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

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Structural study of Be43HfxZr57-x metallic glasses by X-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�

Structural study ^of Be43HfxZr57-x ^metallic glasses by 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 partir

de la combinaison d’une mesure de diffraction neutronique ^en temps ^{de vol dans} l’alliage ^{avec x = 25 at} % ^{et trois}

mesures de diffraction X dans les alliages ^{avec x = 5, 25 et 54 at} % ^en utilisant la substitution isomorphe ^entre

les 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 de mise 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 Hf and Zr atoms. The Bhatia-Thornton partial ^{structure factors are then} deduced. From the partial radial distribution functions the partial coordination numbers are calculated and allow the generalized Warren chemical order parameter 03B11 in the first coordination shell to be determined. The upper radius of the first shell is well defined by

the position of the first minimum of the GNN ^{function located at 3.8} A. Thus, ^{we find a} value of - 0.033 for 03B11 which indicates a slight tendency ^{of chemical} ordering.

Classification Physics ^Abstracts

61. lOF - 61.12D - 61.40D

1. Introduction

Binary

BeHf, ^{BeZr and} BeTi, ^and ternary ^BeHfZr and BeTiZr

amorphous alloys

^{have been}

produced by ultra-rapid liquid quenching

^for

composition

ranges

surrounding

^the

respective

eutectics 34 at

%

Be-Zr, ^{33 at}

%

^{Be-Hf and 37.5 at}

%

Be-Ti. All these

glasses

^{but BeTi are}

readily

fabricable in continuous ribbon form and

they

^{are of}

particular

interest because of their

good

mechanical

properties,

^{such as}

high specific strength [1].

^{A detailed}

understanding

^{of the}

mechanical or

magnetic properties

^{of metallic}

glasses requires

structural information.

In this _paper, we present ^the determination of the

local structure of the

Be43HfxZr57-.

ternary

glasses

which is

basically

^described

by

^{a set of six}

partial

structure factors

IiJ{K).

However the Hf and Zr elements have similar metallic atomic radii

(rw =

1.585

A,

rZr ⁼ 1.597

A)

^and possess the same

hcp

structure; ^moreover

they

^{exhibit a similar chemical}

behaviour when

alloyed

^with Be, characterized

by

very close eutectic

compositions

(as

specified above)

and the same intermetallic

compounds Be2Hf(Be2Zr)

and

Be5Hf (BesZr).

^{For these reasons, we can assume}

that zirconium and hafnium are

isomorphous

^ele-

ments in the BeHfZr

glasses.

^{Then we} may ^treat the ternary glasses

Be43HfxZr57 - x

^as

pseudo-binary glas-

ses, formulated

Be43MT 57 (MT

^{= Hf or}

Zr).

^Conse-

quently

^{their structure is}

simply

^described

by

^three

partial

^structure factors

(PSF).

^{For the} determination of 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

864

This method was

already applied

^for extracting partial functions from X-ray

experiments,

^{such as in}

La (AIGa) glasses

[2] ^or

Ni (ZrHf) glasses

[3] ^Janot

et al. [4] have also used this method for neutron

experiments

^{in the}

pseudo-ternary (FeMn),5P,5clo

glass. ^{Since Fe and Mn have coherent} scattering

lengths

of opposite signs, the substitution between Fe and Mn

drastically

changes ^{the contrast} between metal and metalloid atoms and

consequently,

^the

weights

^of

the

partial

functions in the total interference function.

When

using only

X-rays, ^{the contrast}

brought by

the

isomorphous

substitution method is insufficient to extract all the

partial

^{structure factors, and}

generally

this method is

applied

^{with a} combination of X-ray

and neutron measurements [3]. Moreover, it is often

judicious

^to check the

consistency

^{of the}

partial

structure 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}

%

^which correspond

approximately

^{to the} minimum, ^maximum

and intermediate

compositions

in hafnium. Since the

light

^element (Be) ^{is not visible}

by

X-rays, ^we

realized one

time-of-flight

^neutron

experiment

ⁱⁿ

the

Be43Hf25Zr32 amorphous alloy

which is the most

easily

fabricable

glass

in ribbon form. From the four total interference functions, first the Faber-Ziman _par- tial structure factors

Iij(K)

^are determined, and then the Bhatia-Thornton functions ^are deduced from

Iij(K).

^The calculation of all the

partial

coordination numbers from the radial distribution functions

RDFij(r)

^are

performed,

estimates of ^some of them

were

previously given by

^{us in}

[5].

Finally

^the

generalized

^{Warren chemical} parameter ai is calculated in the first coordination shell, ^{and an}

extension of this parameter ^is

proposed

^for

describing

the 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 thick and 1.5 mm wide were

prepared by

^the

melt-spinning

process. The _average atomic

density

^{of these} ternary

glasses

^{is taken}

equal

^{to 0.0565}

at/A3 (value

^{of the}

Be43Zr57 glass

^measured

by

Tanner et al.

[1]).

^We

checked that this value was in agreement ^{with those} deduced from the

slope

of the reduced distribution functions

G(r)

^{at small r.}

2. 1 X-RAY DIFFRACTION MEASUREMENTS. - The scattered X-ray intensities of the

alloys

^{with x =} 5, ²⁵ and 54 at

%

^{were measured} in transmission

using AgKa

^radiation

(with A

^{= 0.5594}

A)

^{in the conven-}

tional

scanning

20-method, described in

[6].

^The

X-ray samples

^{were formed}

by sticking

^ribbons

parallel

^{to one} another, ^thus

covering

^{the whole}

opening

^{of the holder of 12.5 x 12.5 mm2. The}

samples

were

placed, initially perpendicular

^to the incident

beam, ^{in a vacuum chamber for}

minimizing

^air

scattering.

X-ray diffracted were selected

by

^a

Si(Li)

solid-state detector in

conjunction

^{with a}

single

channel pulse height analyser ^which permitted ^removal

of the white spectrum, the fluorescent radiation and a

large

part ^{of the} Compton

scattering.

^{Raw data were}

registered

^{on a} multichannel

analyser

for diffraction

angles

^{between 20} and 1000 in step ^{of 0.250. The} measured intensities ^were then corrected for

sample absorption, polarization,

^and

Compton scattering,

^as

described elsewhere in

[7].

The values of

Compton scattering

^were calculated for Hf and Zr from the ana-

lytic expressions given by

^Palinkas

[8]

while those of Be were

interpolated

^{from the tables of Cromer}

et al. [9]. ^The normalization of the scattered intensities

was done using ^{the sum} rule of the interference function

I(K)

^which

yielded

the coherent

scattering

per ^atom

Ia(K).

2.2 NEUTRON DIFFRACTION MEASUREMENT. - The

time-of-flight ^neutron diffraction measurement on the

Be43Hf25Zr32

glass ^was

performed

^on the General

Purpose 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

^with

conventional neutron sources. We recall the relation between the

scattering

^{vector K and the}

time-of-flight

of 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 path

between the moderator and the

sample

^{and L the}

diffracted

flight path

^{between the}

sample

^{and the}

detector.

The neutron specimen ^was prepared

by

wrapping

melt-spun

ribbons around a frame such that the final

shape ^{of the}

sample

^{was a}

cylinder

^{of 6 mm diameter}

and 6 cm

height.

^{The mass of}

wrapped

^ribbons

(5.7 g)

and the

cylinder

^{volume lead to an} effective atomic

density peff

^{of 0.026}

at/A’.

^{This value was} used for the calculation of the

absorption

^and

self-shielding

^coef-

ficients. The scattered

intensity

^{was measured}

by

three banks of 16 detectors each, located at the _average

scattering angles

of 1 4.4°, 40.5° and 1 5 1 . 1 ° and

covering respectively

^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} incident energy of ¹ eV). ^{The neutron data of each bank were}

separately

^corrected first for

background, sample absorption, self-shielding

^and

multiple scattering.

The correction factors for

absorption Aa(6, R)

^and

self-shielding ASS(8, ^R)

^are calculated

using

^{the relation}

for

cylinders given by

^{Rouse et al.}

[10] ; they

^are

function of the radius of the

sample cylinder

^{R, the}

effective 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 for incoherent

scattering

^{and for} deviations from the static

approximation using

^{Placzek’s method, which}

was

applied by

^{A. C.} Wright [11] ^to

time-of-flight

measurements for a detector with an

energy-dependent efficiency.

^The

efficiency

^{of He3} detectors is _repre- sented

by

^{1 -}

exp( -

^0.794 A). ^{In table} I, ^we

give

^the

coherent scattering

lengths,

the incoherent and

absorp-

tion cross-sections for the _pure elements taken in the data

analysis.

The

scattering

^{from a} vanadium rod of known incoherent

scattering

allowed, ^{on the one} hand, ^to determine the incident neutron spectrum necessary for Placzek’s correction, ^{and on} the other hand to normalize the scattered

intensity

^{of the}

Be43Hf2sZr 32

glass. ^The

overlappings

^of the normalized intensities of the detector banks at 14.40 and 40.50, ^{and of the}

banks 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 the} HFR at the ILL in Grenoble,

using

^the

respective wavelengths

of 2.52 and 0.94 A. A

supplementary

^cor-

rection was

applied

^{to remove} incoherent

scattering

due to the presence of

hydrogen

^{in the ribbons.}

Using

the values for differential

scattering

cross-section of an

H20

molecule measured

by Beyster [12]

^a

hydrogen

concentration of about 2 mol

%

^{was evaluated to}

account for the observed

background.

3. Results and discussion.

3.1 TOTAL INTERFERENCE FUNCTIONS AND PAIR DISTRI- BUTION FUNCTIONS. ^- When

using

the Faber-Ziman formalism [13], it is usual to define the total inter- ference function I(K) from the coherent

scattering intensity

per atom,

I.(K), by

^the

following

^normaliza-

tion :

where

,fi

^are the atomic

scattering amplitudes (called bi

^for

neutrons, and

fMT = (xjf

^{+ (57 - x)}

fZr)/57). Ci

^are

the atomic concentrations

(note CMT

⁼

0.57).

I(K)

^{is a} linear combination of the three

pair partial

^{structure factors}

I ij( K).

Table I. ^- Values

of

^coherent scattering lengths,

incoherent and

absorption

cross-sections (given

for

A ⁼ 1.8

A) for

^the Be, ^Zr and Hf elements.

In some cases the Bhatia-Thomton formalism [14] ^is

more

advantageous

and the total interference function

or total structure factor, ^noted

S(K),

^{which is a linear}

combination of the three number-concentration struc- ture factors

SN,c(K),

^{is obtained}

^by

^the

^following

normalization :

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 > = 0).

The relation between I(K) ^and S(K) ^is given

by :

The contribution of each PSF in the total interference function

I(K)

^or

S(K)

^is

strongly dependent

^{on the}

value of the

Wij

^{factors. In table II, we}

^give

^{the values}

of

Wij

in both formalisms for the different glasses

studied when

using X-rays

^{or neutrons.}

Figure

^{1 shows the}

I(K)

functions for the

melt-spun alloys

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, ^while

the contribution of

IBeBe(K)

^can

^always

^be

^neglected.

The three X-ray curves are identical and present ^{a well} defined 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).

866

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)

^is

equal

^to 0.9994 and the co-factors

WNc

^and

Wcc

^are

very small in the

SN(K)

^function

(see

^Table

II).

^The

first

peak

^of

IN (K)

^{is centred at 2.69 Å - 1 and a small}

prepeak

^can be observed around

1.4 A-1;

^{the shift}

of the first

peak

^to

higher

K,

compared

^{to this one of}

IX(K),

results from the

larger

contribution of the Be- MT

pairs.

^The uncorrelated La.ue term

f ’ > _ f >2

in the normalization

(1), equal

^{also to}

CBe CMTCfBe - fMT)2

^is

^large

^for

X-rays

and almost

negligible

^for

neutrons

(see

^{values of Table}

I).

^It

explains

^{the diffe-}

rence in

sign

of the limits

Ix(O)

^and

IN(0) .

The Fourier transform 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 - 1}

and 15.15 Å -1

respectively.

These values

correspond

to 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

corresponds

to the MT-MT interatomic distances. This confirms the

isomorphous

behaviour of the Hf and Zr elements.

The

G N(r)

function shows the

splitting

^{of the first}

peak

into three maxima at 2.2, 2.72 and 3.15 A. Since these three distances ^are _very close to those found in the

Be2Hf

^or

Be2Zr compounds (see

^{Table III),}

they

^must

correspond respectively

^{to the first} BeBe, ^BeMT and MTMT interatomic distances. Such a

splitting

^is

quite

seldom because it

requires

^an

important

size effect and atomic concentrations close to 50

%.

3.2 PARTIAL STRUCTURE FACTORS ^AND ATOMIC CORRE- LATION FUNCTIONS. ^- The

partial

^{structure factors}

cannot be obtained

simultaneously by solving

^a system 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 concerning

the 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 by

Edwards et ale [ 15] ;

-

lastly,

^{the function}

IB.B.(K)

^is deduced from

IN(K),

^when

knowing

^{the two} other functions

IMTMT(K)

^and

IBw(K).

^The Bhatia-Thornton PSF

are deduced from the

IiJ{K)’s ^using

^{the well known}

linear relations

given

ⁱⁿ

[14].

- Faber-Ziman formalism :

The function

ImTmT(K),

^{shown in}

figure

3,

strongly

resembles the

I’(K)’s

^{with a first}

peak

^{centred at}

2.55 Å - 1 .

The two other functions

IBeBe(K)

^and

IBeMT(K)

which are obtained

by solving

^{the two linear}

equations

formed

by I3X(K)

^and

IN(K)

^and

using

^{the values of}

IMTMT previously

determined, ^exhibit very

large

^oscilla-

tions and cannot be retained.

Indeed it is _necessary to take into consideration the

errors of

13 (K),1N(K)

^and

IMTMT(K).

The solutions of

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

%.

^This

quite large

^{error takes account} the absence of cor-

rections for the different resolution ^{in K of} the three banks of detectors of the

time-of-flight

spectro-

meter and also for the different resolutions of X-ray

and 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 a12

are the inverse matrices formed

by

the factors

Win

related to

I1X(K)

^and

I2X(K).

^{For instance, at}

K ⁼

10 A-1,

an ^{= -} 1.36 and _(Xt2 ⁼ 2.36 and the

error in

IMTMT(K)

^is

approximately

²²

%.

In the solution

(6), bx(K), 6’(K)

^and

bmT(K)

^are

allowed 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 the range defined in

figure

4 and check the

following inequalities :

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 at} 2.2 Å - 1 and a first

peak

^{at 2.75 Å - 1. The} oscillations of 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

^the

values of

IN(K), IMTMT(K)

^and

I...(K).

^{The function}

IBeBe(K)

^{exhibits a}

prepeak

around 1.70

Å -1,

^which

Fig. ^{3. -} Faber-Ziman partial ^{structure factors}

Iij(K)

^{of the} Be43HfxZr S 7 - x glasses.

indicates a

pseudo-periodicity

^{Be-MT-Be, and a first} peak ^{centred at}

3.4 Å - 1.

The limits of the

partial

functions relative to homoatomic

pairs

^are

negative,

while the limit of the function relative to heteroatomic

pairs

^is

positive;

^these features characterize

chemically

ordered 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 functions}

IB.B. (K)

^and

IB.mT(K)

^{shown in}

figure

^{3 are}

only

868

Fig. ^{4. -} Range ^{of allowed structure factors versus K.}

approximate

solutions. The Fourier transforms of

IMTMT(K), IBeMT(K),

^and

IBeBe(K),

calculated with the upper

integration

limits of

13 Å - 1,

12.9 Å - 1 and

9.4A-’

respectively, yield

^the reduced atomic

pair

distribution functions

GiJ{r),

^{shown in}

^figure

^{5. The}

partial

radial distribution functions are then deduced from

Gij(r) by :

The fitting ^{of the nearest}

neighbour regions ofRDFij(r)

by

^Gaussian components

(as

^{shown in}

Fig. 6) permits

to 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)

^of

the Be43HfxZr 57 - x glasses and Gaussian components ^{of the}

nearest neighbour regions.

discard the

spurious ripples

^{due to} the truncation in the Fourier transform, ^{such as} the oscillation of

RDFB.mT(r)

^{around 2.2 A. The}

partial

coordination number

4r)

^are calculated from the

height

^{and the}

width at

half-height

of the Gaussian

peaks

^{centred at}

rT).

The values of

ziP

^are summed up in table III. For

comparison,

the interatomic distances and the coor-

dination numbers found in the

crystalline compounds Be2Hf

^and

Be2Zr

^{are also}

given

in table III. The lattice 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 large

and can be divided around the

positions

^{2.2 and}

2.86 A.

Concerning

^the distribution of the first

pairs

BeMT and MTMT,

they

^are

asymmetric

^{and can be}

represented by

^two Gaussians; nevertheless the

posi-

tion of the small second Gaussian is

certainly

^affected

by

truncation errors in the Fourier transform. It can

be also noted that there is an inversion of the coordina- tion numbers

ZgtMT

^and

z(2)MTMT

between the

glass

^and

the

crystalline compounds.

In average, the distance

Table III. ^- Interatomic distances and coordination numbers in the

Be43HfxZrS7-x

glasses ^{and the}

crystalline compounds 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 in}

Be2Hf

^or

Be2Zr compounds.

As shown in table III, ^{the first} interatomic distances in the

Be43Hf,,Zr57-x glasses

^are very close to those of 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 (or Be2Zr)

^{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)’s

using the linear relations in

[14],

and shown in

figure

^7.

The

equivalence

^between

SNN(K)

^and

IN(K)

^{is well}

checked, ^{with a first}

peak

ⁱⁿ

SNN(K)

^{at 2.69 A-1}

and a

prepeak

around 1.4 A-1. The first

peak

^of

Scc(K)

^is

quite pronounced,

^{centred at}

2.3 A - I ;

the oscillations of

SNC(K)

^{around zero} reflect the size effect between the two atomic

species

but remain weak

compared

^{to those of}

SNN(K)

ⁱⁿ

spite

^{of a}

high

^ratio

of atomic radii of 1.4.

The Fourier transforms of

K[SNN(K) - 1], K[Scc(Kl ’ 1]

^and

KSNc(K),

^are calculated with truncation values of 15, 11.4 ^{and 13} A-1 respectively,

which

correspond

^to nodes in these functions. The number-concentration correlation functions

GN.c(r),

^so obtained, ^are

presented

ⁱⁿ

figure

^{8. The function}

GNN(R)

is similar ^to

GN(r) ;

the maximum of

GNN(r)

^at

2.72 A

corresponds

^{to a} minimum in

Gcc(r)

^better

pronounced

^{than the} positive

peaks

^{at 2.3 A and 3.17 A}

indicating

^a

preference

for unlike atom pairs.

3.3 CHEMICAL SHORT-RANGE ORDER

(CSRO)

^PARA-

METER. ^- The

generalized

Warren CSRO parameter

a1 relative to the first shell is

given according

^to [6]

by :

where

zie

^and

zMT

^{are the} total coordination numbers of each species. ^{The value pf} ai is

directly dependent

on the _way of

defining

the shell of the first

neighbours,

870

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

by

the abscissa of the first minimum of

GNN

^{located at}

3.8 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 negative

with a value of - 0.035. This value is _very different from - 0.16, ^our

previous

estimate, ^{which was} deduced from a function

ARDF(R) containing

^both

contributions of BeBe and BeMT and calculated for a

first shell limited at

3.4 A (radius

^defined

by

^the

position

of the first minimum of

ARDF(r)).

^This

discrepancy clearly

shows that the limit of the first shell

largely

influences the chemical short _range order parameter ai.

The value of - 0.035 for the

Be4:5Hf ., Zr 5 7 -., glasses

is similar to that calculated for the

Be37.5Ti62.5

Fig. ^{9. -} Evolution of the generalized ^{Warren chemical}

order parameter a(r) ^{as a function of r.}

glass [19]

^with

partial

coordination numbers

equal

^to

ZB.B. = 2.9, ZB.TI = 6.9 and ZTiTi = 8.

In this series of

glasses,

^{the chemical}

ordering

^{is weak}

compared

^{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’

^which

correspond

^{each to the}

position

of the first minimum in

RDFiï

^{If the two}

^species

^are different atomic radii,

the three minima do not coincide with the minimum of

GNN

^and

consequently,

^{the CSRO} parameter ai calculated with

specific r1ij

^can be somewhat different from the value obtained with ^a

unique

^{value rl.}

Therefore for

binary

systems ^with strong ^size effect,

the

importance

^{of the chemical}

ordering

^{and its}

extent could be described

by

^{a function}

a(r)

^defined

in 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

positive beyond

^{3.9 A. The} oscillations of

a(r)

^{around 0}

damp

down

rapidly beyond

^{4.5 A and it shows the local}

character of the chemical

ordering.

This function could be

easily

^{used for a}

comparison

^{of chemical}

orders 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 Los}

Alamos and to the Institut

Laue-Langevin

^{for the}

allocation of beam time at their

respective

^neutron

sources.