- Email: [email protected]
A reverse Monte Carlo study of amorphous Ti67Ni33
] O U R N A L OF
Journal of Non-Crystalline Solids 156-158 (1993) 969-972 North-Holland
~ / S ~ I ~
A reverse Monte Carlo study of amorphous
U
Ti67Ni33
E d g a r W. I p a r r a g u i r r e , Jilt S i e t s m a a n d B a r e n d J. T h i j s s e Laboratory of Materials Science, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands
By applying the reverse Monte Carlo (RMC) simulation technique to X-ray and neutron diffraction data of amorphous Ti67Ni33, a set of atomic coordinates is obtained, which forms a realistic representation of the metallic glass structure. The
atomic positions are analyzed in terms of partial radial distribution functions, nearest-neighbour and bond-angle distributions, and are compared with previously obtained RMC results for NislBIg. Similarities and differences are discussed in terms of composition and atomic size.
1. Introduction In this work, we report results obtained by applying the relatively novel reverse Monte Carlo (RMC) computer simulation technique [1,2] to diffraction data of amorphous Ti67Ni33 . In a similar study on amorphous Ni81B19 [3], we found R M C to be successful in generating a set of atomic coordinates (a 'configuration') that constitutes a physically realistic picture of the metallic glass structure. The present work was initiated to obtain such a picture for a metallic glass of different type and composition as well. An additional purpose was to investigate how R M C behaves if only two instead of three sets of diffraction data are used. Because the neutron scattering lengths of Ti and Ni have opposite signs, Ti67Ni33 is a good candidate for this. First, we present the results of the R M C fit, applied to one X-ray [4] and one neutron [5] total radial distribution function (RDF). Second, the partial R D F s calculated from the final configuration are c o m p a r e d with those for NislB19 previously obtained by RMC. Finally, the configurations of Ti67Ni33 and NialB19 are c o m p a r e d in terms of their nearestneighbour and bond-angle distributions. Such a
Correspondence to: Dr J. Sietsma, Laboratory of Materials Science, Delft University of Technology, Ronerdamseweg 137, 2628 AL Delft, The Netherlands. Tel: +31-15 782 284. Telefax: +31-15 786 730. E-mail: [email protected].
comparison is particularly interesting because (1) the two glasses are typical, respectively, for the m e t a l - m e t a l and m e t a l - m e t a l l o i d glasses, (2) there is a large difference between the related crystalline structures (Ti2Ni, Ni3B) , and (3) contrary to m e t a l - m e t a l l o i d glasses, m e t a l - m e t a l glasses exist in a wide range of compositions M x m l _ x , in which the atom types can even exchange their (M)ajority and (m)inority roles.
2. The RMC procedure The simulation of Ti67Ni33 was started from a random distribution of 1566 atoms in a cubic box of 3 nm edge length. While atoms are given trial moves (of which only some are accepted), the growing agreement between the experimental diffraction data and the calculated R M C data is monitored by a 'goodness-of-fit' parameter, X 2, defined as the sum of the squares of the differences between the experimental and calculated R D F s weighted by the (estimated) experimental errors, tr. The total radial distribution functions as used here are expressed in terms of partial R D F s by the well-known expression G ( r ) = EiF.jW, jGij(r), with r the distance between an i and a j atom. The weighting factors, W~j, are given in table 1. They were corrected for the fact that the neutron experiment was performed on Ti60Ni40 rather than on Ti67Ni33. Generally, ex-
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
E.W. Iparraguirre et aL / RMC study of a-Ti67Ni33
970
Table 1 Estimated experimental errors for G(r), final goodness-of-fit parameters, normalization ratios, and weighting factors for the RMC simulation of Ti67Ni33 o"
Data
X2
(nm-2) X-ray Neutron
1.0 1.0
a exp
l'Vij
OtRMC Ti-Ti 12 34
1.17 1.10
0.378 0.084
Ti-Ni +0.474 -0.340
Ni-Ni 0.148 0.344
perimental RDFs may contain systematic errors because of erroneous normalization of the diffraction data. As shown in ref. [3], this problem can be largely circumvented by multiplying both GeXp(r) and GRMC(r) by their inverse average absolute values (a = (I G ( r ) l ) - l ) , and using F(r) = aG(r) rather than G(r) to compare experiment and simulation. The final configuration was reached after performing 25 × 10 6 atomic movements, of which 6.7 × 10 6 were accepted. The entire procedure took 3.4 × 10 6 cpu s on a DEC-station 3100. Further details are given in table 1.
3. Results
The total RDFs resulting from the RMC simulation of Ti67Ni33 are presented in fig. 1. The agreement with the X-ray data is almost perfect. Small deviations are found for the neutron case. These may be due to systematic experimental errors not fully accounted for. However, in view of the excellent reproduction of all trends and features by the RMC result, these deviations are
,
,
.
0.0
.
.
0.5
.
.
,
r [rma]
.
.
.
.
1.0
,
1.5
Fig. 2. GTiTi(r) of Ti67Ni33 calculated from the RMC results. The inset shows GNiNi(r) of Nis~B19.
-oo-j
,
,
,
.
0.0
.
0.S
.
.
.
.
r [nrn]
.
.
.
.
.
1.0
1.5
Fig. 3. GTiTi(r) of Ti67Ni33 calculated from the RMC results. The inset shows GNiB(r) of Nis1B19.
considered insignificant. It must be noticed that the two experimental sets of diffraction data have different r-ranges. The X-ray data could be used up to r = 1.5 nm, but the neutron data were available only up to r = 1.0 m.
4. Discussion
4.1. Radial distribution functions The effect of fitting two different ranges can be clearly seen in the noise components in figs. 2-4, where the partial RDFs obtained from the Ti67Ni33 configuration are shown. The partials compare well with the Ti60Ni40 partials measured by Fukunaga et al. [6]. This is not a trivial out-
0
r(,)
s 0
-5
0.0
0.5
r [rma]
1.0
1.5
Fig. 1. Final RMC fits (solid curves) of renormalized total RDFs to X-ray and neutron diffraction data for Ti67Ni33 (dashed curves).
--200
1
0.0
,
,
, ~',
~
0.5
. . . .
i
. . . .
r [rtrrt] 1.0
Fig. 4. GNir~i(r)of Ti67Ni33 calculated from the R M C The inset shows GBB(r) of NisIB19.
i
1.5 results.
E.W. Iparraguirre et al. / RMC study of a-Ti67Ni33 come, since o u r R M C results a r e b a s e d on only two t o t a l R D F s , i n s t e a d o f t h e t h r e e t h a t a r e r e q u i r e d . It c a n b e c o n c l u d e d t h a t R M C has f u n c t i o n e d well, d e s p i t e lack o f i n f o r m a t i o n . T h e Ti67Ni33 R D F s a r e also very similar in s h a p e to t h e NistB19 partials, which a r e shown in t h e insets o f figs. 2 - 4 . F i g u r e s 2 a n d 4 a r e p a r t i c u larly illustrative of t h e d i f f e r e n t roles t h a t Ni plays in b o t h m a t e r i a l s ( ' m ' in Ti67Ni33, ' M ' in Ni8tB19). By c o n t r a s t with GBB(r) for Ni81B19 , GNiNi(r) for Ti67Ni33 c o n t a i n s a significant first p e a k a r o u n d r = 0.26 nm. This is r e l a t e d to t h e d i f f e r e n c e in c o m p o s i t i o n o f t h e two a m o r p h o u s m a t e r i a l s . In Ti67Ni33 , t h e m i n o r i t y a t o m s can no l o n g e r avoid b e i n g n e a r e s t n e i g h b o u r s .
4.2. Nearest-neighbour and bond-angle distributions For the determination of the nearest-neighbour (fig. 5) a n d ' b o n d ' - a n g l e (fig. 6) d i s t r i b u t i o n s , t h e n e i g h b o u r s o f an a t o m a r e d e f i n e d as t h e a t o m s at d i s t a n c e s closer t h a n t h e m i n i m u m b e y o n d t h e first p e a k in t h e p a r t i a l R D F s . N e i g h b o u r n u m b e r d i s t r i b u t i o n s a r e i n d i c a t e d by t w o - l e t t e r c o d e s ( w h e r e t h e first l e t t e r d e n o t e s t h e a t o m at t h e origin); b o n d - a n g l e d i s t r i b u t i o n s a r e i n d i c a t e d by t h r e e - l e t t e r c o d e s ( w h e r e t h e angle is c e n t r e d at t h e m i d d l e atom).
971
rf-:-i , ,-3--I
*,-J
....
I
I
0
I
I
Number of nearest neighbours
0
Fig. 5. M-M, M-m and m-M nearest-neighbour distributions. The solid lines corresponds to the distributions for Ti67Ni33, the dashed lines to the distributions for NislBlg.
U s i n g d M / d m = 1.07 for T i - N i a n d d M / d m = 1.42 for N i - B (figs. 2 a n d 3), a n d t a k i n g into a c c o u n t t h e c o m p o s i t i o n s 6 7 - 3 3 a n d 8 1 - 1 9 , estim a t e s o f s o m e e x p e c t e d trivial effects o f a t o m i c d i a m e t e r r a t i o a n d c o m p o s i t i o n can b e calculated. O n e starts with a d e n s e r a n d o m p a c k i n g o f two types o f s p h e r e s o f e q u a l size, a n d o n e subseq u e n t l y a p p l i e s g e o m e t r i c a l c o r r e c t i o n s for t h e c o o r d i n a t i o n n u m b e r a n d for t h e angle u n d e r which a n e i g h b o u r - p a i r of a t o m s is s e e n by a third, c o m m o n n e i g h b o u r - a t o m . R e s u l t s for t h e a v e r a g e n e i g h b o u r n u m b e r s a n d s m a l l - a n g l e max-
Table 2 Expected and observed average coordination numbers, (N), and 'triangle' cosines cos o/t, where a t denotes the i - j - k angle between two nearest neighbour bonds i - j and j - k , for which j and k are neighbours, too Distribution
DRP
Ti67Ni33
function
(N)
Approx. effect of
(N)
comp.
diam. ratio
expected
x0.67 x0.67 x0.33
x1.00 x0.93 xl.08
8.7 8.1 4.6
M-M m-M M-m
~13 ~13 ~13
Nis1B19
COS ~t
M-M-M M-m-M m-M-m
0.5 0.5 0.5
Approx. effect of
(N)
observed
comp.
diam. ratio
expected
observed
7.4 9.6 4.7
x0.81 x0.81 x0.19
×1.00 x0.70 xl.50
10.5 7.4 3.7
12.4 9.6 2.2
COS ~t
-
+ 0.00 - 0.03 + 0.03
COS ~t
expected
observed
0.50 0.47 0.53
0.55 0.52 0.55
expected -
+ 0.00 - 0.19 + 0.16
0.50 0.31 0.66
observed 0.55 0.36 absent
DRP denotes a dense random packing of two types of spheres of equal size, where the types are randomly distributed over the topological network. Trivial effects of actual composition and diameter ratios are indicated. 'M' and 'm' denote majority and minority atoms, respectively.
972
E.W. Iparraguirre et al. / RMC study
of a-Ti67gi33
picture. The Ni-Ni-Ni bond-angles are virtually identical to the Ti-Ti-Ti bond-angles in Ti67Ni33, and the B-Ni-B distribution completely lacks the B-B nearest-neighbour peak at cos a -- 0.5. Note that the observed peak shift between Ni-Ni-Ni and Ni-B-Ni is in good agreement with the expected value - 0.19.
[- ~ - ~ _ r
. . . . ~__3 ,
5. Conclusion -1
cos (bond-~ngle)
1
Fig. 6. M - M - M , M - m - M and m - M - m bond-angle distributions. The solid lines corresponds to the distributions for Ti67Ni33, the dashed lines to the distributions for Nis1B19.
ima of the bond-angle distributions are given in table 2, together with the observed values. Some interesting points can be noted. (i) In Ti67Ni33, a Ti atom has on average 12.1 nearest neighbours (7.4 Ti and 4.7 Ni), and a Ni atom 11.4 (9.6 Ti and (not shown) 1.8 Ni). This result indicates that Ti and Ni play equivalent roles, on a topological network formed by spheres of only a small difference in size. This conclusion is also supported by the similarity of the Ti-Ti-Ti and Ti-Ni-Ti bond-angle distributions. The fact that unlike neighbours occur slightly more often than expected on a random basis points towards a tendency to chemical ordering. Ni has a special behaviour in this respect: the Ni-Ni neighbour peak at cos a = 0.5 in the Ni-Ti-Ni bond-angles is less than that for Ti-Ni-Ti. This Ni-Ni avoidance was already evident in figs. 2 and 4, where the Ti-Ti and Ni-Ni first two coordination peaks are markedly different. (ii) In Nis1B19, a Ni atom has an average of 12.4 nearest Ni neighbours. Since this number is close to the coordination number of close-packed spheres (and to the total number of Ti neighbours in Ti67Ni33), it strongly suggests that the Ni atoms in Nis1B19 form by themselves a dense network, similar to the combined Ti, Ni network in Ti67Ni33. This network implies that the 2.2 additional boron neighbours of Ni in Ni81Bt9 occupy 'interstitial' positions in this metallic network. The bond-angle distributions confirm this
Despite the fact that only two experimental functions GeXp(r) were used, the resulting three partials GiRMC(r)for Ti67Ni33 are very realistic. This result can open new roads to extend RMC simulations to a larger number of glasses, namely, those for which only a single X-ray GeXp(r) and a single neutron GeXp(r) are available. The partial RDFs show that the structures of Ti67Ni33 and NisIB19 are much more similar than could be expected from their related crystal structures (Ti2Ni and Ni3B, respectively). At close range, however, the nearest-neighbour and bond-angle distributions reveal some differences. Most notably, the Ti and Ni atoms are topologically equivalent in Ti67Ni33, while the B atoms occupy interstitial positions in Ni81B19. Analysis of the second and higher coordination shells is underway, to provide more insight in the medium-range structure of amorphous materials. This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research of Matter).
References [1] A.L. Renninger, M.D. Rechtin and B.L. Averbach, J. Non-Cryst. Solids 16 (1974) 1. [2] R.L. McGreevy and L. Pusztai, Mol. Simul. 1 (1988) 359. [3] E.W. Iparraguirre, J. Sietsma and B.J. Thijsse, to be published in Comput. Mater. Sci. [4] B.J. Thijsse, unpublished work (Delft Univ. of Technology). [5] H. Ruppersberg, D. Lee and C.N.J. Wagner, J. Phys. F10 (1980) 1645. [6] T. Fukunaga, N. Watanabe and K. Suzuki, J. Non-Cryst. Solids 61&62 (1984) 343.
Journal of Non-Crystalline Solids 156-158 (1993) 969-972 North-Holland
~ / S ~ I ~
A reverse Monte Carlo study of amorphous
U
Ti67Ni33
E d g a r W. I p a r r a g u i r r e , Jilt S i e t s m a a n d B a r e n d J. T h i j s s e Laboratory of Materials Science, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands
By applying the reverse Monte Carlo (RMC) simulation technique to X-ray and neutron diffraction data of amorphous Ti67Ni33, a set of atomic coordinates is obtained, which forms a realistic representation of the metallic glass structure. The
atomic positions are analyzed in terms of partial radial distribution functions, nearest-neighbour and bond-angle distributions, and are compared with previously obtained RMC results for NislBIg. Similarities and differences are discussed in terms of composition and atomic size.
1. Introduction In this work, we report results obtained by applying the relatively novel reverse Monte Carlo (RMC) computer simulation technique [1,2] to diffraction data of amorphous Ti67Ni33 . In a similar study on amorphous Ni81B19 [3], we found R M C to be successful in generating a set of atomic coordinates (a 'configuration') that constitutes a physically realistic picture of the metallic glass structure. The present work was initiated to obtain such a picture for a metallic glass of different type and composition as well. An additional purpose was to investigate how R M C behaves if only two instead of three sets of diffraction data are used. Because the neutron scattering lengths of Ti and Ni have opposite signs, Ti67Ni33 is a good candidate for this. First, we present the results of the R M C fit, applied to one X-ray [4] and one neutron [5] total radial distribution function (RDF). Second, the partial R D F s calculated from the final configuration are c o m p a r e d with those for NislB19 previously obtained by RMC. Finally, the configurations of Ti67Ni33 and NialB19 are c o m p a r e d in terms of their nearestneighbour and bond-angle distributions. Such a
Correspondence to: Dr J. Sietsma, Laboratory of Materials Science, Delft University of Technology, Ronerdamseweg 137, 2628 AL Delft, The Netherlands. Tel: +31-15 782 284. Telefax: +31-15 786 730. E-mail: [email protected].
comparison is particularly interesting because (1) the two glasses are typical, respectively, for the m e t a l - m e t a l and m e t a l - m e t a l l o i d glasses, (2) there is a large difference between the related crystalline structures (Ti2Ni, Ni3B) , and (3) contrary to m e t a l - m e t a l l o i d glasses, m e t a l - m e t a l glasses exist in a wide range of compositions M x m l _ x , in which the atom types can even exchange their (M)ajority and (m)inority roles.
2. The RMC procedure The simulation of Ti67Ni33 was started from a random distribution of 1566 atoms in a cubic box of 3 nm edge length. While atoms are given trial moves (of which only some are accepted), the growing agreement between the experimental diffraction data and the calculated R M C data is monitored by a 'goodness-of-fit' parameter, X 2, defined as the sum of the squares of the differences between the experimental and calculated R D F s weighted by the (estimated) experimental errors, tr. The total radial distribution functions as used here are expressed in terms of partial R D F s by the well-known expression G ( r ) = EiF.jW, jGij(r), with r the distance between an i and a j atom. The weighting factors, W~j, are given in table 1. They were corrected for the fact that the neutron experiment was performed on Ti60Ni40 rather than on Ti67Ni33. Generally, ex-
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
E.W. Iparraguirre et aL / RMC study of a-Ti67Ni33
970
Table 1 Estimated experimental errors for G(r), final goodness-of-fit parameters, normalization ratios, and weighting factors for the RMC simulation of Ti67Ni33 o"
Data
X2
(nm-2) X-ray Neutron
1.0 1.0
a exp
l'Vij
OtRMC Ti-Ti 12 34
1.17 1.10
0.378 0.084
Ti-Ni +0.474 -0.340
Ni-Ni 0.148 0.344
perimental RDFs may contain systematic errors because of erroneous normalization of the diffraction data. As shown in ref. [3], this problem can be largely circumvented by multiplying both GeXp(r) and GRMC(r) by their inverse average absolute values (a = (I G ( r ) l ) - l ) , and using F(r) = aG(r) rather than G(r) to compare experiment and simulation. The final configuration was reached after performing 25 × 10 6 atomic movements, of which 6.7 × 10 6 were accepted. The entire procedure took 3.4 × 10 6 cpu s on a DEC-station 3100. Further details are given in table 1.
3. Results
The total RDFs resulting from the RMC simulation of Ti67Ni33 are presented in fig. 1. The agreement with the X-ray data is almost perfect. Small deviations are found for the neutron case. These may be due to systematic experimental errors not fully accounted for. However, in view of the excellent reproduction of all trends and features by the RMC result, these deviations are
,
,
.
0.0
.
.
0.5
.
.
,
r [rma]
.
.
.
.
1.0
,
1.5
Fig. 2. GTiTi(r) of Ti67Ni33 calculated from the RMC results. The inset shows GNiNi(r) of Nis~B19.
-oo-j
,
,
,
.
0.0
.
0.S
.
.
.
.
r [nrn]
.
.
.
.
.
1.0
1.5
Fig. 3. GTiTi(r) of Ti67Ni33 calculated from the RMC results. The inset shows GNiB(r) of Nis1B19.
considered insignificant. It must be noticed that the two experimental sets of diffraction data have different r-ranges. The X-ray data could be used up to r = 1.5 nm, but the neutron data were available only up to r = 1.0 m.
4. Discussion
4.1. Radial distribution functions The effect of fitting two different ranges can be clearly seen in the noise components in figs. 2-4, where the partial RDFs obtained from the Ti67Ni33 configuration are shown. The partials compare well with the Ti60Ni40 partials measured by Fukunaga et al. [6]. This is not a trivial out-
0
r(,)
s 0
-5
0.0
0.5
r [rma]
1.0
1.5
Fig. 1. Final RMC fits (solid curves) of renormalized total RDFs to X-ray and neutron diffraction data for Ti67Ni33 (dashed curves).
--200
1
0.0
,
,
, ~',
~
0.5
. . . .
i
. . . .
r [rtrrt] 1.0
Fig. 4. GNir~i(r)of Ti67Ni33 calculated from the R M C The inset shows GBB(r) of NisIB19.
i
1.5 results.
E.W. Iparraguirre et al. / RMC study of a-Ti67Ni33 come, since o u r R M C results a r e b a s e d on only two t o t a l R D F s , i n s t e a d o f t h e t h r e e t h a t a r e r e q u i r e d . It c a n b e c o n c l u d e d t h a t R M C has f u n c t i o n e d well, d e s p i t e lack o f i n f o r m a t i o n . T h e Ti67Ni33 R D F s a r e also very similar in s h a p e to t h e NistB19 partials, which a r e shown in t h e insets o f figs. 2 - 4 . F i g u r e s 2 a n d 4 a r e p a r t i c u larly illustrative of t h e d i f f e r e n t roles t h a t Ni plays in b o t h m a t e r i a l s ( ' m ' in Ti67Ni33, ' M ' in Ni8tB19). By c o n t r a s t with GBB(r) for Ni81B19 , GNiNi(r) for Ti67Ni33 c o n t a i n s a significant first p e a k a r o u n d r = 0.26 nm. This is r e l a t e d to t h e d i f f e r e n c e in c o m p o s i t i o n o f t h e two a m o r p h o u s m a t e r i a l s . In Ti67Ni33 , t h e m i n o r i t y a t o m s can no l o n g e r avoid b e i n g n e a r e s t n e i g h b o u r s .
4.2. Nearest-neighbour and bond-angle distributions For the determination of the nearest-neighbour (fig. 5) a n d ' b o n d ' - a n g l e (fig. 6) d i s t r i b u t i o n s , t h e n e i g h b o u r s o f an a t o m a r e d e f i n e d as t h e a t o m s at d i s t a n c e s closer t h a n t h e m i n i m u m b e y o n d t h e first p e a k in t h e p a r t i a l R D F s . N e i g h b o u r n u m b e r d i s t r i b u t i o n s a r e i n d i c a t e d by t w o - l e t t e r c o d e s ( w h e r e t h e first l e t t e r d e n o t e s t h e a t o m at t h e origin); b o n d - a n g l e d i s t r i b u t i o n s a r e i n d i c a t e d by t h r e e - l e t t e r c o d e s ( w h e r e t h e angle is c e n t r e d at t h e m i d d l e atom).
971
rf-:-i , ,-3--I
*,-J
....
I
I
0
I
I
Number of nearest neighbours
0
Fig. 5. M-M, M-m and m-M nearest-neighbour distributions. The solid lines corresponds to the distributions for Ti67Ni33, the dashed lines to the distributions for NislBlg.
U s i n g d M / d m = 1.07 for T i - N i a n d d M / d m = 1.42 for N i - B (figs. 2 a n d 3), a n d t a k i n g into a c c o u n t t h e c o m p o s i t i o n s 6 7 - 3 3 a n d 8 1 - 1 9 , estim a t e s o f s o m e e x p e c t e d trivial effects o f a t o m i c d i a m e t e r r a t i o a n d c o m p o s i t i o n can b e calculated. O n e starts with a d e n s e r a n d o m p a c k i n g o f two types o f s p h e r e s o f e q u a l size, a n d o n e subseq u e n t l y a p p l i e s g e o m e t r i c a l c o r r e c t i o n s for t h e c o o r d i n a t i o n n u m b e r a n d for t h e angle u n d e r which a n e i g h b o u r - p a i r of a t o m s is s e e n by a third, c o m m o n n e i g h b o u r - a t o m . R e s u l t s for t h e a v e r a g e n e i g h b o u r n u m b e r s a n d s m a l l - a n g l e max-
Table 2 Expected and observed average coordination numbers, (N), and 'triangle' cosines cos o/t, where a t denotes the i - j - k angle between two nearest neighbour bonds i - j and j - k , for which j and k are neighbours, too Distribution
DRP
Ti67Ni33
function
(N)
Approx. effect of
(N)
comp.
diam. ratio
expected
x0.67 x0.67 x0.33
x1.00 x0.93 xl.08
8.7 8.1 4.6
M-M m-M M-m
~13 ~13 ~13
Nis1B19
COS ~t
M-M-M M-m-M m-M-m
0.5 0.5 0.5
Approx. effect of
(N)
observed
comp.
diam. ratio
expected
observed
7.4 9.6 4.7
x0.81 x0.81 x0.19
×1.00 x0.70 xl.50
10.5 7.4 3.7
12.4 9.6 2.2
COS ~t
-
+ 0.00 - 0.03 + 0.03
COS ~t
expected
observed
0.50 0.47 0.53
0.55 0.52 0.55
expected -
+ 0.00 - 0.19 + 0.16
0.50 0.31 0.66
observed 0.55 0.36 absent
DRP denotes a dense random packing of two types of spheres of equal size, where the types are randomly distributed over the topological network. Trivial effects of actual composition and diameter ratios are indicated. 'M' and 'm' denote majority and minority atoms, respectively.
972
E.W. Iparraguirre et al. / RMC study
of a-Ti67gi33
picture. The Ni-Ni-Ni bond-angles are virtually identical to the Ti-Ti-Ti bond-angles in Ti67Ni33, and the B-Ni-B distribution completely lacks the B-B nearest-neighbour peak at cos a -- 0.5. Note that the observed peak shift between Ni-Ni-Ni and Ni-B-Ni is in good agreement with the expected value - 0.19.
[- ~ - ~ _ r
. . . . ~__3 ,
5. Conclusion -1
cos (bond-~ngle)
1
Fig. 6. M - M - M , M - m - M and m - M - m bond-angle distributions. The solid lines corresponds to the distributions for Ti67Ni33, the dashed lines to the distributions for Nis1B19.
ima of the bond-angle distributions are given in table 2, together with the observed values. Some interesting points can be noted. (i) In Ti67Ni33, a Ti atom has on average 12.1 nearest neighbours (7.4 Ti and 4.7 Ni), and a Ni atom 11.4 (9.6 Ti and (not shown) 1.8 Ni). This result indicates that Ti and Ni play equivalent roles, on a topological network formed by spheres of only a small difference in size. This conclusion is also supported by the similarity of the Ti-Ti-Ti and Ti-Ni-Ti bond-angle distributions. The fact that unlike neighbours occur slightly more often than expected on a random basis points towards a tendency to chemical ordering. Ni has a special behaviour in this respect: the Ni-Ni neighbour peak at cos a = 0.5 in the Ni-Ti-Ni bond-angles is less than that for Ti-Ni-Ti. This Ni-Ni avoidance was already evident in figs. 2 and 4, where the Ti-Ti and Ni-Ni first two coordination peaks are markedly different. (ii) In Nis1B19, a Ni atom has an average of 12.4 nearest Ni neighbours. Since this number is close to the coordination number of close-packed spheres (and to the total number of Ti neighbours in Ti67Ni33), it strongly suggests that the Ni atoms in Nis1B19 form by themselves a dense network, similar to the combined Ti, Ni network in Ti67Ni33. This network implies that the 2.2 additional boron neighbours of Ni in Ni81Bt9 occupy 'interstitial' positions in this metallic network. The bond-angle distributions confirm this
Despite the fact that only two experimental functions GeXp(r) were used, the resulting three partials GiRMC(r)for Ti67Ni33 are very realistic. This result can open new roads to extend RMC simulations to a larger number of glasses, namely, those for which only a single X-ray GeXp(r) and a single neutron GeXp(r) are available. The partial RDFs show that the structures of Ti67Ni33 and NisIB19 are much more similar than could be expected from their related crystal structures (Ti2Ni and Ni3B, respectively). At close range, however, the nearest-neighbour and bond-angle distributions reveal some differences. Most notably, the Ti and Ni atoms are topologically equivalent in Ti67Ni33, while the B atoms occupy interstitial positions in Ni81B19. Analysis of the second and higher coordination shells is underway, to provide more insight in the medium-range structure of amorphous materials. This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research of Matter).
References [1] A.L. Renninger, M.D. Rechtin and B.L. Averbach, J. Non-Cryst. Solids 16 (1974) 1. [2] R.L. McGreevy and L. Pusztai, Mol. Simul. 1 (1988) 359. [3] E.W. Iparraguirre, J. Sietsma and B.J. Thijsse, to be published in Comput. Mater. Sci. [4] B.J. Thijsse, unpublished work (Delft Univ. of Technology). [5] H. Ruppersberg, D. Lee and C.N.J. Wagner, J. Phys. F10 (1980) 1645. [6] T. Fukunaga, N. Watanabe and K. Suzuki, J. Non-Cryst. Solids 61&62 (1984) 343.