Modeling the atomic structure of an amorphous Ni71Nb29 alloy produced by mechanical alloying using reverse Monte Carlo simulations

Journal of Non-Crystalline Solids 353 (2007) 1046–1053 www.elsevier.com/locate/jnoncrysol

Modeling the atomic structure of an amorphous Ni71Nb29 alloy produced by mechanical alloying using reverse Monte Carlo simulations J.C. De Lima *, A.R. Jeroˆnimo, T.O. Almeida, T.A. Grandi, C.E.M. Campos, S.M. Souza, D.M. Triches Departamento de Fı´sica, Universidade Federal de Santa Catarina, Trindade, C.P. 476, Cep 88040-900, Floriano´polis, Santa Catarina, Brazil Received 7 April 2006; received in revised form 20 December 2006 Available online 20 February 2007

Abstract The local atomic structure of an amorphous Ni71Nb29 alloy produced by mechanical alloying technique was determined using only one X-ray total structure factor S(K) as input data for reverse Monte Carlo (RMC) simulations. The results showed that the amorphous alloy has a local atomic structure similar to that predicted by the additive hard sphere (AHS) model for a Ni and Nb mixture with same composition of the alloy, and quite different of that found in the rhombohedral NiNb crystal. The obtained coordination numbers for the first neighbors showed that the amorphous alloy has a preference to form homopolar pairs. Ó 2007 Elsevier B.V. All rights reserved. PACS: 61.10.Eq; 61.10.Ht; 61.43.Bn; 05.10.Ln Keywords: Alloys; Mechanical alloying; X-ray diffraction; Monte Carlo simulations; Short-range order

1. Introduction Mechanical alloying (MA) [1] is an efficient method for synthesizing crystalline [2–4], amorphous [5–8] alloys, stable and metastable solid solutions [9,10]. MA has also been used to produce materials with nanometer-sized grains and alloys whose components have large differences in their melting temperatures and are thus difficult to produce using techniques based on melting. The few thermodynamics restrictions on the alloy composition open up a wide range of possibilities for property combinations [11], even for immiscible elements [12]. The temperatures reached in MA are very low, and thus this low temperature process reduces reaction kinetics, allowing the production of poorly crystallized or amorphous materials.

*

Corresponding author. E-mail address: [email protected] (J.C. De Lima).

0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.01.012

The Ni–Nb system was one of the first systems to be studied by MA [13] for which amorphous alloys were obtained. Later, several other structural studies were performed on the Ni–Nb alloys produced by different techniques [14–16]. Svab et al. [15,17] reported results obtained for the local atomic structure of the amorphous Ni60Nb40 and Ni62Nb38 alloys. According to the coordination numbers reported by those workers, the amorphous Ni60Nb40 and Ni62Nb38 alloys show a preference to form homopolar and heteropolar pairs, respectively. It is interesting to note that a small change in the Ni concentration causes strong changes in the local atomic structure of these amorphous alloys. In the present paper we describe the results obtained for the local atomic structure of an amorphous Ni71Nb29 alloy produced by MA using only one X-ray total structure factor S(K) as input data for the RMC simulations. The determined local atomic structure was compared with that predicted by the additive hard sphere (AHS) model for a

J.C. De Lima et al. / Journal of Non-Crystalline Solids 353 (2007) 1046–1053

mixture of Ni and Nb with same composition of the alloy, and with that present in the rhombohedral NiNb crystal. 2. Theoretical summary 2.1. Brief description of a thermodynamics approach for the formation of intermetallic binary alloys by MA To understand the formation of amorphous and crystalline alloys, knowledge of two key considerations is necessary: (i) the two elements must have a large negative relative heat of mixing, and (ii) either one of them must be an anomalously fast diffuser (to produce an amorphous phase). If the two elements have similar diffusion coefficients, a simultaneous diffusion of them occurs, and usually a crystalline phase is formed. Of course, the knowledge of other physical mechanisms is necessary. Recently, De Lima et al. [18] developed a thermodynamic approach that has been used to describe the formation of intermetallic binary alloys by MA. This approach assumes that during the milling a composite powder is formed and that its interfacial component is composed by the mixture of the interfacial components of the elemental powders, which are formed during milling process. This approach also assumes that the nucleation and growing of new phases occur in the interfacial component of composite powder at average temperatures not greater than 373 K. From a thermodynamic point of view, the mixture of the interfacial components has been treated as an ideal solution. Thus, the Gibbs free energy and equilibrium volume equations have been used together with the results obtained for the excess Gibbs free energy for the metals, in nanometric form, to estimate the theoretical activation energy value associated with diffuse process responsible for grain growth, grain boundary migration, atomic migration, and nucleation of new phases. It has been observed that for activation energy values around 0.03 eV the final product of milling shows an amorphous structure; while for values around 0.06 eV the final product shows a nanocrystalline structure. This thermodynamic approach was applied to estimate theoretical values of the activation energy and excess volume theoretical values for different ideal solutions of Ni and Nb

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at 300 and 323 K average temperatures. The obtained values are listed in Table 1. From this Table one can see that for NixNb1x ideal solutions, with 5 at.% 6 x 6 75 at.%, the activation energy values suggest the possibility of obtaining amorphous phases. Then, in order to confirm these predictions, a Ni71Nb29 mixture was prepared and submitted to MA. After 25 h of milling an amorphous phase was observed.

2.2. Faber and ziman partial structure factors The structure of the amorphous binary alloy is described by three pair correlation functions Gij(r), which are the Fourier transformation of the three partial structure factors Sij(K). The total structure factor S(K) is a weighted sum of Sij(K), and it can be derived from the X-ray and/ or neutron scattering measurements. Usually, to determine the Sij(K) factors for an amorphous binary alloy at least three independent S(K) factors are necessary. However, there are several difficulties to obtain independent S(K) factors, and two of them are the following: (1) for neutron scattering measurements, samples can be prepared by using the isotope substitution method. The problem is that there is no disposable isotope for all chemical elements or, otherwise, they are very expensive. (2) For conventional X-ray measurements, the commercial tubes have fixed energy and obtain only one independent S(K) factor. These difficulties were partially overcome with the development of synchrotron sources, which allow tuning the energy of incoming beam near the K-absorption edge of the alloy components. This fact has permitted to carry out the anomalous X-ray scattering (AWAXS) measurements. By using AWAXS, De Lima et al. [19,20] determined the three Sij(K) factors for the amorphous Ni2Zr and NiZr2 alloys. Recently, with the development of RMC method [21–24] a number of local atomic structures of the amorphous alloys were modeled. Several papers are reported in the literature describing those [25–31]. According to Faber and Ziman [32], S(K) is obtained for a binary alloy from the X-ray scattered intensity per atom Ia(K) through

Table 1 Theoretical estimated values of the activation energy (Ea) and excess volume (DVIS = DV/V0) for different ideal solutions of Ni and Nb at 300 and 323 K 300 K

323 K IS

Ni (at.%)

DV

10 20 30 40 50 60 70 80 90

0.443 0.443 0.423 0.423 0.423 0.424 0.424 0.424 0.424

20

Ea 10

0.1911 0.1086 0.0162 0.7100 0.1594 0.2786 0.4295 0.6068 0.8092

J/at

Ea (eV)

Ea 1020 J/at

Ea (eV)

0.011 0.006 0.001 0.004 0.009 0.017 0.026 0.037 0.050

0.2889 0.4197 0.4714 0.1281 0.2452 0.3948 0.5724 0.7765 0.1005

0.018 0.001 0.002 0.007 0.015 0.024 0.035 0.048 0.062

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SðKÞ ¼ SðKÞ ¼

I a ðKÞ  ½hf 2 ðKÞi  hf ðKÞi  hf ðKÞi 2 X

2

W ij ðKÞS ij ðKÞ;

;

ð1Þ ð2Þ

i;j¼1

W ij ðKÞ ¼

ci cj fi ðKÞfj ðKÞ

hf ðKÞi X 2 hf ðKÞi ¼ ci fi2

2

;

ð3Þ

i

and " 2

hf ðKÞi ¼

X

#2 ci fi ðKÞ ;

i h where K ¼ 4p sin , ci is the concentration of atoms of type i k and f(K) is the atomic scattering factor. The total and partial reduced distribution functions c(r) and cij(r) are related to S(K) and Sij(K) by Fourier transformation and they are written as Z 1 cðrÞ ¼ ð2=pÞ K½SðKÞ  1 sinðKrÞ dK; ð4Þ Z0 1 cij ðrÞ ¼ ð2=pÞ K½S ij ðKÞ  1 sinðKrÞ dK; ð5Þ 0

The total and partial pair correlation functions G(r) and Gij (r) are related to the c(r) and cij(r) through the expressions, cðrÞ ¼ 4pq0 r½GðrÞ  1

ð6Þ

and cij ðrÞ ¼ 4pq0 r½Gij ðrÞ  1:

ð7Þ

The total and partial radial distribution functions RDF(r) and RDFij(r) are written as RDFðrÞ ¼ 4pq0 r2 GðrÞ

ð8Þ

and RDFij ðrÞ ¼ 4pq0 cj r2 Gij ðrÞ;

ð9Þ

˚ 3. where q0 is the atomic density of the alloy in atoms/A 2.3. Reverse Monte Carlo method The RMC method is based in statistical mechanics, and its basic idea and the algorithm are described elsewhere [21–24]. Its application for modeling the structure of noncrystalline materials uses as starting point one or more experimental S(K) factors, and has as objective to generate static atomic configurations by a procedure explicitly designed to give best agreement with experimental data. It bypasses the need for any representations of the interatomic forces or atomic potentials. The best match between the simulated and experimental S(K) factors indicates that the static atomic configuration generated can be representative of reality, and can also allow an understanding of

the atomic structure as well as the search for insights behind the raw data. The RMC method allows taking into account properly the effects of experimental resolution [33]. Thus, it is important to determine the experimental S(K) factors in a ˚ 1) in order to K-range as large as possible (typically 50 A achieve the best possible resolution in G(r) function. The resolution Dr is given as 2p/Kmax, where Kmax is the maximum value of K achieved in the measurement of S(K). The forward Fourier transforms of K[S(K)  1] (see Eq. (4)) to obtain c(r) is straightforward, but is subject to a problem that arises from the fact that the data for S(K) extend only to some maximum value of K. The effect of the finite range of K on the Fourier transform is to introduce spurious ripple peaks into the computed c(r) function. This problem can be avoided by multiplying K[S(K)  1] by a modification function M(K) that decreases smoothly to zero at Kmax. However, the Fourier transform of the modified form of K[S(K)  1] will then be convoluted with the Fourier transform of M(K), which means that the peaks in c(r) will be artificially broadened. In order to overcome this problem the RMC method can be used to obtain the G(r), whose Fourier transform best matches the experimental K[S(K)  1] data. It is important to note that although the spurious ripple peaks into the computed G(r) function are overcome the effects of experimental resolution remain. The starting point of the RMC method to study noncrystalline materials is to generate an initial configuration of atoms (a random distribution of atoms) without unreasonably short interatomic distances. In this study, the initial configuration was generated by considering a cubic ˚ , 5000 particles (3550 and 1450 reprebox of edge L = 43 A senting the Ni and Nb atoms, respectively) and a density of ˚ 3. q0 = 0.06407 atoms/A A RMC simulation will evolve to maximize the amount of disorder (entropy) in the configurations generated. Thus, it will give the most disordered atomic configurations that are consistent with the experimental data. There may be a range of configurations that match the data, with different degrees of disorder. Only by maximizing the range of experimental data can this problem be minimized. In order to obtain the most consistent atomic configurations, more than one S(K) factor should be used. In this study we have used only one S(K) factor, which was derived from an X-ray diffraction measurement using Cu Ka radiation (k = ˚ ). Thus, the K maximum value reached was 1.5406 A ˚ 1. Trying to obtain the most disordered final atomic 7A configuration that is consistent with our experimental data, two preliminary procedures were adopted: (i) in the initial atomic configuration, at the beginning, minimum approach (cutoff) distances between the atomic centers of ˚ and rNi–Nb = rNb–Nb = 1.7 A ˚ were fixed to rNi–Ni = 1.8 A act as constraints on the short-range structure, and (ii) entropy maximization of atomic configuration. This step will ensure that the model does not get trapped in a local minimum, and instead the model will converge on the global minimum.

J.C. De Lima et al. / Journal of Non-Crystalline Solids 353 (2007) 1046–1053

Gij ðrÞ ¼

N ij ðrÞ ; 4pr2 qi dr

where Nij(r) is the number of atoms of type j lying within the range of distances between r and r + dr from any atom of type i, and qi = ciq0. During the RMC simulation process the following function is minimized: w2 ¼

m 1X 2 ½S RMC ðK i Þ  SðK i Þ : d i¼1

The sum is over m experimental points and d is related to the experimental error in S(K). In order to minimize the w function, atoms are selected at random, and moved small random distances. If the move reduces, it is accepted. If the move increases, it is accepted with the probability P ¼ expðDw2 =2Þ: As the process is iterated w2 decreases until it reaches a global equilibrium value. Thus, in principle, the final atomic configuration corresponding to the equilibrium should be the most disordered and consistent with our experimental data. Using GRMC ðrÞ and S RMC ðKÞ functions ij ij corresponding to the final atomic configuration, the coordination numbers, the interatomic distances and the bond-angle distributions can be calculated. 3. Experimental procedures A binary mixture of high-purity elemental powders of nickel (particle size < 10 lm) and niobium (particle size < 10 lm) with nominal composition of Ni71Nb29 was sealed together with several steel balls into a cylindrical steel vial under an argon atmosphere. The ball-to-powder weight ratio was 4:1. A Spex Mixer/Mill model 8000 was used to perform MA at room temperature. A ventilation system was used to keep the vial temperature close to room temperature. After 5, 9, 20 and 25 h of milling the process was stopped and the powder analyzed via X-ray diffraction (XRD) technique. The XRD patterns were recorded on a powder Rigaku Miniflex diffractometer, and that corresponding for 25 h of milling also on powder Philips X-Pert diffractometer equipped with a graphite monochromator. ˚ ). Both diffractometers used the Cu Ka line (k = 1.5406 A The analysis of the as-milled powder after 25 h of milling by energy dispersive X-rays analysis in a Philips scanning electron microscope showed a content of Ni and Nb of 71 at.% and 29 at.%, respectively. Small iron contamination (less than 3 at.%) was also observed and not considered. Therefore, the final milling product will be considered as being an amorphous Ni71Nb29 alloy. S(K) was computed from the XRD pattern after corrections for polarization, absorption, and inelastic scattering

following the procedure described by Wagner [34]. The spurious contribution of air scattering to the XRD pattern was eliminated following the procedure described in Ref [35]. The f 0 and f00 values were taken from a table compiled by Sasaki [36]. The density of the amorphous alloy was calculated from the slope of the straight line (4pq0r) fitting the initial part of the computed c(r) function (until the first ˚3 minimum) [34]. The value obtained is 0.06407 atoms/A 3 (7.3 g/cm ). 4. Results Fig. 1 shows the measured XRD pattern for the asmilled Ni71Nb29 powder for 25 h. From this figure one can see the absence of sharp peaks indicating the amorphous nature of the as-milled powder. The scattering observed between 2h = 4° and 20° comes from the air shell located between the sample and detector. Fig. 2 shows the total structure factor S(K), derived from the XRD pattern showed in Fig. 1. According to Eq. (2), the S(K) function is a weighted sum of the partial SNi–Ni(K), SNi–Nb(K) and SNb–Nb(K) structure factors, and their respective Wij(K) values are shown in Fig. 3. From this figure one can see that the contribution of the partial SNb–Nb(K) factor to the total S(K) factor is small. Thus, to get information about the Nb–Nb pairs correlation is very difficulty. The S(K) factor was used as input data together with computational RMC programs to obtain the most representative static atomic configuration. The simulated SRMC(K) factor is also shown in Fig. 2 (thick line), and one can see an excellent agreement between them. RMC RMC Fig. 4 shows the partial S RMC Ni–Ni ðKÞ, S Ni–Nb ðKÞ and S Nb–Nb ðKÞ factors obtained from the RMC simulation. From this figure one can see that the S RMC Nb–Nb ðKÞ shows noise levels greater than the others due to its small contribution to S(K) factor. All the S RMC ðKÞ factors show an intense ij 160 140 120

Intensity (cps)

The individual pair correlation Gij(r) functions are defined as

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100 80 60 40 20 0 0

10 20 30 40 50 60 70 80 90 100 110 120

2θ (degree) Fig. 1. Measured X-ray diffraction pattern for the Ni71Nb29 powder milled for 25 h.

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2

NbNb

Gij (r)

S(K)

1

NiNb

0

NiNi

-1 0

1

2

3

4

5

6

7

0

2

4

6

-1

K (Å ) Fig. 2. Total structure factor for the as-milled Ni71Nb29 powder after 25 h of milling: experimental (noise line) and RMC simulated (thick line).

8 r (Å)

10

12

14

Fig. 5. Pair correlation functions GRMC ðrÞ obtained directly from the ij RMC simulations.

0.6 Table 2 Structural parameters obtained for amorphous Ni71Nb29 alloy

NiNb 0.4

Wij (K)

NiNi

0.2

NbNb

Bond type

Ni–Ni

Ni–Nb

Nb–Ni

Nb–Nb

RMC N1 N2 N1/N2

˚ 7.7 at 2.61 A 22.1 0.39

˚ 3.5 at 2.70 A 10.7 0.33

˚ 8.7 at 2.70 A 26.3 0.33

˚ 3.7 at 2.79 A 9.0 0.41

AHS model ˚ 7.9 at 2.63 A N1

˚ 4.0 at 2.82 A

˚ 9.8 at 2.82 A

˚ 4.8 at 3.00 A

1

2

N and N denote the numbers of the neighbors for first and second shells, respectively.

0.0 0

1

2

3

4

5

6

7

-1

K (Å ) Fig. 3. Calculated weights for the amorphous Ni71Nb29 alloy.

˚ 1 and a second wide and diffuse halo at about K = 2.94 A ˚ 1. less intense one at about K = 4.83 A Fig. 5 shows the pair correlation functions Gij(r) obtained directly from the RMC simulations. Due to the

Sij (K)

NbNb

NiNb

NiNi

1

2

3

4

5

6

7

-1

K (Å ) Fig. 4. Partial structure factors: RMC simulations (thick line) and AHS model (thin line).

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 cos (bond-angle)

0.6

0.8

Fig. 6. Bond-angle distributions (the angle is centered at the middle atom) obtained from the RMC simulations: Nb–Nb–Nb (solid line), Nb–Ni–Nb (square + line) and Ni–Nb–Ni (crosses + line).

J.C. De Lima et al. / Journal of Non-Crystalline Solids 353 (2007) 1046–1053

5. Discussion From Table 2, one can see that Ni and Nb atoms have on average 11.2 and 12.4 nearest neighbors, respectively. This result indicates that Ni and Nb play equivalent roles, on topological network formed by spheres of very similar sizes. This fact is supported by the similarity of the Nb– Nb–Nb and Nb–Ni–Nb bond-angle distributions showed in Fig. 6. Other evidence is that the Ni–Ni neighbor peak at cos a  0.6 in the Ni–Nb–Ni bond-angles is greater than that for Nb–Ni–Nb, which suggests that Nb has a special behavior in the network. Table 2 shows also the coordination numbers for the second neighbors and the ratio of the partial coordination numbers of the first and second shells N 1ij =N 2ij , characterizing the relative packing density of the two coordination spheres. From the ratio values it can be concluded that the packing in the NiNi and NbNb neighbors is much more dense than the packing of NiNb ones. The chemical short-range order (CSRO) in the amorphous alloy is obtained using the Warren parameter aw given by [37]

5 4 3 2 1 0 0

N 12 ; c2 ½c1 ðN 22 þ N 21 Þ þ c2 ðN 11 þ N 12 Þ

where Nij are the first neighbors coordination numbers listed in the Table 2. The aw parameter is null for a random distribution. If there is a preference for forming unlike pairs in the alloy, it becomes negative. Otherwise, it is positive if homopolar pairs are preferred. In this study, the obtained value is aw = 0.017. Based on the calculated aw value, it is interesting to compare the functions obtained in this work with those predicted by the AHS model for a mixture of Ni and Nb with same composition of the amorphous alloy. The Percus–Yevick (PY) equation [27] is applied to systems in which short-range forces are dominant. This equation has an exact solution for a hard sphere potential, making it possible to obtain analytical expression for the pair distribution and structure factor functions. Initially, the PY equation solution was used to determine the structure of single metals in liquid state. The solution was based on a hard sphere potential. Later, this model was extended to binary alloys in the liquid state. Weeks [38] used the PY model to study the atomic structure of metallic glasses,

1

2

3

4

5

6

7

-1

K (Å ) Fig. 7. Experimental and AHS (thin line) total structure factors.

3 2 1

γ (r)

aw ¼ 1:0 

assuming an isotropic and homogeneous phase that does not occur in the solid state. The extension of the PY model to study the glass state is based on the structure of an amorphous state, which can be considered as an extrapolation of the atomic structure of the liquid state. A review of the PY model is given in Ref. [39]. We used a subroutine given in Ref. [39] to calculate the Sij(K) predicted by the AHS model as part of a computer program to calculate the S(K) for a binary amorphous alloy. It is well known that the intensity of the main halo of the SAHS(K), generated by the AHS model, is larger than the experimental one. Thus, SAHS(K) has to be multiplied by an exp (r2K2) function in order to introduce a ‘thermal’ effect. The best results were reached by considering ˚ 2 and a packing fraction of 0.68. Fig. 7 shows r2 = 0.056 A the experimental S(K) and SAHS(K) (thin line) functions, where a good agreement between them can be observed. Fig. 8 shows the reduced c(r) and cAHS(r) (thin line) functions. The density of the AHS mixture was determined

S(K)

poor contribution of the S RMC Nb–Nb ðKÞ to S(K) factor, the GNb–Nb(r) function has also high noise levels. The partial radial distribution RDFij(r) functions (see Fig. 9) were obtained from the Gij(r) functions according to Eq. (9). The interatomic distances for the first neighbors were obtained from the first peak of Gij(r) functions and the coordination numbers from the RDFij(r) functions. These values are shown in Table 2. Fig. 6 presents the Nb–Nb–Nb, Nb–Ni–Nb and Ni–Nb– Ni bond-angle distributions (the angle is centered at the middle atom) obtained from the final atomic configuration.

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0 -1 -2 0

1

2

3

4

5

6

7

8

9

10

r (Å) Fig. 8. Experimental and AHS (thin line) reduced distribution functions.

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by using the same procedure already described for the amorphous alloy and the obtained value is qAHS = 7.7 g/ cm3, which agrees with that obtained for the amorphous alloy. In order to compare the S AHS ðKÞ (thin line) functions ij with those obtained from the RMC simulations, they are shown in Fig. 4. From this figure one can see a reasonable agreement among them. The coordination numbers and interatomic distances for first neighbors were also calculated and are listed in Table 2. Due to the features of the AHS model, different interatomic distances than those obtained from RMC results are expected. Using the coordination numbers obtained from the AHS model, the CSRO parameter obtained was aw = 0.0012, which is of the same order of that obtained from experimental results (RMC). The atomic structure of the amorphous Ni71Nb29 alloy was compared with that presents in the rhombohedral NiNb crystal (JCPDS card no. 42-1208), whose prototype structure is the Fe7W6 crystal. Using the CRYSTALOFFICE software [40] we have calculated all the interatomic ˚ for the NiNi, NiNb, NbNi and NbNb distances until 15 A pairs present in this crystal. The partial S Crystal ðKÞ factors ij were calculated using the expression below S Crystal ðKÞ ¼ 1 þ N j ij

X X senðKrj Þ ; Krj j k

where for each rj value the sum is done over the K-range of the experimental S(K). For i = j yields to S Crystal ðKÞ and ii Crystal S Crystal ðKÞ, while for i 5 j yields to S ðKÞ. The funcjj ij Crystal Crystal tions cij ðrÞ and RDFij ðrÞ were obtained as already described previously. Fig. 9 shows the RDFCrystal ðrÞ functions (thin line) calcuij lated taking the Ni atom at 3a (multiplicity Wyckoff letter) as origin. This figure shows these functions together with those obtained for the amorphous Ni71Nb29 alloy. A

detailed interpretation of this figure is difficult. However, one can see that the RDFNiNi and RDFNiNb functions obtained for the amorphous alloy present some features, which seem to be present in the functions calculated for the rhombohedral NiNb crystal. The RDFNbNb functions are quite different. The rhombohedral NiNb crystal has six Ni–Ni first ˚ , 6 Ni–Nb at 2.85 A ˚ and 9 Nb–Nb at neighbors at 2.47 A ˚ an average distance of 3.04 A. The CSRO parameter value is aw = 0.11, indicating a preference to form homopolar pairs as the amorphous Ni71Nb29 alloy. In general way, both structures are different. 6. Conclusions Several conclusions are taken from the study. The main ones are: 1. The formation of an amorphous Ni71Nb29 phase by mechanical alloy was predicted by the thermodynamic approach mentioned in Section 1 and confirmed experimentally. 2. The partial S RMC ðKÞ, GRMC ðrÞ and RDFRMC ðrÞ funcij ij ij tions were obtained for the amorphous Ni71Nb29 alloy from only one X-ray total structure factor and used as input data for the RMC simulations. The interatomic distances and coordination numbers for the first neighbors were obtained from the GRMC ðrÞ and RDFRMC ðrÞ ij ij functions, respectively. 3. The amorphous Ni71Nb29 alloy shows a preference to form homopolar pairs. 4. The local atomic structure of amorphous Ni71Nb29 alloy is similar to that predicted by the AHS model for a mixture with same chemical composition of the alloy. 5. The local atomic structure of the amorphous Ni71Nb29 alloy is different of that present in the rhombohedral NiNb crystals. Acknowledgements We thank the Brazilian agencies CAPES, CNPq and FAPESC for financial support. We are indebted to Dr Patrı´cia Bodanese for the XRD measurements.

NbNb

RDFij (r)

References NiNb

NiNi 0

1

2

3

4

5

6

7

8

9

10

r (Å) Fig. 9. Partial radial distribution functions: amorphous Ni71Nb29 alloy (thick line) and rhombohedral NiNb crystal (thin line) calculated according to expression described in the text.

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