Int. Journal of Refractory Metals and Hard...

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Nanocrystalline tungstennickel heavy alloy reinforced by in-situ tungsten carbide: Mechanical alloying preparation and microstructural evolution Dongdong Gu , Guoquan Zhang, Donghua Dai, Hongqiao Wang, Yifu Shen College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, 210016 Nanjing, PR China abstract article info Article history: Received 16 June 2012 Accepted 27 October 2012 Keywords: Mechanical alloying Tungsten heavy alloy Tungsten carbide Nanocrystalline Microstructure Mechanical alloying, as a low-temperature solid-state powder processing technique, was applied to prepare ho- mogeneous nanocrystalline WNi heavy alloy reinforced by the in-situ formed WC, starting from the WNigraphite elemental powders. The evolutions of constitution phases, microstructural features, and chemical com- positions of the milled powders at various milling times were studied by the XRD, TEM, EDX, XPS, and laser particle size analyzer. The powder particles experienced a continuous renement during 035 h milling, but had a tendency to coarsen with continued milling up to 45 h, due to the competitive operation between the mechanisms of fracturing and cold-welding. The alloying process including the solid dissolution of C and Ni in W and subsequent chemical composition homogenization was gradually completed after 35 h milling. The 35 h milled powder had a considerably rened particle morphology with a narrow size distribution (D 25 = 1.44 μm, D 50 = 2.49 μm, and D 90 = 5.31 μm), leading to a signicantly elevated specic surface area of 1462.56 m 2 /kg. The nal product was identied as b.c.c. structured W alloyed with Ni, containing 1.07 at.% in-situ formed WC. The powders had a homogeneous nanocrystalline ne structure with a signicantly decreased grain size below 20 nm. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction Nanocrystalline materials are normally polycrystalline materials with grain size of typically below 100 nm. Nanomaterials demon- strate unique physical, chemical, and mechanical properties, as rela- tive to the corresponding conventional coarse-grained materials. Nanocrystalline materials can be synthesized by a number of methods including mechanical alloying (MA) [16]. High-energy MA, as a typical powder metallurgy process, involves the repeated fracturing, cold-welding, and re-fracturing of powder particles in a high-energy ball mill. MA process has demonstrated favorable capa- bilities in the formation of stable and metastable phases including solid solutions [7,8], intermediate phases [9,10], and even amorphous alloys [11,12]. In particular, during MA process the powders being milled undergo heavy macroscopic and microscopic deformations due to the continuous action of ballpowderball collisions, which provides a high possibility for the formation of nanocrystallites in as-milled pow- ders [1315]. On the other hand, combined with a careful design of the chemical compositions of the starting powders, high-energy ball milling and inherent chemical reactions may lead to the formation of in-situ phases, due to the effective mechanochemical process during MA [16]. Tungsten (W), as a refractory metal with a high melting point, is often brittle and hard to work in its raw form. It becomes more useful as an engineering material when alloyed with small quantities of other elements, typically nickel (Ni) and/or iron (Fe), to form a group of products referred to as tungsten heavy alloys [17,18]. These alloys are usually used as kinetic energy penetrators, radiation shields, and balance weights, due to their high density, strength, and ductility [8]. In contrast, tungsten carbide (WC) is the hardest binary carbide at elevated temperatures (~1000 kg/mm 2 at 1000 °C), com- bining with high compressive strength (5 GPa at 20 °C) and fracture toughness (67.5 MPa m 1/2 ) [19,20]. The incorporation of WC with- in a W heavy alloy is expected to further strengthen the material. On the other hand, the preparation of nanocrystalline W heavy alloys is potentially attractive for many applications since the reduction of the crystallite size to the nanometer scale may introduce a number of novel physical and mechanical properties that are absent in the coarsen-grained materials. High-energy MA solid-state process is particularly useful for a successful formation of those nanocrystalline compounds that are difcult to prepare by other conventional pro- cesses [1,21]. In this work, MA process was introduced to prepare ultra-ne nanocrystalline and homogeneous W heavy alloy powder reinforced by the in-situ WC phase, starting from the W, Ni, and graphite ele- mental powders. The evolutions of phases, microstructures, and compositions of the milled nanocrystalline powders were studied Int. Journal of Refractory Metals and Hard Materials 37 (2013) 4551 Corresponding author. E-mail address: [email protected] (D. Gu). 0263-4368/$ see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijrmhm.2012.10.015 Contents lists available at SciVerse ScienceDirect Int. Journal of Refractory Metals and Hard Materials journal homepage: www.elsevier.com/locate/IJRMHM

Transcript of Int. Journal of Refractory Metals and Hard...

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Int. Journal of Refractory Metals and Hard Materials 37 (2013) 45–51

Contents lists available at SciVerse ScienceDirect

Int. Journal of Refractory Metals and Hard Materials

j ourna l homepage: www.e lsev ie r .com/ locate / IJRMHM

Nanocrystalline tungsten–nickel heavy alloy reinforced by in-situ tungsten carbide:Mechanical alloying preparation and microstructural evolution

Dongdong Gu ⁎, Guoquan Zhang, Donghua Dai, Hongqiao Wang, Yifu ShenCollege of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, 210016 Nanjing, PR China

⁎ Corresponding author.E-mail address: [email protected] (D. Gu).

0263-4368/$ – see front matter © 2012 Elsevier Ltd. Allhttp://dx.doi.org/10.1016/j.ijrmhm.2012.10.015

a b s t r a c t

a r t i c l e i n f o

Article history:Received 16 June 2012Accepted 27 October 2012

Keywords:Mechanical alloyingTungsten heavy alloyTungsten carbideNanocrystallineMicrostructure

Mechanical alloying, as a low-temperature solid-state powder processing technique, was applied to prepare ho-mogeneous nanocrystalline W–Ni heavy alloy reinforced by the in-situ formed WC, starting from the W–Ni–graphite elemental powders. The evolutions of constitution phases, microstructural features, and chemical com-positions of the milled powders at various milling times were studied by the XRD, TEM, EDX, XPS, and laserparticle size analyzer. The powder particles experienced a continuous refinement during 0–35 h milling, buthad a tendency to coarsen with continued milling up to 45 h, due to the competitive operation between themechanisms of fracturing and cold-welding. The alloying process including the solid dissolution of C and Ni inW and subsequent chemical composition homogenization was gradually completed after 35 h milling. The 35 hmilled powder had a considerably refined particle morphology with a narrow size distribution (D25=1.44 μm,D50=2.49 μm, and D90=5.31 μm), leading to a significantly elevated specific surface area of 1462.56 m2/kg.The final product was identified as b.c.c. structured W alloyed with Ni, containing 1.07 at.% in-situ formed WC.The powders had a homogeneous nanocrystalline fine structure with a significantly decreased grain size below20 nm.

© 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Nanocrystalline materials are normally polycrystalline materialswith grain size of typically below 100 nm. Nanomaterials demon-strate unique physical, chemical, and mechanical properties, as rela-tive to the corresponding conventional coarse-grained materials.Nanocrystalline materials can be synthesized by a number ofmethods including mechanical alloying (MA) [1–6]. High-energyMA, as a typical powder metallurgy process, involves the repeatedfracturing, cold-welding, and re-fracturing of powder particles in ahigh-energy ball mill. MA process has demonstrated favorable capa-bilities in the formation of stable and metastable phases includingsolid solutions [7,8], intermediate phases [9,10], and even amorphousalloys [11,12]. In particular, during MA process the powders beingmilled undergo heavy macroscopic and microscopic deformations dueto the continuous action of ball–powder–ball collisions, which providesa high possibility for the formation of nanocrystallites in as-milled pow-ders [13–15]. On the other hand, combined with a careful design of thechemical compositions of the starting powders, high-energy ballmillingand inherent chemical reactions may lead to the formation of in-situphases, due to the effective mechanochemical process during MA [16].

rights reserved.

Tungsten (W), as a refractory metal with a high melting point, isoften brittle and hard to work in its raw form. It becomesmore usefulas an engineering material when alloyed with small quantities ofother elements, typically nickel (Ni) and/or iron (Fe), to form agroup of products referred to as tungsten heavy alloys [17,18].These alloys are usually used as kinetic energy penetrators, radiationshields, and balance weights, due to their high density, strength, andductility [8]. In contrast, tungsten carbide (WC) is the hardest binarycarbide at elevated temperatures (~1000 kg/mm2 at 1000 °C), com-bining with high compressive strength (5 GPa at 20 °C) and fracturetoughness (6–7.5 MPa m1/2) [19,20]. The incorporation of WC with-in a W heavy alloy is expected to further strengthen the material. Onthe other hand, the preparation of nanocrystalline W heavy alloys ispotentially attractive for many applications since the reduction ofthe crystallite size to the nanometer scale may introduce a numberof novel physical and mechanical properties that are absent in thecoarsen-grained materials. High-energy MA solid-state process isparticularly useful for a successful formation of those nanocrystallinecompounds that are difficult to prepare by other conventional pro-cesses [1,21].

In this work, MA process was introduced to prepare ultra-finenanocrystalline and homogeneous W heavy alloy powder reinforcedby the in-situ WC phase, starting from the W, Ni, and graphite ele-mental powders. The evolutions of phases, microstructures, andcompositions of the milled nanocrystalline powders were studied

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and the reasonable mechanisms for the microstructural develop-ment during MA were elucidated.

2. Experimental procedures

The starting powder components were: 99.9% purity W powderwith an equiaxed structure and an average particle size of 5 μm(Zhuzhou Kete Industries Co., Ltd., China), 99.9% purity Ni powderwith an irregular shape and a mean particle size of 22.5 μm (HainingFeida Metallurgy Powder Co., Ltd., China), and pure graphite powderwith a sheet-like structure and a mean particle size of 30 μm (ShanghaiShiyi Chemical Reagents Co., Ltd., China). The above-mentioned data onparticle sizes were provided by the powder suppliers. The elementalpowder mixture consisting of 42.24 g W, 5.00 g Ni, and 2.76 g graphitewas weighed and mixed, in which the weight fraction of the Ni compo-nent was 10 wt.%.

MA process was performed in a high-energy Pulverisette 6 plan-etary monomill (Fritsch GmbH, Germany). A hardened chromium–

steel grinding bowl was used, whose useful capacity was 250 ml.50 g powder mixture to be ground and 500 g stainless steel grindingballs (58 Φ10 mm balls plus 187 Φ6 mm balls) were charged intothe grinding bowl, with the ball-to-powder weight ratio of 10:1. Inorder to avoid oxidation of the powders, the MA treatment wasunder the protection of an argon atmosphere. Five different millingtimes, 10 h, 20 h, 25 h, 35 h, and 45 h, were changed, while the rota-tion speed of the main disc was fixed at 300 rpm. In order to preventa significant temperature rise within the grinding bowl, a millingduration of 20 min was followed by an interval of 10 min for aircooling.

Phase transformation of the milled powders was identified by a D8Advance X-ray diffractometer (XRD) (Bruker AXS GmbH, Germany)with Cu Kα radiation (λ=0.15418 nm) at 40 kV and 40 mA, using acontinuous scanmode. A quick scan at 4°/minwas primarily performedwithin a wide range of 2θ=20–110° to give a general exhibition of dif-fraction peaks. A slower scan rate of 1°/min was further used over 2θ=25.0–28.0°, 2θ=39.5–41.0°, and 2θ=41.5–48.5° to give a more accu-rate determination of diffraction peaks. The Scherrer equation wasused to estimate the average crystallite size (Dc) of the milled powder[22]:

Dc ¼ 0:89λ= Bcosθð Þ ð1Þ

where λ is thewave length of X-ray, B is the full width at halfmaximumof diffraction peak, and θ is the diffraction angle. The particle size distri-butions and specific surface areas of the milled powders were deter-mined using a BT-9300H laser particle size analyzer (BettersizeInstruments Ltd., China). Themicrostructural features of as-milled pow-ders such as particle morphology, grain size, and crystal structure wereinvestigated using a Tecnai G2 20 S-TWIN transmission electron mi-croscopy (TEM) (FEI Company, The Netherlands). An EDAX Genesis en-ergy dispersive X-ray (EDX) spectrometer (EDAX Inc., USA)was used todetermine the chemical compositions, using a SUTW-sapphire detectorat 200 kV. The X-ray photoelectron spectra were determined by anESCALAB 250 X-ray photoelectron spectroscopy (XPS) system (ThermoFisher Scientific Inc., USA). The acquisition parameters were: sourcetype Al Kα, spot size 500 μm, pass energy 25.0 eV, and energy stepsize 0.050 eV. The identification of peaks was performed by referenceto the standard XPS database [23].

3. Results and discussion

3.1. Phase

Fig. 1 depicts the XRD spectra of the milled powders at variousmilling durations. For the starting unmilled powder, the diffractionpeaks corresponding to W, Ni, and C were clearly detected (Fig. 1a).

After 10 h milling, the diffraction peaks for C disappeared completely(Fig. 1c), whereas the diffraction peaks for Ni were still visible (Fig. 1aand d). As themilling time prolonged above 20 h, the Ni peaks vanishedgradually from XRD pattern (Fig. 1d). It was accordingly reasonable toconsider that duringMA process of the presentW–Ni–C powder system,the dissolution rate of C inWwas faster than that of Ni inW. On increas-ing the milling time up to 35 h, the diffraction peaks for W becamesignificantly broadened and the peaks' intensity showed a decrease(Fig. 1b), which implied the formation of considerably small-sized crys-tallites in the powders that underwent a long-time milling.

Fig. 2 shows the relationship of the calculated powder grain size, thelattice parameter, and the appliedmilling time. The lattice parameter ofW increased significantly from 0.31652 nm to 0.31667 nm during10–35 h milling, which was corresponded to the rapid refinementin the grain size of W from 24.9 nm (10 h milling) to 19.7 nm(35 h milling). As an even higher milling time of 45 h was applied,the lattice parameters of W, 0.31668 nm, remained almost unchangedand the grain size of W showed a slight coarsening to 21.3 nm.

The changes of lattice parameters and grain sizes of W inas-milled powders are related to the dissolution of C and Ni elementsin W during milling. As the milling lasts 35 h, the alloying processwithin this W–Ni–C system reaches a final equilibrium state, that isto say, the solid dissolution of Ni and C elements in W is completed,the constitution phases are determined, and the crystalline struc-tures are in the most refined form (Figs. 1 and 2). The solid solutionof C in W is interstitial, as reflected by the increase in lattice spacing.The rate of expansion of the W lattice amounts to 7×10–5 nm perat.% C [24]. On the other hand, the W–Ni tends to form substitutionsolid solution. According to the Hume–Rothery rule [25], the exten-sive substitutional solid solution occurs only if the atomic size factor,i.e., the relative difference between the atomic radii of the two spe-cies, is less than 15%. If the difference is larger than 15%, the solubilityis limited. The atomic radii of Ni and W are 0.162 nm and 0.202 nm,respectively, and the atomic size factor is 19.8%, which indicates a lim-ited solid solubility of Ni in W. After 35 h long-term milling, the super-saturated but homogeneousW–Ni solid solution tends to be formed. Asa consequence, the lattice parameter of the 35 hmilledW alloy powderincreases significantly, but remains almost unchanged as the millingprocess is further proceeded (Fig. 2).

3.2. Particle size and morphology

Figs. 3 and 4 illustrate the influence of the applied milling time onthe particle size and its distribution, specific surface area, and character-istic morphology of the milled powders. After 10 h milling, the powderunderwent a preliminary refinement and the average particle size D50

reached 4.40 μm (Fig. 3). The particle size distribution was relativelybroad, i.e., D25=2.40 μm, D75=7.10 μm, and D90=10.04 μm (Fig. 4a).The particles showed a relatively coarsened near-spherical shape, andthe specific surface area, 947.46 m2/kg, was lowest in this instance(Figs. 3 and 4a). On increasing themilling time to 25 h, themean parti-cle size D50 decreased markedly to 3.10 μm, leading to an apparent in-crease in the specific surface area to 1147.90 m2/kg (Fig. 3). Themilled particles had a refined poly-angular structure and the particlesize distribution became narrow, i.e., D25=1.45 μm, D75=5.09 μm,and D90=6.89 μm (Fig. 4b). As the milling time reached 35 h, themilled powder exhibited a considerably refined particulatemorphologyand the particle size distribution, D25=1.44 μm, D75=3.85 μm, andD90=5.31 μm, was very narrow (Fig. 4c). The average particle sizeD50 showed a sharp decrease to 2.49 μmand the obtainable specific sur-face area was elevated significantly to 1462.56 m2/kg (Fig. 3). As aneven higher milling time of 45 h was applied, the milled powder didnot have a tendency to further fracture; instead, the mean particlesize D50 increased slightly to 2.69 μm, hence lowering the specific sur-face area to 1293.01 m2/kg (Fig. 3).

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Fig 1. XRD patterns obtained over a wide range of 2θ degrees showing diffraction peaks of the milled powders at different milling times (a). XRD spectra in the vicinity of the stron-gest diffraction peaks of W (b), C (c), and Ni (d) showing changes of the three constituents during milling.

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Whenever two grinding balls collide duringmilling, some amount ofpowder is trapped in between them. The powder particles are repeated-ly flattened, cold welded, fractured, and re-welded [1]. The impact forceplastically deforms the powder particles, leading towork hardening andfracture. The fresh surfaces created enable the particles to weld

together, leading to an increase in particle size. The competitive actionbetween the mechanisms of cold welding and fracturing, accordingly,determines the final microstructure of as-milled powders. A close ex-amination of the evolution of particle size and morphology during MAof the present W–Ni–C powder system reveals that the milling time of

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Fig 2. Changes of crystallite size and lattice parameter of themilledWwith milling times.

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35 h can be regarded as a critical point corresponding tomicrostructureand mechanism transitions, i.e.,

(i) For a milling time b35 h, the particles experience a continuousrefinement (Figs. 3 and 4a and b), implying the operation of afracturing mechanism.

(ii) For a milling time of 35 h, a balance is maintained betweenfracturing and cold welding of particles and, accordingly, atrue alloying among powder components occurs (Fig. 4c).

(iii) For amilling time>35 h, the particles had a tendency to coarsen(Fig. 3), which indicates that the cold welding mechanismpredominates.

For the W–Ni–graphite system being milled, the base element Wis much harder and more brittle than the additive Ni. The brittle Wcomponent gets fragmented during milling and its particle size is re-duced continuously. Since the fragmentation of brittle W particles fa-cilitates the short-range diffusion, the alloying of ductile Ni and brittleW components that have a reasonable mutual solid solubility tends tooccur during MA. On the other hand, since the as-used graphite pow-der has a sheet-like structure and is extremely soft and weak, its func-tion during the initial stage of milling is similar as a lubricant. Thegraphite adsorbs on the fractured surface of powders and minimizescold welding between neighboring particles, thereby favoring thefracturing mechanism and size reduction of powders. With continuedmilling, the graphite component gets fractured and continuously in-teracts with the W particles, which in turn interstitially dissolves inW lattice or gets incorporated in the form of W–C compound. As the

Fig 3. Effect of milling time on average particle size and specific surface area of themilledpowders.

Fig 4. Particle size distribution and characteristic particle morphology (TEM) of themilled powders at various milling times: (a) 10 h; (b) 25 h; and (c) 35 h.

milling process reaches a critical duration of 35 h, the alloying ofboth W–Ni and W–C is completed and the chemical homogeneitywithin the milling system is achieved. In this situation, a steadystate between the fracturing and cold welding of the powder particlesis obtained. An increase in the particle size of the powder that expe-rienced a milling process up to 45 h implies the predominance ofcold welding mechanism in this case, which is mainly ascribed tothe following two factors. Firstly, the starting W and graphite compo-nents that facilitate the fracturing mechanism are exhausted in the

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milling system via the alloying process during 0–35 h milling. Sec-ondly, the significantly refined particles after 35 h milling have a con-siderably high specific surface area and attendant enhanced kineticsof aggregation via the inter-particle collisions during long-termmilling.

3.3. Microstructure and composition

The characteristic microstructures (e.g., grain size, grain structureand its homogeneity) and chemical compositions of the milled nano-crystalline powders are provided in Fig. 5. Fig. 5a–c shows the brightfield images of themilled powders. After a relatively shortmilling dura-tion of 10 h, the powders were a polycrystallinemixture ofW (the darkgrains) and Ni (the gray grains). Some exceptionally large-sized Wgrains with the size of ~300 nmwere occasionally observed, exhibiting

Fig 5. High-magnification TEM micrographs showing interior crystalline microstructures of thmilled powder (d). EDX analysis showing chemical compositions of 10 h (e) and 35 h (f)milled

a heterogeneous interior grain structure (Fig. 5a). The powders expe-rienced25 hmillinghad equiaxed crystalmorphology containing nano-scale fine grains with an average size of ~30 nm (Fig. 5b). At an evenhigher milling time of 35 h, the powders appeared to have a more ho-mogeneous nanocrystalline fine structure with a significantly reducedgrain size below 20 nm (Fig. 5c). The theoretically calculated grainsize using XRD method (Fig. 2) was accordingly consistent with TEMcharacterization results. Fig. 5d presents the selected area diffractionpattern (SADP) of 35 h milled powders, showing sharp rings and spotimages. The diffraction rings and spots revealed the coexistence ofb.c.c. W–Ni solid solution with W crystals. The chemical compositionsof 10 h and 35 h milled powders were detected by EDX, as revealed inFig. 5e–f. The C elemental content decreased sharply from 11.0 wt.% to6.7 wt.% on increasing themilling time from 10 h to 35 h. It accordinglyreveals that the solid dissolution of the C element in W proceeds

e powders after 10 h (a), 25 h (b), and 35 h (c)milling. The corresponding SADP of 35 hpowders. The presence of Cu element is due to the use of a coppermesh grid in TEM study.

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continuously during milling, so as to realize the homogenization ofchemical compositions after 35 h milling.

In order to accurately determine the category and content of sub-stances in the milled powders, the XPS surveys within different energyranges were performed. Typically, XPS data were acquired for the W4f(28–48 eV), C1s (279.7–284.2 eV), and Ni2p (847–866 eV) scans, asdepicted in Fig. 6. The W4f spectra consisted of four peaks at 31.50 eV,33.60 eV, 35.40 eV, and 38.07 eV, which were identified as WC 7/2, W5/2,WO3 7/2, andWOx/W5/2 (Fig. 6a). The presence of a small amountof oxygen element in the milled powders, as also detected by EDX(Fig. 5e and f), was due to the oxidation phenomenon during the

Fig 6. High-resolution XPS spectra of W4f (a), C1s (b), and Ni2p (c) scans in the powderafter 35 h milling.

normal powder handling process. Furthermore, a XPS peak located at282.70 eV was detected in the C1s spectrum, which corresponded toC1s WC (Fig. 6b). The atomic percentage of the elements concernedwas determined based on the experimentally determined sensitivityfactors (F) and the intensity (I) of a photoelectron peak which wastaken as the integrated area under the peak following the subtractionof a linear background [26]. The quantification of compositions basedon XPS method showed that the atomic fraction of WC compound inthe 35 h milled W–Ni-based powders was 1.07 at.%. The concentrationof the alloying element Ni in the powders was calculated to be 2.68 at.%(Fig. 6c), whichwas in good accordance with the detected Ni elementalcontent 2.7 at.% (i.e., 2.8 wt.%) by EDXmethod (Fig. 5f). Based on the ac-curate XPS and TEM/SADP analysis, it was confirmed that the 35 hmilled powder was Ni-alloyed W containing 1.07 at.% in-situ formedWC.

4. Conclusions

MA process was applied to prepare homogeneous nanocrystallineW–Ni heavy alloy reinforced by the in-situ formedWC, starting fromthe W–Ni–graphite elemental powders. The powder particles expe-rienced a continuous refinement during 0–35 h milling, due to theoperation of a fracturing mechanism. For a milling time larger than35 h, the particles had a tendency to coarsen, as a cold weldingmechanism predominated. The alloying process, which includedthe solid dissolution of C and Ni inW and subsequent chemical compo-sition homogenization, was gradually completed after 35 hmilling. The35 h milled powder had a considerably refined particle morphology,showing a narrow size distribution (D25=1.44 μm, D50=2.49 μm,and D90=5.31 μm) and a significantly elevated specific surface area of1462.56 m2/kg. The final product was identified as b.c.c. structured Walloyedwith Ni, containing 1.07 at.% in-situ formedWCwithin the par-ticles. The as-milled powders had a homogeneous nanocrystalline finestructure with a significantly decreased grain size less than 20 nm.

Acknowledgments

One of the authors (D. D. Gu) is grateful for the financial support fromtheNational Natural Science Foundation of China (No. 51104090) and theAeronautical Science Foundation of China (No. 2010ZE52053).

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