X-Ray Diffraction Study on the Structure of the Metallic
Glasses Mg^Nii 6 and Mg30Ca70
E. Nassif*. P. L a m p a r t e r . and S. Steeb
Max-Planck-Institut für Metallforschung. Institut für Werkstoffwissenschaften. Stuttgart
Z. Naturforsch. 3 8 a , 1206- 1209 (1983); received August 6. 1983
The total structure factors as well as the total pair correlation functions of amorphous
Mg84Ni16 and Mg30Ca70 were determined by X-ray diffraction. The Mg-Ni glass shows rather
strong chemical short range ordering. By Gaussian fit of the total pair correlation function partial
coordination numbers and atomic distances were obtained. Similar surrounding of the Ni atoms
in the amorphous phase and in crystalline Mg 2 Ni was found. The structural features of the
Mg-Ca glass differ from those of the Mg-Ni glass.
Introduction
In recent structural investigations on the metalmetal glasses Mg 8 5 5 Cui4.5 and Mg 7 oZn 3 o [1] c h e m ical short range order ( C S R O ) and correspondence
of the coordination of the Cu atoms in the M g - C u
glass with that in crystalline M g 2 C u was found. T h e
present paper is a continuation of these investigations. T h e first subject was the question w h e t h e r
Mg-Ni glasses also exhibit a C S R O effect and
whether it resembles to the structure of crystalline
Mg 2 Ni. This research was stimulated by t h e r m o dynamic studies on M g - C u - and Mg-Ni-glasses [2],
where evidence for a chemical ordering effect for
both glasses has been given.
T h e second subject was the e x a m i n a t i o n of the
structure
of
a
metal-metal
glass,
namely
Mg 30 Ca70, where both constituents belong to the
same group of the periodic table. As C S R O was
concluded f r o m the t h e r m o d y n a m i c data [3] of this
glass, it was of interest to investigate w h e t h e r such
an effect is also found by X-ray diffraction.
Experimental and Data Reduction
T h e preparation of the melt spun samples, the
diffraction experiments and the evaluation of the
structural data were essentially done as reported
previously [1]. T h e C a - M g samples had to be
alloyed in a glove-box and melt spun i m m e d i a t e l y
after alloying.
* Permanent address: University of Buenos Aires. Engineering Faculty. Department of Physics. Paseo Colon
850. 1063 Buenos Aires. Argentina.
Reprint requests to Prof. Dr. S. Steeb. Max-Planck-Institut
für Metallforschung. Institut für Werkstoffwissenschaften.
D-7000 Stuttgart 1.
The density of a m o r p h o u s Mg 8 4 Nii6 was m e a sured by the s a m e t e c h n i q u e as used in [1] yielding
D = 2.6 g/cm ? . This value, however, is regarded to
be not very exact d u e to the small a m o u n t of the
a m o r p h o u s material available. But it corresponds to
an excess v o l u m e of a b o u t —10 pet, which was
measured also with a m o r p h o u s Mg 85 . 5 Cui4.5. F o r
the Mg3oCa7o the density could not b e m e a s u r e d ,
and therefore the value D = 1 . 6 g / c m 3 according to
ideal mixing of the c o m p o n e n t s was used. T h e real
value is expected to be s o m e w h a t larger.
Results and Discussion
MgMNi]6
From the coherently scattered intensity per a t o m
Ic(Q) the total structure factor S(Q) was o b t a i n e d
according to:
S(Q) = Ic(Q)Kf2(Q)>,
(1)
where
</2(0)>
c\,c2
f\{Q),fi(Q)
Q
20
/.
=C,/,2(0 + C2/22(0,
= m o l a r fractions,
= scattering factors,
=(47rsin0)/x,
= scattering angle,
= wavelength of the X-rays.
The structure factor is plotted in Fig. 1 together
with that of a m o r p h o u s Mg 85 . 5 Cui4.5 taken f r o m [1].
Comparison shows that the general run of both
curves is quite similar. T h e most r e m a r k a b l e f e a t u r e
is the occurence of a strong p r e p e a k in front of the
sharp main m a x i m u m , which gives evidence for
chemical short range order in the M g - N i glass, too.
Both curves show a splitting up of the second
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I
I
|
I
NJ
3
I
I
Table 1. D = density, d, = atomic diameter [9].
Ql =
position of the prepeak and the main peak, respectively, of
the X-ray structure factor. AQ P , AQ1 = width of the peaks.
c c , c T = correlation lengths for chemical and topological
ordering. I ? = amplitude of the prepeak measured from
the dotted baseline in Figure 1. R\ A1 = atomic distance
and total coordination number, respectively, calculated
from the main peak of the total pair correlation function. Rjj, Zjj = atomic distance and partial coordination
number of/-type atoms around an /-type atom.
Mg 8 ^Ni 16
Mgs5, sCiiu^
-
^
S(Q )
O
—.
I
D [g/cm 3 l
excess volume
^Mg/^Cu;
3_
2
QP
-
Jy
1
n
0
J ,
2
Mg 3 0 Ca 7 0
1
U
1
6
1
8
1
10
[A-1]
<2' [A - 1 ]
AQP [A"']
AQ1 [A" 1 ]
7P
1
QP/Q>
12
In
Q [ A" 1 1
Fig. 1. Total structure factors S(Q) of the metallic glasses
Mg 84 Ni 16 , Mg85 5Cu14.5, and Mg3oCa7o.
,
5 ( 0 = 0.860 S N N ( 0 + 0.140 S e c « 2 )
+ 1.89Snc(0.
(2)
On the basis of the assumption that the p r e p e a k of
5 ( 0 is contributed by the partial structure factor
S c c ( 0 , which describes the C S R O , f r o m its
Mg 84 Ni,6
2.54
-10%
3.20/2.56
= 1.25
1.48
2.65
0.83
0.34
0.28
0.56
~ 2.6
—10%
3.20/2.48
= 1.29
1.41
2.68
0.70
0.37
0.33
0.53
9.0
7.6
2n
,8'5
=
l
m a x i m u m where, however, the s u b p e a k height ratio
for Mg 8 4 Nii6 is reversed as c o m p a r e d with that of
Mg 85 .5Cui45. T h e wavelength of the oscillation at
Q ~ 7 A - ' is rather large c o m p a r e d to the following
oscillation in both cases.
In Table 1 structural p a r a m e t e r s o b t a i n e d f r o m
S ( 0 of the Mg-Ni glass are c o m p a r e d with those
of the Mg-Cu glass, which again reflect the similarities of the structure of both glasses. However, slight
differences can be observed: the p r e p e a k 7 P is
somewhat higher in the case of M g 8 4 N i , 6 . W h e r e a s
the correlation lengths of the topological o r d e r i n g
calculated f r o m the width of the main m a x i m a ,
are about the same, the correlation length of t h e
chemical short range ordering
following f r o m
the width of the prepeak, is larger in the M g - N i
glass than in Mg-Cu.
The total structure factor can b e written in t e r m s
of the three Bhatia Thornton partial structure
factors S N N ( 0 , S C C ( 0 , a n d 5 N C ( 0 [4]:
Mg85.5CUi4.5
R [A]
2.70
11.8
2.75
A1
10.2
*MgMg [A]; /?MgCu [A];
[A]; ^MgNi [A];
Z M g M g : ZMgCu; ZCuMg;
7
-i 7-^-MgNi,- ^-NiMg
7
^-MgMg
3.10; 2.71
9.6; 1.4;
3.09; 2.65
f
11.1; 1.7; 8.5
a m p l i t u d e / p the value of Scc(£? P ) c a n
evaluated
by dividing I p by t h e weighting factor of S e c i n (2)
(see [1]). C o m p a r i s o n between M g - N i and M g - C u
yields
S^Ni(<2p)/^c8Cu(ÖP)-1-24.
This suggests that the C S R O is s o m e w h a t stronger
in a m o r p h o u s M g 8 4 N i i 6 t h a n in
amorphous
Mg 8 5 5 Cui4.5, which is supported by the larger correlation length
in the f o r m e r one. In this respect,
however, it must b e noted that these considerations
are based on the a s s u m p t i o n that the partial structure factor S N C ( 0 shows negligible oscillations in
the region of the prepeak. U p to now no experimental data on S N c ( 0 of this type of m e t a l - m e t a l
glasses have been d e t e r m i n e d ; rather this f u n c t i o n
was simulated by hard sphere m o d e l s [5] or even
neglected [6]. In [7]. however, evidence is given that
the influence of S N c ( 0 in the low (2-range m a y be
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significant. Further experimental work is n e e d e d to
clarify this question.
F r o m the total structure factor the p a i r correlation function G(R) was calculated by F o u r i e r
transformation:
I Qjy^;[S(Q)-\]sm(QR)dQ,
(3)
where Qm= 13.4 A - 1 .
Figure 2 shows the G(R) function t o g e t h e r with
that of a m o r p h o u s Mg85.5Cu14.5- Again a g r e e m e n t of
the general features is observed. T h e d o u b l e p e a k
structure of the first m a x i m u m is m o r e p r o n o u n c e d
in the case of Mg-Ni than in the case of M g - C u ,
which is explained by the larger d i f f e r e n c e of the
atomic diameters of both constituents in the f o r m e r
alloy (see Table 1).
T h e total G(R) is a weighted sum of the three
partial pair correlation functions ( j N i N j ( / ? ) , G M g N i ( ^ ) ,
and G M g M g (#):
G(R) = 0.095 GNiUi(R)
Fig. 2. Total pair correlation functions G(R) of the metallic
glasses Mg 84 Ni ]6 , Mg85 5 Cui 4 5 , and Mg3oCa7o.
+ 0.426 G M g N i ( ^ )
+ 0.479 GMgMg(R).
(4)
F r o m the values of the weighting factors and f r o m
the atomic diameters we conclude that the first subpeak belongs to the Mg-Ni correlation and the
second subpeak to the M g - M g correlation, w h e r e a s
the contribution of the N i - N i correlation is rather
small. This has led to the concept of deriving partial
coordination n u m b e r s by fitting the first m a x i m u m
of G(R) with two G a u s s i a n curves for GMg^{R)
and
GMgMg(^). respectively. T h e details of this proced u r e were described previously [1]. F i g u r e 3 shows
the fitting curve (dashed line) together with the
experimental G(R) in the region of the first coordination sphere.
T h e resulting distances /?vigNi and /?MgMg as well
as the partial coordination n u m b e r s Z M g N i , Z N j M g ,
and Z M g M g are listed in Table 1 together with the
corresponding values for a m o r p h o u s Mg85.5Cu14.5T h e distance between unlike atoms R Mg Ni = 2.65 A
is distinctly smaller than the sum of the G o l d schmidt radii of Mg and Ni (2.84 A). T h i s reflects
the chemical interaction between unlike a t o m s in
the a m o r p h o u s phase. However, the distance between the Mg atoms /?MgMg = 3.09 A is also somewhat smaller than the G o l d s c h m i d t d i a m e t e r of M g
(3.2 A).
The values of the partial c o o r d i n a t i o n n u m b e r s
ZvtMg (M = Ni. Cu) are the s a m e within the
accuracy of the fitting m e t h o d , while Z M g M g is larger
in the Mg-Ni glass than in the Mg-Cu glass. For the
Mg-Ni system the crystalline phase M g 2 N i is reported, whose structure is closely related to that of
crystalline M g 2 C u [8]: T h e Ni atoms are s u r r o u n d e d
by 8 Mg neighbours at a m e a n distance of 2.7 A
building a distorted h e x a h e d r o n . The a g r e e m e n t of
these figures with the values /?MgNi = 2.65 A and
ZniMs = 8.5 A obtained with a m o r p h o u s Mg 8 4Nii 6
suggests the n e i g h b o u r h o o d of the Ni a t o m s to be
very similar in the a m o r p h o u s and in the crystalline
phase. This b e h a v i o u r was also observed with
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respect to the surrounding of the C u atoms, in
a m o r p h o u s Mg 855 Cui4.5 and in crystalline M g 2 C u
[1]. Concerning the fitting p r o c e d u r e it should be
noted that the small contribution of the N i - N i pairs,
which has been not taken into account by a s e p a r a t e
Gaussian, is therefore included in Z N i M g = 8 . 5 ,
which thus may be s o m e w h a t too large. O n t h e
other hand, compared to a G a u s s i a n curve the real
^NiMg(^) function is certainly a s y m m e t r i c , t h a t
means broader at its right h a n d side, which w o u l d
imply a larger value for Z N j M g .
The Mg atoms in crystalline Mg 2 Ni are s u r r o u n d ed by 11 Mg neighbours, 3 at 3.0 Ä, 8 at 3.3 A, a n d 4
Ni neighbours at 2.7 A. W h e r e a s Z M g M g in the
a m o r p h o u s and crystalline phase is the same, Z^gNi
is smaller in the a m o r p h o u s phase. T h i s smaller
value is explained by the lower Ni concentration in
the Mg 84 Nii6 glass c o m p a r e d to crystalline M g 2 N i .
Mg30Ca10
The structure factor of a m o r p h o u s Mg 3 0 Ca70 is
plotted in Figure 1. C o m p a r i s o n with the curves of
the Mg-Ni and Mg-Cu glasses shows significant
differences: Instead of a p r e p e a k the M g - C a curve
only exhibits a small b u m p near Q= 1.3 A - 1 . T h e
second m a x i m u m of 5 ( 0 of M g - C a is splitted u p
into a higher first subpeak and a lower second one.
Also the further oscillations are different.
F r o m the equation
S(Q) = 0.958 5 n n ( 0 ) + 0.042
-0.871 S N C ( 0
SCC(Q)
(5)
one can see that the weighting factor of S e c is
rather small. Therefore C S R O , if present in the MgCa glass, hardly can be observed by X-ray d i f f r a c tion. The small b u m p , however, can b e r e g a r d e d as
an indication for a C S R O effect. In T a b l e 2 structural parameters of 5 ( 0 are listed.
Table 2. d, = atomic diameter [9], Qp, Qx = position of the
prepeak and the main peak, respectively, of the X-ray
structure factor. AQ' = width of the mean peak. qt = correlation length for topological ordering. Rl, Nl = atomic
distance and total coordination number, respectively, calculated from the main peak of the total pair correlation
function.
Mg3oCa7()
3.94/3.20= 1.23
- 1.3
2.09
0.33
0.62
0 P [A' 1 ]
Ö' [A-']
AQ'
[A" 1 ]
Qp/Q]
AQ1
R[ [A]
Nl
19.0
[A]
3.75
12.7
ordering up to nine coordination spheres. T h e m a i n
m a x i m u m shows no splitting up, although the
atomic d i a m e t e r ratio is almost as large as that of
Mg-Cu (Table 2). T h e radius of the first c o o r d i n a tion shell Rl and the total coordination n u m b e r N\
evaluated f r o m G(R), are listed in T a b l e 2.
Writing G ( R ) in terms of the partial pair correlation functions,
G(R) = 0.042 GMgMg(R)
+ 0.325 G M g C a ( ^ )
+ 0.633 G0d0d(R),
(6)
one can see that G ( R ) is mainly d e t e r m i n e d by
^MgCa and GcaCa- F r o m the weighting factors it
can be explained that Rl = 3.75 A is closer to
dca = 3.94 A than to dMg = 3.20 A.
As conclusion one can state that the structural
results for a m o r p h o u s Mg3 0 Ca 7 0 derived in the
present work d o not show close relationship to the
structure of Mg-Cu and Mg-Ni glasses.
Acknowledgements
The Fourier transform of S ( Q ) is plotted in
Figure 2. We observe very extended topological
T h a n k s are d u e to Dr. F. S o m m e r and Dr. J. J.
Lee for the p r e p a r a t i o n of the alloys.
[1] E. Nassif, P. Lamparter, W. Sperl, and S. Steeb, Z.
Naturforsch. 38a, 142 (1983).
[2] F. Sommer, G. Bucher, and B. Predel, J. Physique C-8,
563 (1980).
[3] F. Sommer, Z. Metallkde. 72,219 (1981).
[4] A. B. Bhatia and D. E. Thornton, Phys. Rev. B 2, 3004
(1970).
[5] C. N. J. Wagner, D. Lee, L. Keller, L. E. Tanner, and
H. Ruppersberg, Proc. 4th Int. Conf. Rapidly
Quenched Metals, Sendai 1981, p. 331.
[6] M. Sakata, N. Cowlam, and H. A. Davies, Proc. 4th Int.
Conf. Rapidly Quenched Metals, Sendai 1981, P- 327.
[7] P. Lamparter, E. Grallath, and S. Steeb, Z. Naturforsch. 38a, 1210 (1983).
[8] K. Schubert and K. Anderko, Z. Metallkde. 12, 321
(1951).
[9] W. Hume Rothery and G. V. Raynor, The Structure of
Metals and Alloys, Inst. Metals, London 1954.
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