National Key Research and Development Program of China. 2018YFB0703904 National Key Research and Development Program of China. 2017YFE0302600 National Natural Science Foundation of China. 51471114 National Natural Science Foundation of China. 51171128
Materials based on binary immiscible metal systems are widely used in aerospace, nuclear fusion engineering, electronic packaging, anti-armor weapons and other fields. However, due to the positive formation heat and the large differences in the properties of the component, the direct alloying of binary immiscible metals and the preparation of the corresponding materials are very difficult. Varieties of methods have been developed for direct alloying of binary immiscible metals at home and abroad, and the thermodynamic and diffusion mechanism of these methods have been studied. In this review, firstly the principle and thermodynamic mechanism of mechanical alloying, physical vapor deposition and ion beam mixing, as well as their applications in binary immiscible metal powder alloys and nano-multilayer films are reviewed. Then the irradiation damage alloying (IDA) and high-temperature structure induced alloying (HTSIA) methods that are proposed and developed by our group are introduced. Besides, the principle, interfacial microstructure, thermodynamic mechanism, diffusion mechanism and application of these two methods were described in detail. Finally, the development trend of the research on alloying of binary immiscible metals is proposed.
HUANG Yuan, DU Jinlong, WANG Zumin. Progress in Research on the Alloying of Binary Immiscible Metals. Acta Metallurgica Sinica[J], 2020, 56(6): 801-820 DOI:10.11900/0412.1961.2019.00451
大塑性变形(severe plastic deformation，SPD)方法也是一种机械合金化方法。该方法通过在块体材料上施加一个非常高的应变来实现合金化，同时不显著改变试样的原始尺寸并且能够产生优异的晶粒细化效果[30]。目前已经开发的大塑性变形方法主要有：高压扭转(high pressure torsion，HPT)[31,32,33]、累积叠轧(accumulative roll bonding，ARB)[34,35]、等通道转角挤压(equal channel angular extrusion or pressing，ECAE or ECAP)[31,33,36]等。大塑性变形方法实现低固溶度金属相互扩散进而实现合金化的原理和过程如图1所示。
离子束混合[79](ion-beam mixing，IBM)技术是一种亚稳相制备方法，是一种将离子束与薄膜技术结合起来的实现二元互不固溶金属合金化的技术。具体过程为：使用离子束(通常是惰性气体离子)轰击交替沉积的二元互不固溶金属薄膜，轰击过程中离子束与膜中的金属原子碰撞，膜层与膜层之间的原子可以通过这种碰撞实现相互混合，产生扩散的效果。由于离子束的射程设计成与薄膜整体厚度一致，从而在薄膜中形成成分均匀的合金相。由于这种合金相通常为非晶相，薄膜在离子束混合作用下内部实际发生了固态非晶化反应(solid state amorphization reaction，SSAR)，如图3所示。
Fig.11
Variable energy positron annihilation spectroscopy (VEPAS) results of various samples[101] (S is the line shape parameter of Doppler broadening data, SB is the parameter that is normalized to the defect-free S value)(a) S parameter vs positron implantation energy for the pre-annealed pure Mo and the Ag+ implanted Mo
(b) S parameter vs positron implantation energy for the pre-annealed pure Mo and the Mo/Ag laminated samples with a 100 nm thick Ag layer annealed at different temperatures
Fig.12
Cross-section TEM image for the Mo/Ag laminated sample annealed at 800 ℃ for 4 h (a) and the magnified image of the region marked with a white rectangular frame in Fig.12a (b)[101]
Fig.16
HRTEM images of microstructures of theW50Cu50 sintered powder metallurgy materials prepared by milling for 30 h (a) and 40 h (c) and subsequent sintering at 980 ℃ for 3 h, and the corresponding SAED patterns of Figs.16a and c (b, d)[109] (Insets in Figs.16a and c show the EDX results of W50Cu50 sintered powders)
Fig.19
Calculated curves of Gibbs free energy change for the alloying in W-Cu system[109](Einitial—total initial energy of W-Cu system, ΔGalloying—Gibbs energy for the alloying between W and Cu, —Gibbs energy for the formation of W/Cu crystalline phases, —Gibbs energy for the formation of W/Cu amorphous phases)
The preparation of laminar metal matrix composites for immiscible alloy systems was difficult due to the positive formation heat and diffusion difficulty between each other, resulting in no metallurgy combination forming on interfaces. Aiming at this situation, a new irradiation damage alloying method for immiscible and not reacting alloy systems was presented in this work, through irradiation damages were produced by an ion implantation technology in the matrix metal first, and then the metal in the surface layer diffused into the matrix metal through the irradiation damages to form metallurgy combination with the metal. The key of this kind of metallurgy combination is to form amorphous alloy phase in the diffusion layer. By alloying the high-performance Mo/Ag laminar metal matrix composites used in spacecraft were prepared, whose maxium resistance spot welding joint tensile strength reaches 150 MPa, the average 130 MPa. The properties of thees composites exceed the national military standards and the technical requirements specified by astronic users.
AbstractAg50Cu50 alloys are prepared by high energy ball milling at different controlled temperatures, 85 K, 315 K and 453 K, with milling times long enough to reach steady-state. Atom probe field ion microscopy (APFIM) is used to characterize the atomic mixing forced by low temperature milling and to study the nanocomposite materials stabilized by elevated temperature milling. A new method is devised that makes it possible to prepare sharp tips from ball-milled powders. Statistical analysis of the APFIM composition profiles is used to determine the degree of mixing as a function of the length scale. These results are compared with the ones obtained from kinetic Monte Carlo simulations. Cryo-milling results in nearly random mixing of copper and silver, whereas the mixing achieved by milling at 315 K is calculated to be around 70%. 453 K milling results in the decomposition into copper-rich and silver-rich regions at a scale of ≈25 nm.]]>
XiS Q, ZuoK S, LiX G, et al.
Study on the solid solubility extension of Mo in Cu by mechanical alloying Cu with amorphous Cr(Mo)
AbstractThis 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.]]>
Al-AqeeliN, HusseinM A, SuryanarayanaC.
Phase evolution during high energy ball milling of immiscible Nb-Zr alloys
AbstractPure nickel was selected for a detailed investigation of the experimental parameters influencing grain refinement and microstructural evolution during processing by high-pressure torsion (HPT). Samples were examined after HPT using microhardness measurements, transmission electron microscopy and orientation imaging microscopy. Processing by HPT produces a grain size of ~170 nm in pure Ni, and homogeneous and equiaxed microstructures are attained throughout the samples when they are subjected to at least ~5 whole revolutions under applied pressures of at least ~6 GPa. For these conditions, the distributions of grain boundary misorientations are similar in the center and at the periphery of the samples. A simple model is proposed to explain the development of a homogeneous microstructure in HPT.]]>
ValievR.
Nanostructuring of metals by severe plastic deformation for advanced properties
Bulk nanolayered Cu/Nb composites fabricated by accumulative roll bonding (ARB), leading to a nominal layer thickness of 18 nm, were subjected to large shear deformation by high-pressure torsion at room temperature. The evolution of the microstructure was characterized using X-ray diffraction, transmission electron microscopy and atom probe tomography. At shear strains of the crystallographic texture started to change from the one stabilized by ARB, with a Kurdjumov-Sachs orientation relationship and a dominant {1 1 2}(Cu)parallel to{1 1 2}(Nb) interface plane, toward textures unlike the shear texture of monolithic Cu and Nb. At larger strains, exceeding 10, the initial layered structure was progressively replaced by a three-dimensional Cu-Nb nanocomposite. This structure remained stable with respect to grain size, morphology and global texture from strains of similar to 290 to the largest ones used in this study, 5900. The three-dimensional self-organized nanocomposites comprised biconnected Cu-rich and Nb-rich regions, with a remarkably small coexistence length scale, similar to 10 nm. The results are discussed in the context of the effect of severe plastic deformation and strain path on microstructure and texture stability in highly immiscible alloy systems. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd.
WangM, AverbackR S, BellonP, et al.
Chemical mixing and self-organization of Nb precipitates in Cu during severe plastic deformation
Fully dense bulk nanocomposites have been obtained by a novel two-step severe plastic deformation process in the immiscible Fe-Cu system. Elemental micrometer-sized Cu and Fe powders were first mixed in different compositions and subsequently high-pressure-torsion-consolidated and deformed in a two-step deformation process. Scanning electron microscopy, X-ray diffraction and atom probe investigations were performed to study the evolving far-from-equilibrium nanostructures which were observed at all compositions. For lower and higher Cu contents complete solid solutions of Cu in Fe and Fe in Cu, respectively, are obtained. In the near 50% regime a solid solution face-centred cubic and solid solution body-centred cubic nanograined composite has been formed. After an annealing treatment, these solid solutions decompose and form two-phase nanostructured Fe-Cu composites with a high hardness and an enhanced thermal stability. The grain size of the composites retained nanocrystalline up to high annealing temperatures. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd.
QuelennecX, MenandA, Le BretonJ M, et al.
Homogeneous Cu-Fe supersaturated solid solutions prepared by severe plastic deformation
m can be used to characterize the tendency of material strengthening as the strain rate increases. To investigate the impacts of modulation period and interfacial structures upon strain rate sensitivity of nanoscale multilayers, Cu/Ni nanoscale multilayers with different periods (Λ=4 nm, 12 nm, 20 nm) were prepared on Si substrate with e-beam evaporation technologies, while Cu/Nb nanoscale multilayers with different periods (Λ=5 nm, 10 nm, 20 nm) were prepared on Si substrate with magnetron sputtering technologies. Under vacuum conditions, the Cu/Ni nanoscale multilayers of different periods were annealed at 200 and 400 ℃ for 4 h respectively, and the Cu/Nb nanoscale multilayers of different periods were annealed at 200, 400 ℃ and 600 ℃ for 4 h respectively. Microstructures of Cu/Ni and Cu/Nb nanoscale multilayers were characterized with XRD and TEM. Besides, the hardness of nanoscale multilayers was measured by nano-indentation techniques under different loading strain rates (including 0.005, 0.01, 0.05 and 0.2 s-1). The results suggested that strain rate sensitivity was impacted by interfacial structures and grain size. Both increased density of incoherent interfaces and grain size could result in weaker strain rate sensitivity. As the period increases, the density of incoherent interfaces and the grain size of Cu/Ni nanoscale multilayers increased, leading to a decline in the strain rate sensitivity. While for Cu/Nb nano scale multilayers, the density of incoherent interfaces decreased and their grain size was enlarged with longer period, the m value kept unchanged as a result. As the annealing temperature increasing, the strain rate sensitivity of Cu/Ni and Cu/Nb nanoscale multilayers generally tended to decline, which should be ascribed to increased density of incoherent interfaces and grain size in the course of annealing.]]>
The Ag/Cu nanoscaled multilayer films, which had a constant thickness of Ag layer (about 15 nm) and various thicknesses of Cu layer from about 4 to 20 nm, have been deposited by magnetron sputtering technique. The phase composition, microstructure, surface topography and mechanical properties of these films were investigated, respectively. XRD results revealed that both Ag and Cu layers in multilayer films had a polycrystalline fcc structure with preferred growth of (1 1 1) orientation. The crystallite sizes decreased greatly compared with that of pure Ag film. High-resolution TEM analysis indicated that the multilayers exhibited obvious interfaces between Ag and Cu layers and had dense and columnar grain morphology. AFM analysis showed that all the multilayers with various thicknesses of Cu layers were much smoother than their constituent Ag and Cu pure films. As compared to that of pure Ag (1.7 GPa) and Cu (2.1 GPa) films, as well as, the hardness values calculated from the rule-of-mixtures, a remarkable increase of hardness was observed for all the multilayer films. The maximum hardness value of 4.3 GPa was obtained for the multilayer film with about 20 nm Cu layer. The vacuum ball-on-disk tribotest results suggested that the multilayer film with highest hardness showed a slight decrease in friction coefficient and notable increase in wear resistance. Especially, these results about mechanical and tribological properties were discussed as a function of the film microstructure. (C) 2014 Elsevier B.V.
ZhangX, HundleyM F, MalinowskiA, et al.
Microstructure and electronic properties of Cu/Mo multilayers and three-dimensional arrays of nanocrystalline Cu precipitates embedded in a Mo matrix
Based on our previous knowledge on Cu/Nb nanoscale metallic multilayers (NMMs), Cu/W NMMs show a good potential for applications as heat skins in plasma experiments and armors, and it could be expected that the substitution of Nb by W would increase the strength, particularly at high temperatures. To check this hypothesis, Cu/W NMMs with individual layer thicknesses ranging between 5 and 30 nm were deposited by physical vapor deposition, and their mechanical properties were measured by nanoindentation. The results showed that, contrary to Cu/Nb NMMs, the hardness was independent of the layer thickness and decreased rapidly with temperature, especially above 200 degrees C. This behavior was attributed to the growth morphology of the W layers as well as the jagged Cu/W interface, both a consequence of the low W adatom mobility during deposition. Therefore, future efforts on the development of Cu/W multilayers should concentrate on optimization of the W deposition parameters via substrate heating and/or ion assisted deposition to increase the W adatom mobility during deposition. (C) 2014 Elsevier B.V.
WenS P, ZongR L, ZengF, et al.
Evaluating modulus and hardness enhancement in evaporated Cu/W multilayers
AbstractThe microstructure, hardness and elastic modulus of Cu/W multilayers prepared by evaporation deposition were investigated by X-ray diffraction, transmission electron microscopy and nanoindenation. The results show that the multilayers with good modulation structure have asymmetrical interfaces. The W on Cu interfaces are relatively sharp, while the Cu on W interfaces are diffuse, with significant intermixing. The intermixing results in compression of the out-of-plane interplanar spacing of the W layer. The compression increases with decreasing periodicity and leads to modulus enhancement. The hardness values also increase with decreasing periodicity, which is interpreted by the Lehoczky model.]]>
GuoZ Z, SunY, DuanY H, et al.
Structures and properties of Cu/W nanostructured multilayers deposited by sputtering
AbstractIon-beam mixing experiments show that amorphous phases are formed in the Cu70Ta30, Cu65Ta35, Cu60Ta40, and Cu50Ta50 multilayered samples, while a crystalline structure is retained in the Cu75Ta25 sample. These results suggest that the composition limit for forming an amorphous phase is around 30 at.% Ta, which confirms the same value of 30 at.% Ta predicted by recent atomistic modeling. For the metastable crystalline Cu75Ta25 phase, ab initio calculations identify its relatively stable structure to be L12 (fcc type) and determine some associated physical properties, which agree well with those derived from a proven realistic Cu-Ta potential through molecular dynamics simulations. Interestingly, an fcc Cu75Ta25 phase is indeed observed in ion-beam mixing experiments and its lattice constant determined by diffraction analysis matches well with those from theoretical calculations.]]>
GongH R, LiuB X.
Unusual alloying behavior at the equilibrium immiscible Cu-Nb interfaces
Metastable phase formation in the immiscible Cu-Co system studied by thermodynamic, molecular dynamics and ab initio calculations together with ion beam mixing
AbstractRecently, the presence of two Kirkendall planes has been discovered in solid-state diffusion couples in various binary metallic systems in our laboratory, and in this work even three Kirkendall marker planes were found in a couple Ti/TiAl3. The bifurcation and trifurcation of the Kirkendall plane can quantitatively be described using the classical diffusion theory in terms of Kirkendall velocity construction. The position of a Kirkendall plane is revealed in the reaction zone not only by inert markers, but also by a different crystal morphology on either side of the plane. A physico-chemical approach is developed which elucidates the role of the Kirkendall effect in the morphogenesis of interdiffusion systems. The occurrence of one or more Kirkendall planes, characterized by morphology changes in the reaction layers, turns out to be related to different nucleation sites of the product grains. The model is demonstrated using the experimental results in the Co–Si system. It is shown that the predictions using the physico-chemical approach are in good agreement with the experimentally found positions of the Kirkendall plane(s). The presence or absence of inert markers at the Kirkendall planes provides insight into the initial stages of reactive phase formation.]]>
JiaoX Y, WangX H, FengP Z, et al.
Microstructure evolution and pore formation mechanism of porous TiAl3 intermetallics via reactive sintering
[J]. Acta Metall. Sin. (Engl. Lett.), 2018, 31: 440
Molecular dynamics simulations of the bulk and surface melting processeswere performed for metal Cu. The variations of the structure and energy inthe system during bulk melting process were analyzed. The movement of thesolid/liquid interface position during surface melting process wasobserved. The interaction between atoms in the system adopts theembedded atom potential proposed by Mishin. The simulation results showthat the structure and energy in the system vary discontinuously at 1585 Kin bulk melting process and the solid/liquid interface remainsunchanged at 1380 K in the surface melting process. The differentmechanisms of the two melting processes induce lower thermodynamicmelting point (1380 K) than the bulk melting point (1585 K). Surfacemelting is significant in real melting process, so the experimentaldatum measured is the thermodynamic melting point. The simulated meltingpoint coincides well with the experimental one, thus it can be concluded thatthe present melting point simulation method is correct and effective,and the Mishin's embedded atom potential is suitablefor dealing with complicated and disordered systems.
Metastable phase formation in the immiscible Cu-Co system studied by thermodynamic, molecular dynamics and ab initio calculations together with ion beam mixing
... [100]Preparation process of the immiscible W/Ag, Mo/Ag and Mo/Cu laminated metal composites (LMCs) by irradiation damage alloying (IDA)<sup>[<xref ref-type="bibr" rid="R100">100</xref>]</sup>
... [100,102]EDX line-scanning results of the cross-section of the Mo/Cu LMCs<sup>[<xref ref-type="bibr" rid="R100">100</xref>,<xref ref-type="bibr" rid="R102">102</xref>]</sup>
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... [100,102]
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... (a) drift corrected spectrum profile (b) EDX line-scanning profile along the red-line in Fig.7aFig.7
... [100,101]Microscopic characterization for the interface of the Mo/Ag LMCs<sup>[<xref ref-type="bibr" rid="R100">100</xref>,<xref ref-type="bibr" rid="R101">101</xref>]</sup>
EDX line-scanning results of the cross-section of the Mo/Ag LMCs<sup>[<xref ref-type="bibr" rid="R100">100</xref>,<xref ref-type="bibr" rid="R101">101</xref>]</sup>
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... [100,101]
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Induction of diffusion and construction of metallurgical interfaces directly between immiscible Mo and Ag by irradiation-induced point defects
Microscopic characterization for the interface of the Mo/Ag LMCs<sup>[<xref ref-type="bibr" rid="R100">100</xref>,<xref ref-type="bibr" rid="R101">101</xref>]</sup>
... [101] (S为Doppler展宽谱的线性参数，SB为被归一化为无缺陷样品的S值)Variable energy positron annihilation spectroscopy (VEPAS) results of various samples<sup>[<xref ref-type="bibr" rid="R101">101</xref>]</sup> (<i>S</i> is the line shape parameter of Doppler broadening data, <i>S</i><sub>B</sub> is the parameter that is normalized to the defect-free <i>S</i> value)(a) <i>S</i> parameter <i>vs</i> positron implantation energy for the pre-annealed pure Mo and the Ag<sup>+</sup> implanted Mo
(b) S parameter vs positron implantation energy for the pre-annealed pure Mo and the Mo/Ag laminated samples with a 100 nm thick Ag layer annealed at different temperatures ...
... [101] (S is the line shape parameter of Doppler broadening data, SB is the parameter that is normalized to the defect-free S value)(a) S parameter vs positron implantation energy for the pre-annealed pure Mo and the Ag+ implanted Mo
(b) S parameter vs positron implantation energy for the pre-annealed pure Mo and the Mo/Ag laminated samples with a 100 nm thick Ag layer annealed at different temperatures ...
... S parameter values and corresponding depth of the S peak for the Mo/Ag laminated samples annealed at different temperatures[101] ...
... ,101]EDX line-scanning results of the cross-section of the Mo/Ag LMCs<sup>[<xref ref-type="bibr" rid="R100">100</xref>,<xref ref-type="bibr" rid="R101">101</xref>]</sup>
... [101]Cross-section TEM image for the Mo/Ag laminated sample annealed at 800 ℃ for 4 h (a) and the magnified image of the region marked with a white rectangular frame in Fig.12a (b)<sup>[<xref ref-type="bibr" rid="R101">101</xref>]</sup>Fig.12
Schematic view of the forming process of the Kirkendall voids in the Mo/Ag laminated sample<sup>[<xref ref-type="bibr" rid="R101">101</xref>]</sup> (IIPDs—irradiation-induced point defects )
Schematic view of the forming process of the Kirkendall voids in the Mo/Ag laminated sample<sup>[<xref ref-type="bibr" rid="R101">101</xref>]</sup> (IIPDs—irradiation-induced point defects )
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... [101]Schematic view of the forming process of the Kirkendall voids in the Mo/Ag laminated sample<sup>[<xref ref-type="bibr" rid="R101">101</xref>]</sup> (IIPDs—irradiation-induced point defects )
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... [101] (IIPDs—irradiation-induced point defects )
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Building metallurgical bonding interfaces in an immiscible Mo/Cu system by irradiation damage alloying (IDA)
EDX line-scanning results of the cross-section of the Mo/Cu LMCs<sup>[<xref ref-type="bibr" rid="R100">100</xref>,<xref ref-type="bibr" rid="R102">102</xref>]</sup>
... [107]Preparation process of the Nb/Cu joint by high-temperature structure induced alloying (HTSIA)<sup>[<xref ref-type="bibr" rid="R107">107</xref>]</sup> (<i>F</i>—force)Fig.14<strong>5.2 </strong>高温结构诱发合金化所构建界面的显微组织
... [109]HRTEM observation of the W/Cu interface of W/Cu joint prepared through the direct diffusion bonding<sup>[<xref ref-type="bibr" rid="R109">109</xref>]</sup>
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... [109]
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... (c) filtered image of the region marked with blue rectangle in Fig.15bFig.15
HRTEM images of microstructures of theW<sub>50</sub>Cu<sub>50</sub> sintered powder metallurgy materials prepared by milling for 30 h (a) and 40 h (c) and subsequent sintering at 980 ℃ for 3 h, and the corresponding SAED patterns of Figs.16a and c (b, d)<sup>[<xref ref-type="bibr" rid="R109">109</xref>]</sup> (Insets in Figs.16a and c show the EDX results of W<sub>50</sub>Cu<sub>50</sub> sintered powders)Fig.16
DSC curves of the 40 h milled W<sub>50</sub>Cu<sub>50</sub> powder mixture before and after being annealed<sup>[<xref ref-type="bibr" rid="R109">109</xref>]</sup>Fig.18
Calculated curves of Gibbs free energy change for the alloying in W-Cu system<sup>[<xref ref-type="bibr" rid="R109">109</xref>]</sup>(<i>E</i><sub>initial</sub>—total initial energy of W-Cu system, Δ<i>G</i><sub>alloying</sub>—Gibbs energy for the alloying between W and Cu, <span class="formulaText"><inline-formula><math id="M11"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msubsup></math></span></inline-formula></span>—Gibbs energy for the formation of W/Cu crystalline phases, <span class="formulaText"><inline-formula><math id="M12"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">a</mi></mrow></msubsup></math></span></inline-formula></span>—Gibbs energy for the formation of W/Cu amorphous phases)Fig.19
DSC curves of the 40 h milled W<sub>50</sub>Cu<sub>50</sub> powder mixture before and after being annealed<sup>[<xref ref-type="bibr" rid="R109">109</xref>]</sup>Fig.18
Calculated curves of Gibbs free energy change for the alloying in W-Cu system<sup>[<xref ref-type="bibr" rid="R109">109</xref>]</sup>(<i>E</i><sub>initial</sub>—total initial energy of W-Cu system, Δ<i>G</i><sub>alloying</sub>—Gibbs energy for the alloying between W and Cu, <span class="formulaText"><inline-formula><math id="M11"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msubsup></math></span></inline-formula></span>—Gibbs energy for the formation of W/Cu crystalline phases, <span class="formulaText"><inline-formula><math id="M12"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">a</mi></mrow></msubsup></math></span></inline-formula></span>—Gibbs energy for the formation of W/Cu amorphous phases)Fig.19
... [109]DSC curves of the 40 h milled W<sub>50</sub>Cu<sub>50</sub> powder mixture before and after being annealed<sup>[<xref ref-type="bibr" rid="R109">109</xref>]</sup>Fig.18
Calculated curves of Gibbs free energy change for the alloying in W-Cu system<sup>[<xref ref-type="bibr" rid="R109">109</xref>]</sup>(<i>E</i><sub>initial</sub>—total initial energy of W-Cu system, Δ<i>G</i><sub>alloying</sub>—Gibbs energy for the alloying between W and Cu, <span class="formulaText"><inline-formula><math id="M11"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msubsup></math></span></inline-formula></span>—Gibbs energy for the formation of W/Cu crystalline phases, <span class="formulaText"><inline-formula><math id="M12"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">a</mi></mrow></msubsup></math></span></inline-formula></span>—Gibbs energy for the formation of W/Cu amorphous phases)Fig.19
Calculated curves of Gibbs free energy change for the alloying in W-Cu system<sup>[<xref ref-type="bibr" rid="R109">109</xref>]</sup>(<i>E</i><sub>initial</sub>—total initial energy of W-Cu system, Δ<i>G</i><sub>alloying</sub>—Gibbs energy for the alloying between W and Cu, <span class="formulaText"><inline-formula><math id="M11"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msubsup></math></span></inline-formula></span>—Gibbs energy for the formation of W/Cu crystalline phases, <span class="formulaText"><inline-formula><math id="M12"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">a</mi></mrow></msubsup></math></span></inline-formula></span>—Gibbs energy for the formation of W/Cu amorphous phases)Fig.19
... [109]Calculated curves of Gibbs free energy change for the alloying in W-Cu system<sup>[<xref ref-type="bibr" rid="R109">109</xref>]</sup>(<i>E</i><sub>initial</sub>—total initial energy of W-Cu system, Δ<i>G</i><sub>alloying</sub>—Gibbs energy for the alloying between W and Cu, <span class="formulaText"><inline-formula><math id="M11"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msubsup></math></span></inline-formula></span>—Gibbs energy for the formation of W/Cu crystalline phases, <span class="formulaText"><inline-formula><math id="M12"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">a</mi></mrow></msubsup></math></span></inline-formula></span>—Gibbs energy for the formation of W/Cu amorphous phases)Fig.19
... [109](Einitial—total initial energy of W-Cu system, ΔGalloying—Gibbs energy for the alloying between W and Cu, —Gibbs energy for the formation of W/Cu crystalline phases, —Gibbs energy for the formation of W/Cu amorphous phases)Fig.19
