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Study on the solid solubility extension of Mo in Cu


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Acta Materialia xxx (2008) xxx–xxx www.elsevier.com/locate/actamat

Study on the solid solubility extension of Mo in Cu by mechanical alloying Cu with amorphous Cr(Mo)
Shengqi Xi a,*, Kesheng Zuo b, Xiaogang Li a, Guang Ran a, Jingen Zhou a
a

State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China b College of Earth Science and Land Resources, Chang’an University, Xi’an 710023, China Received 19 April 2008; received in revised form 8 August 2008; accepted 9 August 2008

Abstract This paper presents the extension of the solid solubility of Mo in Cu by a mechanical alloying technique. Two binary systems, Cu– 10 wt.% Mo and Cr–50 wt.% Mo, and one ternary system, Cu–20 wt.% Cr(Mo), are investigated. The solid solubility of Mo in Cu has been shown to be less than 4.3 at.% when the Cu–Mo system is mechanically alloyed, whereas when the Cr–Mo system is mechanically alloyed all of Mo dissolves into Cr, forming an amorphous Cr(Mo). Similarly, all of 10 wt.% Mo dissolve into Cu when Cu–20 wt.% amorphous Cr(Mo) is mechanically alloyed. Based on Miedema’s model, the Gibbs free-energy changes in these three alloy systems during the formation of solid solutions are calculated to be positive, which means that thermodynamic barriers exist for the formation of these three alloy systems in solid solution states. The mechanism of solid solubility extension in these mechanical alloyed systems is discussed. The conclusion is that the extension of solid solubility is favoured by adding a third element, such as Cr, to the Cu–Mo system. ? 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Mechanical alloying; Solid solubility extension; Copper alloys; Interface di?usion; Amorphous Cr(Mo) alloy

1. Introduction Copper and copper alloys are widely used in engineering because of their excellent electrical and thermal conductivities, outstanding resistance to corrosion, easy fabrication, and good strength and fatigue resistance [1]. In many applications, such as the marine, automotive and electronic industries, copper and copper alloys are required to have higher strength as well as good electrical and thermal conductivities. Many approaches, such as solid solution strengthening, precipitation strengthening and composite strengthening, have been employed to improve the properties of copper alloys. In general, the electrical conductivity would decrease when alloying elements are introduced into copper as the solid solution strengthening mechanism. Strengthening copper with ceramic particles, e.g. Al2O3

*

Corresponding author. Tel.: +86 29 82668614; fax: +86 29 82663453. E-mail address: xishq@mail.xjtu.edu.cn (S. Xi).

and SiC, is also unfavorable to electrical conductivity because they are insulators [2]. Compared to the above two methods, precipitation strengthening is more e?ective, in which the supersaturated alloying elements (solute atom), which have little or no solubility in copper at equilibrium, will form precipitates in the copper matrix. The supersaturation state of solute atoms in many alloy systems can be achieved by non-equilibrium processing methods, such as rapid solidi?cation processing from the liquid state (RSP), mechanical alloying solid elements (MA), vapor deposition, laser processing, sputtering and ion beam mixing [3]. In all of these non-equilibrium processing methods, RSP and MA are often used to obtain bulk supersaturated solid solutions for practical engineering applications. RSP includes transformation from a liquid state to a solid state. Only when quenched under the equilibrium temperature T0, at which the solid and liquid phases have the same free energy for a given composition, can a supersaturated solid solution be obtained by RSP [4–6]. To prevent the equilibrium phases being formed

1359-6454/$34.00 ? 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.08.013

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by full di?usion during RSP, the liquid should be cooled at a rate as high as 105–106 K s?1, which could be achieved by melt spinning. Using this method, however, only a thin strip of material can be obtained. MA, on the other hand, is a solid-state process. As a non-equilibrium process, not only amorphous alloys, metastable phases and quasi-crystals but also extended solid solution and nanocrystalline materials can be synthesized by MA [7–9]. The extension of solid solubility beyond the equilibrium values has been reported for a number of alloy systems, including many metallic systems and a few ceramic systems [10–15]. Since the maximum deviation from the equilibrium achievable by MA is higher than that by RSP for a given alloy system [16,17], it is expected that MA can achieve a larger solid solubility extension than RSP. It has been shown, for example, that the solid solubility extension achieved by MA is much higher than that achieved by other methods, such as RSP, evaporation and sputtering, for the Fe–Cu system [18]. In Cu-based binary alloys, the extended solubility limits of di?erent solute elements in copper achieved by MA have been reported and compared. Two important factors, atomic radius and electronegativeity, have been identi?ed as having a strong in?uence on the extended solubility limit during MA [18]. In all cases, the solid solubility limit was considerably increased by MA, but the di?erence in the atomic size between the solute atom and the copper should be within 15%, as suggested by Hume-Rothery et al. for solid solution formation [19]. Girgis [20] presented a modi?ed Dark–Gurryele (electronegativity vs. atomic size) plot for a mechanically alloyed copper-based powder mixture, and pointed out that elements that falls into the ellipse of drawn with ±15% atomic size and ±0.4 U electronegativity would exhibit high solid solubility. However, not all experiments follow this rule, nor does it particularly apply to solid solubility extension by MA. According to this role, Mo should have a large solubility in Cu, but recent reports have shown that dissolving Mo in Cu by MA is rather dif?cult [21,22]. Another example is Ag, which does not satisfy with the rule, but can form a complete solid solution in Cu by MA [23,24]. With respect to the thermodynamic driving force, an alloy system with a negative heat of mixing, i.e. a miscible system, would be easily alloyed by MA as a solid-state process. However, the formation of supersaturated solid solutions by MA in some alloy systems, such as Cu–Fe and Cu–Co [25,26], with positive heats of mixing has also been reported. It is more noteworthy that supersaturated solid solution is formed by MA in liquid- and solid-immiscible systems than in only solid-immiscible systems. The mechanism responsible for the enhanced solid solubility in alloy systems with positive heat of mixing is not yet clear. Although nanocrystalline structures are always produced via mechanical alloyed powders with extra energies stored at the interfaces of the nanocrystalline materials, it is doubtful whether these interfacial energies are su?cient to serve as the thermodynamic driving force to form the

supersaturated solid solution in liquid-immiscible alloy systems. In this paper, the solid solubility of two binary alloys – one a Cu–Mo alloy that is both liquid- and solid-immiscible and the other a Cr–Mo alloy this is only solid-immiscible – was studied. Since the solid solubility of Mo in Cu by MA was expected to be very low, the third element, Cr, was added to extend the solid solubility of Mo in Cu during MA in the present study. Mechanically alloyed Cr–Mo alloy was ?rst studied and an amorphous Cr(Mo) alloy was found to be formed by MA. The mechanical alloyed amorphous Cr(Mo) alloy was then mechanically alloyed with Cu to investigate whether Mo could dissolve in the Cu matrix, thus extending the solid solubility of Mo in Cu. 2. Experiment details The three raw powder materials of Cu, Mo and Cr used in this study are speci?ed in Table 1. All of the milling operation was carried out with the designed powder mixtures using a self-made attritor in an argon atmosphere at a speed of 300 rpm. Hardened steel balls were used in the milling, which have a weight ratio of ball-to-powder of 20. The mixture of 10 wt.% Mo and 90 wt.% Cu was milled for di?erent milling times from 5 to 50 h, while the attritor was cooled by water at the ambient temperature. For Cr– Mo binary alloy, the mixture with 50 wt.% Mo was milled at –30 °C for 6, 12 and 24 h, respectively. As for the Cu– 10 wt.% Cr–10 wt.% Mo ternary system, two di?erent mixtures were milled at –30 °C for 36 h. One was a mixture of 80 wt.% Cu powder with 20 wt.% amorphous Cr(Mo) powder synthesized by mechanical alloying Cr–50 wt.% Mo for 24 h. The other was a mixture of 80 wt.% Cu powder, 10 wt.% Cr powder and 10 wt.% Mo powder. The powder mixtures obtained by milling were analyzed with a PHILIPS X’pert pro X-ray di?ractometer, using Cu Ka radiation (k = 0.15406 nm) and a graphite crystal monochromator. The phase evolutions in these mixtures during mechanical alloying were characterized by their Xray di?raction patterns. Based on the X-ray di?raction spectra, the interplanar spacing d, grain size L and solid solution limit were calculated as follows. The interplanar spacing d was calculated in terms of Bragg’s law
Table 1 Raw Materials Elements Cu Mo Purity (%) P99.7 P99.9 Powder size (lm) <150 <100 Produced by Shanpu Chemical Engineering Ltd., Shanghai, China Shuangqiao Chemical Engineering Factory, Beijing, China Shanpu Chemical Engineering Ltd., Shanghai, China

Cr

P99.7

<150

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k ? 2d hkl sinh where k is the wavelength of the X-ray beam (= 0.15406 nm), dhkl is the interplanar spacing for the plane with Miller indices hkl and h is the di?raction angle. In general, the grain size is determined by measuring the full-width at half-maximum intensity of the Bragg di?raction peak using the Scherrer formula B cos h ? 0:9k=L where L is the crystallite size, k is the wavelength of Xradiation, B is the peak width, which is in?uenced by the particle size, and h is the Bragg angle. In this equation it is assumed that XRD peaks are broadened only due to the small particle size in material, but in fact there is a large lattice strain in the milled powder, which also contributes to the peak broadening. In consideration of this factor, the following modi?ed equation was used to calculate the grain size in our experiment [27] B cos h ? 0:9k=L ? 4g sin h where g represents the strain. According to this equation, when Bcosh is plotted against 4sinh, a straight line is obtained with slope g and intercept 0.9k/L. Using this formula, not only grain size L but also lattice strain g can be calculated. The solid solubility of Mo in Cu by MA is expected to be very low. The Vegard formula given below was used to estimate the solid solubility of the milled powder [28]. ?1 ? x?a1 ? xa2 ? a where a1 and a2 are the lattice parameter of the pure solvent element and solute element, respectively, a is the lattice parameter of solution alloy and x is the solid solubility. Using this equation, it is assumed that both solvent and solute elements have a face-centred cubic crystal structure with coordination number 12, and the relationship between lattice parameter, a, and atom radius of element, r, is a=4r/31/2. In addition, the morphologies of the milled powders were examined using a Hitachi S400 scanning electron microscope (SEM), and the energy-dispersive X-ray spectra of the milled powder were obtained simultaneously by this SEM equipped with energy-dispersive X-ray spectrum analyzer (EDXA). The chemical composition of the milled powder was analyzed using an S4 Pioneer of X-ray ?uorescence analysis (XRF) instrument.

DGS ? DH S ? RT ?C A ln C A ? C B ln C B ? m where CA and CB are the atomic concentrations of elements A and B in solid solution, respectively, and CA + CB = 1. R is the universal gas constant. T is the temperature at which a solid solution is formed by mechanical alloying, which in this case takes the value of T=300 K. DH S is the enthalpy of mixing, which comprises three items m as shown below [29]: DH S ? DH C ? DH E ? DH S m where, DHC is the chemical contribution, which is the same for liquid and solid solutions, DHE represents the elastic mismatch energy in the solid solutions and DHS represents the lattice stability energy. The three terms in the expression are determined as follows. The full expression for calculating the ?rst item, DHC, for binary A–B alloy was introduced by Miedema [30] as   2=3 2=3 2Pf ?C s ? C A V A ? C B V B DH C ? ? ??1=3 ? ??1=3 nA ? nB ws ws ! Q R 2 ? 1=3 2 ? ??DU ? ? ?Dnws ? ? P P assuming that H solin B ? n A
2=3 P ?V A ? ?1=3 ?1=3

?nA ? ws

? ?nB ? ws

?

o. 2 !

Q R ? ??DU ? ? ?Dn1=3 ?2 ? ws P P
? 2

and H solin A ? n? B P ?V B ? o. ? ? ? A ?1=3 ? nB ?1=3 2 nws ws
2 2=3

? ??DU? ? ?

! Q ? 1=3 ?2 R Dnws ? ; P P

The expression can be simpli?ed as ? ?? ? DH C ? f C S C A H solin B ? C B H solin A A B for solid solution, f ?C s ? ? C S C S ; C S and C S are deterA B A B mined as CS ? A CAV A
2=3 2=3 2=3

CAV A ? CBV B

and

CS ? B

CBV B
2=3

2=3 2=3

CAV A ? CBV B

3. Thermodynamic analyses for the formation of Cu-based solid solution alloys 3.1. Binary Cu–Mo and Cu–Cr solid solution alloys Forming an disordering A(B) solid solution from a mixture of pure elements A and B, the free-energy change can be calculated as follows when the original pure elements are taken as the standard state

where VA and VB are the molar volumes of atoms A and B, respectively; U* is the work function of constituent elements; nws is the electron density; and P, Q and R are constants related to constituent elements. For transition group elements, P=14.1 kJ V?2 cm?1, Q=132.54 kJ V?1, and R/P takes zero. The second item, DHE, i.e. elastic mismatch energy in solid solution, is determined by the following formula [31] DH E ? C A C B ?C A DEA in B ? C B DEB in A ?

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where DEA in B is the elastic mismatch energy caused by element A dissolved in element B, and the same is for DEB in A. They can be calculated as DEA in B ? DEB in A ? 2K A uB ?V B ? V A ? 3K A V B ? 4uB V A
2

and
2

2K B uA ?V A ? V B ? 3K B V A ? 4uA V B

where K and u are the elastic modulous and shear modulous per unit volume for relevant constituent elements, respectively. The third item, DHS, i.e. the structure contribution, related to the number of valence electrons per atom Z, is a small positive value and can be neglected in the estimation. Another possible state for powder mixture during mechanical alloying may be amorphous. For an alloy at this state, both the elastic energy due to size mismatch and the structural stability can be neglected. In such a state, the mixing enthalpy, DHamorphous, can be determined by the following formula [32] DH amorphous ? DH C ? aT fuse where T fuse ? C A T mA ? C B T mB ; a ? 3:5 J mol?1 K?1

calculated results for these two alloy systems are shown in Figs. 1 and 2, respectively. In both the Cu–Mo and Cr–Mo alloy systems, the free-energy changes for forming either solid solution or amorphous are positive, which indicates that there are no driving forces with respect to the thermodynamic conditions for both systems to form a solid solution or amorphous phase. Additional energy, such as input during mechanical alloying, should be provided to overcome the thermodynamic barriers for these two systems to form a solid solution or amorphous alloy from the element mixtures. In both the Cu–Mo and Cr–Mo alloy systems, the freeenergy change for forming an amorphous alloy is larger

For Cu–Mo alloy system, TmCu = 1357.6 K, TmMo=2890.2 K. From the above analysis, the free-energy changes (DG) for forming a disordered solid solution and an amorphous alloy from the mixture of pure elements A and B are expressed in terms of the constitute elements CA and CB. Selecting suitable parameters in the above formulas for the A–B alloy system, one can obtain the relationship between DG and CA and/or CB. To verify the above expressions, the mixing enthalpies and elastic mismatch energies for the Ni–W alloy system are calculated using the corresponding parameters, and the following results are obtained: H solin B ? ?14:2kJ mol?1 ; H solin A ??11:1 A B kJ mol?1 ; DEA in B = 53.5 kJ mol?1 and DEB in A = 62.5 kJ mol?1, which are consistent with the results reported in the literature [33]. This indicates that the above expressions are valid and can be used for the calculation of free-energy change. The required parameters for calculating the free-energy changes of both the Cu–Mo and Cr–Mo alloy systems are given in Table 2. All of the energy calculations are assumed at 300 K, because the mechanical alloying is conducted at room temperature and is cooled by water. The
Table 2 Parameters for free-energy changes calculation [30,33,34] Elements Cu Mo Cr P kJ V?2 cm?1 14.1 14.1 14.1 Q kJ V?1 132.54 132.54 132.54 n1/3cm?1 1.47 1.77 1.73 U* V 4.45 4.65 4.65

Fig. 1. The calculated Gibbs free-energy change of Cu–Mo binary system.

Fig. 2. The calculated Gibbs free-energy change of Cr–Mo binary system.

K 1010N m?2 13.7 26.12 16.02

u 1010N m?2 4.8 12.56 11.53

V cm3 mol?1 7.1 9.4 7.12

Tm K 1357.6 2890.2 2130.0

T/K 300 300 300

R/P 0 0 0

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than that for forming a solid solution alloy for the same composition. It can be expected that the formation of a solid solution is easier than that of an amorphous alloy in these two alloy systems. The maximum Gibbs free-energy change in the Cu–Mo alloy system is about 18 kJ mol?1, whereas that in the Cr– Mo alloy system is less than 5 kJ mol?1. These two di?erent alloy systems will exhibit di?erent behavior during mechanical alloying, because of the di?erence in the thermodynamic energy needed to form a solid solution. This is discussed further in the following section. 3.2. Ternary Cu–Cr–Mo solid solution alloy In a ternary alloy system, even though there is only one more constituent element than in a binary alloy system, there is much great di?culty in calculating the Gibbs free-energy change. Only a few articles have discussed the Gibbs free-energy change of ternary alloy systems [35,36]. To calculate the Gibbs free-energy change in the Cu– Cr–Mo ternary alloy system, the mixing enthalpies of the binary alloy system are ?rst calculated based on the aforementioned Miedema model, then the mixing enthalpies of the ternary alloy system are obtained by interpolation methods. Taking xA, xB and xC as the atomic concentrations of constituent elements A, B and C, respectively, the following expression is obtained [35]: xB xC DH ? DH AB ?xA ; 1 ? xA ? ? DH AC ?xA ; 1 ? xA ? 1 ? xA 1 ? xA   xB xC 2 ; ? ?xB ? xC ? DH BC xB ? xC xB ? xC Fig. 3 presents the calculated Gibbs free-energy change for forming (a) a solid solution and (b) an amorphous alloy, and (c) the di?erence between the two. It can be seen that the free-energy changes in forming either a solid solution or amorphous alloy are positive. In this ternary alloy system, there are no thermodynamic driving forces to form a solid solution or an amorphous alloy. As in the binary Cu–Mo alloy system, additional energy is required to overcome the thermodynamic energy barrier to form a solid solution or amorphous alloy in the Cu–Cr–Mo ternary alloy system. As shown in Fig. 3(c), the Gibbs free-energy change for forming a solid solution is smaller than that for forming an amorphous for the same composition of Cu–Cr–Mo alloy. 4. Experimental results 4.1. Mechanical alloying of binary Cu–10 wt.% Mo alloy The XRD patterns of Cu–10 wt.% Mo powders are shown in Fig. 4. It can be seen that the intensities of all peaks decrease with milling time while the width at the half height of every peak increases. These trends are due to the decrease in crystallite sizes of Cu and Mo during the mill-

ing process. The crystallite sizes of Cu and Mo were estimated using the modi?ed Scherrer formula and are shown as a function of milling time in Fig. 5. With prolonged milling time, the Cu and Mo crystallite sizes decrease, and after 50 h both have reached about 10 nm. It is noticeable that the grain size in all the powders has reduced to 10–15 nm, resulting in a nanocrystalline structural material. According to the Bragg’s law, the interplanar spacing values (d) of both Cu and Mo during mechanical alloying were calculated, and the variations of the interplanar spacing d with milling time are shown in Fig. 6. With increasing milling time, the interplanar spacing d of Mo decreases slightly, but that of Cu increases signi?cantly. For fcc structures, the relationship between lattice parameter?? a p and interplanar spacing d(1 1 1) is given by d ?1 1 1? ? 33 a. Therefore, the lattice parameter a increases when the interplanar spacing d of Cu increases with milling time. It can be inferred that part of Mo has dissolved into Cu. To estimate the solubility of Mo in Cu using the Vegard formula, the d values of planar (1 1 1) in fcc Cu and Mo should be given. Since the structure of Mo is bcc, ?rst, its crystal lattice was transformed into an fcc structure, then, according to the relationship between d and atom radii r, q?? d ?1 1 1? ? 8r, the d(1 1 1) of Mo was calculated to be 3 0.22258 nm. The d value of planar (1 1 1) in fcc Cu is 0.20865 nm, and the d value of Cu(Mo) solution in the powder milled for 50 h is 0.20925 nm. According to the Vegard formula, the solid solubility of Mo in Cu after milling for 50 h has achieved 4.3 at.% (i.e. about 6.4 wt.%). The morphology of the milled powder and the distributions of the three elements, Cu, Mo and Fe (impurity), along one scanning line are shown in Fig. 7, which was obtained by TEM and EDXA. During milling, the surfaces of the ball and vial are easily covered with a thin ?lm of Cu, such that the content of the impurity Fe element was less than 5 wt.% (see Table 3, the chemical composition analyzed by XRF). On the scale of one particle size, the spectra of Mo and Cu are uniform and almost compatible with each other. There are no free and coarse Mo particles in the milled powder. All of Mo is dispersed uniformly into Cu matrix, although not all of the Mo element dissolves into the Cu matrix. 4.2. Mechanical alloying of binary Cr–50 wt.% Mo alloy The XRD patterns of Cr–50 wt.% Mo mixed powders milled for 6, 12 and 24 h are shown in Fig. 8. It can be seen that, after milling for only 6 h, fcc Cr is present in the mixed powders. With prolonged milling time up to 12 h, the intensities of all peaks on the XRD pattern have decreased and their widths have increased. The peak position of fcc Cr shifts from 43.312° (milled 6 h) to 43.115° (milled 12 h). After milling for 24 h, all other peaks have disappeared except for a broad and di?used peak at 43.1°. The results reported above demonstrate that the Cr– 50 wt.% Mo powder mix has experienced a series of phase

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Fig. 3. The free-energy changes of Cu–Cr–Mo ternary alloy.

changes during milling. Firstly, after milling for a short time, the crystal structure of Cr has transformed from bcc into fcc. It has been reported that others elements, such

as Nb, Zr and Ti, exhibit similar behavior during milling [37–39]. Thus, as milling time is prolonged, Mo dissolves into fcc and bcc Cr, with bcc Cr continuing to transform

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Fig. 4. The XRD pattern of Cu–10 wt.% Mo mixing powder milled for di?erent times.

into fcc Cr. Eventually, all of the fcc Cr has transformed into amorphous Cr(Mo). 4.3. Mechanical alloying of ternary Cu–10 wt.% Cr–10 wt.% Mo The XRD patterns of the 80 wt.% Cu–20 wt.% Cr(Mo) powder mix milled for 35 h and the 80 wt.% Cu–10 wt.% Cr–10 wt.% Mo powder mix milled for 35 h are shown in Fig. 9, as curves (a) and (b), respectively. On curve (a), all of the Mo element peaks have disappeared, which means that Mo has dissolved into the Cu matrix after the 80 wt.% Cu–20 wt.% Cr(Mo) powder mix has been milled for 35 h, and hence the Cu peak positions shifts to a slightly smaller angle. Unlike on curve (a), one peak of Mo exists on curve (b), albeit with a weak intensity. This means that Mo has not totally dissolved into Cu after the 80 wt.% Cu–10 wt.% Cr–10 wt.% Mo powder mix was milled for 35 h. Interestingly, there are no peaks of Cr element on either curve (a) or curve (b), which indicates that, in both powder mixes, the Cr has totally dissolved into the Cu. Furthermore, not only the peaks of Cu element but also the peaks of Cu2O compound appear on the X-ray pattern of curve (a). The oxygen in the Cu2O compound is suspected to be associated with amorphous Cr(Mo). Because the amorphous Cr(Mo) as synthesized by mechanical alloying is highly reactive, the oxygen can be easily adsorbed on the surfaces of amorphous Cr(Mo) particles before these particles are brought into the milling jar. 5. Discussion The solid solubility of an element depends on its atomic size and electronegativity, etc. The atomic radius, crystal

Fig. 5. The change in crystalline size with milling time.

Fig. 6. The change in interplanar spacing d with milling time.

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Fig. 7. (a) The morphology of Cu–10 wt.% Mo powder milled for 35 h; (b) the distributions of the three elements, Cu, Mo and Fe.

Table 3 Chemical composition of milled powders (mass%) Milled powder Elements Cu Cu–Mo mixed powder milled 24 h Cu–Cr(Mo) amorphous milled 36 87.35 75.54 Mo 7.535 5.78 Cr – 7.34 Fe 1.925 3.36 C 1.83 1.52 O 1.26 6.46

structure, electronegativity and valence of Cu, Mo and Cr elements are listed in Table 4. From the table, it can be seen that, in the Cu–Mo alloy system, the di?erence in electronegativity is small and the di?erence in the atomic sizes of Cu and Mo is 6.48%, which is below the critical value of 14–15%. According to Hume-Rothery’s empirical rules [19], this is favorable for the formation of substitutional solid solutions in the Cu–Mo alloy system. However, the crystal structures of Cu and Mo are di?erent, so that it is unfavorable for the Cu–Mo alloy system to form a solid solution. It is expected that forming a solid solution with

unlimited solubility is in fact impossible in the Cu–Mo alloy system. On the other hand, the free-energy change calculated for the Cu–Mo alloy system to form a solid solution is positive across the entire range of Mo content, which means that there is no thermodynamic driving force for the system to form a solid solution. As is well known, Cu is immiscible with Mo in an equilibrium state [41,42]. Many non-equilibrium processing technologies, such as RSP, ion beam mixing, vapor deposition and MA, have been applied to extend the limit to which Mo dissolves into Cu. According to the results of the present study, a very limited solid solubility (less than 4.3 at.%) was achieved for Cu–10 wt.% Mo alloy by MA. This result is similar to what was achieved on mechanically alloyed Cu–8 at.% Mo for 100 h by Aguilar et al. [22]. However, by ion beam mixing, Zhao et al. [43] gained a Cu–15 at.% Mo solid solution and Chen et al. [44] gained a Cu–34 at.% Mo solid solution, in which the Mo solubility was increased dramatically. Therefore, the solid solubility of binary alloys depends not only on their thermodynamic condition, but also on their dynamics of alloying in a non-equilibrium

Fig. 8. The XRD patterns of Cr–50 wt.% Mo powder milled for di?erent times.

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Fig. 9. The XRD patterns of Cu–Cr–Mo powder mix milled for 35 h.

Table 4 Some physical parameters of Cu and Mo [40] Elements Cu Mo Atomic radius/nm 0.1278 0.1363 Crystal structure fcc bcc Electronegativity 1.9 1.8

process. As a result, the di?usion of atoms should be considered during alloying. During the early stage of MA, Cu powder particles may experience severe plastic deformation, resulting in repeated cold working, shearing and fracturing, and rewelding. This process can lead to the formation of lamellar structures of alternate layers of Cu; because Mo is hard and brittle, the Mo powder particles can be broken and embedded in the lamellar Cu matrix. With continuous milling the interlamellar spacing is decreased, and the compositional inhomogeneity can be reduced in a mixed powder, as show in Fig. 7. As the milling time is prolonged, the crystalline sizes of both Cu and Mo decrease (see Fig. 5), and a mixed Cu and Mo nanocrystalline structure is formed uniformly in a mechanically alloyed powder. Meanwhile, interdi?usion may take place across the interfaces due to the reduced diffusion distances and increased di?usivity, as aided by the creation of lattice defects and the increase in temperature during MA. When considering interdi?usion in a mixed Cu and Mo nanocrystalline structure, it can be assumed that the average Mo content has reached a nominal composition, which in the present case is about 10 wt.% Mo. Nordlund and Averback [45] found that the di?usion coe?cient of atoms with a high melting temperature is smaller than those of atoms with lower melting points. Since the melting temperature of Mo is much higher than that of Cu, as shown in Table 2, the di?usion coe?cient of Mo in Cu should be

much smaller than that of Cu in Mo. Veltel et al. [46] suggested that the energy stored in the grain boundaries of nanocrystalline materials is the driving force for the formation of solid solution. Free-energy increases due to the creation of new interfaces as a result of reduction in crystallite size. The free-energy change is estimated by using the formula DGc = c(A/V)m [47,48], where c is the grain boundary energy, A/V is the surface/volume ratio and m is the molar volume. In a mixed Cu and Mo nanocrystalline structure it is easy for Cu to dissolve into Mo to form an interface layer because the di?usion coe?cient of Cu in Mo is larger than that of Mo in Cu. However, as the maximum energy stored in nanograin boundaries during milling is estimated to be about 6.6 kJ mol?1 when the minimum crystallite size of Cu is about 2 nm using the formula DGc = c(A/V)m, the Mo content in this interface layer, according to Fig. 1, would not be less than 90 at.%. To consume Mo thoroughly by means of Cu dissolving into Mo, i.e. to decrease the Mo content from 100% to the nominal average compoΔG ΔGmax Δ Gnom ΔGb

Mo (B)

C in Mo C in B

Cc

C nom

C in Cu C in A

Cu (A)

Fig. 10. Schematic plot of the free-energy change with element composition in binary solid solution.

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sition, Cnom, as shown schematically in Fig. 10, the Mo content would pass a critical value in the Cu–Mo system, Cc. At this concentration the free-energy change is a maximum. Since the maximum free-energy change in this alloy system, DGmax, is about 18 kJ mol?1, which is much higher than the energy stored in the interface layer, DGb, the Mo content in the interface layer would not be decreased. Furthermore, there is also residual Mo in the mixed powder during the milling, as shown in Fig. 4. In the mixed Cu–Mo nanostructure, brought about by di?usion of Mo into Cu, the Mo content in the Cu layer, Cin Cu, according to Fig. 1, would not exceed 5 at.% when the energy stored in nanocrystalline Cu is lower than 6 kJ mol?1. This is consistent with the present results, which show that the solubility of Mo in Cu during MA is less than 4.3 at.%. As shown in Fig. 10, the Mo content in Cu would not reach the nominal composition Cnom as much more energy than DGb would need to be provided to increase the Mo in the Cu. In the Cr–Mo alloy system, during MA, a powder with mixed nanaocrystalline structures of Cr and Mo can be formed due to severe plastic deformation in the same way as occurred in the Cu–Mo alloy system. Interdi?usions between nanocrystalline Cr and Mo would also take place. In the Cr–Mo alloy system, the free-energy change for forming solid solution in the whole composition range is positive, as in the Cu–Mo alloy system, but the maximum free-energy change, DGmax, of the Cr–Mo alloy system is about 5 kJ mol?1 (see Fig. 2), which is slightly less than the energy stored in nanograin boundaries during milling, DGb, which is about 6.8 kJ mol?1, as estimated when the minimum crystallite size of Cr is about 2 nm using the formula DGc = c(A/V)m. In addition, as the di?erence between the melting points of Cr and Mo is much smaller than that between Cu and Mo, the di?erence between the di?usion coe?cients of Cr and Mo should likewise be small. Due to these two reasons, the interdi?usion behavior of the Cr–Mo alloy system is di?erent from that of Cu–Mo alloy during MA. In a mixed nanocrystalline structure of Cr and Mo, the di?usion of Cr into Mo could cause the Mo content to decrease to a nominal average composition, and vice versa. The thermodynamic barrier would be overcome by the additional energy provided by MA during the milling. In the Cr–Mo alloy system, not only solid solution but also amorphous alloy could form during MA. Amorphous alloys can be produced by mechanical alloying in many alloy systems, but most of these alloy systems have a negative heat of mixing. In the Cr–Mo alloy system, with a positive heat of mixing, the free-energy change for forming amorphous alloy is about 6 kJ mol?1 when the Mo content is about 50 wt.%, as shown in Fig. 2. As previously estimated, the energy stored in nanograin boundaries during the milling is 6.8 kJ mol?1, which is slightly higher than that needed for forming amorphous alloy in the Cr–Mo alloy system. With respect to thermodynamics, it is quite

possible to form amorphous Cr(Mo) alloy during the milling. Formation of amorphous alloy is dependent not only on the driving force derived from the thermodynamic free energy, but also on the kinetic coe?cients. There are many crystalline defects, such as vacancies and dislocations, induced in milling powders. Martin and co-workers [49– 51] developed dynamical phase changes as triggered by the coupling of point defect ?uxes to solute ?uxes, which could explain the formation of Cr(Mo) amorphous alloy during milling, but further research is still needed. According to the calculations of this study, in the Cu– 10 wt.% Cr–10 wt.% Mo ternary alloy system, the freeenergy change for forming a solid solution is increased compared to the Cu–10 wt.% Mo alloy system. Adding Cr into the Cu–Mo alloy system would not reduce the thermodynamic barrier for forming solid solution. However, the present results show that it is easy to form amorphous Cr(Mo) when Cr and Mo powders are milled together. Amorphous Cr(Mo) possesses higher energy and provides more di?usion paths, which promotes Cr and Mo dissolving into the Cu matrix. In Cu and amorphous Cr(Mo) mixture, the amorphous Cr(Mo) possesses higher energy and more di?usion paths. Therefore, it is not necessary for Cu to di?use into Mo in order to consume pure Mo, as occurs in Cu–Mo alloy during MA, to form an interface layer. As the Mo in Cr(Mo) possesses higher energy, it is energetically preferred for Mo to di?use into Cu rather than the other way around, as happened in the Cu–Mo binary system, resulting in the total dissolution of Mo (indicated by curve (a) in Fig. 9) when Cu and amorphous Cr(Mo) are milled. When pure Cu, Mo and Cr powders were milled, three di?erent contacting interfaces may form during the early stage, i.e. the Cu–Cr, Cu–Mo and Cr–Mo interfaces. As Cr and Mo can easily to form amorphous Cr(Mo) during milling, a Cu-amorphous Cr(Mo) contact interface would form in the powder mix as the milling continued. Finally, the Mo atoms in Cr(Mo) would dissolve into Cu, as occurred in milling the Cu–Cr(Mo) mixed powder. On the other hand, the Mo in the Cu–Mo mixed region would not dissolve totally, so that there would still be some Mo left in the ?nal powder, as shown on curve (b) in Fig. 9. 6. Conclusions Mechanical alloying of the Cu–Mo, Cr–Mo and Cu– Cr(Mo) systems was conducted to extend the solid solubility of Mo in Cu by adding amorphous Cr(Mo) during MA. Based on the Miedema’s model, the Gibbs free-energy change in these three alloy systems from mixed elements to form a solid solution and an amorphous phase have been calculated. The Gibb’s free-energy changes in these three alloys are all positive. Therefore there are no purely thermodynamic driving forces for all of these three alloys to form a solid solution or an amorphous phase. Additional energy as provided by MA is needed for this transformation to occur.

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The maximum free-energy change in the Cr–Mo alloy system, which represents the thermodynamic barrier for forming solid solution, is about 5 kJ mol?1. This is smaller than that of Cu–Mo alloy system, which is 18 kJ mol?1. The additional energy, which is stored in the grain boundaries of nanocrystalline materials during MA, would be the driving force to overcome this thermodynamic barrier for the formation of a solid solution. By mechanically alloying the Cu–10 wt.% Mo powder mix, the solid solubility of Mo in Cu is less than 4.3 at.%, most of Mo element being uniformly dispersed in the Cu matrix, but for Cr–50 wt.% Mo alloy, an amorphous Cr(Mo) alloy is synthesized and all of Mo dissolves into Cr. These results could be attributed to the di?erence in the thermodynamic barrier of phase transformation and their interdi?usion coe?cients during MA. Using this mechanical alloyed amorphous Cr(Mo) powder, all of the 10 wt.% Mo dissolves into Cu during mechanical alloying Cu–20 wt.% Cr(Mo). Although the free-energy change for forming a solid solution is not decreased by adding Cr to the Cu–Mo alloy system, the interdi?usion condition of Cu–Cr–Mo is di?erent from that of Cu–Mo. The formation of a solid solution and the extension of solid solubility between binary alloy elements is improved when a third element such as Cr is added to the Cu–Mo system. Acknowledgements The authors would like to acknowledge the ?nancial support of a Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050698018). This research is also supported by the Program for New Century Excellent Talents in University (No. NCET-05-0839) and by the Key Project of Chinese Ministry of Education (No. 105159). The authors also thank Prof. Liu from Carleton University and Dr.Wu and Dr.Chen from the National Research Council Canada, respectively, for their valuable discussions. References
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Please cite this article in press as: Xi S et al., Study on the solid solubility extension of Mo in Cu ..., Acta Mater (2008), doi:10.1016/ j.actamat.2008.08.013


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