Nanostructured amorphous SiAu alloys — Structure and atomic correlations

MATERIALS SCIENCE & ENGINEERING ELSEVIER

Materials Science and Engineering B32 (1995) 295-306

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Nanostructured amorphous S i - A u alloys -- structure and atomic correlations A. Sturm, A. Wiedenmann, H. Wollenberger Hahn-Meitner-Institut Berlin GmbH, A G NM, Glienicker Str. 100, 14109 Berlin, Germany

Abstract Nanostructured amorphous Si~_xAUxalloys (0.1 ~
Keywords: Amorphous materials; Neutron scattering; Grain boundaries; Small-angle scattering

1. Introduction During the last decade, a new class of solids has been developed--the so-called nanostructured materials. T h e s e materials are p r o d u c e d by compacting powders consisting of grains of several nanometres in diameter. T h e properties of nanostructured materials are determined by the fact that almost equal volume fractions of atoms belong to the interior of the grains and the interfacial regions. Powders with such grain sizes can be p r o d u c e d by different methods, e.g. inert gas condensation or high energy ball milling (for a review of the synthesis, structure and correlated properties, see Ref. [1]). For archetypical nanostructured materials, produced by compacting crystalline grains, a high volume fraction of defects (mainly grain boundaries) are e m b e d d e d in regions with crystalline structure. T h e single crystallites are randomly oriented with respect to each other. T h e thickness of the interfaces between the crystallites is about 1 nm. T h e atomic arrangements in 0921-5107/95/$9.50 © 1995 - Elsevier Science S.A. All rights reserved SSDI 0921-5107(95)03020-4

the interfacial regions are characterized by a reduced density and different atomic nearest neighbour correlations compared with the crystal. Based on this conception, it was speculated that an analogous situation might occur when amorphous particles are compacted. According to a simple hypothesis, each particle has the glass structure characteristic of, for example, the melt-spun volume glass. Since the particles solidify when isolated, and are compacted in r a n d o m orientations at the temperature at which they are configurationally frozen, the interfaces between two formerly isolated, now adjacent, particles should exhibit a reduced atomic density and a random distribution of atomic spacings instead of the shortrange order of the volume glass, similar to the situation found in shear bands in metallic glasses [2,3]. In this paper, we present the results and interpretation of a small-angle neutron scattering (SANS) study and density measurements on a set of nanostructured amorphous Sil_xAu x alloys (0.1~
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MaterialsScience and Engineering B32 (1995) 295-306

wide-angle neutron scattering (WANS). SANS supplies information on modulations of atomic density or composition on a scale typically between 1 nm and several 100 nm, and it has been proven to be a powerful technique for qualitatively and quantitatively determining the microstructure of nanostructured crystalline materials [4-7]. WANS supplies information about the atomic correlations on a scale between 0.1 and 1 nm, i.e. the atomic distance distributions as well as coordination numbers. 2. Experimental details 2.1. Sample preparation The nanostructured amorphous samples were produced by an inert gas condensation method with subsequent in situ consolidation, which is almost identical to the method used to prepare nanostructured crystalline samples [8] and is described in detail in Refs. [9] and

[10]. A high vacuum system at 10-7 mbar was filled with 3 mbar 99.999% pure He. Au and Si were thermally evaporated from the molten alloy. The vapour condensed in a small nucleation and growth zone in the vicinity of the evaporation source to form nanometresized amorphous particles. The particles were transported via convective flow of the He gas to a liquidnitrogen-cooled surface where they adhered and were scraped off. When enough powder had accumulated to form a sample, evaporation was stopped, a high vacuum was re-established and the powder was transferred to an in situ mechanical consolidation system. The powder was consolidated under high vacuum at 1.6 GPa for 120 s. For all samples, the powder was pressed with the same external parameters. The nanostructured amorphous samples were 8 mm diameter discs typically 150-500/~m thick. The sample composition was determined by energy dispersive X-ray fluorescence measurements with a scanning electron microprobe. The composition of the samples varied by _+ 1 at.% across the surface. 2. 2. Density measurements The macroscopic density was determined by the Archimedes method in diethylphthalate (C12H1404) [9,10]. From the measured weights, the geometrical density PGeo (given by the total sample volume including open and closed porosity), the effective density PE (given by a reduced sample volume including only the closed porosity) and the volume fraction of open porosity fop = 1 - (PC,eo/PE) were estimated. The open and closed porosities are the parts of the total porosity which can be filled or not filled with liquid respectively.

2. 3. Neutron scattering experiments The SANS measurements were carried out using the small-angle cameras D17 and D11 at the high flux reactor (ILL, Grenoble), PAXE (LLB, Saclay) and on the SANS spectrometer of the BER II reactor (HMI, Berlin). The differential scattering cross-section do(Q)/dQ was estimated by the standard treatment of the scattering data [9] as a function of the momentum transfer Q (Q = (4:r/2) sin 0, where 20 is the scattering angle and 2 is the wavelength) in absolute units of barn sr- 1 atom- 1. The WANS measurements were carried out at the spectrometer 7C2 (LLB, Saclay)[9].

3. Results and discussion 3.1. Sample preparation Amorphous Si~ _xAux samples were produced in the Au concentration range 0.1 ~
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measured. The volume fraction of open porosity v a r i e s f r o m s a m p l e to s a m p l e b e t w e e n 4 a n d 15 vol.%. From an understanding of the mechanisms which occur d u r i n g t h e c o m p a c t i o n o f d i s p e r s e d p o w d e r s (see p. 114 in Ref. [16]), initially, p a r t i c l e r e a r r a n g e m e n t a n d sliding t a k e place. T h e n u m b e r o f c o n t a c t s a n d t h e contact area between the particles increase, and geometrical densities between 70% and 80% of the t h e o r e t i c a l d e n s i t y a r e a c h i e v e d . P o w d e r s w i t h a size distribution of grains reveal higher densities than m o n o d i s p e r s e d grains. F o r a f u r t h e r i n c r e a s e in t h e density, p l a s t i c d e f o r m a t i o n o f t h e g r a i n s is n e c e s s a r y . Following these arguments, from the measured geom e t r i c a l d e n s i t i e s o f t h e n a - S i - A u s a m p l e s , it c a n b e c o n c l u d e d that p a r t i c l e r e a r r a n g e m e n t a n d sliding a r e the dominant mechanisms during compaction. S i n c e all s a m p l e s w e r e c o n s o l i d a t e d w i t h t h e s a m e external compaction parameters, characteristic param e t e r s o f t h e p o w d e r , such as t h e g r a i n size, s h o u l d b e r e s p o n s i b l e f o r t h e d i f f e r e n t r e l a t i v e effective d e n s i t i e s PE/PF a n d t h e o p e n p o r o s i t y fop.

3.3. Small-angle neutron scattering Fig. 2 s h o w s t h e d i f f e r e n t i a l s c a t t e r i n g c r o s s - s e c t i o n d o ( Q ) / d f 2 f o r s a m p l e s with d i f f e r e n t r e l a t i v e effective densities, a n d as a f u n c t i o n o f t h e m o m e n t u m t r a n s f e r

Table 1 Geometrical density PGeo and effective density p~: of nanostructured amorphous Si-Au samples, volume fraction of open porosity f,p and relative densities P/Ce,,,E//PF obtained from a comparison with the density of amorphous Si-Au films PF from Ref. [ 15] Sample

XAu (at.%)

PG~o (g cm s)

PE (g cm -3)

f,p (vol.%)

PSe,,/PV (%)

PE/P~' (%)

A.23 A.22 A.00 A.13 A.07 A. 11 A.06 A.09 A.15 A.04 A.14 A.12 A.18 A.19 A.08 A.20 A.01

9.2 12.0 13.3 13.4 13.7 14.4 14.5 14.9 15.0 15.2 16.0 16.0 16.2 17.1 18.1 18.1 28.2

2.72_+0.01 3.27 -+ 0.01 3.44-+0.01 3.31 -+0.01 3.00 -+0.01 3.03 _+0.04 3.11 _+0.01 3.08 _+0.02 3.59_+0.03 3.24_+0.02 3.43_+0.02 3.52_+0.01 3.36_+0.01 3.66 _+0.01 3.04 _+0.02 3.11 _+0.02 3.77 + 0.02

3.02_+0.01 3.54 _+0.01 3.68_+0.01 3.50+0.01 3.25 _+0.01 3.31 _+0.01 3.48_+0.01 3.47 _+0.01 3.65_+0.01 3.39_+0.01 3.63_+0.01 3.69_+0.01 3.72_+0.01 3.85 _+0.01 3.43 + 0.01 3.33 _+0.01 4.22 _+0.01

9.9_+0.2 7.6 _+0.2 6.6-+0.1 5.6_+0.2 7.5 _+0.2 8.5 _+0,2 10.6_+0.2 11.3 _+0.3 1.8_+0,5 4.3_+0,4 5.4-+0.3 4.7_+0.1 9.8_+0.2 4.7 _+0.1 11.3 _+0.5 6.7 -+ 0.3 10.7 _+0.3

74_+6 79 -+ 6 79-+6 75-+6 68 -+ 5 67 -+ 6 68_+5 71 + 6 77_+6 69-+6 71 _+6 73_+6 69_+5 73 _+6 59 _+5 60 _+5 55 + 5

82_+4 85 _+4 84-+3 80_+3 73 _+3 73 _+3 76+3 75 _+3 79_+3 75-+3 75_+3 77_+2 77_+3 77 _+3 67 _+2 65 _+2 62 _+2

B.14I B.I 4II B. 161 B. 16II B.22I

22.9 29.2 30.7 31.6 33.0

4.01 _+0.02 3.94 _+0.02 5.19 -+ 0.02 5.30 + 0.02 5.64 _+0.02

4.69 + 0.01 4.58 _+0.01 5.96 _+0.02 6.23 _+0.02 6.68 _+0.02

14.5 _+0.2 14.1 + 0.2 12.9 _+0.2 15.0 _+0.2 15.6 _+0.3

68 _+5 66 _+5 72 _+5 72 + 6 75 _+6

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Fig. 3. Example of the best fit for dcr(Q)/dQ (full line) to the observed data (circles), including the contributions according to the model described in the text (broken lines).

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Q. Double logarithmic scales are used because the data extend over several decades. For the sample with the highest relative density of 88%, a power law of the scattering cross-section d o ( Q ) / d Q - Q-~ over almost two orders of Q and five orders of intensity was observed below Q = 1 nm 1 T h e exponent a of the power law was 3.37. For all other samples, an additional scattering contribution occurs, overlapping the power law in the middle of the investigated Q range. Apparently, the scattering curves show a systematic variation as a function of the relative effective densities PE/Pv achieved during the preparation. For samples with decreasing relative effective density, the intensity of the scattering contributions in the medium Q range increases, while the intensity at low Q decreases. A quantitative analysis of the SANS data was carried out using the standard p r o c e d u r e of calculation of d o ( Q ) / d Q on the basis of a modelled microstructure, which is described in detail in Ref. [10]. Our model included contributions from the following scattering structures. (1) Large inhomogeneities characterized by power law scattering at small Q, as described by daa( Q)/dff2Q - % with a = 3.37. (2) Spherical particles with radii of several nanometres and log-normal size distribution e m b e d d e d in a matrix of reduced scattering length density formed by grain boundaries and free volumes. Their scattering contrast Ar/G = q~ - ~/M is attributed to density fluctuations leading to a curved scattering contribution in the medium Q range. (3) Incoherent background scattering at large Q, denoted as 10.

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T h e contributions to the scattering intensity were assumed to be independent of each other. T h e modelled structure function was fitted to the data by an interactive trial and error procedure. Two size distributions (grain (G), pore (P)) were necessary to fit the experimental curves satisfactorily. A n example of such a fit for d o ( Q ) / d ~ derived from our scattering model, together with the single contributions according to (1)-(3), is plotted in Fig. 3. It should be noted that the model curves describe the measured scattering curves rather well over more than two decades in Q and more than four decades in the scattering intensity. A n example of the distribution functions resulting from the fitting p r o c e d u r e of the curve in Fig. 3 is plotted in Fig. 4.

3.3.1. Scattering in the medium observed Q range In this Q range, particle scattering supplies the dominant contribution to the scattering intensity.

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From the size distribution Nn(R), the average particle radius (Rn) was determined. Fig. 5 shows the correlation between the average particle size and the relative effective density. For a density increase from 73% to 83%, the average particle size for the first distribution (denoted G) decreases from about 2.7 nm to 1.8 nm, while the second distribution (denoted P) decreases from about 1.5 nm to 1 nm. In the sample with 88% relative effective density, the particles must be so small that their (weak) scattering contribution is no longer resolved beyond the strong power law contribution. Keeping in mind the results of the density measurements (Section 3.2), smaller grain sizes of the powder are likely to be responsible for higher relative effective densities. The size distribution denoted G was attributed to the amorphous grains for the following reasons: (1) during the inert gas condensation, particles with a log-normal size distribution are produced [17]; (2) rearrangements and sliding of the grains are the dominant compaction mechanisms; smaller grains exhibit higher relative densities when applying the same external compaction parameters (see above); (3) for a higher compaction, the number of contacts between the grains increases and the number of boundaries between the grains and the free volume decreases; therefore the scattering contrast in the sample decreases, resulting in a decreasing scattering intensity in the medium Q range. Assuming a constant composition of the grains and the surrounding matrix (i.e. only density fluctuations), and also that the grains have a maximum density equal

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Fig. 6. Volume fraction of the amorphous grains obtained following the two-phase model described in the text vs. the relative effective density PE/Pv.

to the density of the amorphous Si-Au films of the same Au content, i.e. PG = Pv, the volume fraction of grains fG and the matrix density PM/PFwere estimated. As shown in Fig. 6, the volume fraction of the amorphous grains is between 30 and 50 vol.%, and increases slightly with increasing relative effective density. At the same time, the density of the matrix increases from about 60% to about 75% of the grain density, as shown in Fig. 7(a). The volume fractions of the grains and densities of the matrix in the na-Si-Au alloys are very similar to the corresponding values observed in nanostructured crystalline (nc) materials prepared by the same method. Following a similar model, Jorra et al. [4] estimated, in nc-Pd, a volume fraction of grains between 23 and 36 vol.% and a matrix density of 4 0 % - 6 0 % of the grain density. Wagner et al. [6] determined, in nc-Fe, about 50 vol.% grains and a matrix density of about 40%. In na-Si-Au, the observed increase in the matrix density was attributed to a decreasing volume fraction of the free volume. This implies an almost constant density of the interfaces between the grains, which seems reasonable since rearranging and sliding are the dominant compaction mechanisms. As a reference, the sample with the highest relative effective density of 88%, for which only power law scattering was observed, was assumed to consist only of grains and interfaces. Using this assumption, an equation to calculate the relative density of the interfaces can be derived [10]. An almost constant density of the interfaces of about 80% of the grain density is determined, as shown in Fig. 7(b). Furthermore, the additional fraction of free volume in the other samples, compared with the sample with 88% relative effective density, can be estimated. As

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shown in Fig. 7(c), this additional volume fraction decreases from about 30 vol.% to about 5 vol.%. Therefore, together with the volume fraction of the grains (Fig. 6), the volume fraction of the interfaces can be estimated to be between 40 and 60 vol.%. T h e density values of the interfaces are in good agreement with the values determined in nc materials. For the unrelaxed grain boundaries in nc-Pd, Klingel [18] estimated a relative density of 80%. Wagner et al. [5] determined, in nc-TiO2, compacted at 550 °C, an

interfacial density of 70% of the bulk rutile density, covering 27 vol.% of the specimen volume. While the densities of the interfaces in na and nc samples agree well within the measured error, there is a significant difference in the volume fraction. This is because of a greater n u m b e r of interfaces, a larger interface thickness, or both, in na-Si-Au. To estimate the average thickness of the interfaces, the interface was assumed to be a spherical shell with thickness {6i) around a spherical grain with radius {Ro). T h e average thickness of the interface between two grains 2(6i) is plotted in Fig. 8 vs. the relative effective density. It decreases from about 1.7 nm in samples with 73% relative effective density to about 0.9 nm in samples with 85% relative effective density. In nc-Pd, the thickness of the grain boundaries was determined by high-resolution electron microscopy ( H R E M ) to be between 0.4 and 0.6 nm [19] or larger than 0.6 nm [20]. It should be noted that the initial state of the grain boundaries can be influenced by the sample preparation for H R E M . From the segregation of hydrogen in nc-Pd, the average thickness of the grain boundaries was calculated to be between 0.8 and 1.1 nm [21]. Thus the absolute thicknesses of the interfaces in na-Si-Au samples and nc-Pd agree well with each other. Taking into account that na-Si-Au samples with higher relative density contain smaller grains, the ratio of the shell thickness {di) to the grain radius (RG) is obtained. T h e result is shown in Fig. 9. A n almost constant value of 0.3, independent of the relative effective density, is found. T h e same calculation yields, for nc-TiO2 with the data from Ref. [5], a thickness of the grain boundary

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between 1 and 1.7 nm and a ratio of the interface thickness to the grain radius of 0.1, independent of the relative density. This hints at a different structure of the interfaces in na-Si-Au samples and nc materials. While the thickness of the interfaces is about the same in both materials, in na-Si-Au the relative thickness is significantly higher. In contrast with this result, in na-Pdv0Fe3Siz7 , from M6ssbauer spectroscopy data, an interface thickness of 0.4 nm was determined [22]. These different results may be attributed to different atomic correlations in na and nc materials. For example, in crystalline materials, on the basis of the Peierls-Nabarro model, an increasing core size with decreasing interatomic coupling is found in dislocations [23]. A similar effect could be responsible for the different interface structures and thicknesses.

3.3.2. Scattering at large Q and background scattering An additional size distribution Np(R) improved the fit of the experimental curves around Q = 1.6 nm -~. The average particle radius (Rv) determined from this distribution is included in Fig. 5. (Rp) decreases slightly with increasing relative effective density, but not as strongly as (RG), which was attributed to the amorphous grains. Furthermore, the relative width of this second size distribution Np is much smaller than the width of NG, as shown in Fig. 4. Since this second size distribution was observed in all samples and is also correlated with the relative effective density, it is attributed to closed pores. From powder metallurgy, it is known that during compaction the free volume is partly encapsulated in closed pores. The size of these pores decreases with increasing compaction, while their volume fraction is decreasing [16], which is in

301

agreement with the results observed in this investigation. The volume fraction of these closed pores was estimated to be between 1 and 6 vol.%. These values of the closed porosity, which is part of the "matrix" surrounding the amorphous grains, are lower than the estimated values of the additional free volume shown in Fig. 7(c). We can conclude that up to 50% of the free volume of the matrix consists of spherical closed pores with radii between 1 and 1.5 nm. However, these values must be considered as a lower limit, because a vacuum was assumed inside the pores. If these pores were filled with gas or vapour, the contrast would be lower and the volume fraction higher. The constant value I 0 of the intensity, observed at Q > 2 nm-1, varies between the samples from 0.7 to 1.4 barn sr- 1 atom- l, and is ascribed to the incoherent scattering of 10-20 at.% hydrogen absorbed during the preparation.

3.3.3. Scattering at low Q The most interesting feature of the power law doa( Q)/df2 ~ Q-a, observed over the whole concentration range (0.1 ~
do(Q)/d~2=PmQ -(om)

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Materials Science and Engineering B32 (1995) 295-306

, and the scattering law corresponds to 4.5

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where the fractal dimension is 2 ~ ~, where Z is the cut-off parameter; structures larger than g can no longer be described as a fractal), whereas for very rough surfaces (D,<3), exponents between a = 3 and a = 4 are expected. In this picture, the power law scattering observed in na-Si-Au alloys must therefore be attributed to a surface fractal with the fractal dimension of Ds = 2.63, i.e. on a scale between 3 nm and at least ~/Qm~n= 200 nm, the surface shows a scale invariant structure, while no cut-off is observed. The intensity parameter P, is proportional to the total fractal surface S [26] Ps = 27rA G2SF(5 - D~) sin[Tr(D~- 1)/2]

(3)

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where the relevant scattering contrast AT/s is equal to the average scattering length density of the sample ~/AuSi"The total fractal surface S increases slightly with increasing relative effective density. From this observation, we may conclude that the fractal surface structure is built up during the compaction process. In order to check whether the power law really results from a fractal surface, the scattering of a sample immersed in a contrast liquid was measured. A sample with an Au content of 14.5 at.% and relative density of pE/pv=76% was immersed in CS2 in order to fill the open porosity. The scattering length density of CS2, r/(CS2)=l.23x101° cm -2, is less than ~/auSi= 1.86 X 101° cm -2, and therefore the contrast is modified to A~s(CS2) =(b)RE-/](CS2)

=A~]s-

~](CS2)

(5)

which is not completely matched. The resulting scattering curve is compared in Fig. 10 with the corresponding curve measured without the liquid, together with the fit of the model. There is a striking decrease in intensity at low Q, resulting in a ratio of the constants P s ( C S z ) / P s = 0.353. However, the exponent a = 3.37 is not modified by the immersion liquid, which confirms that the fractal surface is the origin of the scattering at low Q. The fraction of the surface covered by contrast liquid, Scov/S, is calculated according to

Scov/S= [1

-

Ps(CS2)/P,]/[1

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A ~]s2(CS2)/At]s 2]

(6)

Actually, 73% of the total fractal surface was covered by the immersion liquid.

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By filling the open pores with the contrast liquid, the scattering length density of the matrix ~/M(CS2)= r/M +fop~/(CS2) should be increased and the contrast with the individual grains AqG(CSz) should be reduced to A,7o(CS2) = ,7o - 'TM(CS2)= A'lo -fo

'7(CS2)

(7)

This is effectively observed: the scattering curve in the medium Q range can be fitted exactly using the same parameters for the size distribution as for the curve without CS2, with the exception of the intensity parameters. From the ratio between the intensity parameters da(Q)/df~(CSz)/do(Q)/d~ = 0.563, the volume fraction fop of the open porosity can be evaluated. The value of f,p = 17 vol.% was determined, which compares favourably with the value of 12 vol.% found from density measurements. The small discrepancy may be ascribed to the large size of the C12H]404 molecules, which cannot enter the smallest channels. It should be emphasized that, for the formerly discussed fluctuation model [24], immersion in a contrast liquid will not change the intensity at all (except for minor effects at the external surface of the sample). In this model, the contrast results only from the density profile inside the "domains", which remains unaffected by the contrast liquid. In conclusion, the formation of the surface fractal in na-Si-Au alloys must result from the compaction of individual grains. Very recently, the scattering law has been calculated for a regular model assembly of spheres of uniform scattering length density [26]. The zero-order approximant is a sphere of radius a 0. The

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Materials Science and Engineering B32 (1995) 295-306

approximant of order n is obtained from the preceding approximant by adding spheres of radius aoZ " (2 ~
303

4. Atomic correlations in nanostructured amorphous Si71Au29 Inorganic, non-crystalline solids are generally characterized as belonging to either of the following two classes: metallic systems with an atomic structure resembling a dense random packing of hard spheres (DRPHS), which are characterized by a coordination number similar to that of dense packed crystalline phases ( 12 neighbouring atoms in the first coordination shell), or amorphous solids with covalent bonding and with a lower coordination number (e.g. four nearest neighbours for amorphous Si), which can be described as continuous random network structures (CRNS). In both types of system, the local order is characterized by correlations between atomic positions extending to several nearest neighbour spacings. The local order in na-Si-Au alloys was investigated by WANS and compared with analogous X-ray measurements (WAXS)[13]. Fig. 12 shows the characteristic modulation of the neutron scattering intensity •(20) as a function of the scattering angle 2 0, resulting from the atomic correlations in the amorphous state. In contrast with WAXS, the intensity, normalized to the scattering per atom, is much higher than expected from the scattering of Si-Au alone and decreases continuously at large values of 2 0. This behaviour is typical for materials containing hydrogen.

14.0

I

'F:

I

I

r" \A

E

"

before ~

I

I

I

I

I

I

1 I

90

•~

6.5

4.0

-0~ ~

LJ 1.5

i 0

Fig. 11. (a) Two- dimensional analogue of the third-order approximant of a non- random surface fractal built up by an assembly of spheres of uniform scattering length density [26]. (b) Model of a surface fractal structure of dimension D~ = 2.36 from Ref. [30]. In the case of na-Si-Au samples, the microstructure is composed of spherical substructures of densely packed grains (density PE) and interconnected channels of free volumes (open porosity).

after hydrogen correction i i ~ i I r i 25 50 75 100 Scattering angle 2e / degrees

i 125

Fig. 12. WANS intensity •(20) vs. the scattering angle 20 for an na-Si71Au29 sample. The much higher scattering intensity than expected from the scattering of Si-Au alone (about 4 barn per atom) and the continuously decreasing trend at large scattering angles are due to hydrogen. The calculated structureless intensity function of hydrogen is shown in the inset for different effective masses M/m. After the hydrogen correction, the scattering curve shows the broad modulations characteristic of an amorphous material.

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Materials Science and Engineering B32 (1995) 295-306

Subtracting the form factor for hydrogen (inset in Fig. 12) according to the correction procedure of Chieux et al. [31] leads to the curve ("after hydrogen correction") in Fig. 12, with oscillations around the expected constant value at large 20. This analysis yields a hydrogen content of about 10 a t . ° In an additional WANS experiment on samples which were never exposed to air, a similar hydrogen content was found, showing that it originates from the production process. By Fourier transformation of the total structure function S(Q), we obtain the total pair correlation function g(r), which describes the distribution of atoms around a central atom as a function of the interatomic distance r. Fig. 13 compares g(r) achieved from WANS and WAXS. For WAXS, g(r) is characterized by the existence of only two maxima at about r = 0.24 nm and r = 0.28 nm, while for WANS, g(r) clearly exhibits a third maximum in addition to the first two around r= 0.39 nm. Nevertheless, both experiments reveal correlations only between first and second nearest neighbours. The experimentally accessible total pair correlation function g(r) is the weighted sum of the partial correlation functions gAB(r)(A, B -= Au, Si)

g(r) = WAAgAA(r) 4- WBBgBB(r)+2 WABgAB(r)

(8a)

independent experiments, in the present case, three independent experiments are not available, but we can obtain detailed information from a comparison of WAXS and WANS. The calculated weighting factors (Eq. (8b)) for XAu=0.29 (see Table 2) show that the contribution of the Si-Si correlations to g(r) is about 9% for WAXS but 44% for WANS. While WAXS strongly represents the Au contributions, WANS more strongly represents the Si correlations. Therefore the third peak in g(r) observed by WANS is attributed to an Si-Si correlation. Furthermore, by comparing the heights of the two main peaks in g(r) for WAXS and WANS, we can conclude that the maximum at 0.24 nm corresponds to an Si correlation and the maximum at 0.29 nm corresponds to an Au correlation. To estimate the partial atomic correlations and the coordination numbers, the peaks in g(r) were fitted by a series of gaussian functions attributed to certain atomic pair correlations. While three partial correlations (Si-Si, Au-Si, Au-Au) are expected, only two maxima were observed in g{r). Various fits with nearly the same fit quality were possible as shown in Fig. 14. Combining the WAXS and WANS results, the atomic distances and numbers of nearest neighbours were estimated and compared with different structural models.

with WAB= (CACBbAbB)/(CAbA2 + CBbB2) where c is length. For correlation varying the

'

the concentration a binary system, functions, which weighting factors

'

'

i

'

'

'

(8b)

and b is the scattering there are three partial can be estimated by WAB with at least three

i

'

'

,

i

Table 2 Normalized weighting factors WAB(see Eq. (Sb)) of the partial pair correlation functions for an na-Si7~Au2, ) sample Correlation

X-rays

Au-Au Au-Si Si-Si

Neutrons

(%,)

(%)

49 42 9

24 32 44

'

2.0 tO

1.6

t--

1.2

g

t-

o

.m ,....,

~'N//f~

Neutrons

0.8 0.4

g o

1.6

0 .m

1.2 0.8

o.o

0'.2

'

o14

'

'

i

0.6

'

'

'

o.~

Atomic distance r / nm Fig. 13. Pair correlation functions g(r) as obtained from WANS and WAXS. With WAXS only two maxima are resolved, whereas with WANS a third maximum is observed at larger atomic distances r. Nevertheless, only correlations between first and second nearest neighbours are detected.

/

,\

/'X

\

/ "

'

i

\

/

0.4 0.0 0.20

0.25

0.30

0.25

0.30

0.35

Atomic distance r / nm

Fig. 14. Fitting of the total pair correlation function g(r) with a series of gaussian functions, each corresponding to a certain partial atomic correlation (also see Table 3).

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Materials Science and Engineering B32 (1995) 295-306

Table 3 Coordination numbers ZABcorresponding to the assignment of different partial atomic correlations to the gaussian functions in Fig. 14. The most probable assignment is printed in bold numbers (see text) Figure

r (nm)

ZAuAu

ZAuSi

Zsisi

14(a)

0.243 0.284 0.241 0.269 0.293 0.240 0.249 0.287 (I.238 0.246 0.286

3.6 5.3 2.0 6.2 1.3 1.2 3.2 5.0 0.7 3.4 5.3

3.3 4.9 1.8 5.7 1.2 1.1 2.9 4.6 0.6 3.1 4.9

5.0 7.5 2.7 8.6 1.9 1.7

14(b) 14(c) 14(d)

4.4

7.0 1.0 4.7 7.4

T h e local order in na-Si 7 lAU29 is characterized by: (1) an A u - A u nearest neighbour distance of 0.283 nm with about five nearest neighbours; when compared with 12 nearest neighbours in a dense packed metallic system, this scales roughly with a r a n d o m distribution of Au neighbours around an Au central atom in the first nearest neighbour shell; (2) correlation at about 0.244 nm is attributed to A u - S i nearest neighbours, with two Si atoms around an Au atom; (3) Si-Si correlations exhibit a broad distribution of nearest neighbour spacings ranging from 0.233 nm up to almost 0.3 nm; the correlation at about 0.39 nm is attributed to second nearest neighbours. Nanostructured amorphous Si71Au29 alloys, prepared by inert gas condensation and in situ compaction, exhibit a significantly reduced short- range order compared with metallic glasses with a D R P H S structure or amorphous solids with covalent bonding and CRNS. Nevertheless, this reduced short-range order is not due to the novel production technique, but is a characteristic of the S i - A u system itself. This is characterized by a broad distribution of nearest neighbour distances, similar to metallic Si-Si correlations in the melt.

5. Conclusions

Nanostructured amorphous Si~ _ xAux alloys (0.1 ~
305

Density measurements revealed that particle rearrangement and sliding are the dominant compaction mechanisms. From the SANS investigations, the observed background scattering at Q > 2 nm-~ is ascribed to the incoherent scattering of 1 0 - 2 0 at.% hydrogen, resorbed during the preparation. T h e SANS signal in the medium observed Q range is due to the contrast between amorphous grains and a matrix of lower density. Smaller particle sizes are correlated with higher relative effective densities. A higher density of the matrix, which is built up of grain boundaries and free volumes, is due to a decrease in free volume, while the density of the grain boundaries is almost constant and about 80% of the grain density. At small Q, power law scattering with an exponent a = 3.37 is observed, which is attributed to a surface fractal structure of dimension D~=2.63. During the compaction of the powder, agglomerates are formed on any scale, consisting of amorphous grains, grain boundaries and (closed) pores, as well as a system of interconnected channels of open porosity across the whole sample. T h e internal surface of the assembly of agglomerates exhibits fractal behaviour. WANS investigation of an na-Si71Au29 sample reveals a local order which is characterized by atomic correlations only between first and second nearest neighbours. A broad distribution of, in particular, Si-Si nearest neighbour spacings and low coordination numbers are found. T h e r e f o r e this material exhibits a significantly reduced short-range order compared with metallic glasses with a D R P H S structure or amorphous solids with covalent bonding and CRNS. T h e results suggest that na-Si71Au29 resembles the structure of frozen-in, non-simple liquids, formed by certain group IV and V elements and some of their alloys [32].

References

[1] H. Gleiter, Prog. Mater. Sci., 33(1989) 223. [2] T. Masumoto, H. Kimura, A. Inoue and Y. Waseda, Mater. Sci. Eng., 23(1976) 141. [3] EE. Donovan and W.M. Stobbs, Acta Metall., 29 (1981) 1419. [4] E. Jorra, H. Franz, J. Peisl, G. Wallner, W. Petry, R. Birringer, H. Gleiter and T. Haubold, Philos. Mag. B, 60 (1989) 159. [5] W. Wagner, R.S. Averback, H. Hahn, W. Petry and A. Wiedenmann, J. Mater. Res., 6 ( 1991 ) 2193. [6] W. Wagner, A. Wiedenmann, W. Petry, A. Geibel and H. Gleiter, J. Mater. Res., 6 ( 1991 ) 2305. [7] M. Miiller-Stach, H. Franz, U. Herr, J. Peisl, W. Petry and G. Wallner, J. Appl. Crystallogr., 24 ( 1991 ) 603. [8] R. Birringer, U. Herr and H. Gleiter, Suppl. Trans. Jpn. Inst. Met., 27(1986) 43. [9] A. Sturm, Thesis, TU Berlin D83, Fortschritt-Berichte VDI Reihe 5 Nr. 313, VDI-Verlag GmbH, Diisseldorf, 1993.

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[10] A. Sturm, A. Wiedenmann and H. Wollenberger, Nanostructured Matreials, 4 (1994) 417. [11] S. Takayama, J. Mater. Sci., 11 (1976) 164. [12} J. Weissmtiller, R. Birringer and H. Gleiter, Phys. Lett. A, 145(1990) 130. [13] J. Weissmiiller, J. Non-Cryst. Solids, 142 (1992) 70. [14] A. Sturm, A. Wiedenmann, H. Wollenberger and J. Weissmiiller, to be published. [15] Ph. Mangin, G. Marchal, C. Mourcy and Chr. Janot, Phys. Rev. 1:1,21 (1980) 3047. [ 16] R.D. German, Powder Metallurgy Science, MPIE Princeton, NJ, 1984. [17] C.G. Granqvist and R.A. Buhrman, J. Appl. Phys., 47 (1976) 2200. [18] M. Klingel, Thesis, Universit~it des Saarlandes, 1992. [19] G.J. Thomas, R.W. Siegel and J.A. Eastman, Scr. Metall., 24 (1990)201. [20] W. Wunderlich, Y. Ishida and R. Maurer, Scr. Metall. Mater., 24 (1990) 403. [21] T. Miitschele and R. Kirchheim, Scr. Metall., 2l (1987) 1101.

[22] J. Jing, R. Kr~imer, R. Birringer, H. Gleiter and U. Gonser, J. Non-Cryst. Solids, 113(1989) 167. [23] R. Bullough and V.K. Tewary, in ER.N. Nabarro (ed.), Dislocations in Solids, Vol. 2, North-Holland, Amsterdam, New York, Oxford, 1979, p. 5. [24] B. Boucher, P. Chieux, E Convert and M. Tournarie, J. Non-Cryst. Solids, 61/62 (1984) 511. [25] M. Schaal, E Lamparter and S. Steeb, Z. NaturJbrsch. Teil A, 44(1989)4. [26] P.W. Schmidt, J. Appl. Crystallogr., 24 ( 1991 ) 414. [27] P.W. Schmidt, J. Appl. Crystallogr., 15(1982) 567. [28] J. Teixeira, J. Appl. Crystallogr., 21 (1988) 781. {29J J.E. Martin and A.J. Hurt, J. Appl. Crystallogr., 20 (1987) 61. [30] H. Pape and J.R. Schopper, in K.K. Unger (ed.), Characterisation of Porous Solids, Proc. 1UPAC Symp., Bad Soden, 198Z Elsevier, Amsterdam, 1988, p. 473. [31] P. Chieux, R. de Kouchkovsky and B. Boucher, J. Phys. F, 14(1984)2239. [32] R.M. Waghorne, V.G. Rivlin and G.I. Williams, J. Phys. k, 6 (1976) 147.