Structure study of amorphous Gd-Y Alloys

Structure study ^of amorphous ^Gd-Y Alloys

M. Laridjani (*) and J. F. Sadoc (**)

(*) Service de Physique des Solides et Résonance Magnétique, ^C.E.N. Saclay, ^B.P. 2, 91190 Gif-sur-Yvette, ^France.

(**) Laboratoire de Physique ^des Solides, ⁹¹⁴⁰⁵ Orsay, ^France.

(Reçu ^{le 16} février 1981, accepté ^{le 21 mai} 1981)

Résumé. 2014 Les alliages amorphes ^{Gd-Y avec} différentes compositions depuis Gd0,9Y0,1 jusqu’à Gd0,1 Y0,9 ^{ont été}

étudiés par diffraction des rayons X. Les fonctions d’interférence et de distribution radiale sont présentées. ^Leurs

évolutions montrent clairement l’existence d’un ordre chimique ^{à courte distance.}

Les structures de ces alliages ^{ne sont} pas explicables par ^un ordre polytétraédrique compact. ^{Un modèle obtenu} par ^un mélange ^{de sites} tétraédriques ^et octaédriques ^est proposé.

Abstract.

Amorphous ^Gd-Y alloys ^{with different} compositions in the range Gd0.9Y0.1 ^to Gd0.1Y0.9 ^{have been}

studied by X-ray diffraction. Interference and radial distribution function are presented. ^{The behaviour of these}

functions clearly ^{indicates a chemical} short-range ^order.

The structure of these alloys ^{cannot be} explained by the tetrahedral close packing ^{model. A} model obtained by mixing tetrahedral and octahedral sites is proposed.

Classification Physics Abstracts 61.40

1. Introduction.

A variety of amorphous ^metallic alloys, produced by ^dif’erent techniques, ^{can be}

subdivided into two main categories :

1. Alloys ^{of two} metallic elements with _very dif- ferent atomic sizes ;

2. Metal-metalloid alloys, systems in which the small atomic size of the non-metal element is essential for glass ^formation.

However, ^to date, ^{there seems to be no} experimental

evidence of the alloying ^{of two} metallic elements with identical radii such as gadolinium (Gd)-yttrium (Y) (rGd

^1.802 Â, r,

1.801 Â).

Yttrium was chosen as a diluting material because it possesses the following ^two characteristics :

-

it has the same crystal ^structure (hexagonal ABAB...) with almost the same lattice parameter ^{as Gd}

-

it has similar outer electrons (one ^{d electron}

and two s electrons).

These two elements form a complete series of solid solutions in the hexagonal system [1]. Therefore, ^we expect ^{that the use} of yttrium ^{in this} investigation may

give ^some understanding of the role of atomic size in the structure of metallic amorphous alloys, ^and may

yield information on short-range ^order (chemical- disorder) which will be very helpful ⁱⁿ indentifying

non-resolved atomic arrangements of metal-metal

alloys.

2. Expérimental ^method.

^The amorphous ^metal-

lic alloy ^was prepared by high-rate sputtering ^with

an AI substrate at 78 K under Ar pressure of 2 x 10-4 torr with a sputtering ^{rate of 1 x 104} Â/h.

The inlet argon gas was of 99.995 % purity. ^The sputtering ^{chamber was evacuated to a} pressure 10-6 torr before admitting argon. This sputtering system ^{had a triode} configuration which consists of a

hlament, ^a floating substrate, ^{an anode and a} target (cathode); the cathode can be powered by ^{a D-C}

power supply (0-4 ⁰⁰⁰ kV).

The target ^{material was} prepared by ^levitation melting ^{in an} argon atmosphere.

By using ^this technique ^the compositions 10, 30, 50, 70, ^{90 at} % ^Gd (Gd ^99.9 %) ^{and Y} (99.9 %) ^were prepared. The various compositions ^{of the} sputtered alloys ^were obtained in uniform (5-10 gm) ^{foils of}

70 ^x 7 mm. The deposits ^{have metallic mirror sur-}

faces.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019810042090129300

The purity ^{of the} samples ^{was checked} by X-ray

emission spectroscopy (fluorescence analysis). ^This analysis ^{did not show any metallic} impurities ^or gas contamination such ^as _argon. Moreover, ^{a similar} experiment ^on amorphous ^rare earth-transition metals and Pd-Si alloys ^{did not show} argon gas ^or any metal- lic impurities. The latter were also tested by ^ionic micro-analysis ^with again ^no sign ^of any contami- nation.

All foils used were first checked by ^a diffraction pattern ^{with a} Debye-Scherrer technique.

A single foil of each sample ^was glued ^{to the} top ^of

a glass capillary ^{and the} sample ^was exposed ^{to an} X-ray ^beam. By using ^this method, ^the effects of

shadowing by ^{Gd did not} affect the picture. CoKa

radiation was used at 30 kV, 28 mA. The length ^of

exposure ^was 34 hrs.

In order to reduce the fluorescence background ^we interposed ^{a thin foil} (20 y) of iron between the _spe- cimen and film.

These diffraction patterns ^were characteristic of

amorphous solids without _any evidence of Bragg

lines.

The X-ray pictures ^of sputtered ^{films of} pure Gd and Y indicate a single phase ^{H.C.P. structure which}

is similar to that of Gd and Y. The absence of (100)

and (110) reflections shows that this phase ^{is a H.C.P.}

textured structure and that, therefore, ^{we do not}

observe _any oxide phases in pure Gd and Y sputtered

films.

Subsequent quantitative X-ray measurements were

obtained with a CGR diffractometer using Ag ^radia- tion ; ^each sample ^was scanned from 2 0

40 to 130°

at 0.010 _per min. in the reflection and transmission geometry. ^This angular range corresponds (for K1

^{4 7c sin} 0/À ^and K2

^{4 7r sin} O/Â2 ^{in which}

À1KpAg = ^{0.561 and À1KexAg}

^{0.497) to :}

In order to avoid fluorescence, the scattered beam

was recorded by ^an energy-dispersive detector of lithium-drifted silicon {(Si(Li)}, ^{and its} pulses ^accu-

mulated in a multichannel _energy analyser comprising

512 channels.

3. Results and discussion.

Figure ^{1 shows the}

reduced interference function F(K) derived from the measured intensities for Gd x Y 1 - x alloys (0.1 ^{X x} 0.9). Although ^the F(K) of the Gd-Y

alloys ^look similar, detailed observation shows clear differences between the F(K) corresponding ^{to the}

different compositions :

-

The first peak ^appears sharper ⁱⁿ Gdo.sYo.s

than in _any other composition and it is asymmetrical

for Gd0.1Y0.9.

-

The second rings ^resemblé each other but there is no evidence of a second ring shoulder which is

Fig. ^1.

Five reduced interférence functions F(K), derived from measured intensity data with five different compositions ^{of Gd-Y} alloys.

characteristic of the tetrahedral packing ^{in the clas-}

sical metallic amorphous alloys, ^{such as} Ni0.75-P0.25

and COO.75-PO.25 [2]. Previously, the absence of a

second peak shoulder has been interpreted by ^Sinha

and Duwez [3] ^{in terms of a} high degree of disorder and a large difference in atomic size between the elements. This explanation is thus inconsistent with

our present ^results given ^the equivalent radii in the

case of Gd-Y alloys.

Later Dixmier and Sadoc [4] predicted ^{that amor-} phous alloys ^{such as Au-Si seem to have a} short-range

order which generates such random networks without

giving ^a shoulder in the second peak.

3.1 1 THE REDUCED RADIAL DISTRIBUTION FUNCTION

( W(r)).

^{In order to clarify this apparent} discrepancy

the interference functions for all the compositions ^were

Fourier analysed ^to obtain reduced radial distribu- tion functions (R.D.F.). Figure ² shows that the features of the five radial distribution functions _vary somewhat with the composition. They ^{are characte-}

rized by ^{a first} peak (2 ^r

0") corresponding ^to approximately ¹² neighbours ^and by the second ring exhibiting ^an asymmetric profile.

The radial distribution functions of Gd0.1Y0.9 ^and Gdo.3yO.7 (Fig. 2a) ^have one common feature which is a shoulder on the small r side of the first peak ^which

indicates that there is a small interatomic distance of about 3 A. Changing the upper limit of integration (Kmax) produces ^no qualitative changes ^{in the R.D.F.}

of these compositions and their subpeaks ^remain

visible under termination ripples. Thus it is concluded

that these subpeaks ^have physical meaning.

Fig. ^2.

Experimental reduced radial distribution functions, W(r)

of different alloy compositions

a

Gdo.i Yo.9-Gdo.3 Y 0,7’ b

Gdo.7 Yo.3-Gdo.9 Yo i,

c

Gdo.s Y0.5.

When the concentration is increased the shoulder at 3 A becomes less pronounced.

The radial distribution functions obtained with different compositions ^{of Gd-Y} alloys ^{show some}

evolution of the second ring. The second ring ^of Gd0.9Yo.1 ^{1 and} Gd0.1Yo.9 ^are very similar, increasing slowly as ^{r increases and} falling just after the maximum value. This second peak ^is very different from the second peak ⁱⁿ the R.D.F. of the tetrahedral close

packing ^structure in which there is a shoulder cor-

responding ^to twice the first interatomic distance.

Figure 2c shows the R.D.F. of Gdo.5YD._, ^{which is} quite different. The first peak ^is sharper ^{and the second} ring ^more symmetrical than for the other composi-

tions. The other noticeable characteristic of this

curve is the appearance ^{of the} light ^{shoulder on the} high ^r spider of the second. As the concentration of Gd increases this shoulder becomes less and less pro- nounced and finally disappears. ^{Note also that the} subpeak ^{at 3 A is not} observed for this composition.

The value of the distance, .J2 ^u, corresponding ^to

the small ^r side of the 2nd ring appears ^to have a

minimum value for the Gdo.5 y 0.5 composition. ^Hence

it seems to us that the structure of Gdo.5 y 0.5 might

be an intermediate case between tetrahedral close

packing (R.D.F. ^{curve with} splittings, Fig. 5) ^and

other structures more appropriate ^{for the} Gdx y 1- X alloys (with ^{X 0.5 or} X > 0.5).

3.2 DIscussION.

An attempt ^{will now be made}

to describe the evolution of the R.D.F. resulting ^from changes ^{in the} composition.

-

In the crystalline phase ^{Gd-Y is a} solid solution for all compositions. Therefore it seemed a reasonable first hypothesis ^to consider the structure of this alloy

as a pure metallic structure for the study of the R.D.F.

in the amorphous ^{state. In such a case a} tetrahedral

packing ^{model would seem to be a} good starting point

to describe the R.D.F. but the experimental ^results

show that this hypothesis ^{is wrong} (Figs. ^{2a, b,} c).

All the Gd-Y, ^{R.D.F. are} characterized by ^{4 inter-}

atomic distances : the first distance Q which corres-

ponds ^to the first peak, and three other distances which contribute to the 2nd ring (J2 ^{Q, 1.75 cr and}

2 (j). ^The distance.J2 (j is characteristic of octahedra ;

the distance 1.75 u is associated with pentagonal ^bi- pyramids (Fig. 7a). ^The profile of the 2nd ring ^{of the}

R.D.F. suggests ^the occurrence of octahedral sites

mainly ^for compositions ^{different from} Gdo.5yo.5 (Figs. ^2a, b). ^The structure cannot be explained by ^a

pure tetrahedral packing.

-

If the amorphous alloy ^{was a solid solution}

without chemical order (ideal solution) ^{the three} partial R.D.F.’s would be identical _{and any} combi- nation of these functions would give ^{the same total}

radial distribution function and would be independent

of the composition. ^The evolution of the experimental

R.D.F. with the composition ^{does not} corroborate this hypothesis. ^{For instance, the} distribution func- tions of Gd0.5Y0.5 shows that the structure is an

intermediate case between tetrahedral close packing

and some other structure of the GdxY, -x alloys.

The number of interatomic distances V2- (J ^{for the}

Gdo.5YO.5 alloy is smaller than in the other compo- sitions and a shoulder corresponding ^{to the distance}

2 6 appears ^on the righ r side of the 2nd peak ^{of this} composition..

For low Gd content alloys ^{we observed some}

interatomic distance near 3 Á (Fig. 2a), ^{which is} surprising since the metallic radius for both Gd and Y atoms is 1.80 Á. Is it possible ^to explain this small distance by valence fluctuations of the Gd atoms ? As the Gd electronic structure is normally ^considered

to be a stable structure with half filled f-bands, ^this explanation ^is generally rejected. ^However in crys- talline Gd-Y alloys with low Gd content, ^{an increase} of the magnetic ^{moment of the Gd} atoms, ^{and the low} temperature specihc ^{heat behaviour can be} explained by valence fluctuations [5]. Nevertheless it is not the usual theory currently ^{held to} explain these effects [6].

Thus there exists no convincing model which can account for the 3 Á distance.

That the structure of a Gd-Y alloy depends ^{on its} composition indicates that there is a chemical effect

on this structure, probably resulting from chemical

ordering ^{in the} amorphous form of this material.

Consequently ^{we have the} paradoxal ^conclusion

that the chemical local order is more important ^{in the} amorphous form than in the crystalline ^form. Perhaps long-range order in the crystalline phase, by setting

an identical local order topology around all atoms, does not facilitate the existence of chemical order.

4. Structural model.

The radial distribution func- tions show an interatomic distance near.,/-2 ^{a, which}

is characteristic of octahedral sites. A packing ^of

tetrahedra and octahedra is an adequate hypothesis

for the amorphous ^{Gd-Y structure.}

The packing ^of regular polyhedra like tetrahedra and octahedra is not necessarily possible ^{in real} space

but _space curvature can allow such a packing. ^One

of us [7, 8] showed that this is the case, for instance,

with a tetrahedral packing.

It is well known that tiling of space by regular

tetrahedra is impossible, ^{but a} regular packing ^of

tetrahedra ^can be defined in a space of positive ^cur-

vature [9, 10]. Amorphous structures like tetrahedral close packed structures are derived from the packing

of the curved space by mapping ^onto the Euclidian space. This mapping introduces length distortions and

topological ^defects.

Tiling ^of 3-dimensional _space with a mixture of octahedra and tetrahedra is possible if there is the combination of two tetrahedra for one octahedron.

In this _way a crystalline ^structure is obtained.

For other ratios of octahedra to tetrahedra, only

curved space ^can be tiled. One useful configuration

occurs when there are 4 tetrahedra for 1 octahedron.

This mixture gives ^a semi-regular polytope (polytope

is equivalent ⁱⁿ 4-dimensional _space to a polyhedron

in the Euclidian 3-dimensional space). ^{In this} polytope

there are 2 400 tetrahedra and 600 octahedra, ^{if the}

interatomic distance is 1 the radius of the circumsphere (a 3-sphere in 4-dimensional space) ^{is 3.225} [5, 6].

This radius is relatively large compared ^{to the radius}

obtained for a pure tetrahedral packing (1.618).

In this semi-regular polytope ^{there are two kinds of}

vertices (called ^{A and} B). ^{Each B vertex} is coordinated with 12 A vertices giving ^an icosahedron. There are

120 B vertices in each polytope. ^{Each A vertex is}

coordinated with 10 B vertices and 2 A vertices forming

a polyhedron ^with 5 square and 10 triangular ^faces.

There are 720 A vertices. Consequently ^{we can use the}

notation A6/7B 1/7 ^{for this} structure. If we consider the

amorphous structure, ^{to be a} regular ^{structure in}

curved _space distorted by ^the mapping ^{on the Eucli-}

dian _space, this polytope ^{is a} good hypothetical

structure for the amorphous ^Gd-Y alloys.

By putting ^{Gd atoms on the A} vertices and Y atoms

on the B vertices, ^{we can} describe the structure of

Gd6/7y1/7. Conversely by placing ^{Y atoms on the A}

vertices and Gd atoms on the B vertices the structure of Gd1/7y6/7 ^{can be built up.}

As in the tetrahedral close packing ^structure (T.C.P.)

an important basic unit is a cluster of 7 atoms that form a pentagonal bi-pyramid (5 tetrahedra with a common edge). In tetrahedral close packing ^{two of}

these clusters can be assembled, ^{with a common vertex}

and a common pentagonal ^{axis, to obtain an icosa-}

hedron (Fig. 7b). ^{In the structure described} A6/7B1/7’

the icosahedral order remains around the B vertices,

but around the A vertices two pentagonal bi-pyramids

are assembled in such a way ^{as to} build half an octa-

Fig. ^3.

Partial radial distribution function for a

Gd-Y, P(r).

a

PCA(r), ^b

Pcc(r), c

P AA(r).

hedron. This configuration could be described as a

twisted icosahedron (Fig. 7c).

Each pentagonal bi-pyramid ^{contins 6 A vertices}

and 1 B vertex ; each tetrahedron contains 3 A vertices and 1 B vertex ; each octahedron contains 6 A vertices.

An amorphous ^{structure can} be obtained by map-

ping ^the polytope (with ^{atoms located on} the vertices onto the Euclidian _space.

This provides ^two hypothetical structures for alloys

with compositions ^{close to} Gdo.8,6YO.14 ^and Gdo.14Yo.86. ^{For other} compositions ^{it is} possible ^to

suppose ^some substitution of one kind of atom by ^the

other.

The R.D.F. deduced from the model provides ^an

excellent means of testing ^the validity of the model.

It is possible ^to obtain the R.D.F. directly ^{from the} polytope ^{structure defined on a} 3-dimensional curved space ; its R.D.F. is built _up from delta functions since

a polytope ^{is a} regular figure. Broadening ^{of delta}

functions with a factor simulating distortions occur-

ring during ^the mapping ^{onto Euclidian} space is a

way ^to obtain a realistic R.D.F.

These functions are represented ⁱⁿ figure ^4. They

are calculated in two cases which correspond ^{to the} compositions Gd6/7 Y 1/7 ^and Gd1/7y6/7 ^{with X-ray} scattering ^factor.

The radial distribution functions are obtained by ^a

combination of 3 partial Pij(r) functions ; Pi j(r) ^being

the probability ^of finding j ^{atoms at a distance r}

from an i atom

P(r) - (Ci f 2 Pii + Cj f 2 Pjj +

+ 2 Ci Cj ^if fj Pjil(Ci fi ⁺ Cj fi) 2

Partial PAA(r), PBB(r) ^and PBA(r) ^{functions are also} presented ⁱⁿ figure ^3.

The calculated functions _agree relatively ^{well with}

the Gdo.1 y 0.9 ^and Gdo.gYo.l experimental ^functions

if interatomic distances are 3.6 À for dAA ^{and 3.3 A}

for dBA. (If ^{A atoms form a} regular icosahedron the distance from the centre of the icoahedron (B atom)

Fig. ^4.

Calculated pair distribution functions for the mixture of tetrahedra and octahedra.

Fig. ^5.

Calculated pair distribution function for tetrahedral

packing. ^{In this} figure ^{the 3rd} peak (splitting) corresponds ^{to 2 or.}

to the vertex (A atom) is smaller than the edge length,

and therefore dAA > dBA.)

The maxima positions ^{for both} experimental ^and

theoretical functions are identical and the profiles ^of

the rings ^are comparable. Nevertheless, ^the broadening

factor seems to be small for large ^distances.

This result supports ^the hypothesis ^{of a} mixing ^of

tetrahedral and octahedral sites in the ratio 4 to 1.

If concentrations are slightly ^{different from} A6/7B1/7

it is then possible ^to suppose ^some substitution.

When the concentration is in the _range A1/2B1/2

the experimental results show that there are more

tetrahedral sites (Fig. 2c). ^{We simulated a R.D.F.} by combining ^a Pl(r) ^function, corresponding ^{to the} A6/7B1/7 ^{(Fig. 6a) (with Gd and Y randomly} distributed

on A or B positions) ^{with a} P 2(r) ^function (Fig. 6), corresponding ^{to a} tetrahedral close packing ^struc-

ture with Q

3.6 À.

Figure ⁶ represents ^{two curves} calculated with

P(r)

nP 1 (r) ⁺ (1

n) P 2(r) ^{for n}

0.5 and 0.7.

Experimental results fit the curve shown in figure ^6b (n

0.7). The ratio between the number of octa- hedral sites and the number of tetrahedral sites in this case is 1/7.

Nevertheless this last attempt, ^{which is at least a} qualitative representation ^{of the} short-range order,

Fig. ^6.

Calculated P(r) distribution for Gdo,5 Yo. s a : ⁿ

0.5,

b : n = 0.7.

c

Fig. ^7.

^{a :} pentagonal pyramid ; b : ^an icosahedron ; ^{c : a twisted} icosahedron or a polyhedron with 5 square faces and 10 triangular

faces. b and c are obtained by joining ^two pentagonal bi-pyramids (a)

with a common 5-fold symmetry ^{axis in} staggered (b) ^and eclipsed (c) configurations.

is certainly ^{not a} model. It is only ^a hypothesis ^to

describe this structure. It is impossible ^{to deduce at}

this time whether there is a local order coherent with this ratio between the number of tetrahedra and ^octa-

hedra, ^{or if there are} local order fluctuations between the pure T.C.P. and the A6/7B1/7 ^structure.

5. Conclusion.

The structure of the binary ^Gd-Y alloy, ⁱⁿ spite ^{of its} constituting ^elements having ^the

same atomic size, ^{is not an} approximation ^{of a} pure metal when it is prepared ^{in an} amorphous ^form.

Chemical order explains the radial distribution beha- viour when,the concentration is changed. There is also

a strong change ^{in the} atomic size of some atoms when the Gd content is low. A model using ^a mixing ^{of tetra-}

hedral and octahedral sites can account for the radial distribution functions. There are approximately ⁴

tetrahedra for 1 octahedron at low concentrations

(Gdo.86YO-14 ^or Gd0.14Y 0.86), and there is an increase in the tetrahedron number when the composition ^is

about Gd).5Y).5. ^{In order to} understand ^more clearly

the chemical order and the atomic size fluctuations,

EXAFS experiments, ^{which are very sensitive to the}

nearest neighbours, ^are proposed.

Acknowledgments.

^We would like to express ^our

gratitude ^{for the} great help and valuable advice from D. Luzet in the preparation ^{of the} alloys. The authors

are indebted to Dr. J. Dixmier for his critical review of the manuscript.

References

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[2] SADOC, J. F., DIXMIER, J. and GUINIER, A., J.N.C.S. 18 (1973) 46.

[3] SINHA, ^{A. K. and} DUWEZ, P., Appl. Phys. ³⁶ (1965) ^2267.

[4] DIXMIER, J. and SADOC, ^J. F., Metallic Glasses-American Society for ^metals (1978).

[5] ALLAIN, Y., BONNEROT, J., ^et al., ^J. Physique ²⁴ (1967) ^98.

[6] COQBLIN, B., The electronic structure of ^Rare Earth Metals and

Alloys : ^The Magnetic Heavy ^{Rare Earth} (Academic Press) ^1977.

[7] SADOC, ^J. F., 1980a, Proceeding of the L.A.M. 4 Conf., ^J.

Physique Colloq. ⁴¹ (1980) ^C8-326.

[8] SADOC, ^J. F., ^{J.N.C.S. 44} (1981) ^1.

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[10] ^{MACKAY, A. L., J.} Phys. ^{A 13} (1980) ^3373.