Solid State Communications, Vol.44,No.7, pp.983-986, 1982. 0038-1098/82/430983-04$03.00/O Printed in Great Britain. Pergamon Press Ltd.

PARTIAL PAIR CORRELATION NNCTIONS OF La l_x(Al-Ga-Au)

METALLIC GLASSES FROM X-RAY DIFFRACTION DATA* x

Arthur Williams

W. M. Keck Laboratory of Engineering Materials, California Institute of Technology, Pasadena, California 91125

(Received 29 June 1982 by H.Suhl)

X-ray diffraction studies of Lal_xAlx, Lal_x(A10 5Ga0.5)x, Lal_xGax

and La l_xAux metallic glasses have been performed for x = 0.20, 0.24

and 0.28. Similarities in the radial distribution functions for these materials as well as other data suggest that these alloys are iso- structural. Experimental data from different alloys have therefore been used to separate the three different pair distribution functions, which are then compared to dense random packing models and data for other metallic glasses.

Introduction

Diffraction studies of amorphous metal alloys have usually been complicated by the multiconstituent nature of these materials which results in diffraction intensity profiles which are sums of the contributions from a num- ber of individual pair correlation functions from each pair of constituent elements. In a previous study, two of the three partial pair correlation functions for some binarylanthanum- based metallic glasses were obtained through the isomorptous substitution of Al and Ga in the alloys. In this study, three lanthanum-based alloys of Al, Ga, and Au which can be rapidly quenched into the glassy state have been found from x-ray diffraction studies to have similar short range order, and isomorphous substitution has been used to obtain all three partial pair correlation functions. The results show a type of short range order different from either that of the transition metal-metalloid (TM-M)

glasses: or the dense random packing (DRP)

models.

Experimental

Twelve alloys were prepared with the com- positions shown in Table 1 by rf levitation melting of the appropriate constitutents under an argon atmosphere on a water cooled silver boat. Ingots were remelted several times and then broken apart and visually inspected for homogeneity.

Amorphous samples in the form of foils about 40 microns thick and typically 1 to 2 centimeters in diameter were obtained by rapidly quenching from the liquid melt by the piston and anvil technique4 under a helium atmosphere.

A flat mosaic of samples several foils thick was built up on a Pyrex slide using

thinned Duco cement and made thick enough to effectively eliminate any scattering from the substrate. Accurate x-ray diffraction measure- ments were performed on the mosaics using MO Ku radiation with a curved LiF monochromator in the diffracted beam, which was scanned from

28 Q 5' to 160'. As many as four complete stags were performed on each sample and then added together in order to obtain asatisfactory signal to noise ratio.

Table 1. Atomic densities and x-ray scattering weights of individual pairs of atomic species of the alloys studied.

0.8950 0.1021 0.0029 0.02909

0.8317 0.1605 0.0077 0.02966

0.7749 0.2107 0.0143 0.03018

0.5516 0.3822 0.0662 0.02945

0.8701 0.1253 0.0045 0.03071

0.7945 0.1937 0.011.9 0.02083

0.7283 0.2502 0.0215 0.03098

O.b838 0.4235 0.0927 0.03001

0.8037 0.1197 0.0066 0.03109

0.7560 0.2270 0.0170 0.03133

0.6813 0.2882 0.0305 0.03107

0.1222 0.4551 0.1227 0.03053

Densities of the amorphous metal alloys studied were measured by the hydrostatic weigh- ing technique using toluene as the working fluid. An average of the densities measured for each of three or four foils was taken for each composi- tion in Table 1.

* Work supported by the Department of Energy, Proj. Agree. No. DE-AT03-81ER10870 under Contract No. DE-AM03-76SF00767.

983

984 PARTIAL PAIR CORRELATION

Results

FUNCTIONS OF La l_x(Al-Ga-Au)x Vol. 44, No. 7

justifiable by the similarity in their G(r) as well as by the facts that Al and Ga are iso- electronic simple metals and form the same inter- metallic compounds with La. The contributions from iAl_A1(K) and iGa_Ga(K) to the total i(K)

are very small as can be seen from Table 1 which

After making corrections for background, polarization and Compton scattering the coherent x-ray scattering intensity I,,(K) for each of the 12 alloys was normalized in the usual manner by the high angle method5 and used to compute the reduced interference functions i(K)= K[I(K) -11. The IK(K) for the Lal_xAux metallic glasses are unusual in-that they exhibit small prepeaks near K % 1.5 A-l, which are well separated from thepri- mar-y diffraction band, as shown for La 6Au24 in

Fig. 1. The intensities of the prepea s were ;! found to scale with Au concentration in thealloys, suggesting a large Au-Au correlation distance on the order of 2*/K % 4.2 6;. The Au-Au contribu- tion to the total scattering, however, which is a linear combination of three partial pair terms, is unfortunately too small to be observeddirectly in the total G(r), where

I I I

0.0 2.0 4.0 6.0 8.0 I

K &',

Fig. 1. X-ray coherent scattering intensity, IN(K) of the metallig glass La76Au24, displaying

prepeak at K = 1.46 A-l.

G(r) = 4nr[p(r)-po] = <s-i(K) sin(Kr)dK,

although the first maximzm is split as a result of the strong contributions from La-La and La-Au pairs as first observed by Logan for LagOAu20.6 The total G(r) of all twelve alloys exhibit second neighbor peaks at Q 1.73 but not at 2.0 times the nearest neighbor distance. An isomor- phous substitution of elements was therefore used to separate the three independent partial pair correlation functions GLa_La(r),GLa_Au(r) and GAu_Au(r) in order to acquire a more detailed

understanding of the nature of these metallic glasses. First, analysis of diffraction data from La 1 xAl, and Lal_xGax was performed on the

assumption that Al and Ga perform identicalroles in the structure of the glassy alloys, deemed

shows the average coefficients of the three partial reduced interference functions to the total i(K) for each alloy, and were neglected to allow calculation of i La-La(K) and iLa_Al(K)'

Diffraction data from the ternary alloys La l-x(A10.5Ga0.5)x allowed redundant calcula-

tions to be made for the two partial pair re- duced interference functions as a cross check and were found to be quite consistent for all three compositions x = 0.20, 0.24, 0.28. Further, identical functions for i La-La(K) and

iLa-A1(K) were obtained from combining the data

from Lal_xAlx, La1 xGax and Lal_xAux, assuming

the latter glass to also be isomorphous with the former two. In this case the Au-Au contri- bution is significant enough to allow iAu_Au(K)

to be obtained as well in a complete solution of all three i

a$' Again, solutions were also ob-

tained using the ternary as a cross check with quite consistent results.

I I

12.

i - La-La

IO. II --_--- La-”

8. II n-n

L Ii

Fig. 2. The three partial pair reduced inter- ference functions icrB(K) for isomorphic La76A124,

=a76Ga24' and La76Au24 metallic glasses.

The three partial pair reduced interference functions iLa_La(K), iLa M(K). and h I,i(K) for

La76M24, where M = Al, Ga, Au are shown inFig. 2.

The t a-La

and i La_M have been multiplied by an

exponential convergence factor e -0.005K2.

$iM(K) was cut off at about K = 8 i-l, since

Vol. 44, No. 7 PARTIAL PAIR CORRELATION FUNCTIONS OF Lal_x(Al-Ga-Au)x 985

c

Fig. 3. The three partial pair reduced radial distribution functions G ij(r) for isomorphic

La l_xAlx, Lal_xGax and Lal_xAux metallic glasses

for x = 0.20, 0.24, and 0.28.

essentially nothing but noise was accessible beyond this point and is shown multipli d by an

.015K 1 exponential convergence factor e- . It can be seen that the prepeak in IN(K) does indeed

manifest itself at about 1.5 is1 as the primary maximum in iMM(K). The three partial pair

reduced radial distribution functions, Gij(r) = 4nr[pij(r)/Cj-PO], for LagOM20,

La76Mz4 and La,2M28 are shown in Fig. 3, all of

which exhibit primary maxima in the GI,fM(r) at

about 5 i. Table 2 lists the primary peak Posi- tions for all the pij(r) as w;il as coordination

numbers computed from n.. = iJ I

0

4ar2 pij(r) dr

where Ro is the minimum in P ij(r) following the

primary maximum. The widths listed are FWHM of

the pij(r) corrected for convergence and termi-

nation broadening effects.

Discussion

From Table 2 the average La-La nearest neighbor distance for the La l_xMx metallic

glasses is just twice the La Goldschmidt radius,

1.87 %. The total La coordination is close to 12, that of the pure metal and of the inter- metallic compound La3(Al-Ga). The La-La coordi-

nation number changes little with composition, (no trend is visible at least within theresolu- tion of the experiment), and both the observed

'ILa-La and 'La-M are little different from those

expected from a completely disordered alloy. Using (1-x)nLa as the La-La and xqLa as the

La-M coordinations for a disordered Lal_xMx alloy

yields 'lLa_La = 9.22, 9.80, and 9.57 and

'La-M = 2.30, 3.09, and 3.72 for x = 0.20, 0.24,

and 0.28 respectively, all very close to the coordination numbers observed for the metallic glasses. The M-atom coordinations, on the other hand, show distinct signs of chemical ordering. Using (l-x)nMLa and xnM_La (since

there were no M-M nearest neighbors ob:erved), again as the expected coordinations for a com- pletely disordered alloy yields qM_La = 6.24,

Table 2. First maxima positions of the atomic density functions, pij(r) and their

full widths at half maximum and coordination numbers for several amorphous alloys and for crystalline La3Al.

Alloy Ta-La R~a_~ S-M "%a-La ARLa-M ARM-M 'La-La 'La-M 'La 'M-La %I-M

(+0.04i) (LO.05i) (+0.2i) (+o.oli) (+o.oli) (?O.lh (c0.7) kO.2) (50.9) kO.9) kl.5)

La3Al

3.73 3.27 5.11 0.43 0.14 0.51 9.57 1.95 11.52 7.80 8.09

3.75 3.22 5.02 0.49 0.15 1.02 9.84 3.05 12.89 9.66 9.28

3.71 3.25 4.94 0.49 0.16 1.23 9.54 3.75 13.29 9.64 8.60

3.60 3.60 5.093 a 4 12 8 6

2.55 2.32 3.34 0.43 0.33 0.70 10.1 2.09 12.19 8.9 -

986 PARTIAL PAIR CORRELATION FUNCTIONS OF Lal_x(Al-Ga-Au)x Vol. 44, No. 7

7.34, and 6.94, and t&M = 1.56, 2.32, and2.70.

The fact that no M-M nearest neighbors were found, (or at least, considerably < l), is strong evidence for chemical ordering in these materials similar to that found in amorphous TM-M alloys of CO-P.~

Using R,a_M - @La_La to evaluate the M

atom size in the matrix produces an average

value of % 1.38 % + 0.38 R for the three groups of alloys,-which is-somewhere between the metallic and covalent radii of Al-Ga-Au. In fact, the sharpness of the primary maximum of G La_M(r) and the closeness of the La-M nearest

neighbors demonstrates a rather well defined La-M bond length in the metallic glass.

Crystalline La3A1 has the Cu3Au structure

with Al on a cubic lattice and La occupying the faces of the cube. No Al-Al near neighbors exist in this structure, and the coordination numbers shown in Table 2 are not too different

from those of the compositionally close metallic glass, La76M24. Also, the atomic density of

La,,Al, computed from the lattice parameter, is

0.03028 atoms/i3, nearly identical to that of the metallic glass. In crystalline La3A1 however, Al

atoms reside in very large octahedral holes in a very compressed La matrix, and the La-La and La-Al nearest neighbor separations are therefore very different from those in metallic glasses.

The GLa-La (r) in Fig. 3 have second maxima

of R2/Rl = 1.73, 1.75 and 1.74 respectively for

LaSOMzO, La76M24, and La72M28, which are all very

close to5, the position occurring in the DRP, as opposed to Q 1.63 which occurs more commonly for typical transition metal-metalloid glasses. Unlike either the DRP or most other metallic glasses however, no peak at all occurs neag 2Rl.

The second peak in GLa_W(r), r 2 6.5 A, is

about equal in each case to the separation of La and M atoms on opposite sides of a tetrahe- dral base of La atoms. A similar configuration may explain the only observed maximum in G &M(r)'

Conclusion

The short range order of the Lal_$Al-Ga-Au)x

metallic glasses is quite different from that of more typical amorphous TM-M alloys. Although chemical ordering is obvious in both the amor-

phous La-M and TM-M alloys', the former appear to exhibit considerably less topological order- ing as opposed to chemical ordering. It seems quite likely that many different amorphous structures will be necessary to describe the various different structures of amorphous metal alloys such as La-(Al-Ga-Au) and the related TM-M and early transition metal-late transition metal alloys. Input parameters to successful models of these structures will have to include some reason- able estimation of the interatomic potentials in order to introduce a basis for the chemical order- ing in these materials, as well as size ratios, boundary conditions, and other topological param- eters.

REFERENCES

1. WILLIAMS, A., J. Non-Cryst. Solids, 45, 183 (1981). 2. SADOC, J. F. and DIKMIER, J., Mat. Sci. and Eng., 2, 187 (1976). 3. FINNEY, J. L., Nature (London) 266, 309 (1977). 4. PIETROKOWSKY, P., Rev. Sci. Instrum., 34, 445 (1963). 5. CARGILL, G. S. III, Solid State Physics, 30, 227 (1975). 6. LOGAN, J., Scri. Metall., 2 379 (1975).