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J. Phys. Chem. B 2005, 109, 9362-9367
Nonequilibrium Solid Phase Formation Studied by Lattice Dynamics Calculation and Ion Beam Mixing in an Immiscible Co-Ag System Y. Kong, H. B. Guo, H. F. Yan, and B. X. Liu* AdVanced Materials Laboratory, Department of Materials Science and Engineering, Tsinghua UniVersity, Beijing 100084, China, and State Key Laboratory of Solid-State Microstructure, Nanjing UniVersity, Nanjing 200039, China ReceiVed: December 7, 2004; In Final Form: March 24, 2005
For the equilibrium immiscible Co-Ag system, a proven realistic ab initio derived n-body potential is applied to study the nonequilibrium solid phase formation at three chemical stoichiometries of Co/Ag ) 1:3, 1:1, and 3:1. To predict the structural stability, the elastic constants and the phonon spectra are calculated at the chosen stoichiometries with a total of eight hypothetical crystalline structures. The calculated results suggest that four compounds, that is, D03 CoAg3, B1 CoAg, B2 CoAg, and D03 Co3Ag, are unstable, as they all feature negative elastic constants as well as imaginary phonons, and that another four compounds of both fcc-type L12 and hcp-type D019 structures at chemical stoichiometries of Co/Ag ) 1:3 and 3:1, respectively, may elastically be favored and therefore obtainable under some specific conditions. It is also found that all the calculated elastic constants and phonon spectra are coincident within the framework of the elastic theory. Moreover, the calculated elastic constants are in good agreement with those acquired directly from ab initio calculations, lending support to the validity of the ab initio derived n-body Co-Ag potential as well as its resultant elastic constants and the phonon spectra. Interestingly, some of the predicted nonequilibrium solid phases, that is, two hcp-type compounds at chemical stoichiometries of Co/Ag ) 1:3 and 3:1, respectively, are indeed obtained in ion beam mixing experiments and their lattice constants determined by diffraction analysis are in good agreement with those from calculations.
1. Introduction In the past decades, some new materials processing techniques have been developed to produce various nonequilibrium metallic alloys of either an amorphous or crystalline structure.1-3 Among these techniques, ion beam mixing (IBM) of multiple metal layers was introduced in the early 1980s and has been proven as one of the most powerful means not only in producing a variety of new nonequilibrium alloys in the equilibrium miscible and immiscible binary metal systems but also in studying the underlying scientific issue, namely, the nonequilibrium solid phase formation and transformation under far-from-equilibrium circumstances.4 It is well-known that ion irradiation is capable of promoting some local atomic rearrangements and therefore modifying the microstructure of the materials/solids and that the atomic rearrangement and microstructural modification are sensitively dependent on the physical and chemical interactions between the constituent metals/elements, for example, the miscibility/immiscibility of the system concerned, as well as on the interfacial free energy stored in the studied multilayered films. Take the formation of metallic glasses as an example: in liquid melt quenching (LMQ), the formation of metallic glasses is through a process of liquid-to-solid phase transformation, whereas, in IBM, it is through an entirely different process of solid-solid phase transformation. Naturally, such a difference in the phase transformation process would certainly result in a significant difference between LMQ and IBM in their capabilities of producing the metallic glasses. In fact, IBM is capable of producing metallic glasses not only in those binary metal * To whom correspondence should be addressed. E-mail: dmslbx@ tsinghua.edu.cn.
systems with negative heats of formation (∆Hf) defined and calculated by Miedema’s model5 but also in those equilibrium immiscible systems with positive ∆Hf, in which the two constituent metals could not even be co-melted together to form any alloy. It follows that some basic concept and understanding of metallic glasses established previously based mainly on the observations from LMQ practice should somehow be modified or refined, for instance, the previously defined glass-forming ability (GFA) or glass-forming range (GFR), the consequently defined glass-forming and non-glass-forming systems, and so forth. Besides the experimental studies, much attention has also been paid to the theoretical modeling concerning the formation and structural characteristics of the nonequilibrium solid phases.6-8 In this respect, some researchers have studied the stability of the nonequilibrium solid phases by calculating their free energies under the framework of Miedema’s thermodynamic model.9,10 Generally speaking, thermodynamic calculation is still at a semiquantitative stage, and to approach a better understanding at a depth of electronic structure, first principles calculation is necessary. By performing relevant first principles calculation, one can determine the lattice constants and cohesive energies of some hypothetical crystalline structures at some specific chemical stoichiometries of a binary metal system of interest, and from the sequence of the determined cohesive energies of the hypothetical crystalline structures, one can predict an energetically favored structure for a specific chemical stoichiometry to appear as a nonequilibrium solid phase in the system. In recent years, the approach of first principles calculations to predict nonequilibrium solid phase formation has been applied successfully for some equilibrium immiscible systems.11-14
10.1021/jp044449g CCC: $30.25 © 2005 American Chemical Society Published on Web 04/20/2005
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TABLE 1: Calculated Equilibrium Properties (Lattice Constants (a and c/a), Atomic Volumes (V), Cohesive Energies (Ec)) of Co-Ag in the Eight Hypothetical Crystalline Structures CoAg3 a (Å) c/a V (Å3/atom) Ec (eV)
D03
L12
6.455
4.054
16.810 -3.280
16.657 -3.312
CoAg D019 2.866 1.635 16.667 -3.311
Nonetheless, there are still some open questions requiring further investigation. For example, in an equilibrium immiscible system characterized by a positive ∆Hf value, whether a crystalline phase with the lowest cohesive energy predicted by the first principles calculation could really be a nonequilibrium solid phase. It is well-known that the free energy is a determinate factor of the phase stability and that the internal energy, the contribution of lattice dynamics, and the thermal electronic contribution are parts of the free energy of a metallic system.15 A survey of the theoretical and experimental literature seeking to quantify the effect of lattice vibrations on the phase stability indicates that the contribution of lattice vibrations can be significant.16,17 Consequently, only considering the cohesive energy, that is, the internal energy of an alloy system, is not sufficient to predict the stability of a nonequilibrium solid phase in an equilibrium immiscible system. Moreover, there have been some reports showing that even if a crystalline structure seems to be elastically stable, its phonon spectra may feather imaginary frequencies at the Brillouin zone (BZ) boundary, which suggests that the crystalline structure is unstable.18,19 In fact, a relatively stable nonequilibrium solid phase should not only be favored in terms of its cohesive energy but also be elastic as well as vibrational stable under a specific condition. In this regard, we have recently shown the feasibility of calculating the phonon spectra based on a proven realistic Cu-Ta potential to predict the structural stability of the nonequilibrium solid phase in the equilibrium immiscible Cu-Ta system.20 In the present study, we focused on studying the nonequilibrium solid phase formation in the equilibrium immiscible Co-Ag system by lattice dynamics calculations and by an ion beam mixing experiment. Choosing the Co-Ag system is based on the following considerations. First, it has recently been noted that the granular materials made of CoAg alloys feature a giant magnetoresistance (GMR) effect and have a consequent potential for practical applications.21,22 Second, it has been found that though the Co-Ag system is essentially immiscible at equilibrium, an effective intermixing did take place at the Co-Ag interface under some specific circumstance.23,24 Third, a proven realistic Co-Ag potential under the second moment approximation of the tight-binding scheme (TB-SMA) has been constructed and the potential was able to reproduce some static properties as well as to reflect some dynamic properties of the Co-Ag system.6, 25 2. Methods and Computational Details Since the theoretical basis of the computations has been described in many texts and papers,26,27 only a brief summary of the computation methods is presented here. 2.1. Lattice Dynamics. Applying the derived TB-SMA Co-Ag potential, the elastic constants are calculated following Johnson’s method that the second-order elastic constants are the second derivatives of the single atom energy.28 To obtain the phonon spectra, there are basically three approaches for determining the force constants: analytic calculation, supercell calculation, and linear-response calculation.17 In the present
Co3Ag
B1
B2
D03
L12
5.404
3.198
6.121
3.844
19.727 -3.088
16.353 -3.501
14.333 -3.791
14.200 -3.829
D019 2.718 1.627 14.142 -3.827
study, we perform analytic calculation with the TB-SMA Co-Ag potential to obtain the phonon spectra for the possible CoAg3, Co3Ag, and CoAg compounds with some hypothetical crystalline structures. On the basis of the Born-von Ka´rma´n model,27 using the TB-SMA Co-Ag potential, the interatomic force constants (ΦRβ(r bij)) between atom i and atom j can be obtained under the harmonic approximation. Consequently, the phonon spectra can be calculated through the dynamical matrix DRβ(q b,kk′), which is the Fourier transformation of the interatomic force constant.
|DRβ(q b,kk′) - mkmk′ω2(q b)δRβδkk′| ) 0 where mk is the mass of the k atom, ω is the phonon frequency, b q is the wave vector, and δ is the Kronecker function. 2.2. Ab initio Calculation. The well-established Vienna ab initio simulation package (VASP) is employed to acquire some physical properties for fitting the TB-SMA potential, such as the cohesive energies and lattice constants of some possible nonequilibrium solid phases in the Co-Ag system. Concerning the detailed procedure of the ab initio calculations as well as the details of deriving the TB-SMA potential, the readers are referred to our recent publications.7,25 In addition, the elastic constants of eight hypothetical crystalline structures are also calculated by another wellestablished ab initio simulation software named CASTEP to verify the results obtained form the TB-SMA potential.29 In the CASTEP calculation, we first perform the geometry optimization to find the ground state of the studied structures, and the elastic constants are then calculated with the same setting for the geometry optimization. The calculations are conducted in a plane-wave basis with a maximum plane-wave cutoff energy of 330 eV, using fully nonlocal Vanderbilt-type ultrasoft pseudopotentials to describe the electron-ion interaction.30 The exchange and correlation items are described by the generalizedgradient approximation (GGA) proposed by Perdew and Wang.31 The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used in the geometry optimization.32 The qualities of the convergence are all set to be ultrafine, so that the energy convergence is less than 5.0 × 10-6 eV/atom. After the final self-consistency cycle, the remaining forces on all the atoms are less than 0.01 eV/Å, and the remaining stress is less than 0.02 GPa. The pseudopotential representation is in a reciprocal space. The integration in the BZ is done on the special k points determined according to the Monkhorst-Pack scheme.33 3. Results and Discussion In this section, we first present and discuss the calculation results and then compare the calculated results with the experimental observations. 3.1. Theoretical Results. Structure Parameters. In the calculation, we chose the D03, L12, and D019 structures as the hypothetical crystalline structures for the possible nonequilibrium CoAg3 and Co3Ag compounds, as the previous studies suggest that these three structures are energetically favored, and
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TABLE 2: Elastic Constants (GPa) of the Eight Hypothetical Crystalline Structures in the Equilibrium Immiscible Co-Ag System Calculated from the TB-SMA Co-Ag Potential CoAg3 CoAg Co3Ag
structure
C11
C12
C44
D03 L12 D019 B1 B2 D03 L12 D019
107.4 144.7 181.9 214.8 103.7 131.2 177 227.4
116.8 102.6 90.3 15.8 124.6 141.5 123 106.5
73.1 58.1 33.1 -14.1 83.1 96.1 77 43.1
C13
C33
77.2
193.6
89.1
243.9
C′ -4.7 21.1 45.8 99.5 -10.5 -5.1 27 60.5
the simple crystalline structures of the open-packed bcc, the close-packed fcc, and hcp structures are the most common structures in the binary metal systems.11,13 The calculated lattice constants (a) and cohesive energies (Ec) of these hypothetical crystalline structures are listed in Table 1. For another possible nonequilibrium CoAg compound, we chose the B1 and B2 structures as the hypothetical crystalline structures and the calculated results are also listed in Table 1. From the table, one sees that, at a chemical stoichiometry of Co/Ag ) 1:3 (or 3:1), the energies of the L12 and D019 structures are very close, reflecting the well-known fact that the fcc and hcp structures have essentially similar atomic configurations, while the energy of the D03 structure is a little higher than those of L12 and D019, and that, at a chemical stoichiomety of Co/Ag ) 1:1, the B2 structure has a lower energy than the B1 structure. Elastic Constants. On the basis of the derived TB-SMA Co-Ag potential, the elastic constants of the eight hypothetical crystalline structures are obtained and listed in Table 2. From the table, one sees some unusual features in their elastic behavior. First, the shear elastic constants C′ ) (C11 - C12)/2 of the D03 structure and the B2 structure are both negative, implying the D03 structured CoAg3 and Co3Ag and B2 structured CoAg compounds are dynamically unstable under elastic shearing. Second, the shear elastic constant C44 of the B1 structure is also negative, highlighting an elastic instability of the B1 structured CoAg compound. Third, the shear elastic constants C44 and C′ of the D019 and L12 structures are both positive, suggesting that the closed-packed D019 and L12 structured CoAg3 and Co3Ag compounds may elastically be stable. Phonon Spectra. We first present the calculated results for the phonon spectra of the hypothetical crystalline structures of the CoAg3 compound along the high symmetry directions of the Brillouin zone (BZ) in Figure 1. For convenience, we use the negative y axis to plot the imaginary frequencies. In general, one sees that the imaginary phonons appear along high symmetry directions of the BZ for the D03 structure, whereas the phonon frequencies are all real for the D019 and L12 structures. One can find out some details by carefully inspecting the figure. First, for the D03 structure from Figure 1a, the initial slope of the transverse acoustic (TA) phonon branch along [110] is negative, while the TA phonon branches along [100] are initially positive and later become imaginary phonons at the BZ boundary. The phonon branches along the [111] direction, however, are all positive. Second, for the L12 and D019 structures from parts b and c of Figure 1, respectively, one sees that there are 12 and 24 phonon branches in the L12 and D019 structures and coincidence with four and eight atoms in the conventional cells of the L12 and D019 structures, respectively, and all the phonon frequencies are positive. We now present the calculation results for the Co3Ag compound. Figure 2 shows the phonon spectra for the Co3Ag
Figure 1. Obtained phonon spectra of the (a) D03, (b) L12, and (c) D019 structures of the equilibrium immiscible CoAg3 compounds.
compound with three hypothetical crystalline structures, and they are similar to the counterparts of the CoAg3 compound; that is, the imaginary phonons appear in the D03 structure, and the phonon frequencies of L12 and D019 are all positive. A different point between the Co3Ag and CoAg3 compounds is that the maximum frequency of the Co3Ag compound is near 8 THz, while it is near 6 THz for the CoAg3 compound. This difference can be explained by the different average atom volumes of the two compounds. From Table 1, one can note that the average atom volume is about 16 Å3/atom for CoAg3, and for Co3Ag, it is about 14 Å3/atom. Since the atoms in the Co3Ag compound have a smaller space to vibrate compared with the atoms in the CoAg3 compound, their maximum vibration frequencies should be higher than the atoms vibrating in the CoAg3 compound with a larger space. For the two hypothetical crystalline structures of the CoAg compound, the obtained phonon spectra are shown in Figure 3. The B1 structure is of the typical NaCl structure. At the [100] and [110] directions, the initial slope of the TA phonon branches is negative, and the longitudinal acoustic (LA) phonon branches become imaginary phonons near the BZ boundary. At the [111] direction, however, there is no such imaginary phonon appear-
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Figure 3. Obtained phonon spectra of the (a) B1 and (b) B2 structures of the equilibrium immiscible CoAg compounds.
Figure 2. Obtained phonon spectra of the (a) D03, (b) L12, and (c) D019 structures of the equilibrium immiscible Co3Ag compounds.
ing. As for the B2 structure, it is of the CsCl type. The phonon spectra of the B2 structured CoAg compound show some different features compared with those of the B1 structured CoAg compound. In the B2 structured CoAg compound, only imaginary phonons appear along the [110] direction and no imaginary phonons appear along the [100] and [111] directions. The initial slope of one of the TA phonon branches along the [110] direction is negative, while only the LA phonon branch becomes imaginary phonons at the BZ boundary and another TA phonon branch is still positive, differing significantly from the B1 structured CoAg compound. In short, imaginary phonons appear in the two studied hypothetical crystalline structures, that is, B1 and B2, of the CoAg compound, indicating an internal instability of the positions of the nuclear coordinates. It should be noted that, according to the elastic theory,34 in the long wavelength limit, the elastic waves in the principal propagation directions in the cubic crystals have the following relations: (1) Along the [100] direction, the LA phonon branch is equal to C11 and the TA phonon branch is equal to C44. (2) Along the [110] direction, the LA branch is equal to 1/2(C11 + C12 + 2C44) and the TA phonon branch is degenerated into two branches; that is, one is equal to C44, and the other is equal to
C′. (3) Along the [111] direction, the LA branch is equal to 1/ (C 3 11 + 2C12 + 4C44) and the TA branch is equal to 1/ (C 3 11 - C12 + C44). Apparently, these relationships are all held in the obtained phonon spectra. For example, only the C44 value of the B1 structured CoAg compound is negative, so that, along the [100] direction, only the initial slope of the LA phonon branch of the B1 structured CoAg compound is negative among all the studied structures. For the B1 structured CoAg compound, along the [111] direction, the obtained results for LA ) 1/ (C + 2C + 4C ) ) 63.3 GPa and TA ) 1/ (C - C + 3 11 12 44 3 11 12 C44) ) 61.6 GPa from the calculated elastic constants are very close, so that the longitudinal and transverse phonon branches are almost overlapped. It is the same reason that the longitudinal and transverse phonon branches are almost overlapped along the [110] direction for the B1 structured CoAg compound and along the [100] direction for the B2 structured CoAg compound. Consequently, the coincidence between the phonon spectra and the elastic constants could lend some support to the relevance of the present lattice dynamics calculation. In summary, the above lattice dynamics calculations show that, at a chemical stoichiometry of Co/Ag ) 1:3 (or 3:1), the D03 crystalline structures are unstable and the close-packed L12 and D019 crystalline structures are relatively stable, which coincides with the conclusion based on the comparison of the cohesive energies and the elastic constants among these hypothetical crystalline structures, as it is shown that the L12 and D019 structures have lower cohesive energies and are elastically stable. At a chemical stoichiometry of Co/Ag ) 1:1, the B1 and B2 structures both feature imaginary phonons, and their shear elastic constants are both negative, clearly indicating a lattice instability of these hypothetical compounds. Elastic Constants from CASTEP. To verify the validity of the calculations based on the derived empirical TB-SMA Co-Ag potential, we recalculated the elastic constants of the four hypothetical crystalline structures featuring negative elastic constants, that is, the D03 CoAg3, B1 CoAg, B2 CoAg, and
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TABLE 3: Elastic Constants (GPa) of the Four Featuring Negative Elastic Constant Crystalline Structures in the Equilibrium Immiscible Co-Ag System Calculated from CASTEP CoAg3 CoAg Co3Ag
structure
C11
C12
C44
D03 B1 B2 D03
116.7 295.2 121.4 125.3
120.2 15.3 148.6 216.5
76.5 -30.1 99.3 74.6
C13
C33
C′ -1.75 139.95 -13.6 -45.6
D03 Co3Ag compounds, from CASTEP, and the results are listed in Table 3. From the table, one can note that although some numerical quantities of the elastic constants are slightly different from the two calculation methods, the obtained results from CASTEP show that the four hypothetical crystalline structures also have similar unusual elastic behaviors revealed by the calculations based on the derived empirical TB-SMA potential, which also correctly resulted in a large difference between C11 and C12 of the B1 structured CoAg compound. It is therefore concluded that the calculated results from the empirical TB-SMA potential are in good agreement with those obtained from CASTEP, implying the calculated elastic constants and the phonon spectra from the TB-SMA Co-Ag potential are, at least, qualitatively reasonable, since they are both the second derivatives of the energy of the Co-Ag alloys. 3.2. Comparison with the Ion Beam Mixing Experiment. Since the recent discovery of the GMR in granular materials, much attention has been devoted to the Co grains embedded in the Ag medium and there have been some interesting experimental observations reported in the literature. For example, it has been reported that the Co nanoparticles in the 10 nm size regime could sink below the surface when deposited on Ag(100) at 600 K and that such a sink process is likely due to the so-called burrowing effect.35 Concerning the nonequilibrium solid phase formation, Li et al. have reported that some nonequilibrium solid phases could be formed in the Co-Ag system by 200 keV Xe+ ion beam mixing of the Co-Ag multilayers.36 Besides, a nonequilibrium fcc structured Ag3Co alloy has been formed in thin films upon ion irradiation,13 and Amirthapandian et al. have observed an hcp structured CoAg3 phase (DO19) in an amorphous matrix in an ion beam mixing experiment.24,37 In fact, these experimental observations strongly support the above lattice dynamics calculations. From the above calculated elastic constants and phonon spectra, it is concluded that, at a chemical stoichiometry of Co/Ag ) 1:3, the nonequlibrium CoAg3 compound of either L12 or D019 structure can be relatively stable under some specific conditions. It is well-known that ion beam mixing is a far-from-equilibrium process and is very powerful in synthesizing nonequlibrium solid phases and that the predicted L12 and D019 structures of the CoAg3 compounds were indeed obtained in the IBM experiments mentioned above. For the Co-rich side, however, there has been less studied experimentally. According to the above lattice dynamics calculations, it is predicted that the L12 and D019 structures are also likely to appear at the Co-rich side, as they are both phonon stable and elastic stable. To confirm the above prediction, we prepared seven multilayered samples with overall compositions of 20, 25, 30, 35, 40, 50, and 75 atom % of Ag, respectively, and then had the as-deposited samples subjected to 200 keV xenon ion irradiation at 300 K at the doses ranging from 5 × 1014 to 9 × 1015 Xe+/cm2. The detailed experimental procedure will be discussed elsewhere.38 The experimental results show that a nonequilibrium crystalline phase of hcp
structure in the Co-rich side was indeed observed, and the indexing results for the newly formed hcp phase showed that the lattice parameters were a ) 2.84 Å and c/a ) 1.64, respectively. Recalling the results from the lattice dynamics calculations, the hcp-type D019 structure has lattice parameters of a ) 2.72 Å and c/a ) 1.63, respectively, which are in good agreement with the present experimental results. As for a chemical stoichiometry of Co/Ag ) 1:1, there are not any reports claiming the formation of the nonequilibrium solid phase, and in our experiments, no metastable phase has so far been observed either. According to the above lattice dynamics calculation, although the B2 structure has a relatively low energy, it may still be unstable, suggesting the difficulty to obtain any alloy at this chemical stoichiometry. 4. Concluding Remarks The elastic constants were calculated by an ab initio derived TB-SMA Co-Ag potential at three chemical stoichiometires of Co/Ag ) 1:3, 1:1, and 3:1, respectively, with a total of eight hypothetical crystalline structures in the Co-Ag system, and the results showed that four crystalline structures, that is, D03 CoAg3, B1 CoAg, B2 CoAg, and D03 Co3Ag, are elastically unstable, as they all feature negative elastic constants. The phonon spectra of the eight hypothetical crystalline structures were also calculated by the standard lattice dynamical methods, based on the ab initio derived TB-SMA Co-Ag potential. The obtained phonon spectra suggested that the fcctype L12 and hcp-type D019 structures may relatively be stable at a chemical stoichiometry of Co/Ag ) 1:3 (or 3:1) under some specific circumstance and that, for a chemical stoichiometry of Co/Ag ) 1:1, a nonequilibrium solid phase is hard to obtain. It is also found that all the calculated elastic constants and phonon spectra are coincident within the framework of the elastic theory. Moreover, the calculated elastic constants of the four crystalline structures featuring negative elastic constants based on the ab initio derived n-body Co-Ag potential are in good agreement with those acquired directly from ab initio calculations, lending support to the validity of the derived Co-Ag potential as well as its resultant elastic constants and the phonon spectra. In ion beam mixing experiments, the hcp-type Co-Ag phases at stoichiometries of Co/Ag ) 1:3 and 3:1, respectively, were indeed obtained, lending strong support to the feasibility of lattice dynamics calculation to predict the formation of nonequilibrium solid phases in the Co-Ag system. Acknowledgment. The authors are grateful for the financial support from the National Natural Science Foundation of China, The Ministry of Science and Technology of China (G20000672), and Tsinghua University. References and Notes (1) Liu, B. X.; Johnson, W. L.; Nicolet, M. A.; Lau, S. S. Appl. Phys. Lett. 1983, 42, 45. (2) Schwarz, R. B.; Johnson, W. L. Phys. ReV. Lett. 1983, 51, 415. (3) Koch, C. C.; Cavin, O. B.; McKamey, C. G.; Scarbrough, J. O. Appl. Phys. Lett. 1983, 43, 1017. (4) Liu, B. X.; Lai, W. S.; Zhang, Q. Mater. Sci. Eng., R 2000, 29, 1. (5) de Boer, F. R.; Boom, R.; Mattens, W. C. M.; Miedema, A. R.; Niessen, A. K. Cohesion in Metals: Transition Metal Alloys; NorthHolland: Amsterdam, The Netherlands, 1989. (6) Li, J. H.; Kong, L. T.; Liu, B. X. J. Phys. Chem. B 2004, 108, 16071. (7) Gong, H. R.; Kong, L. T.; Lai, W. S.; Liu, B. X. Phys. ReV. B 2002, 66, 104204. (8) Mura, P.; Demontis, P.; Suffritti, G. B. Phys. ReV. B 1994, 50, 2850. (9) Guillermet, F. A. J. Alloys Compd. 1995, 217, 69.
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