO).

REFERENCES

i ) F.E. Luborsky, H.H. Liebermann, J.J. Becker, J.L. Walter, Proc. Third I n t . Conf. on Rapidly Quenched A l l o y s , Sussex, 1978.

2) B.D. Sawicka & J.A. Sawicki, Nucl. I n s t r . Meth. 209/210 (1983) 799; B.D.

Sawicka, p r i v a t e communication.

3) A.S. Schaafsma, " M e t a l l i c Glasses", Ph.D.-thesis (1981), Solid State Phy- sics Laboratory, University of Groningen, The Netherlands.

4 H.C. Theuerer & J.J. Hauser, Trans. Metall. Soc. AIME, 233 (1965) 588.

5 C.L. Chien & K.M. Unruh, Phys. Rev. B, vol. 25, no. 9 (1982) 5790.

6 A.R. Miedema, F.R. de Boer & P.F. de Ch~tel, Physica IOOB (1980) i . 7 A.R. Miedema & F. van der Woude, Physica IOOB (1980) 145.

8 F. van der Woude & A.R. Miedema, Solid State Comm. 39 (1981) 1097.

9 H.B. Michaelson, IBM J. Res. Develop., vol. 22, no. i (1978) 72.

10 J.D. Eshelby, Solid State Physics (edited by F. Seitz and D. T u r n b u l l ) , vol. 3, p. 116 (Academic Press, New York, 1956).

i i ) C. K i t t e l , I n t r o d u c t i o n to Solid State Physics, 5th e d i t i o n , p. 85 (John Wiley & Sons, I n c . , New York, 1976).

12) R. I n g a l l s , F. van der Woude & G.A. Sawatzky, M~ssbauer Isomer Shifts ( e d i - ted by G.K. Shenoy and F.E. Wagner), p. 405 (North-Holland Publishing Com- pany, Amsterdam, 1978).

13) A.M. van der Kraan & K.H.J. Buschow, Phys. Rev. B 25, no. 5 (1982) 3311.

14) A.M. van der Kraan & K.H.j. Buschow, Phys. Rev. B 27, no. 5 (1983) 2693.

15) M. Tegze, p r i v a t e communication.

16) G. Czjek, J. Fink, F. G~tz, H. Schmidt, J.M.D. Coey, J.P. R e b o u i l l a t & A.

Li~nard, Phys. Rev. B 23 (1981) 2513.