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Short range structure of mechanically alloyed amorphous Ni2Zr investigated by anomalous X-ray scattering
I O U R N A L OF
Journal of Non-Crystalline Solids 150 (1992) 386-390 North-Holland
WW_[~/'~I|.[_II~~ll|_l~ INll-~|tI 0 uilllllll 1,
Short range structure of mechanically alloyed amorphous Ni2Zr investigated by anomalous X-ray scattering F. Buffa, A. Corrias, G. L i c h e r i a n d G. N a v a r r a Dipartimento di Scienze Chimiche, Unit'ersithdi Cagliari, L,iaOspedale 72, 09124 Cagliari, Italy D. R a o u x Laboratoire de Cristallographie, CNRS, Ace. des Martyrs 38042 Grenoble, France
The differential anomalous scattering technique has been used to study the local order in an amorphous Ni2Zr sample, prepared by mechanical alloying. The resulting structural parameters are compared with previous data obtained for a sample prepared by rapid quenching.
I. Introduction
Faber-Ziman [4,5]:
One of the main problems regarding amorphization processes is to determine whether amorphous samples having similar composition, but prepared by different methods, have similar atomic distributions. In this paper, we report the use of the differential anomalous scattering (DAS) technique to compare the local structure of an Ni~Zr amorphous alloy, prepared by mechanical alloying (MA), with that of a sample of similar composition prepared by rapid quenching (RQ) and extensively studied by different techniques (neutron diffraction [1], X-ray diffraction [2] and extended X-ray absorption fine structure spectroscopy (EXAFS) [3]). For a binary amorphous system, the total structure factor (TSF), a(s, E), obtainable from X-ray scattering data, is a weighted sum of three
a(s, E ) = WAn(S, E)aAA(S )
partial structure
factors (PSFs)
+ 2WAB(S, E)aAB(S)
+ wB,(s, E)a~.(s), wij(s, E ) = c i c j f i f j * / ( f ) 2,
(2)
( f ) 2 = i c A f A + cBfB 12,
(3)
where s is the scattering vector, E is the photon energy, and c i and fi =fi( s, E) are the concentration and the atomic scattering factor of species i, respectively. The anomalous X-ray scattering (AXS) method is based on the energy dependence of the scattering factors due to anomalous dispersion phenomena [6]. The X-ray atomic scattering factors can be written as f / ( s , E ) = f i ° ( s ) + f i ' ( s , E ) + ifi"(s, E ) ,
Correspondence to: Dr A. Corrias, Dipartimento di Scienze Chimiche, Universit~ di Cagliari, via Ospedale 72, 09124 Cagliari, Italy. Tel: +39-70 668 047. Telefax: +39-70 669 272.
(1)
(4)
where fi ° is the Fourier transform of the electron density and fi' and fi" are the real and imaginary parts of the anomalous dispersion correction. The dependence of these terms on the scattering an-
0022-3093/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
F. Buffa et al. / Structure o f a-Ni2Zr
gle is negligible but they change abruptly when the energy of the incident beam is tuned near the absorption edge of the i species. The DAS technique involves collecting two diffraction patterns, at photon energies respectively near and far from an absorption edge of an atomic species A, and taking the difference between these two sets of data [7]. Since only the scattering factor of atom A changes significantly, the differential structure factor (DSF), related to atom A, contains only two contributions: DSFA(S, El, E2) = AwAAaAA( S ) + AwABaAB( S),
(5) wi ( s, El) -wij(s, E2) AWij =
( f l ) 2 __ ( f 2 ) 2
,
(6)
the coefficient AWBB being practically zero. The Fourier sine transform of DSFA(s) gives the differential distribution function DDFA(r) which describes the structure around atom A. Therefore, more information on the structural details can be obtained by taking the DDFs around each atomic species.
2. Experimental
2.1. Sample preparation and characterization The sample was prepared by high energy milling the elemental powders. Pure elemental crystalline nickel and zirconium powders were initially mixed to give the desired composition
Table 1 Anomalous scattering factors (electrons) calculated at the different energy values (keV) [12] Energy
f/~i
f/~i
fir
fir
El= E2= E 3= E4= E5=
-3.82 - 7 . 5 3 a~ -0.04 0.27 0.27
0.49 1.76 a) 2.13 1.12 1.06
-0.34 -0.37 -0.97 -3.00 - 7 . 4 2 a)
2.17 2.11 1.10 0.56 1.02 a~
8.200 8.329 12.000 17.400 17.989
4) Values obtained from experimental absorption data by means of the optical theorem and a Kramers-Kr6nig integration [11], with estimated uncertainties of +0.05 electrons.
387
(NizZr). The milling was carried out in a planetary ball mill with steel vials under an argon atmosphere. The change to amorphous phase was monitored by X-ray diffraction spectra taken on portions of the powder at different milling steps. After 38 h, the crystalline peaks of elemental Ni and Zr had completely disappeared and only a broad halo typical of amorphous alloys was present. Fe contamination from the ball mill was measured and was 2% in the final product.
2.2. X-ray diffraction measurements The X-ray diffraction data were collected at Lure (Laboratoire pour l'Utilisation de la Rayonnement Electromagnetique, Orsay, France) using the DCI synchrotron radiation source. The sample was placed in a vacuum chamber to avoid any air scattering contribution to the measured signal. The experimental apparatus consists of a two circle diffractometer equipped with a Solid State multidetector comprising 12 Si:Li detectors [8]. With this apparatus, the time needed to obtain a good signal/noise ratio was reduced. Five photon energies were selected; they are shown in table 1, together with the values of f ' and f " used in the data analysis. The energies E 2 and E 5 were selected to fall at slightly smaller values then those of the K-edges of Ni and Zr, respectively, in order to reduce fluorescence. The energies E I and E 4 were selected far enough from the edges to yield a significant change in f ' , but not too far in order to take advantage of the cancellation of systematic errors in the difference between the two data sets [9]. The fifth energy was chosen far from both the Ni and Zr edges. At least 20 independent measurements were collected for each energy.
2.3. Data analysis Great care was necessary in the preliminary steps of the data analysis [4,5,10], in particular in the rejection of the Ka fluorescence, the subtraction of the Compton scattering and the normalization to obtain the absolute scattering per atom. For the energies nearest to the Ni and Zr K-edges,
17. Buffa et al. / Structure of a-Ni 2Zr
388
the values of f~i and f i r , respectively, were calculated using the Kramers-Kr6nig relationship [11], starting from experimental absorption data; otherwise tabulated values [12] were used. Each data set was independently processed to obtain the total structure function (TSF). These functions were analyzed to check for good behaviour and good compatibility between them. After the rejection of bad data sets, the remaining sets were then averaged and used to calculate the differential structure functions. The two energies Ea-E 5 were used to evaluate DSFzr, but the two energies E2-E3, instead of the more obvious E~-E 2 pair, were used to evaluate DSFNi. In the latter case, some distortions were discovered in the resulting DSFNi probably due to systematic errors which did not cancel in calculating the difference.
3. Results
The four TSFs corresponding to the energies used are shown in fig. 1 together with the rescaled diffraction lines for crystalline Ni and Zr. Some preliminary observations can be made. (i) The differences between the averaged TSFs are small due to the small values of f ' and f " with respect to f0. This fact makes the precise knowledge of the dispersion corrections a crucial factor in AXS analysis. (ii) The curves exhibit a very good sign a l / noise ratio which is mostly due to the imple-
TSF
2 1
3
DSF
1 0 2 1
s,~
0 0
4
8
12
16
Fig. 2. Differential structure factors, DSFs, measured at the N i (a) and Zr (b) K-edges. The experimental DSFs (full lines) are compared with DSFs simulated from neutron data [1] (dashed lines).
mentation of the multidetector. (iii) Some features in the spectra, due to the influence of crystalline peaks, are ascribable to residual metallic Zr. The crystalline peak evident at s = 2.25 .A coincides with the position of the (100) diffraction peak for elemental Zr, and the shoulder on the left side of the main peak probably contains contributions from the (002) and (101) reflections. Further, these features are less evident at energies near Zr K-edge since the scattering power of Zr decreases due to the anomalous corrections. Figure 2 shows the DSFs calculated near the Ni and Zr K-edges. It is important to note the high quality of the two signals and the absence of strong Zr crystalline contributions in DSFNi which were in practice cancelled out during the subtraction procedure. This effect was expected as the scattering power of Zr is the same at the two energies used to calculate DSFNi. On the contrary, the crystalline contributions are enhanced in DSFzr.
1 1
4. Discussion
1 0
s,A-1 0
4
8
12
16
Fig. 1. Total structure factors, a(s, E), corresponding to the four energies used in this work: (a) 8.329 keV, (b) 12.000 keV, (c) 17.400 keV and (d) 17.989 keV. The diffraction lines for crystalline Ni (dashed lines) and Zr (full lines) are also indicated (arbitrary units).
In order to make a comparison with previous results, we used experimental data relating to amorphous Ni2Zr prepared by rapid quenching [1]. In fig. 2 our DSFs are compared with DSFs simulated from the neutron data. The latter were calculated using eq. (5) starting from the partial structure factors obtained from the neutron mea-
389
F. Buffa et al. / Structure of a-Ni2Zr
DDF
40
20 10 0
"
10 0
~ ,
-
a r,A
0
2
4
6
8
Fig. 3. Differential distribution functions, DDFs, measured at the Ni (a) and Zr (b) K-edges. The DDFs from the experimental DSFs (full lines) are compared with the DDFs from the simulated DSFs in fig. 2 (dashed lines).
surements and kindly supplied by Lefebvre [1]. T h e differential distribution functions obtained by Fourier transformation of these DSFs are shown in fig. 3. T h e a g r e e m e n t between these functions is very good suggesting that the same structure is present in both samples. T h e most evident difference between the two samples consists of a small shift in the position of the first peak in all of the DSFs. This and o t h e r small differences are probably due to the residual crystalline phase in the mechanically alloyed sample. A further comparison with previous results can be made using structural parameters. Nearest neighbour distances and coordination n u m b e r s were obtained from a profile analysis in real space of the first peak of the D D F s by expressing it as a sum of two Gaussian distributions, i.e., N i - N i and N i - Z r distances for DDFNi and Z r - N i
and Z r - Z r distances for D D F z r . N o t e that the first p e a k in D D F z r is split into two subshells, while only an unresolved p e a k appears in DDFNi due to both the shorter range in s-space and the small difference between the N i - N i and N i - Z r distances. Best fit values for the structural parameters are reported in table 2, where they are c o m p a r e d with analogous results obtained from an A X S investigation [13] of a m o r p h o u s N i 2 Z r p r e p a r e d by rapid quenching [1]. Keeping in mind the different preparation m e t h o d s for the two samples, the presence of crystalline peaks in the M A sample and the poor s i g n a l / n o i s e ratio for the R Q sample m e a s u r e m e n t s [13], the structural parameters exhibit good a g r e e m e n t within the experimental errors. In table 2, the results obtained by E X A F S spectroscopy [3,14] for both samples are also shown. It appears that all o f the distances from the E X A F S m e a s u r e m e n t s are shorter than those from the A X S technique. This is a usual situation in studying metallic glasses and can be attributed to the different sensitivities of E X A F S and A X S at low r. Taking this into account, the comparison with E X A F S data confirms the reliability of our results.
5. Conclusion In summary the results reported in this paper suggest two main conclusions.
Table 2 Comparison of distances, R (,~), and coordination numbers, N (atoms), for the first shell in real space for both the MA and RQ samples MA sample
RQ sample
present work Ni-Ni Ni-Zr Zr-Ni Zr-Zr
EXAFS [14]
AXS [2]
EXAFS [3]
R
N
R
N
R
N
R
N
2.60 2.76 2.68 3.34
5.0 5.6 10.4 6.1
2.53 2.63 2.65 3.28
5.3 4.5 8.9 5.0
2.56 2.76 2.76 3.36
5.9 5.5 9.7 7.0
2.52 2.66 2.66 3.26
6.0 5.0 8.5 5.0
Structural parameters reported from EXAFS studies are calculated by averaging the values obtained performing a multi-shell fitting procedure on both Ni and Zr K-edges. Estimated uncertainties are AN= _+0.5 atoms and AR = _+0.05 A for EXAFS and AN = _+0.5 atoms and AR = _+0.03 ,~ for AXS results, respectively.
390
F. Buffa et al. / Structure of a-gi2Zr
(1) T h e D A S t e c h n i q u e can o b t a i n accuracies similar to n e u t r o n scattering with isotopic substitution; thus these two t e c h n i q u e s can be r e g a r d e d as c o m p l e m e n t a r y . (2) T h e rapid q u e n c h i n g a n d m e c h a n i c a l aUoying m e t h o d s may p r o d u c e a m o r p h o u s samples with the same local structure. This work has b e e n s u p p o r t e d by the R e g i o n e A u t o n o m a della Sardegna.
References [1] S. Lefebvre, M. Harmelin, A. Quivy, J. Bigot and Y. Calvayrac, Z. Phys. Chem. 157 (1988) 365. [2] J.C. de Lima, J.M. Tonnerre and D. Raoux, J. Non-Cryst. Solids 106 (1988) 38. [3] A. Sadoc and Y. Calvayrac,J. Non-Cryst. Solids 88 (1986) 242. [4] B.E. Warren, X-ray Diffraction (Addison-Wesley, Reading, MA, 1969).
[5] M. Magini, G. Licheri, G. Piccaluga, G. Paschina and G. Pinna, X-ray Diffraction of Ions in Aqueous Solutions: Hydration and Complex Formation (CRC, Boca Raton, FL, 1988). [6] Y. Waseda, Novel Application of Anomalous (Resonance) X-ray Scattering for Structural Characterization of Disordered Materials, Lecture Notes in Physics 204 (Springer, Berlin, 1984). [7] P.H. Fuoss, P. Eisenberger, W.K. Warburton and A. Bienenstock, Phys. Rev. Lett. 46 (1981) 1537. [8] G. Nicoll, R. Andouart, C. Barbier, D. Dagneaux, M. De Sanctis and D. Raoux, Soc. Ital. Fis. Conf. Proc. 25 (1990) 353. [9] K.F. Ludwig Jr., W.K. Warburton, L. Wilson and A.I. Bienenstock, J. Chem. Phys. 87 (1987) 604. [10] S. Aur, D. Kofalt, Y. Waseda, T. Egami, R. Wang, H.S. Chen and B.K. Teo, Solid State Commun. 48 (1983) 111. [11] P. Dreier, P. Rabe, W. Malzfeldt and W. Niemann, J. Phys. C17 (1984) 3123. [12] S. Sasaki, KEK Report 83-22, Nat. Lab. for High Energy Physics, Tsukuba, Japan. [13] J.C. de Lima, PhD thesis, Universit6 de Paris-Sud (1989). [14] A. Corrias, G. Licheri, G. Vlaic, D. Raoux and J.C. de Lima, Soc. ltal. Fis. Conf. Proc. 25 (1990) 689.
Journal of Non-Crystalline Solids 150 (1992) 386-390 North-Holland
WW_[~/'~I|.[_II~~ll|_l~ INll-~|tI 0 uilllllll 1,
Short range structure of mechanically alloyed amorphous Ni2Zr investigated by anomalous X-ray scattering F. Buffa, A. Corrias, G. L i c h e r i a n d G. N a v a r r a Dipartimento di Scienze Chimiche, Unit'ersithdi Cagliari, L,iaOspedale 72, 09124 Cagliari, Italy D. R a o u x Laboratoire de Cristallographie, CNRS, Ace. des Martyrs 38042 Grenoble, France
The differential anomalous scattering technique has been used to study the local order in an amorphous Ni2Zr sample, prepared by mechanical alloying. The resulting structural parameters are compared with previous data obtained for a sample prepared by rapid quenching.
I. Introduction
Faber-Ziman [4,5]:
One of the main problems regarding amorphization processes is to determine whether amorphous samples having similar composition, but prepared by different methods, have similar atomic distributions. In this paper, we report the use of the differential anomalous scattering (DAS) technique to compare the local structure of an Ni~Zr amorphous alloy, prepared by mechanical alloying (MA), with that of a sample of similar composition prepared by rapid quenching (RQ) and extensively studied by different techniques (neutron diffraction [1], X-ray diffraction [2] and extended X-ray absorption fine structure spectroscopy (EXAFS) [3]). For a binary amorphous system, the total structure factor (TSF), a(s, E), obtainable from X-ray scattering data, is a weighted sum of three
a(s, E ) = WAn(S, E)aAA(S )
partial structure
factors (PSFs)
+ 2WAB(S, E)aAB(S)
+ wB,(s, E)a~.(s), wij(s, E ) = c i c j f i f j * / ( f ) 2,
(2)
( f ) 2 = i c A f A + cBfB 12,
(3)
where s is the scattering vector, E is the photon energy, and c i and fi =fi( s, E) are the concentration and the atomic scattering factor of species i, respectively. The anomalous X-ray scattering (AXS) method is based on the energy dependence of the scattering factors due to anomalous dispersion phenomena [6]. The X-ray atomic scattering factors can be written as f / ( s , E ) = f i ° ( s ) + f i ' ( s , E ) + ifi"(s, E ) ,
Correspondence to: Dr A. Corrias, Dipartimento di Scienze Chimiche, Universit~ di Cagliari, via Ospedale 72, 09124 Cagliari, Italy. Tel: +39-70 668 047. Telefax: +39-70 669 272.
(1)
(4)
where fi ° is the Fourier transform of the electron density and fi' and fi" are the real and imaginary parts of the anomalous dispersion correction. The dependence of these terms on the scattering an-
0022-3093/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
F. Buffa et al. / Structure o f a-Ni2Zr
gle is negligible but they change abruptly when the energy of the incident beam is tuned near the absorption edge of the i species. The DAS technique involves collecting two diffraction patterns, at photon energies respectively near and far from an absorption edge of an atomic species A, and taking the difference between these two sets of data [7]. Since only the scattering factor of atom A changes significantly, the differential structure factor (DSF), related to atom A, contains only two contributions: DSFA(S, El, E2) = AwAAaAA( S ) + AwABaAB( S),
(5) wi ( s, El) -wij(s, E2) AWij =
( f l ) 2 __ ( f 2 ) 2
,
(6)
the coefficient AWBB being practically zero. The Fourier sine transform of DSFA(s) gives the differential distribution function DDFA(r) which describes the structure around atom A. Therefore, more information on the structural details can be obtained by taking the DDFs around each atomic species.
2. Experimental
2.1. Sample preparation and characterization The sample was prepared by high energy milling the elemental powders. Pure elemental crystalline nickel and zirconium powders were initially mixed to give the desired composition
Table 1 Anomalous scattering factors (electrons) calculated at the different energy values (keV) [12] Energy
f/~i
f/~i
fir
fir
El= E2= E 3= E4= E5=
-3.82 - 7 . 5 3 a~ -0.04 0.27 0.27
0.49 1.76 a) 2.13 1.12 1.06
-0.34 -0.37 -0.97 -3.00 - 7 . 4 2 a)
2.17 2.11 1.10 0.56 1.02 a~
8.200 8.329 12.000 17.400 17.989
4) Values obtained from experimental absorption data by means of the optical theorem and a Kramers-Kr6nig integration [11], with estimated uncertainties of +0.05 electrons.
387
(NizZr). The milling was carried out in a planetary ball mill with steel vials under an argon atmosphere. The change to amorphous phase was monitored by X-ray diffraction spectra taken on portions of the powder at different milling steps. After 38 h, the crystalline peaks of elemental Ni and Zr had completely disappeared and only a broad halo typical of amorphous alloys was present. Fe contamination from the ball mill was measured and was 2% in the final product.
2.2. X-ray diffraction measurements The X-ray diffraction data were collected at Lure (Laboratoire pour l'Utilisation de la Rayonnement Electromagnetique, Orsay, France) using the DCI synchrotron radiation source. The sample was placed in a vacuum chamber to avoid any air scattering contribution to the measured signal. The experimental apparatus consists of a two circle diffractometer equipped with a Solid State multidetector comprising 12 Si:Li detectors [8]. With this apparatus, the time needed to obtain a good signal/noise ratio was reduced. Five photon energies were selected; they are shown in table 1, together with the values of f ' and f " used in the data analysis. The energies E 2 and E 5 were selected to fall at slightly smaller values then those of the K-edges of Ni and Zr, respectively, in order to reduce fluorescence. The energies E I and E 4 were selected far enough from the edges to yield a significant change in f ' , but not too far in order to take advantage of the cancellation of systematic errors in the difference between the two data sets [9]. The fifth energy was chosen far from both the Ni and Zr edges. At least 20 independent measurements were collected for each energy.
2.3. Data analysis Great care was necessary in the preliminary steps of the data analysis [4,5,10], in particular in the rejection of the Ka fluorescence, the subtraction of the Compton scattering and the normalization to obtain the absolute scattering per atom. For the energies nearest to the Ni and Zr K-edges,
17. Buffa et al. / Structure of a-Ni 2Zr
388
the values of f~i and f i r , respectively, were calculated using the Kramers-Kr6nig relationship [11], starting from experimental absorption data; otherwise tabulated values [12] were used. Each data set was independently processed to obtain the total structure function (TSF). These functions were analyzed to check for good behaviour and good compatibility between them. After the rejection of bad data sets, the remaining sets were then averaged and used to calculate the differential structure functions. The two energies Ea-E 5 were used to evaluate DSFzr, but the two energies E2-E3, instead of the more obvious E~-E 2 pair, were used to evaluate DSFNi. In the latter case, some distortions were discovered in the resulting DSFNi probably due to systematic errors which did not cancel in calculating the difference.
3. Results
The four TSFs corresponding to the energies used are shown in fig. 1 together with the rescaled diffraction lines for crystalline Ni and Zr. Some preliminary observations can be made. (i) The differences between the averaged TSFs are small due to the small values of f ' and f " with respect to f0. This fact makes the precise knowledge of the dispersion corrections a crucial factor in AXS analysis. (ii) The curves exhibit a very good sign a l / noise ratio which is mostly due to the imple-
TSF
2 1
3
DSF
1 0 2 1
s,~
0 0
4
8
12
16
Fig. 2. Differential structure factors, DSFs, measured at the N i (a) and Zr (b) K-edges. The experimental DSFs (full lines) are compared with DSFs simulated from neutron data [1] (dashed lines).
mentation of the multidetector. (iii) Some features in the spectra, due to the influence of crystalline peaks, are ascribable to residual metallic Zr. The crystalline peak evident at s = 2.25 .A coincides with the position of the (100) diffraction peak for elemental Zr, and the shoulder on the left side of the main peak probably contains contributions from the (002) and (101) reflections. Further, these features are less evident at energies near Zr K-edge since the scattering power of Zr decreases due to the anomalous corrections. Figure 2 shows the DSFs calculated near the Ni and Zr K-edges. It is important to note the high quality of the two signals and the absence of strong Zr crystalline contributions in DSFNi which were in practice cancelled out during the subtraction procedure. This effect was expected as the scattering power of Zr is the same at the two energies used to calculate DSFNi. On the contrary, the crystalline contributions are enhanced in DSFzr.
1 1
4. Discussion
1 0
s,A-1 0
4
8
12
16
Fig. 1. Total structure factors, a(s, E), corresponding to the four energies used in this work: (a) 8.329 keV, (b) 12.000 keV, (c) 17.400 keV and (d) 17.989 keV. The diffraction lines for crystalline Ni (dashed lines) and Zr (full lines) are also indicated (arbitrary units).
In order to make a comparison with previous results, we used experimental data relating to amorphous Ni2Zr prepared by rapid quenching [1]. In fig. 2 our DSFs are compared with DSFs simulated from the neutron data. The latter were calculated using eq. (5) starting from the partial structure factors obtained from the neutron mea-
389
F. Buffa et al. / Structure of a-Ni2Zr
DDF
40
20 10 0
"
10 0
~ ,
-
a r,A
0
2
4
6
8
Fig. 3. Differential distribution functions, DDFs, measured at the Ni (a) and Zr (b) K-edges. The DDFs from the experimental DSFs (full lines) are compared with the DDFs from the simulated DSFs in fig. 2 (dashed lines).
surements and kindly supplied by Lefebvre [1]. T h e differential distribution functions obtained by Fourier transformation of these DSFs are shown in fig. 3. T h e a g r e e m e n t between these functions is very good suggesting that the same structure is present in both samples. T h e most evident difference between the two samples consists of a small shift in the position of the first peak in all of the DSFs. This and o t h e r small differences are probably due to the residual crystalline phase in the mechanically alloyed sample. A further comparison with previous results can be made using structural parameters. Nearest neighbour distances and coordination n u m b e r s were obtained from a profile analysis in real space of the first peak of the D D F s by expressing it as a sum of two Gaussian distributions, i.e., N i - N i and N i - Z r distances for DDFNi and Z r - N i
and Z r - Z r distances for D D F z r . N o t e that the first p e a k in D D F z r is split into two subshells, while only an unresolved p e a k appears in DDFNi due to both the shorter range in s-space and the small difference between the N i - N i and N i - Z r distances. Best fit values for the structural parameters are reported in table 2, where they are c o m p a r e d with analogous results obtained from an A X S investigation [13] of a m o r p h o u s N i 2 Z r p r e p a r e d by rapid quenching [1]. Keeping in mind the different preparation m e t h o d s for the two samples, the presence of crystalline peaks in the M A sample and the poor s i g n a l / n o i s e ratio for the R Q sample m e a s u r e m e n t s [13], the structural parameters exhibit good a g r e e m e n t within the experimental errors. In table 2, the results obtained by E X A F S spectroscopy [3,14] for both samples are also shown. It appears that all o f the distances from the E X A F S m e a s u r e m e n t s are shorter than those from the A X S technique. This is a usual situation in studying metallic glasses and can be attributed to the different sensitivities of E X A F S and A X S at low r. Taking this into account, the comparison with E X A F S data confirms the reliability of our results.
5. Conclusion In summary the results reported in this paper suggest two main conclusions.
Table 2 Comparison of distances, R (,~), and coordination numbers, N (atoms), for the first shell in real space for both the MA and RQ samples MA sample
RQ sample
present work Ni-Ni Ni-Zr Zr-Ni Zr-Zr
EXAFS [14]
AXS [2]
EXAFS [3]
R
N
R
N
R
N
R
N
2.60 2.76 2.68 3.34
5.0 5.6 10.4 6.1
2.53 2.63 2.65 3.28
5.3 4.5 8.9 5.0
2.56 2.76 2.76 3.36
5.9 5.5 9.7 7.0
2.52 2.66 2.66 3.26
6.0 5.0 8.5 5.0
Structural parameters reported from EXAFS studies are calculated by averaging the values obtained performing a multi-shell fitting procedure on both Ni and Zr K-edges. Estimated uncertainties are AN= _+0.5 atoms and AR = _+0.05 A for EXAFS and AN = _+0.5 atoms and AR = _+0.03 ,~ for AXS results, respectively.
390
F. Buffa et al. / Structure of a-gi2Zr
(1) T h e D A S t e c h n i q u e can o b t a i n accuracies similar to n e u t r o n scattering with isotopic substitution; thus these two t e c h n i q u e s can be r e g a r d e d as c o m p l e m e n t a r y . (2) T h e rapid q u e n c h i n g a n d m e c h a n i c a l aUoying m e t h o d s may p r o d u c e a m o r p h o u s samples with the same local structure. This work has b e e n s u p p o r t e d by the R e g i o n e A u t o n o m a della Sardegna.
References [1] S. Lefebvre, M. Harmelin, A. Quivy, J. Bigot and Y. Calvayrac, Z. Phys. Chem. 157 (1988) 365. [2] J.C. de Lima, J.M. Tonnerre and D. Raoux, J. Non-Cryst. Solids 106 (1988) 38. [3] A. Sadoc and Y. Calvayrac,J. Non-Cryst. Solids 88 (1986) 242. [4] B.E. Warren, X-ray Diffraction (Addison-Wesley, Reading, MA, 1969).
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