Radial distribution function of amorphous NiPtP alloys

J. Phys. Chem. Solids

Pergamon Press 1971. Vol. 32, pp. 267-277.

Printed in Great Britain.

RADIAL DISTRIBUTION FUNCTION AMORPHOUS Ni-Pt-P ALLOYS*

OF

ASHOK K. SINHA and POL DUWEZ

W. M. Keck Laboratory of Engineering Materials, California Institute of Technology, Pasadena, Calif. 91109, U.S.A.

(Received 13 March 1970) Abstract--Accurate X-ray diffraction measurements were made upon five amorphous alloys having the composition (Ni~Ptt00-~)TsP25 with 20 ~ x ~ 60, which were obtained by rapid quenching from the liquid state. The shapes of the interference function a(K), and of the atomic radial distribution function (RDF) curves are strikingly similar to those observed for metallic liquids. Contrary to what was observed in previously studied amorphous metallic alloys, there is no shoulder on the high angle side of the second peak of a(K) and the R D F does not have a double peak beyond the first maximum. The ratio of second to first near-neighbor atomic distances is 1.86___0-02, a value which is larger than that ( - 1.7) observed for previously known amorphous foils. The first coordination number is close to 12. On the basis of these and further experimental studies on the first band of various amorphous metallic alloys, it is concluded that the present alloys possess a higher degree of disorder than that found in any of the existing amorphous metallic materials. The degree of disorder is comparable to that present in fused silica. The factors contributing towards successful synthesis of these alloys are discussed. 1. INTRODUCTION

THE RADIAL distribution function (RDF) data for amorphous or glassy materials are of fundamental importance in the description of their atomic configuration [I], and this in turn provides a useful means for understanding the electrical properties of metallic conductors in the glassy state[2]. Thus, a successful treatment of the electronic transport phenomena in disordered structures involves the use of the X-ray interference function a(K), which enters in the equation for electron scattering cross-section, the latter being proportional to electrical resistivity [3,4]. The interference function as well as its Fourier transform, R D F , may be obtained through X-ray diffraction measurements. In recent work [5] on a series of amorphous N i - P t - P alloys, it was shown that these alloys possess quite interesting electrical properties. Whereas both N i and Pt have negative thermoelectric power at 300°K, these amorphous alloys have a positive ther-

moelectric power which increases linearly with temperature in the range 77-300°K. The temperature coefficient of electrical resistivity was found to be composition dependent in the range 4.2-420°K: it was negative for Ptrich alloys, increasing with increasing Ni/Pt ratio and changed sign from negative to positive at around equiatomic ratio of Ni to Pt. Such electrical behavior reflects the high degree of disorder present in these alloys, and can be adequately explained in terms of the temperature and composition dependence of a(K) for these alloys [5]. In the present work, accurate X-ray diffraction measurements were made upon a series of amorphous alloys having the general composition (NixPt100-~)75P2s where 20 ~< x ~< 60. The interference function a(K) as well as the atomic radial distribution function have been obtained. The alloy chemistry principles involved in synthesis of glassy metallic alloys are briefly reviewed. 2. EXPERIMENTAL PROCEDURE

*This work was supported by the U.S. Atomic Energy Commission.

The starting materials were metal powders of 99-99_ purity and reagent grade red phos267

268

A S H O K K. S I N H A and POL D U W E Z

phorus powder. About 2 gms of the alloy constituents were mixed and compacted into ¼in. dia. briquettes using 50,000 psi pressure. They were encapsulated into pyrex tubes under vacuo and sintered by slowly heating at the rate of about 20°C per hr. up to about 500°C and then holding there for 2 days. The sintered briquettes were then melted in evacuated fused silica capsules by slowly heating up to 650°C. The total weight loss during the whole procedure was always less than 2 per cent and for this reason the alloys will be referred to by their nominal (analyzed) compositions. Rapid quenching (at rates approaching 106°C/sec) from the melt was achieved using the piston and anvil technique [6]. The quenched foils were about 2.5 cm in dia. and 35/x thick. To guard against any 'misquench', all the foils were carefully checked by taking their X-ray diffraction pattern in the region of first broad band. A step-scan diffractometer with Cu Ko~ radiation was used. Any second crystalline phase could be detected by the presence of a few weak but relatively sharp peaks superimposed upon the smooth broad band characteristic of the amorphous phase. Such foils were rejected, the rejection rate for present alloys being about 10 per cent. The X-ray diffraction patterns were recorded using a G.E. diffractometer fitted with a curved LiF crystal monochromator in the diffracted beam, a pulse-height analyzer and a scintillation counter. The specimen consisted of four foils glued together with thinned Duco cement on a bakelite substrate. Such a specimen may be considered as being infinitely thick for the purpose of absorption correction. Mo Kot radiation at 45 kV and 38 mA was used. Since it takes about ten days to record the entire diffraction pattern of each alloy, it was necessary to check for the stability of the X-ray tube, as well as that of the counter and associated electrical circuitry. This was done as explained in Ref. [7]. The diffraction pattern was recorded in the range 12° <~ 20 ~< 160 ° with a scanning rate of 0.02 ° per 100 sec up to about 130°, and then 0.04 ° per 100 sec

for higher values of 20. The beam divergence employed was 1° in the range 12° ~< 20 ~< 64 ° and 3° in the range 60° ~< 20 ~< 160°. All the measurements could be normalized to a single divergence using the overlapping data in the range 60 ° ~< 20 <~ 70 °. The number of counts was printed every 100 sec. (0.02 °) in the range 12° ~< 20 ~< 28 ° and then every lO00sec. (0.2 ° or 0.4 °) at higher angles. 3. EXPERIMENTAL RESULTS AND ANALYSIS OF DATA

The X-ray data for each alloy were recorded in the form of a plot of the diffracted intensity, lex~, (arbitrary units) vs. diffraction angle, 20 (Fig. 1). When corrected for polarization and absorption, l~xp is the sum of the coherently scattered intensity 1~, the compton modified scattering l~n~and the background lb: iex,,/(P . A ) = lc + li.,: + lb.

(1)

The polarization factor P for a LiF monochromater having Bragg angle 0 corresponding to a (200) reflection is: P = (1 + C o s "

2/3 Cos 2 20)/(1 + C o s 2 2/3). (2)

As pointed out earlier, the specimen may be considered to be infinitely thick so that the absorption factor A is independent of angle. Also the use of a diffracted beam monochromator removes most of the fluorescent radiation as well as Compton modified scattering at high angles [8] leaving only a small part of (line "at"Ib), which together act as the effective background In. Using the experimentally determined shape of IB vs. 20 curve, it was only necessary to make small systematic adjustments in order to get exact values of IB(20). Rewriting equation (1): (lex,,/P -- I~)o~ = lc e~'

(3)

where all quantities except a are functions of

RADIAL DISTRIBUTION

FUNCTION

OF AMORPHOUS

Ni-Pt-P ALLOYS

269

500

A

40C

'\

~ 3O0 z

200

I00 12

I 14

/ 16

I 18

I 20

I 22

I 24

I 26

I 28

28 (*) 200 A

u

180

o. O

150

>" 140 1-Z

I00

I00

50

24

I

I

I

I

l

32

40

48

56

64

20 (*)

60

I

,2o

,~o

,~o

20 (*)

Fig. 1. Diffracted intensity (le~,) vs. diffraction angle 20 for amorphous (Niz0Pt,a)~sP~.~. Broken portion o f curve l shows typical data points. The beam divergence for curves l and 2 was l*, and that for curve 3 was 3*.

20, or K which is the modulus of the scattering vector: K = (4zr/h) Sin 0, h being the wavelength. The normalization constant a converts the coherent intensity from arbitrary units into that in electron units per atom of the alloy. Since the intensities were available for values of K up to 17-4 ,~-~, ot could be determined by the high angle method [9] in which:

!c e`` ~ ~ Xmfm 2 for K > I0 ~-1

(4)

i'll

where, m, n, p refer to the alloying elements Ni, Pt and P; xm is the atomic fraction of element m in the alloy, and f,, is the modulus of the atomic scattering factor[10] corrected for anomalous dispersion [11]. Figure 2 shows the normalized coherent intensity per atom, lce', vs. K for the alloy (Ni~0Pts0)TsP~_5. On the same graph is also shown the curve x,,Jm 2 corresponding to independent scattering by the component atoms of the alloy.

While deducing the R D F from these data, it must be remembered that in a ternary alloy like the present one there are six pair atomic distribution functions corresponding to the combinations Ni-Ni, Pt-Pt, P-P, Ni-Pt, N i - P and Pt-P. Using data from a single X-ray diffraction experiment one obtains a convolution broadened weighted average atomic density function p(r) for the alloy as a whole[12, 13]. As will be shown below, the atomic density function p(r) may be related to the reduced electron density function g(r). A general expression for the latter may be written as follows [14, 15];

I~e" = ~, Xmfm 2 "+'fe2 f 47rr2 rn o X(~ xmNm)[g(r)--go]SinKr/Krdr

(5)

270

ASHOK K. SINHA and POL DUWEZ '

I

'

I

'

I

'

5O

3o Z 20

8 ,oi 4

6

8

I0 K (~-I)

12

I

I

Fig. 2. Coherently scattered intensity, Ic e", from amorphous (Ni=oPt, o)75P..~ (oscillating curve). The smoothly varying curve represents the average scattering power, Y,x,,,f,.2, corresponding to independent scattering by the atoms of the alloy.

where N., is a constant coefficient assumed to be equal to the effective number of electrons for atoms of type m (atomic number Z,.) and the function fi(K) is the effective scattering factor per electron. The coefficient N,. may be evaluated using the following approximations [14, 15]:

N,. = f.,(K)/fi( K )

g(r) = (,,~ xmN,n) p(r)

(10)

go and p0 refer to the average electronic and atomic density respectively in the alloy, and are, of course, also related through equation (10). Using equations (6), (7) and (10), equation (5) may be rewritten as:

(6)

K [ a ( K ) - - 1] = .r 47rr[p(r)--po] S i n K r d r and,

0

(11) where the interference function a(K) given by:

If the number of atoms m, n, p in an interval dr at a radial distance r from the center of any atom m are at., a., ap, then g(r) and p(r) are defined by:

47rr2g(r) dr = ~. a,.N.,

(8)

tit

47rr"-p(r) dr = ~. a.,.

(9)

From equations (8) and (9) it may be seen that the ratio of g(r) to p(r) may be equated to the total number effective electrons per atom, i.e.,

_-, +

is

x,,,.o), (12)

Figure 3 shows the variation of a(K) vs. K for amorphous (NixPtloo-~)75P~ alloys. The a(K) curve has a relatively sharp peak at values of K, between 2.67 and 2-87A -I (Table 1). At higher angles, the peaks get smaller and eventually only weak modulations about the horizontal line a ( K ) = l, remain. This line represents a completely random structure and corresponds to the curve of

RADIAL DISTRIBUTION FUNCTION OF AMORPHOUS Ni-Pt-P ALLOYS

' ' ' ' ' ' ' ' ' ' ' '

271

' ' ] Fig 2 f or which

Ice"= ~, X.fm~. m

C~

50

Coming back to equation (11), as stated earlier, p(r) is a weighted average atomic density function and it can be written in terms of the pair distribution functions pm.(r), as follows [13]:

X=60

v o

p(r) = E E WmnPmn(r)

g,,,o

m

X=50

I-(D Z

lq

(13)

where the weighing factor w.,. is given by:

Wm. = xmNr~N./ ( xmNm) 2.

X:40

Z bJ n-" b_l

In order to perform the Fourier inversion of equation (11), win. should be independent of K. This is not quite so in case of X-ray diffraction by most alloys; however, the errors introduced in the R D F due to the assumption of a constant w,.. become vanishingly small as we approach a completely random structure[13]. Performing the Fourier inversion, we get:

W

z~ 2<)

X :30

X:20

°°oI

2

4

6

a'

I0

12

14

16

W(r)=2/Tr f K [ a ( K ) - - l ] S i n K r d K

[e

K (~,-I)

(15)

0

Fig. 3. Interference function, a ( K ) , for amorphous (Ni~Pq0o-~)75Pzs alloys (with shifted zeroes) vs. K (=4~r/h. SinO). Horizontal line at a ( K ) = l would represent a completely uncorrelated structure.

where W(r) is the atomic distribution function with,

W(r)

=

47rr[p(r) - - P 0 ] -

Table 1. Structure results for amorphous N i - P t - P alloys Max. position in interference function, a ( K ) , (~-') Alloy composition

(Ni20Pts0)rsP~,~ (Nia0PtTo)7~P2s (Ni4oPt6o)75P~s (NisoPtso)TsP25 (Ni6oPt4o)7sP2s

(14)

Max. position in distribution Coordination function, W(r), number CN P0 (A) from R D F (atoms/A 3)

Kt

K2

K3

r,

r..,

r.~

2"67 2"73 2"78 2"82 2"87

4"93 4"95 4"98 4"99 5'08

7"08 7"26 7"25 7-27 7"40

2"85 2"83 2"82 2.80 2"77

5"35 5"28 5"26 5'20 5"10

7"80 7-27 7"27 7"03 6"98

!1-4±0"5 !I-0±0-5 11"5±0"5 11"9±0-5 11"8±0"5

0"063 0"065 0"067 0-069 0"071

(16)

272

A S H O K K. S I N H A and P O L D U W E Z

Figure 4 shows a plot of W(r) vs. the radial distance r. The maxima in W(r) correspond to the interatomic distances in the amorphous phase and these are tabulated in Table 1. Rearranging the terms of equation (15) gives the R D F :

are shown in Fig. 5. Also shown is the average density curve 47rr2po vs. r. The value ofpo was experimentally determined using a pycnometer. The area under the first peak of R D F gives the coordination number CN (Table 1): g

4rrr2p(r) = 41rr2po+ 2r/zr f K [ a ( K )

-

-

CN = f 47rr2p(r) dr

1]

0

x Sin KrdK.

(17)

These computations were done using an IBM 360 computer. The R D F for the present alloys I

I

I

I

where, r, and r2 are the values of r below which p(r)= 0 and that corresponding to the first minimum in R D F , respectively. The relevant structural parameters deduced from I

I

I

I

I

I

12

II

I0 o<~ E 0 O

v v

8

l._

\,.. %% 0 I--

6

z IJ_ z 0 I.-.-

R\

5

\~

X,40

130 I,u3 Eb

~J

',..3 2

X: 3 0 0

I

X:20

\ \

0

(18)

rl

,

I

I

I

2

I 4

I 5

I 6

I 7

I 8

I 9

10

Fig. 4. Atomic distribution function, W (r), for amorphous (Ni=Pt~o0_~)~5 P,s alloys (with shifted zeroes).

RADIAL

DISTRIBUTION

FUNCTION

OF AMORPHOUS

Ni-Pt-P

ALLOYS

273

16C

14C

12C

.4 10C

o o "2

8(3

u_" 60 r'~ or40

20

0 0

I

z

3

4

5

6

~

s

9

Jo

r(~.) Fig. 5. Atomic radial distribution function ( R D F ) for amorphous (NixPhoo-x)7sP2s alloys (oscillating curve). T h e smoothly rising curve represents the average atomic density 4~rrZpo. T h e zeroes have been systematically shifted for alloys having x greater than 20.

Figs. 3-5 are summarized in Tables 1 and 2. Errors in the determination of the normalization constant a show up as spurious ripples in the W (r) plot especially in the region of low values of r (Fig. 4) [16]. Judging from the small amplitude of these ripples it may be concluded that this error was not large. The other sources of error are due to termination of the integration in equation (15) at a finite value of K[16],

and inaccuracies in the experimental data particularly at large values of K. To compensate for effects due to both of these errors, a convergence factor[15], exp. (-0.01 Kz), was applied to the intensity function K [a (K) -- 1] before carrying out the integration in equation (15). The X-ray data obtained for several amorphous alloys using Cu Kot radiation are listed

Table 2. Relative positions o f maxima in a( K ) and W (r) KdK, Alloy composition (NizoPtso)7.~P~s (Ni~oPtTo)7sP,_,~ (Ni4oPtro)75P~.~ (NisoPtso)75P2.~ (NiroPho)7~Pz~

•I.P.C.S. Voi. 32 No. 1~R

r~/r~

i=l

i----2 i = 3

i=l

i=2

i=3

K~.r,

I'00 I'00 1"00 1"00 1"00

1"85 1"81 1"79 1 "77 1"77

1"00 i'00 I'00 1"00 1"00

1-88 1"87 1"86 I "86 1"84

2"74 2"57 2"58 2"51 2"52

7"61 7"73 7"84 7"90 7"95

2"65 2"66 2"61 2"58 2"58

274

A S H O K K. S I N H A and POL D U W E Z

in Table 3. Only the first band was studied and the position of the maximum (Kmax) and the width at half maximum A20 were determined. The band-widths were related to the size of ordered domains using Scherrer formula[15]. 5. DISCUSSION

A comparison of the foregoing results with those obtained for existing liquid-quenched amorphous metallic alloys, namely Pd-Si [17], F e - P - C [18], P d - N i - P [7], P d - F e - P [7], M n - P - C [19] and P d - N i - B [20] reveals a number of interesting differences. Contrary to what was observed for these latter alloys, there is no shoulder on the high angle side of the second peak of the present interference function, a(K) (Fig. 3). Also, the distribution function, W(r) (Fig. 4) as well as the R D F (Fig. 5) do not have a double peak beyond the first maximum. The ratio of second to first near neighbor distance, r2/r~, for the present alloys has a relatively large value of - 1.86 (Table 2) as compared with

teristic of liquid metals, in which 1.8 ~< rd r~ ~< 2-0121]. In addition to the present alloys, only two other systems, namely (Pdjo0-xMx)s0P20 where M = Ni or Fe, involving a series of amorphous alloys have been studied. In both of these cases, the peaks in a(K) as well as in W(r) were observed to shift regularly with change in the ratio of Pd to (Pd + M ) . As a direct consequence of this fact, it was found that the positions of the first peaks in a(K) and W(r) were related as follows: K , . r, = const. (-- 8.0).

(19)

It is interesting to note that the compositiondependent shift in the position of the peaks of the X-ray diffraction pattern or a(K) is not at all uniform in the case of present alloys (Table 2). With increasing Pt-concentration, the shift in the first peak towards lower Kvalues is much greater than the corresponding shifts for second and third peaks, i.e. K2/K~, K3/KI are not constant with respect

Table 3. X-Ray results on first band of amorphous alloys (CuKa radiation) Position of maximum K, Alloy composition (Ni2oPtso)TaPz.~ (NiaoPtTo)rsP2~ (Ni4oPt~o)rsP2.~ (NisoPt.~o)7.~Pz5 (N i6oPho)7.~P'.,5 Ni53Pd2rP20 Fe4., Pd:,eP..,0 Ni4,Pd4,B,s Pds0Si20 PdsoSi,oGe,0 FersP,sC,o (FesoMn.~o)75Pl~C,o MnT.~PtsCt0 Fused SiOz

r,,_/rl = -

Width at half-max. A2O

Size parameterL

(A-,)

(*)

(h)

2-69 2"74 2'79 2"85 2"89 2"97 2"88 2.91 2.82 2.82 3-04 3.03 3.00 ! .50

I I" 12 10"24 9"60 9" 12 8"40 7'30 6.24 6-88 5.80 5'36 5.45 6.14 5-90 8.05

7"6 8"2 8"8 9'3 10" 1 11-7 13-6 12.4 14"6 15-8 15"7 13-9 14.5 10.0

1.7-1.7 for the previously studied alloys. On the other hand, both the shapes of the present a(K), W(r) and R D F curves as well as r2/r~ value are close to those charac-

to composition. It is, therefore, clear that no simple relation such as equation (19) may be assumed to exist between the position parameters in the real (r-) and Fourier (K-) space

R A D I A L D I S T R I B U T I O N F U N C T I O N O F A M O R P H O U S N i - P t - P ALLOYS

of a highly disordered structure like the present one, even though r~ and 1/K~ are both linearly dependent functions of composition (Figs. 6, 7). In order to further confirm the relatively high degree of disorder in these alloys, the first X-ray diffraction peaks of these as well as a number of other amorphous alloys were analyzed. Application of Scherrer formula to the broad band yields a parameter L which has dimension of length, and may be defined as: L = 51h/(A20) cos 0

2'90

I

2-85

I

t

I

I

I

(20) I

I

I

"l~{.....4~k.~t..

o< 2.80 2.75 2.70 I

~0

I

20

I

30

I

40

I

50

I

60

L

t

70

I

80

9o

~00

RATIO Ni/(Ni +Pt) (%)

Fig. 6. First near neighbor distance r~ vs. Ni-content. x (= Ni/Ni + Pt) for amorphous (Ni,Pt,0o-~)7.~P2., alloys. I

T

]

I

I

[

I

I

I

0"39 0"38

"4

0.37 0"36 0"35 0"34

N.

N.

N.

0"33

"N "N

0"32 I

I

I

I

I

I

I

I

i

~0

20

30

40

5o

60

7o

80

90

~00

RATIO N i / ( N i + P t ) (%)

Fig. 7. I/K~ (= h/47rSinO0 corresponding to the first peak in interference function vs. Ni-content, x (= Ni/ Ni + Pt) for amorphous (Ni~Pt,oo-~)75Pz,~ alloys.

where, A20 is the full width in degrees at half height of the first band. For the model based upon random stacking of close packed layers,

275

L corresponds to the size normal to these layers. As would be clear from later discussion such an interpretation is probably not applicable to the L values for present alloys. In any case, L provides a useful 'domainsize' parameter for comparison of structural disorder in different amorphous alloys, particularly since the present X-ray diffraction patterns were all recorded under identical experimental conditions. The L values for N i P t - P alloys are distinctly lower than those for other amorphous metallic alloys and are comparable to that observed for fused silica (Table 3). Previous attempts at interpreting the R D F of liquid-quenched amorphous alloys have mostly involved the quasi-crystalline approach[13]. This method consists of randomizing the atoms on a suitably chosen lattice. In the case of amorphous P d - N i - P and PdF e - P , a 'Pd4P' structure was assumed as the 'parent' lattice[7], and in the case of amorphous F e - P - C , a f.c.c, structure was chosen [18]. For chemically deposited amorphous N i - P alloys, a model based upon random stacking of spherically close-packed layers (cubooctahedral coordination) was proposed [22]. More recently, the R D F of electrodeposited amorphous N i - P alloys has been interpreted in terms of Bernal's model[2326]. A dense random packing of spherical Ni-atoms was postulated[27], with P-atoms filling up the larger holes[28]. One feature shared by the above three approaches is that the metallic atoms are considered as being equal-sized spheres. All of them succeed in accounting for the splitting of second peak in the R D F curve and hence for the low value of r.,_[rl. They are also compatible with the observed value of coordination number, which is roughly equal to twelve. The average value of first coordination number, CN, in present alloys is also close to twelve, indicating a dense packing of neighboring atoms. However, in view of an eleven per cent difference in the atomic diameters of Ni and Pt, it is probable that the nearly

276

A S H O K K. S I N H A and POL D U W E Z

12-fold coordination results from an approximately icosahedral arrangement of atoms, and not from a cubooctahedral one. An icosahedral assemblage of thirteen atoms represents good topological packing of two atomic species having diameters differing by about 10 per cent. Since the five-fold symmetry of the icosahedron precludes a lattice-like arrangement, the resulting structure is intrinsically close to Bernal's continuous random model. In addition to the tetrahedron, Bernal has listed four other types of polyhedral holes associated with dense random packing of equal-sized spheres. However, it is reasonable to expect that a topologically dense random packing would predominately favor the smaller tetrahedral holes [29]. This is an interesting and significant conclusion: Results of electrical resistivity, thermoelectric power and magnetic measurements indicate that in amorphous N i - P t - P , P-atoms exist in a highly ionized state[5]. These P-atoms, stripped of their valence electrons, then are small enough to fit in the tetrahedral holes, thus effectively locking the icosahedra together. In view of the highly amorphous nature of these alloys, it is of interest to briefly enumerate the factors contributing to their successful synthesis by rapid quenching from the liquid state. In liquids proper, one may distinguish between two kinds of disorder[30]. The first kind is a primarily temperaturedependent motional disorder which is manifested in a large coefficient of self-diffusion and a large amplitude of thermal vibrations. The second kind is a structural or configurational type of disorder which reflects the breakdown of crystal lattice in the liquid state. Judging from the very low value of temperature coefficient of resistivity in these and other amorphous metallic alloys, it may be concluded that most of their disorder is of the latter kind (configurational). The factors favoring retention of configurational disorder upon rapid liquid quenching are just those which suppress nucleation from the melt. These are, (1) a tendency for the liquid to supercool.

This tendency is most marked at compositions corresponding to a deep eutectic, a feature which is usually encountered in metal-metalloid systems. Glass formation occurs if an ultimate cooling rate is exceeded[33]. (2) Increased number and/or complexity of the equilibrium crystalline phases; hence the observation that a ternary amorphous alloy is easier to quench than a binary one (Table 3). In the case of amorphous N i - P t - P alloys, an additional factor may be present. This is related to differing sizes of the metallic components and possible electro-chemical effects which favor topologically-dense-randompacking of the metallic atoms with P-ions fitting into some of the small tetrahedral holes.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

14. 15. 16. 17. 18. 19. 20. 21. 22.

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