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Structural study of Be43HfxZr57-x metallic glasses byX-ray and neutron diffraction

M. Maret, C.N.J. Wagner, G. Etherington, A. Soper, L.E. Tanner

To cite this version:M. Maret, C.N.J. Wagner, G. Etherington, A. Soper, L.E. Tanner. Structural study of Be43HfxZr57-x metallic glasses by X-ray and neutron diffraction. Journal de Physique, 1986, 47 (5), pp.863-871.<10.1051/jphys:01986004705086300>. <jpa-00210269>

863

Structural study of Be43HfxZr57-x metallic glassesby X-ray and neutron diffraction

M. Maret (+), C. N. J. Wagner (+ +), G. Etherington (+ +), A. Soper (*) and L. E. Tanner (**)

(+) Institut Laue-Langevin, 156X, 38042 Grenoble, France(+ +) Materials Science and Engineering Department, University of California,Los Angeles, California 90024, U.S.A.(*) Los Alamos National Laboratory, Los Alamos, New Mexico 87545, U.S.A. (1)(**) Lawrence Livermore National Laboratory, University of California, Livermore, California 94551, U.S.A.

(Rep le 23 septembre 1985, révisé le 27 dgcembre 1985, accepti le 10 janvier 1986)

Résumé. 2014 Les facteurs de structure partiels de Faber-Ziman des amorphes Be43HfxZr57-x sont calculés à partirde la combinaison d’une mesure de diffraction neutronique en temps de vol dans l’alliage avec x = 25 at % et troismesures de diffraction X dans les alliages avec x = 5, 25 et 54 at % en utilisant la substitution isomorphe entreles atomes d’hafnium et de zirconium. Les facteurs de structure partiels de Bhatia-Thornton sont ensuite déduits.A partir des fonctions de distribution radiale partielles, les nombres de coordination partiels sont calculés et per-mettent de déterminer le paramètre d’ordre chimique généralisé de Warren 03B11 dans la première couche de coor-dination. Le rayon extérieur de la première couche est bien défini par la position du premier minimum de la fonc-tion GNN situé à 3,8 A. Nous trouvons ainsi une valeur de - 0,033 pour 03B11, qui montre une faible tendance demise en ordre chimique.

Abstract. - The Faber-Ziman partial structure factors of the Be43HfxZr57-x glasses are calculated from the com-bination of one time-of-flight neutron diffraction measurement in the alloy with x = 25 at % and three X-ray dif-fraction measurements in the alloys with x = 5, 25, and 54 at % using the isomorphous substitution between Hfand Zr atoms. The Bhatia-Thornton partial structure factors are then deduced. From the partial radial distributionfunctions the partial coordination numbers are calculated and allow the generalized Warren chemical orderparameter 03B11 in the first coordination shell to be determined. The upper radius of the first shell is well defined bythe position of the first minimum of the GNN function located at 3.8 A. Thus, we find a value of - 0.033 for 03B11which indicates a slight tendency of chemical ordering.

J. Physique 47 (1986) 863-871 m 1986,

Classification

Physics Abstracts61. lOF - 61.12D - 61.40D

1. Introduction

Binary BeHf, BeZr and BeTi, and ternary BeHfZrand BeTiZr amorphous alloys have been producedby ultra-rapid liquid quenching for compositionranges surrounding the respective eutectics 34 at %Be-Zr, 33 at % Be-Hf and 37.5 at % Be-Ti. All theseglasses but BeTi are readily fabricable in continuousribbon form and they are of particular interest becauseof their good mechanical properties, such as highspecific strength [1]. A detailed understanding of themechanical or magnetic properties of metallic glassesrequires structural information.

In this paper, we present the determination of the

local structure of the Be43HfxZr57-. ternary glasseswhich is basically described by a set of six partialstructure factors IiJ{K). However the Hf and Zrelements have similar metallic atomic radii (rw =1.585 A, rZr = 1.597 A) and possess the same hcpstructure; moreover they exhibit a similar chemicalbehaviour when alloyed with Be, characterized byvery close eutectic compositions (as specified above)and the same intermetallic compounds Be2Hf(Be2Zr)and Be5Hf (BesZr). For these reasons, we can assumethat zirconium and hafnium are isomorphous ele-ments in the BeHfZr glasses. Then we may treat theternary glasses Be43HfxZr57 - x as pseudo-binary glas-ses, formulated Be43MT 57 (MT = Hf or Zr). Conse-quently their structure is simply described by threepartial structure factors (PSF). For the determinationof PSF’s we use the isomorphous substitution method.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01986004705086300

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This method was already applied for extractingpartial functions from X-ray experiments, such as inLa (AIGa) glasses [2] or Ni (ZrHf) glasses [3] Janotet al. [4] have also used this method for neutronexperiments in the pseudo-ternary (FeMn),5P,5cloglass. Since Fe and Mn have coherent scattering lengthsof opposite signs, the substitution between Fe and Mndrastically changes the contrast between metal andmetalloid atoms and consequently, the weights ofthe partial functions in the total interference function.When using only X-rays, the contrast brought by

the isomorphous substitution method is insufficientto extract all the partial structure factors, and generallythis method is applied with a combination of X-rayand neutron measurements [3]. Moreover, it is oftenjudicious to check the consistency of the partialstructure factors extracted from three measurements

by redundant measurements.For the structural analysis of the Be 43 HfZr . 57-.,

glasses, we performed three X-ray diffraction experi-ments in the alloys with x = 5, 25 and 54 % whichcorrespond approximately to the minimum, maximumand intermediate compositions in hafnium. Sincethe light element (Be) is not visible by X-rays, werealized one time-of-flight neutron experiment inthe Be43Hf25Zr32 amorphous alloy which is the mosteasily fabricable glass in ribbon form. From the fourtotal interference functions, first the Faber-Ziman par-tial structure factors Iij(K) are determined, and thenthe Bhatia-Thornton functions are deduced from

Iij(K). The calculation of all the partial coordinationnumbers from the radial distribution functions

RDFij(r) are performed, estimates of some of themwere previously given by us in [5].

Finally the generalized Warren chemical parameterai is calculated in the first coordination shell, and anextension of this parameter is proposed for describingthe chemical ordering as a function of the distance r.

2. Experimental technique and data analysis.The ribbons of Be43Hf,,Zr,7-,, glasses 35 J.1m thickand 1.5 mm wide were prepared by the melt-spinningprocess. The average atomic density of these ternaryglasses is taken equal to 0.0565 at/A3 (value of theBe43Zr57 glass measured by Tanner et al. [1]). Wechecked that this value was in agreement with thosededuced from the slope of the reduced distributionfunctions G(r) at small r.

2. 1 X-RAY DIFFRACTION MEASUREMENTS. - Thescattered X-ray intensities of the alloys with x = 5, 25and 54 at % were measured in transmission usingAgKa radiation (with A = 0.5594 A) in the conven-tional scanning 20-method, described in [6]. TheX-ray samples were formed by sticking ribbons

parallel to one another, thus covering the wholeopening of the holder of 12.5 x 12.5 mm2. The sampleswere placed, initially perpendicular to the incidentbeam, in a vacuum chamber for minimizing air

scattering. X-ray diffracted were selected by a Si(Li)

solid-state detector in conjunction with a singlechannel pulse height analyser which permitted removalof the white spectrum, the fluorescent radiation and alarge part of the Compton scattering. Raw data wereregistered on a multichannel analyser for diffractionangles between 20 and 1000 in step of 0.250. Themeasured intensities were then corrected for sampleabsorption, polarization, and Compton scattering, asdescribed elsewhere in [7]. The values of Comptonscattering were calculated for Hf and Zr from the ana-lytic expressions given by Palinkas [8] while those ofBe were interpolated from the tables of Cromeret al. [9]. The normalization of the scattered intensitieswas done using the sum rule of the interferencefunction I(K) which yielded the coherent scatteringper atom Ia(K).2.2 NEUTRON DIFFRACTION MEASUREMENT. - The

time-of-flight neutron diffraction measurement on theBe43Hf25Zr32 glass was performed on the GeneralPurpose Diffractometer at the pulsed neutron spal-lation source of the WNR Facility in Los Alamos,utilizing the high epithermal flux to extend measure-ments to higher values of K than are possible withconventional neutron sources. We recall the relationbetween the scattering vector K and the time-of-flightof neutron t(À) given by :

where mn is the mass of neutron, h is Planck’s constant,2 0 the scattering angle, Lo the incident flight pathbetween the moderator and the sample and L thediffracted flight path between the sample and thedetector.The neutron specimen was prepared by wrapping

melt-spun ribbons around a frame such that the finalshape of the sample was a cylinder of 6 mm diameterand 6 cm height. The mass of wrapped ribbons (5.7 g)and the cylinder volume lead to an effective atomicdensity peff of 0.026 at/A’. This value was used for thecalculation of the absorption and self-shielding coef-ficients. The scattered intensity was measured bythree banks of 16 detectors each, located at the averagescattering angles of 1 4.4°, 40.5° and 1 5 1 . 1 ° and coveringrespectively the K-ranges of 0.5 to 5 A-1, 1.4 to

10 A-’ and 7 to 25 A -1 (the upper limits were deter-mined by a strong resonance of Hf around an incidentenergy of 1 eV). The neutron data of each bank wereseparately corrected first for background, sampleabsorption, self-shielding and multiple scattering.The correction factors for absorption Aa(6, R) andself-shielding ASS(8, R) are calculated using the relationfor cylinders given by Rouse et al. [10] ; they arefunction of the radius of the sample cylinder R, theeffective atomic density peff and the absorption cross-section for Aa(9, R) or the total scattering cross-

section for ASS(e, R). Data were then corrected forincoherent scattering and for deviations from thestatic approximation using Placzek’s method, which

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was applied by A. C. Wright [11] to time-of-flightmeasurements for a detector with an energy-dependentefficiency. The efficiency of He3 detectors is repre-sented by 1 - exp( - 0.794 A). In table I, we give thecoherent scattering lengths, the incoherent and absorp-tion cross-sections for the pure elements taken in thedata analysis.The scattering from a vanadium rod of known

incoherent scattering allowed, on the one hand, todetermine the incident neutron spectrum necessaryfor Placzek’s correction, and on the other hand tonormalize the scattered intensity of the Be43Hf2sZr 32glass. The overlappings of the normalized intensitiesof the detector banks at 14.40 and 40.50, and of thebanks at 40.50 and 151° was checked by complemen-tary neutron measurements on the same sample res-pectively on the DIB and D2 spectrometers at theHFR at the ILL in Grenoble, using the respectivewavelengths of 2.52 and 0.94 A. A supplementary cor-rection was applied to remove incoherent scatteringdue to the presence of hydrogen in the ribbons. Usingthe values for differential scattering cross-section of anH20 molecule measured by Beyster [12] a hydrogenconcentration of about 2 mol % was evaluated toaccount for the observed background.

3. Results and discussion.

3.1 TOTAL INTERFERENCE FUNCTIONS AND PAIR DISTRI-BUTION FUNCTIONS. - When using the Faber-Zimanformalism [13], it is usual to define the total inter-ference function I(K) from the coherent scatteringintensity per atom, I.(K), by the following normaliza-tion :

where

,fi are the atomic scattering amplitudes (called bi forneutrons, and fMT = (xjf + (57 - x) fZr)/57). Ci arethe atomic concentrations (note CMT = 0.57).

I(K) is a linear combination of the three pairpartial structure factors I ij( K).

Table I. - Values of coherent scattering lengths,incoherent and absorption cross-sections (given forA = 1.8 A) for the Be, Zr and Hf elements.

In some cases the Bhatia-Thomton formalism [14] ismore advantageous and the total interference functionor total structure factor, noted S(K), which is a linearcombination of the three number-concentration struc-ture factors SN,c(K), is obtained by the followingnormalization :

and

with

The normalization (3) is more general than the norma-lization (1), since it is still applicable to a zero alloy(i.e. when b &#x3E; = 0). The relation between I(K) andS(K) is given by :

The contribution of each PSF in the total interferencefunction I(K) or S(K) is strongly dependent on thevalue of the Wij factors. In table II, we give the valuesof Wij in both formalisms for the different glassesstudied when using X-rays or neutrons.Figure 1 shows the I(K) functions for the melt-spunalloys obtained from X-ray (Ix(K)) and neutron(IN(K») data. It is clear from table II that the IX(K)functions are dominated by the MT-MT pairs, whilethe contribution of IBeBe(K) can always be neglected.The three X-ray curves are identical and present a welldefined first peak at 2.56 Å -1. The neutron curve IN(K)is equivalent to SNN(K), because IN (K) and SN(K) are

Table II. - Values of the Wijfactorsfor the Be43HfxZrS7-x glasses using X-rays(XR) for K = 0, and neutrons(N).

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Fig. 1. - Total interference functions I(K) of the

Be43HfxZrs7-x glasses measured by X-rays for x = 5, 25,54 at % and by neutrons for x = 25 at %.

identical since the ratio b )2/ b2 ) in equation (5) isequal to 0.9994 and the co-factors WNc and Wcc arevery small in the SN(K) function (see Table II). Thefirst peak of IN (K) is centred at 2.69 Å - 1 and a smallprepeak can be observed around 1.4 A-1; the shiftof the first peak to higher K, compared to this one ofIX(K), results from the larger contribution of the Be-MT pairs. The uncorrelated La.ue term f ’ &#x3E; _ f &#x3E;2in the normalization (1), equal also to CBe CMTCfBe -fMT)2 is large for X-rays and almost negligible forneutrons (see values of Table I). It explains the diffe-rence in sign of the limits Ix(O) and IN(0) . The Fouriertransform of K [I(K) - 1] yields the reduced distribu-tion function G(r) :

Figure 2 shows the curves of G(r) for the

Be43Hf2sZr32 glass obtained from X-rays and neu-trons, using the upper integration limits of 15.45 Å - 1and 15.15 Å -1 respectively. These values correspondto nodes in the K(I(K) - 1) functions.

Fig. 2. 2013 Reduced distribution functions G(r) of the

Be,3Hf,,Zr3l glass obtained from X-rays and neutrons.

The three G X (r) functions (only one shown) are

identical with a first peak at 3.18 A, which correspondsto the MT-MT interatomic distances. This confirmsthe isomorphous behaviour of the Hf and Zr elements.The G N(r) function shows the splitting of the first peakinto three maxima at 2.2, 2.72 and 3.15 A. Since thesethree distances are very close to those found in the

Be2Hf or Be2Zr compounds (see Table III), they mustcorrespond respectively to the first BeBe, BeMT andMTMT interatomic distances. Such a splitting is quiteseldom because it requires an important size effectand atomic concentrations close to 50 %.3.2 PARTIAL STRUCTURE FACTORS AND ATOMIC CORRE-LATION FUNCTIONS. - The partial structure factorscannot be obtained simultaneously by solving asystem of three linear equations such as (2) or (3),chosen among the four total interference functions,because any combination yields a very small deter-minant of the matrix formed by the factors Wij.Therefore, we used the following procedure concerningthe Faber-Ziman formalism :- first, the function IMTMT(K) is derived from the

Ix(K) 1 function of Be43HfsZrs2 and I;(K) of

Be43Hf54Zr3 by neglecting the contribution of

I BeBe (K).- then the function IBMT(K) is determined from

the two other interference functions Ix(K) and IN (K)of Be43Hf25Zr32, and the partial function IMTMT(K),using an algorithm similar to the one proposed byEdwards et ale [ 15] ;- lastly, the function IB.B.(K) is deduced from

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IN(K), when knowing the two other functions

IMTMT(K) and IBw(K). The Bhatia-Thornton PSFare deduced from the IiJ{K)’s using the well knownlinear relations given in [14].- Faber-Ziman formalism :

The function ImTmT(K), shown in figure 3, stronglyresembles the I’(K)’s with a first peak centred at2.55 Å - 1 .

The two other functions IBeBe(K) and IBeMT(K)which are obtained by solving the two linear equationsformed by I3X(K) and IN(K) and using the values ofIMTMT previously determined, exhibit very large oscilla-tions and cannot be retained.

Indeed it is necessary to take into consideration theerrors of 13 (K),1N(K) and IMTMT(K). The solutionsof IBeMT(K) and IBeBe(K) are then given by :

A-1 is the inverse matrix of A =

the coefficients are relative to x = 25 at %.After the data treatment, we estimate the relative

errors in the total interference function at 6 %. Thisquite large error takes account the absence of cor-rections for the different resolution in K of the threebanks of detectors of the time-of-flight spectro-meter and also for the different resolutions of X-rayand neutrons methods. By neglecting errors in the co-factors Wij, the absolute error in IMTMT(K) is equal to± (I (XII 0.06 1 lx(K) I + I (X12 0.06 If(K) I). x 11 and a12are the inverse matrices formed by the factors Winrelated to I1X(K) and I2X(K). For instance, at

K = 10 A-1, an = - 1.36 and (Xt2 = 2.36 and theerror in IMTMT(K) is approximately 22 %.

In the solution (6), bx(K), 6’(K) and bmT(K) areallowed to vary respectively between ± 0.06 1 Ix(K) [± 0.06 I IN(K) I and

We keep the solutions of IB,,MT(K) and IBeBe(K)obtained by equation (6) which both fall inside therange defined in figure 4 and check the followinginequalities :

and

For each K an average value of these retained solu-tions is calculated. The function IBeMT(K), so obtained,is shown in figure 3 and presents a minimum at2.2 Å - 1 and a first peak at 2.75 Å - 1. The oscillationsof the function IBeBe(K) evaluated by the same pro-cedure damp down too rapidly; so it is better to

finally deduce IBeBe(K) from equation (2) using thevalues of IN(K), IMTMT(K) and I...(K). The functionIBeBe(K) exhibits a prepeak around 1.70 Å -1, which

Fig. 3. - Faber-Ziman partial structure factors Iij(K) of theBe43HfxZr S 7 - x glasses.

indicates a pseudo-periodicity Be-MT-Be, and a firstpeak centred at 3.4 Å - 1. The limits of the partialfunctions relative to homoatomic pairs are negative,while the limit of the function relative to heteroatomicpairs is positive; these features characterize chemicallyordered systems (such NiB [16] or NiTi [17] glasses).For liquid alloys these limits are related to the thermo-dynamic data [18]. We must precise that the functionsIB.B. (K) and IB.mT(K) shown in figure 3 are only

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Fig. 4. - Range of allowed structure factors versus K.

approximate solutions. The Fourier transforms of

IMTMT(K), IBeMT(K), and IBeBe(K), calculated with theupper integration limits of 13 Å - 1, 12.9 Å - 1 and9.4A-’ respectively, yield the reduced atomic pairdistribution functions GiJ{r), shown in figure 5. The

partial radial distribution functions are then deducedfrom Gij(r) by :

The fitting of the nearest neighbour regions ofRDFij(r)by Gaussian components (as shown in Fig. 6) permitsto divide the first shell into sub-shells and also to

Fig. 5. - Reduced atomic pair distribution functions Gij(r)of the Be43HfxZrs-x glasses.

Fig. 6. - Partial radial distribution functions RDFij(r) ofthe Be43HfxZr 57 - x glasses and Gaussian components of thenearest neighbour regions.

discard the spurious ripples due to the truncation in theFourier transform, such as the oscillation of

RDFB.mT(r) around 2.2 A. The partial coordinationnumber 4r) are calculated from the height and thewidth at half-height of the Gaussian peaks centred atrT). The values of ziP are summed up in table III. Forcomparison, the interatomic distances and the coor-dination numbers found in the crystalline compoundsBe2Hf and Be2Zr are also given in table III. Thelattice constants of Be2Hf and Be2Zr with the hexago-nal AIB2 structure type are respectively ao = 3.786 A,Co = 3.163 A and = 3.81 A, co = 3.23 A.The distribution of the first pairs BeBe is quite largeand can be divided around the positions 2.2 and2.86 A. Concerning the distribution of the first pairsBeMT and MTMT, they are asymmetric and can berepresented by two Gaussians; nevertheless the posi-tion of the small second Gaussian is certainly affectedby truncation errors in the Fourier transform. It canbe also noted that there is an inversion of the coordina-tion numbers ZgtMT and z(2)MTMT between the glass andthe crystalline compounds. In average, the distance

869

Table III. - Interatomic distances and coordination numbers in the Be43HfxZrS7-x glasses and the crystallinecompounds Be2Hf and Be2Zr.

(*) Errors are only related to the Gaussian parameters and do not account for the inaccuracy of the RDFij functions.

Fig. 7. - Bhatia-Thornton partial structure factors SN,c(K)of the Be43HfxZrs7 -x glasses.

MTMT is shorter in the amorphous phase than inBe2Hf or Be2Zr compounds.As shown in table III, the first interatomic distances

in the Be43Hf,,Zr57-x glasses are very close to thoseof the crystalline compounds Be2Zr (or Be2Hf),except for the distance BeBe at 2.86 A which lies

between the distances of 3.16 (or 3.23 A) in Be2Hf (orBe2Zr) and 2.635 A of the crystalline compound Be5Zr.- Bhatia-Thornton formalism

The Bhatia-Thornton number-concentration struc-ture factors SN,c(K) are deduced from the Iij(K)’susing the linear relations in [14], and shown in figure 7.The equivalence between SNN(K) and IN(K) is wellchecked, with a first peak in SNN(K) at 2.69 A-1and a prepeak around 1.4 A-1. The first peak ofScc(K) is quite pronounced, centred at 2.3 A - I ;the oscillations of SNC(K) around zero reflect the sizeeffect between the two atomic species but remain weakcompared to those of SNN(K) in spite of a high ratioof atomic radii of 1.4.The Fourier transforms of K[SNN(K) - 1],

K[Scc(Kl ’ 1] and KSNc(K), are calculated withtruncation values of 15, 11.4 and 13 A-1 respectively,which correspond to nodes in these functions. Thenumber-concentration correlation functions GN.c(r), soobtained, are presented in figure 8. The function

GNN(R) is similar to GN(r) ; the maximum of GNN(r) at2.72 A corresponds to a minimum in Gcc(r) betterpronounced than the positive peaks at 2.3 A and 3.17 Aindicating a preference for unlike atom pairs.3.3 CHEMICAL SHORT-RANGE ORDER (CSRO) PARA-METER. - The generalized Warren CSRO parametera1 relative to the first shell is given according to [6] by :

where zie and zMT are the total coordination numbersof each species. The value pf ai is directly dependenton the way of defining the shell of the first neighbours,

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Fig. 8. - Number-concentration correlation functions

GN,,(r) of the Be,, Hf.Zrl 7 -., glasses.

since the numbers zij are, obtained from :

The upper radius of the first shell, r’, is defined bythe abscissa of the first minimum of GNN located at3.8 A. The lower limits r"" allow to discard the

spurious ripples in RDFJ. Using the integrand (9)with rl = 3.8 A, I Z1BeMT and z1MTMT are equal to 4.2,7.4 and 8.2 respectively. Thus, a1 is slightly negativewith a value of - 0.035. This value is very differentfrom - 0.16, our previous estimate, which was

deduced from a function ARDF(R) containing bothcontributions of BeBe and BeMT and calculated for afirst shell limited at 3.4 A (radius defined by theposition of the first minimum of ARDF(r)). Thisdiscrepancy clearly shows that the limit of the firstshell largely influences the chemical short range orderparameter ai.The value of - 0.035 for the Be4:5Hf ., Zr 5 7 -., glassesis similar to that calculated for the Be37.5Ti62.5

Fig. 9. - Evolution of the generalized Warren chemicalorder parameter a(r) as a function of r.

glass [19] with partial coordination numbers equal toZB.B. = 2.9, ZB.TI = 6.9 and ZTiTi = 8.

In this series of glasses, the chemical ordering is weakcompared to those existing in metal-metalloid glasses :(Ni8oB20 [16]) or, metal-metal glasses (Ni33 Y 67 [20]).We must emphasize that in most previous structural

studies of metallic glasses, the zi’j numbers are calculat-ed with different upper integration limits r’ whichcorrespond each to the position of the first minimumin RDFiï If the two species are different atomic radii,the three minima do not coincide with the minimumof GNN and consequently, the CSRO parameter aicalculated with specific r1ij can be somewhat differentfrom the value obtained with a unique value rl.

Therefore for binary systems with strong size effect,the importance of the chemical ordering and itsextent could be described by a function a(r) definedin the same way as al, i.e. :

with

Figure 9 shows the variation of a(r) for the

Be43HfxZrs7_x glasses. Between 3 and 4.25 A a(r)is an increasing function, which becomes positivebeyond 3.9 A. The oscillations of a(r) around 0 dampdown rapidly beyond 4.5 A and it shows the localcharacter of the chemical ordering. This functioncould be easily used for a comparison of chemicalorders in different glasses.

Acknowledgments.This research was supported in part by grant DMR80-07939 and 83-10025 from the National Science Foun-dation. Thanks are due to the WNR Facility in LosAlamos and to the Institut Laue-Langevin for theallocation of beam time at their respective neutronsources.

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