Local Electronic Structures and Chemical Bonds in Zr-Based Metallic Glasses

Materials Transactions, Vol. 45, No. 4 (2004) pp. 1172 to 1176 Special Issue on Bulk Amorphous, Nano-Crystalline and Nano-Quasicrystalline Alloys-V #2004 The Japan Institute of Metals Local Electronic Structures and Chemical Bonds in Zr-Based Metallic Glasses Yoshihiro Takahara and Nobutaka Narita Department of Applied Science for Integrated System Engineering, Graduate School of Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan Local electronic structures of Zr-based metallic glasses have been calculated using the discrete variational X cluster molecular orbital method. The cluster models are constructed for Zr-Cu, Zr-Ni and Zr-Pd metallic glasses on the base of local structure parameters determined by extended X-ray absorption fine structure analysis. The valence-band X-ray photoelectron spectra computed from the local electronic structures agree well with experimental spectra. Based on the feature of chemical bonds in those glasses evaluated from the electronic structures, we discuss the relationship between the chemical bond and the stability of supercooled liquid state. The strength of the Zr-Ni bond is larger than that of Zr-Cu bond, while the Cu-Cu bond strength is nearly equal to the Ni-Ni bond. Moreover, the Zr-Zr bond strength is larger in Zr-Cu glass than in Zr-Ni glass. This indicates that the formation of primary crystalline phase is more difficult in Zr-Cu glass than in Zr-Ni glass. The difficulty contributes to the relative stabilization of supercooled liquid state in Zr-Cu glass compared with that in Zr-Ni glass. It is also shown that local atomic structures of Zr-Pd glass are well described by the icosahedral atomic configuration. (Received October 20, 2003; Accepted February 16, 2004) Keywords: zirconium-based metallic glass, supercooled liquid state, molecular orbital method, local electronic structure, chemical bond 1. Introduction Recently, bulk metallic glasses have attracted much attention because of the importance in materials science and the extension of their application fields. 1) Bulk metallic glasses are characterized by a wide supercooled liquid region, T x which is defined as the temperature interval between glass transition temperature, T g and crystallization temperature, T x. The appearance of the wide supercooled liquid region implies the high resistance against crystallization, leading to large glass-forming ability. The stable supercooled liquid state enables the production of bulk metallic glasses. It is therefore quite important to understand the reason for the stabilization of the supercooled liquid state from the viewpoint of interests in materials science as well as development of new bulk metallic glasses. The three empirical rules have been proposed by Inoue 2) in order to explain the origin of the wide supercooled liquid region and good glass-forming ability in bulk metallic glasses. It is also suggested that the stability of the supercooled liquid state is strongly correlated with their local structure. 3 6) Alamgir et al. 7,8) have investigated the relation between the electronic structure and the glass-forming ability in Pd-Ni-P glassy alloys, and pointed out that the existing electron models are not fully adequate to explain the high glass stability of the Pd 40 Ni 40 P 20 alloy. However, little is known about the relation of the chemical bond among constituent atoms with the stability of supercooled liquid state in bulk metallic glasses. The present study is intended to investigate the local electronic structures and the chemical bonds among constituent atoms in Zr-based metallic glasses, and to clarify the relation between the chemical bond and the stability of supercooled liquid state. The local electronic structures are calculated for Zr-Cu, Zr-Ni and Zr-Pd metallic glasses using the discrete variational (DV) X cluster molecular orbital method. 9) The cluster models are constructed on the base of local structure parameters determined by extended X-ray absorption fine structure (EXAFS) analysis. The feature of chemical bonds in these glasses is evaluated from the calculated electronic structures. 2. Experimental Procedure Metallic glasses of Zr 65 Cu 35,Zr 65 Ni 35 and Zr 65 Pd 35 were used in this investigation. Those specimens were prepared by Prof. H. Kimura of Tohoku University with a single roller melt-spinning technique in a purified argon atmosphere. These were ribbons with about 5 mm in width and 30 to 40 mm in thickness. The amorphicity of the ribbons was examined by X-ray diffraction with Cu K radiation. The thermal properties were measured by differential scanning calorimetry (Rigaku DSC-8230B) at a heating rate of 0.33 K/ s in a purified argon flow. A powdery Al 2 O 3 was used as a reference material. For EXAFS measurements, the samples were thinned by polishing to an optimum thickness. The measurement was carried out in the transmission mode by the use of an EXAC800 laboratory EXAFS system (Technos Corp.) which consists of rotating anode X-ray generator, curved-crystal monochromator and solid state detector. Johansson-type Ge(220) crystal (2d ¼ 0:400 nm) was used as the monochromator. The local electronic structures of the model clusters were calculated using DV-X molecular orbital method. The magnitude of chemical bonds was evaluated by the Mulliken population analysis 10,11) of the calculated electronic structure. In order to confirm the validity of the calculated electronic structure, we estimated the valence-band X-ray photoelectron spectroscopy (XPS) spectra from the electronic structure, and compared them with the measured X-ray photoelectron spectra. The measurements of the spectra were carried out with an ULVAC-PHI 5500MC spectrometer using AlK monochromatic X-rays. The surface on each sample was cleaned in high vacuum by Ar-ion etching before recording a spectrum. 3. Results and Discussion Figure 1 shows the DSC curves of the Zr-based binary metallic glasses used here. As can be seen from the figure, the Zr-Ni glass has no supercooled liquid region but the Zr-Cu and Zr-Pd glasses exhibit an obvious endothermic reaction

Local Electronic Structures and Chemical Bonds in Zr-Based Metallic Glasses 1173 Fig. 3 Radial structure function for the Zr 65 Cu 35 metallic glass. Fig. 1 Differential scanning calorimetry (DSC) curves of as-prepared Zr 65 Ni 35,Zr 65 Cu 35 and Zr 65 Pd 35 metallic glasses. Fig. 4 Comparison between EXAFS experimental data (closed circle) and curve-fitting result (solid line) for the Zr 65 Cu 35 metallic glass. Fig. 2 Cu K-edge EXAFS spectrum for the Zr 65 Cu 35 metallic glass. due to the glass transition followed by a supercooled liquid region. Such differences suggest that the chemical interaction (chemical bond) between constituent atoms is closely related to the stability of supercooled liquid state in those metallic glasses. In this study, we evaluated the overlap population for the chemical bonds from the local electronic structures in those glasses which were calculated using the DV-X cluster method. First of all, local atomic structures were investigated by EXAFS analysis in order to construct the cluster models for those metallic glasses. The Cu K-edge EXAFS spectrum for the Zr 65 Cu 35 metallic glass is shown in Fig. 2. The EXAFS signals were extracted from the raw data using a standard procedure. 12) The absorption background below the K-edge was extrapolated to the EXAFS region by a Victoreen fit, and the atomic absorption was approximated by a polynomial expression. Figure 3 shows the radial structure function FðrÞ obtained for the Zr 65 Cu 35 glass. The structure function represents a single peak well isolated in the vicinity of 0.22 nm. The inverse Fourier transformation of FðrÞ was employed to the isolated peak to obtain a filtered EXAFS function in k (wave vector) space. The filtered EXAFS function obtained is shown in Fig. 4 (solid circle). The nearest neighbor distance r and coordination number N around Cu atom were determined from the filtered EXAFS function by a curve-fitting method. In the curve-fitting, we used the theoretical values of the backscattering amplitudes and phase shifts calculated by the FEFF program. The result of the fitting is illustrated by solid line in Fig. 4. The values of r and N obtained are summarized in Table 1. These values agree well with those in parentheses which are evaluated from X-ray diffraction measurements by Chen and Waseda. 13) It is evident from the Table that the total coordination number around Cu is about 12. Based on the result, we constructed the HCP-like cluster model of first approximation to the local atomic structure of the Zr 65 Cu 35 metallic glass. The cluster model is illustrated by Fig. 5. On the other hand, it is reported that a tetragonal Zr 2 Ni phase is precipitated as the primary phase in the melt-spun Zr 70 Ni 30 glass 14) The formation of the tetragonal Zr 2 Ni phase as the primary phase implies that a tetragonal Zr 2 Ni-like shortrange ordering exists in the glassy state. By taking the fact

1174 Y. Takahara and N. Narita Table 1 Structure parameters obtained from curve-fitting for Cu K edge EXAFS of the Zr 65 Cu 35 metallic glass: r is the interatomic distance, N is the coordination number and is the Debye-Waller factor. r Terms N (nm) 0.247 4.4 Cu-Cu (0.253) (4.6) Zr 65 Cu 35 0.274 7.7 Cu-Zr (0.277) (7.4) (nm) 0.02 0.02 z y x Zr Cu Fig. 6 Comparison between experimental (closed circle) and simulated (solid line) valence-band XPS spectra for the Zr 65 Cu 35 and Zr 65 Ni 35 metallic glasses. Fig. 5 Geometry of HCP-like cluster. into consideration, we calculated the electronic structure for the tetragonal cluster model used as a first approximation of the local atomic structure in the Zr 65 Ni 35 metallic glass. In the calculation of local electronic structure for each cluster model, the interatomic distances in the clusters were employed as in the following. (1) For the Zr 65 Cu 35 glass, the interatomic distances of Cu- Cu and Cu-Zr were taken from Table 1 and that of Zr-Zr was taken from the experimental data reported by Chen and Waseda. 13) (2) The interatomic distances for the Zr 65 Ni 35 glass were take from the literature reported by Saida et al. 14) In order to confirm the validity of the calculated electronic structures, we estimated the valence-band XPS spectra from the electronic structures, and then compared them with the measured valence-band XPS spectra. The results are shown in Figs. 6(a) and (b). In the figures, the experimental valenceband XPS spectra for the Zr 65 Cu 35 and Zr 65 Ni 35 metallic glasses are illustrated by closed circles. It is observed that the valence bands of these two glasses are formed by two components. One lies close to the Fermi energy E F, and the other appears at a higher binding energy. The components close to E F in both glasses correspond to the Zr 4d-bands. The component at a higher binding energy in the Zr 65 Cu 35 glass corresponds to the Cu 3d-band, and that in the Zr 65 Ni 35 glass corresponds to the Ni 3d-band. The solid lines in Figs. 6(a) and (b) represent the calculated valence-band XPS spectra for each cluster. The calculated spectra are in good agreement with the measured spectra for each metallic glass, which demonstrates the validity of the local electronic structures calculated in this study. On the other hand, we used an icosahedral cluster model as a first approximation to the local atomic structure of the Zr 65 Pd 35 metallic glass. The interatomic distances for the Zr 65 Pd 35 glass were employed from the experimental data reported by Waseda and Chen. 15) The valence-band XPS spectrum was evaluated from the local electronic structure which was calculated for the icosahedral cluster model using the DV-X molecular orbital method. The comparison of the calculated valence-band XPS spectrum (solid line) with the measured spectrum (closed circle) is shown in Fig. 7. The valence band of this glass is formed by two well separated components. The component lying close to E F corresponds to the Zr 4d-band, and that appearing at a higher binding energy corresponds to Pd 4d-band. In Fig. 7, the valence-band XPS spectrum (broken line) calculated for the HCP-like cluster is also shown for comparison. The calculated spectrum for the icosahedral cluster agrees well with the measured spectrum, implying that the local atomic structure of the Zr 65 Pd 35 glass is well described by the icosahedral atomic configuration. This result is consistent with the suggestion of the existence of icosahedral short-range ordering in the Zr-Pd glass. 16) However, the agreement between the observed spectrum and the calculated spectrum for the icosahedral cluster is not so

Local Electronic Structures and Chemical Bonds in Zr-Based Metallic Glasses 1175 5 Cu-Cu Cu-Zr Zr-Zr 0.143 0.210 0.418 Energy, E / ev 0-5 -10 Anti- -0.4 0 0.4-0.4 0 0.4-0.4 0 0.4 5 Ni-Ni Ni-Zr Zr-Zr Fig. 7 Comparison between experimental (closed circle) and simulated valence-band XPS spectra for the Zr 65 Pd 35 metallic glass. The solid line shows the spectrum for the icosahedral cluster and the broken line shows the spectrum for the HCP-like cluster. good compared with that in the Zr 65 Cu 35 and Zr 65 Ni 35 glasses. Hence, further analysis of the calculated local electronic structure was not performed for the Zr 65 Pd 35 glass. In this study, we employs the Mulliken population analysis to estimate the magnitude of chemical bondings. The overlap population Q ij ðlþ of the lth molecular orbital between i (ith atomic orbital) and j (jth atomic orbital) is defined by 10) Q ij ¼ X Z f l c il c jl i ðrþ j ðrþdr; l where the C il are coefficients, f l is the occupation number of the lth molecular orbital. The overlap population can be used as a measure of strength of the covalent bonding. Figure 8 shows the overlap population diagrams for Cu-Cu, Cu-Zr and Zr-Zr bonds obtained for the Zr-Cu cluster, and for Ni-Ni, Ni- Zr and Zr-Zr bonds obtained for the Zr-Ni cluster. Those diagrams are made by convoluting the overlap population at each molecular orbital with Gaussian function of 0.5 ev full width at half-maximum. The right part of each diagram shows the bonding contribution and the left part shows the anti-bonding contribution. The integration of both bonding and anti-bonding contributions up to the highest occupied molecular orbital (Fermi level) provides the bond overlap population for each bond. The values of the bond overlap population are indicated in each diagram. By comparing these values between the Zr-Cu and Zr-Ni glasses, it is evident that the strength of the Zr-Ni bond is larger than that of the Zr-Cu bond, and the Cu-Cu bond strength is almost identical to the Ni-Ni bond. This is consistent with that the heats of mixing for the Zr-Ni pair ( 49 kj/mol) are significantly negative relative to that for the Zr-Cu pair ( 23 kj/mol). Further, the Zr-Zr bond strength is larger in the Zr-Cu glass than in the Zr-Ni glass. Hence, we will discuss these results in relation to the formation of primary crystalline phase in these two metallic glasses. It has been reported that the Zr 2 Cu and Zr 2 Ni phases are formed as a Energy, E / ev 0-5 -10 primary phase in the Zr 65 Cu 35 and Zr 65 Ni 35 metallic glasses, respectively. 17,18) Considering that somewhat strong interaction between atoms of different types is required to form the crystalline phase (compound) in the glassy matrix (see Fig. 8), it is strongly suggested that the formation of primary crystalline phase is more difficult in the Zr-Cu glass than in the Zr-Ni glass. Therefore, we can conclude that the difficulty contributes to the relative stabilization of supercooled liquid state in the Zr 65 Cu 35 glass compared with the Zr 65 Ni 35 glass. 4. Conclusions Anti- 0.144 0.259 0.374-0.4 0 0.4-0.4 0 0.4-0.4 0 0.4 Overlap Population, n / ev -1 Fig. 8 Overlap population diagrams for the bonds between constituent atoms in the Zr 65 Cu 35 and Zr 65 Ni 35 metallic glasses. We have performed the discrete variational X cluster model calculation for the local electronic structures in Zrbased metallic glasses. The feature of chemical bonds in those glasses is estimated from the electronic structures, and the relation between the chemical bond and the stability of supercooled liquid state is discussed. The results obtained are summarized as follows: (1) In the Zr-Cu and Zr-Ni glasses, the strength of the Zr-Ni bond is larger than that of Zr-Cu bond, while there is no difference between the Cu-Cu bond strength and the Ni-Ni bond. Furthermore, The Zr-Zr bond strength is larger in the Zr-Cu glass than in the Zr-Ni glass. This means that the formation of primary crystalline phase is more difficult in the

1176 Y. Takahara and N. Narita Zr-Cu glass than in the Zr-Ni glass, which results in the stabilization of supercooled liquid state in the Zr-Cu glass relative to the Zr-Ni glass. (2) The existence of the icosahedral local atomic configuration in the glassy state is suggested in the Zr-Pd glass. Acknowledgements The authors are indebted to Profs. A. Inoue and H. Kimura in IMR, Tohoku University for the supply of samples and to Dr. S. Towata in Toyota Central R&D Laboratories for the XPS experiments. We also thank Prof. O. Haruyama in Tokyo University of Science and Dr. N. Nishiyama in RIMCOF for stimulating discussions. REFERENCES 1) A. Inoue: Acta Mater. 48 (2000) 279 306. 2) A. Inoue: Mater.Trans., JIM 36 (1995) 866 875. 3) E. Matsubara, T. Tamura, Y. Waseda, A. Inoue, M. Kohinata and T. Masumoto: Mater. Trans., JIM 31 (1990) 228 231. 4) E. Matsubara, T. Tamura, Y. Waseda, A. Inoue, M. Kohinata and T. Masumoto: Mater. Trans., JIM 33 (1992) 873 878. 5) T. Ikeda, E. Matsubara, Y. Waseda, A. Inoue, T. Chang and T. Masumoto: Mater. Trans., JIM 36 (1992) 1093 1096. 6) S. Sato, E. Matsubara, S. Tanaka, M. Imafuku, Y. Waseda, T. Zhang and A. Inoue: Proc. Int. Conf. on Solid-Solid Phase Transformations 99 (JIMIC-3), (Japan Inst.Metals, 1999) 1211 1214. 7) F. M. Alamgir, H. Jain, A. C. Miller, D. B. Williams and R. B. Schwarz: Phil. Mag. B79 (1999) 239 247. 8) F. M. Alamgir, H. Jain, R. B. Schwarz, O. Jin and D. B. Williams: J. Non-Cryst. Solids 274 (2000) 289 293. 9) H. Adachi, M. Tsukada and C. Satoko: J. Phys. Soc. Jpn. 45 (1978) 875 883. 10) R. S. Mulliken: J. Chem. Phys. 23 (1955) 1833 1840. 11) H. Adachi: Introduction to Quantum Materials Chemistry-Approach with DV-X method-, (Sankyo Press, Tokyo, 1991) pp. 24 53. 12) Y. Udagawa (Ed.): Extended X-ray Absorption Fine Structure, (Japan Scientific Societies Press, Tokyo, 1993). 13) H. S. Chen and Y. Waseda: Phys. Status Solidi (a) 51 (1979) 593 599. 14) J. Saida, M. Kasai, E. Matsubara and A. Inoue: Ann. Chim. Sci. Mat. 27 (2002) 77 89. 15) Y. Waseda and H. S. Chen: Proc. 3rd Int. Conf. On Rapidly Quenched Metals, (1978) 412 418. 16) J. Saida, M. Matsushita, C. Li and A. Inoue: Philos. Mag. B79 (1999) 239 247. 17) J. Saida, M. Matsushita, K. Yaoita and A. Inoue: Mater. Trans., JIM 40 (1999) 1117 1122. 18) J. Saida, M. Matsushita and A. Inoue: Materia Japan 41 (2002) 199 205.