LOCAL ORDER IN THE EUTECTIC Mg.72 Zn.28 ALLOY

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LOCAL ORDER IN THE EUTECTIC Mg.72 Zn.28

ALLOY

P. Andonov, P. Chieux

To cite this version:

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LOCAL ORDER

IN THE

EUTECTIC Mg.,2 Zn.28 ALLOY

P. Andonov and P. ~ h i e u x *

Laboratoire de MagnQtisme, C. N. R. S . Be ZZevue, 1, Place Aristide Briand 92195 Meudon PrincipaZ Cedex, France

* ~ n s t i t u t Laue-Langevin, B.P. 156 X, 38042 GrenobZe, France

R6sm6

-

Les facteurs de structure globaux S(Q) et les fonctions de corr6la- tion G(R) de l'alliage amorphe Mg.72 Zn.z8 ont 6t6 obtenus par diffraction des rayons X et des neutrons.Ltordre chimique B courte distance est discut6 dans lefomlisme de Bhatia;-Thornton et les nombres de coordination partiels sont extraits.La cornparaison de llamorphe et du cristal MgslZnzo indique une faible diff6rence de l'ordre local due B un nombre de premiers voisins de mSme type supe'rieur dans la phase d6sordo~e'e.L'6volution structurale au cours de la cristallisation de l'amorphe et de la solidification du liquide surfondu a 6t6 observde in situ par diffraction neutronique.Les variations de GCR) sont en ac- cord avec les premiers r6sultats.Les alliages amorphe ou liquide 'cristallisent dans la phase orthorhombique MgSIZnLO;ltarrangement atomique est obtenu en deux e'tapes successives.

Abstract -The total structure factors S(Q) and the total pair correlation functions G(R) of the amorphous alloy Mg. 72Zn. 8 have been investigated by X-ray

and neutron diffraction.The chemical short range order is discussed in the Bhatia-Thornton formalism and the partial coordination numbers are extracted. Comparison with thestructure of crystalline MgslZnno shows a weak difference in the local order due to a preference for like type atoms at the first interatomic distances in the disordered phase.To confirm these results, new measurements were performed by neutron diffraction.The structural evolution during the crystallization of the amorphous phase or the solidification of the undercooled melt are observed in situ.The changes of G(R) are in good agreement with the previous results. Amorphous and liquid alloys crystallize to the single phase of crystal Mg51Zn20; the approach of the crystalline local atomic arrangement is obtained by two successive steps.

I

-

INTRODUCTION

The crystallization process of amorphous alloy Mg.70Zn30 was studied by many resear- chers /1,2,3/. This alloy, near its eutectic composition, crystallizes into the single phase MgS1Znz0 defined by Higashi et a1 /4/. The atomic structure of metallic glass has been investigated experimentally by EXAFS /5,6/ and X-ray diffraction/7,8/ as well as neutron diffraction techniques /9,10,11/. The usual conclusion is that this alloy shows a local structure similar in the glassy and crystalline states. But a difference between these states may exist.

The aim of the present work is to study the structural evolution of eutectic alloy in different states :amorphous, liquid and undercooled melt. The chemical short range order (C.S.R.O.) and the partial coordination numbers are investigated from X-ray and neutron diffraction. For this alloy, the structure changes are observed for the first time in situ, the temperature variation taking place in the neutron beam. I1

-

RECALL OF THEORETICAL BASIS

The total structure factors were evaluated using the Faber-Ziman definition /12/ or the Bhatia-Thornton definition /13/ : ₍_SFZ(Q)

= 1 ~ ~ ~ ~ ( ~ ) - ( < f ~ > - < f > ~ ) } /<f>'

2

I

SBT(Q) = Icoh(Q) /<f >

with Icoh(Q) = corrected and normalized intensity, f = scattering l e n g t h , ~ = 4 ~ ~ i ~ ~ / h

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C8-82 JOURNAL DE PHYSIQUE

s c a t t e r i n g vector and c l , c2 = atomic f r a c t i o n of the constituents 1,2. The t o t a l function G(R) i s obtained by Fourier transform of SFZ(Q):

G(R) = 2/ll

/ow

Q{ SFZ(Q)-1) sinQR dQ

G(R) = 4'R _{P ( ~ ) - P ~ )}_{and the r a d i a l d i s t r i b u t i o n function RDF(R)} ₌_{4 l I ~ ~ p ( ~ )} with po=mean atomic number density and p(R) = atomic number density a t the distance R The coordination number N1 i s calculated from the area of the main peak of the RDF between R1 and RZ positions of minima flanking t h i s peak.

G(R) can be expressed i n terms of the three p a r t i a l p a i r correlation functions Gij(R)

as following: c l 2 f l 2 C 2 2 f2 2 2clc,f,f2

G (R) = ---;-- G1 (R) + - G,, (R) + G 1 2 (R)

<f > <f > 2 <f > 2

G..(R), t h e d i s t r i b u t i o n of j-type atoms around an i-type atom, i s r e l a t e d t o the

11 p a r t i a l d i s t r i b u t i o n function p _{1 3}- . (R) according t o : G .

.

(R) = 4(IRi (p

.

(R) ,c. -p

11 11 1 0

To describe the S.R.O., SRT(Q) can be expressed i n terms of the three p a r t i a l _--

f a c t o r s : _{t f > 2} _{c i c z ~ f ~} _2Af<f>

S,,(Q) = SNN(Q) + S C C ( Q ) + < f 2 >

< f 2 > SNC (Q)

<f 2 >

h ( Q ) i s the p a r t i a l structure f a c t o r of the correlations between density f l u c - tuations, it describes the topological order

Scc(Q) i s the p a r t i a l structure f a c t o r of the correlations between concentration fluctuations, it describes the C.S.R.O.

SNC(Q) i s the p a r t i a l s t r u c t u r e f a c t o r of the cross correlations, it represents the s i z e e f f e c t s

The generalized Warren S.R.O. parameter /14/ i s an another way t o describe the local

orde?: pi(R) represents the number of atoms

= I-PIZ ( R ) / [ ~ ~ { C Z P ~ (R)+cipn (R)

9 _wr

_velum_about _an_{i-twe atom} p. .(R):the number of j-type atoms about an i-type atom.

a(R)<O indicates a preference f o r unlike neighbors I11

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EXPERIMENTAL

Sample preparation : The amorphous e u t e c t i c material Mg.72Zn.28 was prepared a t the Laboratory of Magnetism (R.Krishnan and P.Rougier) by rapid quenching from the melt with the "single r o l l e r technique". The amorphous structure was cheked by X-ray d i f - f r a c t i o n and D.T.A. The alloy composition matches the stoichiometry of the single c r y s t a l l i n e phase MgslZnzo. For neutron d i f f r a c t i o n , the quenched material, obtained as s t r i p s , i s wound on an aluminium frame t o form a sample of volume = 0.3 cm3. For X-ray d i f f r a c t i o n , by transmission technique, one layer (e=30um) i s s u f f i c i e n t ; four o r f i v e layers a r e superposed t o work by r e f l e c t i o n technique. The l i q u i d sample of same composition i s obtained by melting small a l l o y l ~used t o prepare amorphous s material. The specimen was maintained i n a vacuum = 10- Torr i n a vanadium container The sample d e n s i t i e s and experiment temperatures are reported i n Table I .

Experimental procedure : Neutron d i f f r a c t i o n experiments were c a r r i e d out using the

D2 spectrometer a t I.L.L. (Grenoble,France). The flux of monochromatic neutrons was obtained by r e f l e c t i o n on the (111) planes of a copper monochromator. The exact A,the counter arm zero and the instrument resolution were determined from the positions and the width of the f i r s t f i v e well resolved peaks of a s i l i c o n powder sample. X-ray scattering measurements were performed on three goniometers:

- a standard C.G.R. powder diffractometer operating i n the transmission and r e f l e c - t i o n mode, equipped with a Si(Li) s o l i d s t a t e detector. With AgKa radiation and a channel width = 200eV, the Q uncertainty i s <0.4%.

-

a Guinier camera and a Siemens goniometer, equipped with a auartz monochromator i n the incident beam and precise s l i t s f o r the small angle s c a t t e r i n g . These two ap- paratus, using CuKa radiation i n the transmission mode, allow a good control of the i n t e n s i t y i n the low Q range: 0-2.5A-l. In a l l cases, the instrument adjustement and the resolution t e s t s were obtained from the peaks of the same s i l i c o n powder sample.

(see i n t h e Table - I - the experiment parameters)

IV

-

RESULTS

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Alloy state amorphous partially

1

crystallizeaj liquid ;;wooledJ partially

has been made from the SFZ(~) (Q) of h4g. 72zn.28 and Pd. 82~Si. 1 7 5 (Fig. 1). The second

maximum of the first alloy shows two well splitted subpeaks when only a shoulder is

Table I : description of experiments observed in the second one. The damping of the oscilla- tions is weakly more superior.

So the metal-metal glass ap- pears more structured. But the range of correlations between the density fluctuations (topological short range order), represented by the correlation length lccd, is the same in the two alloys

(lCcd'2q/AQ). See results in table I1 The most apparent difference is the prepeak observed in MgZn alloy at 1.5a-l. To cha- racterize the S.F..O. effect, the structure factor of this alloy is described in terms of B.T. partial factors from

and SBT (n) (Q)

.

SBT(x) j2ie Fig. 2)

At ~=1.51-l:

SBT(~) (Q) = 0.7879 SNN + 0.21Z0 SCC + 1 .8202 SNC(x) SBTcn) (Q) = 0.99g3 SNN + 0.0006 SCC + 0.11 l6 SNC(x) SCC contribution is negligible in the neutron diffraction, the prepeak of SBT(x)(Q)

must be attributed to SCC or SNC.

Since S shows up the size effect, its peak positions are mainly determined by the atomic #$meters of the constituents and strong C.S.R.0. effects cannot modify the SNC(Q) curve, like it was explained by Nassif et a1 /8/. The atomic diameter ratio is close to 1 for h4gZn alloy (D~~/D~~=3.20/2.76 = 1.16), the contribution of SNc must be small in the low Q region. The error is expected negligible in the calculation of the Partial factors, using for SNC(Q), the values calculated from the Percus-Yevick approximation generalized to a blnary alloy/l5/ in which C.S.R.O. effects are not ta-

0.6 - 16.65 0.7

-

5.0 3.00 0.5

-

2.2 1°K 293tO.l 343t0.2 37310.2 618=Tft2 816=Tf+200 599=Tf-17 3- 2- 0 2 4 6 8 1 0 1 2 1416 Fig.1-Total structure factors SFZ(,)

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C8-84 JOURNAL DE PHYSIQUE

ken into account. The theoretical hard-sphere model curves S~c(x) and SI\TC~~) have been calculated using different mean atomic densities and different hard-sphere dia- meters. The best agreemegt for the position Q1 and the amplitude S(Q ) was obtained with: p = 0.052

atom.^-^

h.s.DM, = 2.828 h . s . ~ ~ ~ = 2.42;

"

The partial factors are shown in Table I1 :-local order in amorphous alloy Fig.3, SCC contribution is much

-structural parameters in reciprocal space stronger than the other ones. This confirms the hypothesis that the AQi=width at halt m a x i m intensity of the _{prepeak has}

to be attributed to tor-

(i) peak in A-'

Qi =position of the (i) maximum in

8-I

relations between the concentration _{fluctuations. From the prepeak width}

c .

=ratio S(Q. ) /S(Q ; S (Q- ) =maximum am- the spatial extension gf the

plitude o$ the ti) peak C.S.R.O. is about 10a.

pp=index relative to the prepeak

i I 1 I !

"

' I mean peak

1

0

Fig.3-Partial B.T.structure factors kwrphous Alloy OPP Q1 Q2 or{::: Q3 Q4 S(Qpp) S(Q,)

err'

222 c3 (4 A Q ~ P AQl

b) igteratogic distances and

so_ordi~rlarien-n~e_rs

-

G

cn)

CR) G (x) mF (n) (R) and

RDF{,) (R) are calculated from Pd.825Si.175 F.Z. Fornlalirn experiments ( x ) 2.70 4.75 7.01 9.05 3.10 O 0

I

0.40 0.37 0.40 J 1'b.72Zn.28 A.L. Formalism H.S. Model

Correlation length of: 'FZ (n) and SFZ(x)

.

The radius of

concentration fluctuations lCcf the first coordination shells

density 1 1 lCdf Rz (,I, R1 and the total coor-

dination numbers N1 fn) ,N1 (x-) are (

-

2.65 4.84 -

-

3.31

-

0.42 ng.7~Zn.28 8.T. Formalism experiments J I 1 obtained from: I n )

-

2.61 4.75 - -

-

3.44 - -

--

- - --

-

0.38 Mg.72zn.28 F . I . Formalfsm experiments ( x ) 1.50 2.65 4.45 15.20 6.85 9.35 0.55 3.28 -

-

0.63 0.44 RDF and RDF

.

The atomic distances Rij (i,j=1,2) and the partial coordination numbers Nij are determined from the main peaks of the RDF functions corresponding to G1p) and G1cXi fitted by three gaussian repartitions. The fitting parameters were de lned from t e crystalline phase MgslZnzo as following:

the maximum positions are the mean distances dmij calculated from the distribution of all the first crystalline distances dij, taklng the atomic coordination of all the sites into account.

( x ) 1.55 2.62 4.45 15.20 6.85 9.35 0.60 3.33 0.50

1

,.,a 0.35 0.31 0.63 0.45 (n)

-

2.60 4.40 (5.13 6.65 8.70

-

3.51

-

- - - - 0.40

6 . . =

-

Ad- .k with Ad.. = the total dispersion of crystalline distances dij

lJ

x2

13 kl' = disorder factor -1 :25 I n ) - 2.60 4.40 5.13 6.65 8.70 - 3.51 0.45

lo

..

0.33 0.30

-

0.40

Sij = area of the gaussians 2 2 S..

RDFl[R) = R C C

i=l j=l " : e x p { L ( ~ - d m ~ ~

-

2 1'1

Nij were calculated from &dmij .aij aoij

the area with: cif i2 2c.f .f.

N.. = S . . /and N.. = S../ '1

11 11

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decrease of the unlike neighboring atoms and a increase of the Zn-Zn coordination. numerical values) Table I11 : local order, structural parameters in direct space 3

( see Fig.4 the decomposition of the peaks and Table I11 the

2

Fig.4

-

aldistribution of the interatomic distances

1

in the crystalline phase M R S O Z ~ Z o 0 2.5 3.0 3.0 3.0 3.5

~ ( i )

0 4 C ,-.? VI c .k .I? * ? 2 * ." % '+ u VI _c m m 5 g C_VI * O .- m u 0. u C .,- .- g 5 * m _L_n0 c m o, C) .r c 0

-

'z C r y s t a l Mg51Zn20 2.71 d ~ n . z n d m ~ . ~ n = 2'787 2.60 d ~ g - ~ n = 2.9E2 [3.20 m"g'in 2.82 d ~ g - ~ g dm = 3.203 13.65 Mg-Mg AZn-Zn = 0.36 AMg-Zn = 0.60 AM,, -, = 0.88 A 1 ( x ) 9.9 mean atoms Al(n) 11.9 mean atoms

zn[::;

t:;

NTa(x)=11.2 N z n - z n l ( x ) 8.6

'lg[(n) 8.5 N ~ a ( n ) = 1 1 ' 4 N ~ n - M g & Amorphous a l l o y Mg.72Zn.28

R,:position of the first peak

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JOURNAL DE PHYSIQUE

+Hi. Zn-Zn

-

Mg-Zn

Fig.4-

b)decomposition of the first peak

15

++++ Zn-Zn

---- Mg-Mg

2 . 5 3 . 0 3.5

IV2 - crystallization of the disordered states

-

R

(i)

To confirm the previous results, the structure of

liquid alloy was studied by neutron diffraction. In the liquid, R1 is inferior to the amorphous value ( Rl in liquid = 3.02a < R1 in amorphous = 3.051 ) . This feature does not agree with the thermal dilatation and can be explained only by an increase of Zn-Zn correlation in the more disordered state. At the crystallization, in the both cases, RL attains progressively the maximum observed in the crystalline repar- tition ( R1 in the crystal = 3.16a )

.

The solidification of the liquid is controlled at different temperatures. An undercooling domain is observed in which the main peak S (Q1) varies progressively though Gl (R) does not change. Then S (Q1) shows the same variations than the ones observed in the crystallization of the amorphous alloy. The final state is always the orthorhombic crystalline phase J4g51Zn20.

(results to be published) REFERENCES

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,

Narumi ,H.

,

Arai ,H.

,

Walkatsuki ,K. ,Sasa ,Y. and Mizoguchi ,T. Proc. 4th Int. Conf. on Rapidly Quenched Metals Sendai (1981) 667

/3/ Matsuda,T. and Mizutani,U., Proc, 4th Int. Conf. on Rapidly Quenched Metals Sendai (1981) 1315

/4/ Higashi, I., Shiotani,N., Uda,M. ,Mizoguchi ,T. and Katoh ,J. J. of Solid State Chemistry 36 (1981) 225

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,

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,

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.

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.

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=

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