Microstructure characterization of nanocrystalline TiC synthesized by mechanical alloying

Microstructure characterization of nanocrystalline TiC synthesized by mechanical alloying

Materials Chemistry and Physics 120 (2010) 537–545 Contents lists available at ScienceDirect Materials Chemistry and Physics journal homepage: www.e...

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Materials Chemistry and Physics 120 (2010) 537–545

Contents lists available at ScienceDirect

Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys

Microstructure characterization of nanocrystalline TiC synthesized by mechanical alloying B. Ghosh a , S.K. Pradhan b,∗ a b

Department of Physics, Ramananda College, Bishnupur, Bankura, West Bengal, India Department of Physics, The University of Burdwan, Golapbag, Burdwan 713104, West Bengal, India

a r t i c l e

i n f o

Article history: Received 30 April 2009 Received in revised form 24 November 2009 Accepted 30 November 2009 Keywords: Nanocrystalline TiC Ball milling XRD HRTEM

a b s t r a c t Nanocrystalline TiC is produced by mechanical milling the stoichiometric mixture of ␣-Ti and graphite powders at room temperature under argon atmosphere within 35 min of milling through a selfpropagating combustion reaction. Microstructure characterization of the unmilled and ball-milled samples was done by both X-ray diffraction and electron microscopy. It reveals the fact that initially graphite layers were oriented along 0 0 2 and in the course of milling, thin graphite layers were distributed evenly among the grain boundaries of ␣-Ti particles. Both ␣-Ti and TiC lattices contain stacking faults of different kinds. The grain size distribution obtained from the Rietveld’s method and electron microscopy studies ensure that nanocrystalline TiC particles with almost uniform size (∼13 nm) can be prepared by mechanical alloying technique. The result obtained from X-ray analysis corroborates well with the microstructure characterization of nanocrystalline TiC by electron microscopy. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Metal carbides are in use for several years in high temperature structural applications because of their high melting temperature, high strength and ductility at high temperatures and they deform like fcc metals. They are also being used in surface coating for protecting corrosion attack and improving sharpness of cutting edges. Carbide preparation in a conventional ceramic route requires a very high temperature furnace with inert gas atmosphere. Among different kinds of carbides, the titanium carbide (TiC) is a material of commercial interest because it is one of the hardest metal carbide [1] having excellent thermal stability, very high melting temperature (∼3100 ◦ C), low density, excellent chemical stability, and displays relatively high thermal and electrical conductivity. Owing to this excellent combination of properties, TiC is often used in abrasives, high-speed cutting tools, electrical discharge machining, grinding wheels and coated cutting tips [2–10]. Due to high melting temperature of both ␣-Ti (1670 ◦ C) and graphite (3826 ◦ C), TiC production by melting method requires expensive high temperature equipment. However, mechanical alloying (MA) is relatively a new technique and being utilized successfully in preparing materials which are very difficult to produce by any conventional method due to high melting temperatures of elements. Among several advantages, the chief advantage of MA

∗ Corresponding author. E-mail addresses: [email protected] (B. Ghosh), skp [email protected] (S.K. Pradhan). 0254-0584/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2009.11.048

renders a fine homogeneous nanocrystalline powder that can be consolidated and shaped according to a specific requirement by conventional powder metallurgy process. Nanocrystalline TiC powder had already been produced by MA with the elemental ␣-Ti and C powders [1,5–8,11–18] but the microstructure of the prepared materials in terms of lattice imperfections was not studied so far in detail by any of the authors. In most of the cases, TiC preparation takes a long duration, from 2 to 70 h, but we prepared the stoichiometric TiC powder within 35 min of milling. This article describes in detail the influence of lattice imperfections in the formation mechanism of TiC phase within a record minimum time of milling. High density of lattice imperfections produced by MA is usually manifested in peak broadening of X-ray line profile of cold-worked ␣-Ti and TiC reflections [19,20]. In addition to that, peak asymmetry and peak-shift (with respect to their unmilled counterpart) may also be observed in the XRD patterns of ball-milled powders containing fcc phase due to the presence of planar imperfections, like stacking faults. A careful analysis of all these modifications in XRD pattern due to lattice imperfections results in quantitative measure of several microstructure parameters like, change in lattice parameter, residual stress, stacking fault probabilities of intrinsic, extrinsic and twin faults, coherently diffracting domain size (particle size), r.m.s. lattice strain, dislocation density and stacking fault energy. As the microstructure parameters are directly related to physical properties of a material, a control on the microstructure parameters helps one to prepare ‘tailor made’ materials having desirable properties. The objectives of the present work are (i) to produce nanocrystalline TiC by high-energy ball milling the elemental ␣-Ti

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and C (graphite) powders at room temperature in a minimum time, (ii) to characterize the microstructure of the prepared materials in terms of lattice imperfections and (iii) finally to find the reason of TiC formation. 2. Experimental Pure titanium (M/s Alfa Aesar; purity 99.5%, 200 mesh) and graphite (M/s Loba Chemie; purity 99.5%, 50 ␮m) powders were used as the starting ingredients and mixed in 1:1 molar ratio and then sealed in a chrome steel vial of 80 ml volume together with chrome steel balls of 10 mm diameter, in a glove bag under Ar atmosphere. The ball-to-powder mass ratio (BPMR) was 40:1 and the rotation speed of the disk was 200 rpm. The milling was performed at room temperature using a highenergy planetary ball mill (Model-P5, M/s FRITSCH, GmbH, Germany). The milling was interrupted after a selected milling time and powder was collected from the vial. X-ray diffraction (XRD) with Ni-filtered CuK␣ radiation from an X’pert-pro powder diffractometer (Panalytical) operated at 40 kV and 40 mA was used to monitor the structural changes of the milled powders at different interval of time varying from 5 min to 6 h. For detailed X-ray line profile analysis, step-scan data (of step size 0.05◦ 2 and counting time 30 s) of unmilled and all ball-milled samples were recorded for the entire angular range 15–120◦ 2. The high-resolution transmission electron microscopy (HRTEM) images of 6 h ball-milled TiC powders were taken from a TEM operated at 200 KV (Model HRTEM 2100F and 2010, JEOL) for microstructure characterization of TiC powder. Size of TiC particles, formed after 35 min of milling, was measured by scanning electron microscope (SEM; Model S-530, HITACHI, Japan).

3. Microstructure characterization by X-ray diffraction Microstructure characterization in terms of lattice imperfections in unmilled and all ball-milled samples has been done employing both the Rietveld’s whole profile fitting method [21–24] and modified Warren–Averbach’s [20,25–27] method of line profile analysis (WAMLPA). The formation mechanism of nanocrystalline TiC phase has also been monitored employing both these methods of analyses. Following the changes in XRD patterns of ball-milled samples, the phase transition time was recorded. The content of individual phases was obtained from the Rietveld analysis as the method is based on structure simulation and refinement considering all overlapping and individual reflections of a particular phase once at a time. However, the WAMLPA is based only on line profile fitting methodology which primarily reveals the microstructure and content of individual phases can also be obtained if the recorded reflections are isolated. 3.1. The Rietveld method The Rietveld analysis software, MAUD 2.06 [24] is specially designed to refine simultaneously both the structural and microstructure parameters through a least-squares method. The background of each pattern was fitted by a polynomial function of degree 4. For microstructure characterization the experimental profiles were fitted with the pV analytical function, as the Lorentzian and Gaussian functions approximate particle size and strain broadening respectively of the experimental profile in a better way [21–24]. Considering the integrated intensity of the peaks as a function of both structural and microstructural parameters, the Marquardt least-squares procedure is adopted for minimization the difference between the observed (Io ) and simulated (Ic ) powder diffraction patterns. Structure and microstructure refinement of experimental data continues till convergence is reached with the value of the quality factor, GoF very close to 1 (in present case, it varies between 1.1 and 1.4). Microstructure parameters like particle size and lattice strain values of ball-milled samples are also obtained from this analysis along with all structural parameters. The Rietveld’s analysis is one of the best methods for quantitative phase estimation and has been adopted in the present case to monitor the progress of ball milling towards required TiC phase and phase transformation kinetics during ball milling.

3.2. The Warren–Averbach’s method of line profile analysis Three distinct changes may be observed in the XRD pattern of a cold-worked (ball-milled) sample with respect to its bulk counterpart. They are peak-shift, peak broadening and peak asymmetry and in the present case first two effects are predominant in all ball-milled samples. 3.2.1. Peak-shift analysis The relative peak-shift ( (2 ◦ )hkl ) between successive pairs of [(2 0 0)–(1 1 1), (2 2 0)–(2 0 0), (3 1 1)–(2 2 0)] annealed standard (in present case, the unmilled mixture) and cold-worked samples (in present case, all ball-milled samples) of a fcc structure contains information regarding (a) stacking fault probabilities of intrinsic (˛/ ) and extrinsic (˛// ) nature, (b) change in lattice parameter (a/a0 ) and (c) long-range residual stress () [19,20,26,27]. As the effect of residual stress is insignificant for powder materials, the peak-shift analysis has been done by considering the composite effect of lattice parameter change (a/a0 ) and net deformation stacking fault probability, ˛ = ˛/ − ˛// . 3.2.2. Size strain analysis The basic consideration of this analysis is the modeling of the diffraction profiles (broadened due to instrumental settings, small particle size, r.m.s. lattice strain, stacking and twin faults) by analytical pV function and an exponential asymmetry function. Being a linear combination of Lorentzian and Gaussian functions, the pV function is the most reliable peak-shape function and is being widely used in Rietveld’s structure refinement and WAMLPA software [20–29]. Due to anisotropy in particle size and lattice strain in closepacked structures, profiles of different Miller indices are broadened in different manner and fitting of this non-uniform peak broadening is a difficult tusk in Rietveld structure refinement [24,28]. However, an anisotropy model of both particle size and lattice strain incorporated in MAUD software improves the profile fitting to a large extent. Anisotropic particle size, (De )hkl and r.m.s. lattice strain (ε2  1/2 )hkl values along some principal direction are also obtained from WAMLPA. Both SEM and TEM images reveal that particles in ball-milled samples are of different sizes and shapes. Considering the lognormal distribution of particle size (diameter) and lattice strain, profile fitting has been improved to a great extent and Rietveld’s analysis reveals the most probable value of particle size (diameter) and lattice strain distribution over a certain distance from the center of lattice distortion. 4. Results and discussion Fig. 1(a) illustrates XRD patterns of the stoichiometric (1:1 mol) mixture of unmilled (0 h) ␣-Ti and graphite powders, milled at room temperature for different durations. It is clearly evident from the figure that all peaks in unmilled sample are quite sharp and high angle reflections are well resolved into Cu K␣1- ␣2 components, which indicates that particle sizes of both elements are quite large and elements are almost free from lattice strain. The relative intensity (r.i.) ratios of ␣-Ti (hcp) reflections are in accordance with the reported value (JCPDF file # 44-1294) but those of graphite (hexagonal) powder (JCPDF file # 41-1487) are extremely oriented along 0 0 2. This kind of preferred orientation is a major problem in determining the average particle size as well as the quantitative estimation of phases in a multiphase material. After just 5 min of milling, all ␣-Ti reflections become broaden and some of the high angle reflections are almost absent in the XRD pattern. It is also evident that peak broadening of some reflections is relatively large. It suggests that these atomic planes are more prone to lattice deformation, and are known as ‘fault-affected’ reflections of hcp lattice

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Fig. 1. (a) X-ray powder diffraction patterns of unmilled and ball-milled stoichiometric mixture of elemental ␣-Ti and graphite powders (1:1 molar ratio) milled for different duration under argon medium. (b) Indexed SAED pattern of TiC phase after 6 h ball milling. (c) HRTEM micrograph of TiC phase after 6 h ball milling showing (1 1 1) plane of a nanocrystalline particle.

[20]. It is also interesting to note that in the course of milling, intensities of (0 0 2) (r.i. = 30%) and (1 0 1) (r.i. = 100%) reflections of ␣-Ti become gradually almost equal which reveals the fact that the ␣-Ti particles are oriented slowly along 0 0 2. As the graphite layers are already oriented along 0 0 2, it is more likely that the ␣-Ti particles are embedded on the graphite layer and also aligned along the same direction due to structural similarity. It is also noticed that the texturing effect continues to stay up to 34 min of milling—just before the TiC phase formation. With the progress of milling up to 34 min, the (0 0 2) graphite reflection disappears gradually and at the same time ␣-Ti peaks broaden continuously without any shift in peak positions. It indicates there is no change in lattice parameters of ␣-Ti phase and the possibility of formation of a Ti–C interstitial solid solution within this period of milling may be ruled out. It appears that within this short duration of milling, crystalline graphite powder becomes amorphous carbon due to high-energy impact. Lohse et al. [30] also observed the absence of graphite reflections in ball-milled XRD patterns of Ti–C system and presumed the amorphisation of graphite was induced by ball milling. Ye and Quan [1] pointed out the mass absorption coefficient of CuK␣ for ␣-Ti is 208 m2 g−1 and

that for C is only 4.6 m2 g−1 . This would make graphite very difficult to be detected by XRD analysis in the presence of ␣-Ti, if it presents as thin layers sandwiched in between ␣-Ti layers. It may also happen that C atoms are located at the junction of many grain boundaries of ␣-Ti particles during milling and would also hinder the detection of graphite by XRD. Wu et al. [13] noticed the absence of graphite peaks in a ball-milled Ti–C mixture and from XPS study found the location of C atoms at the grain boundaries of ␣-Ti grains prior to the combustion reaction. However, the crystallinity (crystalline or amorphous) of graphite powder was not reported in their work. We found the XRD pattern of pure graphite powder milled for 1 h contains the sharp line (0 0 2) reflection. It confirms that graphite powder remained crystalline at least up to 1 h of milling and therefore, the possibility of amorphisation of graphite powder at the initial stage of milling can be ruled out. In the present case, the absence of the graphite reflections after short duration of milling, broadening of ␣-Ti reflections without any peak-shift and texturing of ␣-Ti particles along graphite layers reveal the fact that there may be a transitional bonding state between some of C and ␣-Ti atoms, preferably located on the nanocrystalline ␣-Ti grain boundaries [13,17,30]. The amount of

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Table 1 Microstructure parameters of unmilled and ball-milled mixture of ␣-Ti and graphite powders obtained from both Warren–Averbach’s method of line profile analysis and Rietveld method of analysis. Milling time

Phase present

Mol fraction (± 10−3 to 10−2 )

C Ti C Ti C Ti Ti Ti TiC TiC TiC TiC TiC

0 min 5 min 15 min 30 min 34 min 35 min 45 min 1h 2h 6h

0.71 0.29 0.41 0.59 0.29 0.71 1 1 1 1 1 1 1

Lattice parameter (10−10 m) (±10−5 to 10−4 )

WAMLPA

a

˛ × 103

(a/a0 ) × 103

˛ × 103

ˇ × 103

– – – – – – – – – 1.822 3.660 5.562 7.606

– – – – – – – – – 0.795 0.859 0.988 0.880

– – – 3.338 – 2.734 2.119 1.956 – – – – –

– – – 0.053 – 1.662 2.916 3.019 – – – – –

c

Rietveld

WAMLPA

Rietveld

2.4623 2.9511 2.4684 2.9523 2.4846 2.9506 2.9525 2.9527 2.9485 4.3261 4.3259 4.3230 4.3187

– 2.9530 – 2.9523 – 2.9563 2.9518 2.9533 4.3266 4.3294 4.3280 4.3197 4.3181

6.7109 4.6867 6.7136 4.6844 6.7230 4.6821 4.6850 4.6781 – – – – –

lattice imperfections generated in ␣-Ti lattice is measured quantitatively through microstructure characterization employing both WAMLPA and Rietveld’s methods and are shown in Tables 1 and 2. It can be seen that the full formation of cubic TiC (JCPDF File # 32-1383; space group Fm3m) phase just happened after 35 min of milling, through a mechanically induced self-propagating reaction (MISPR). Though MISPR was observed earlier in several cases of TiC formation [13,15–17,30], in the present case, the most probable reason for MISPR may be due to the fact that high-energy ball milling results in rapid decrease in particle size and thereby rapid accumulation of defects that lowers the activation energy for the reaction and brings the powder to a critical pre-combustion condition. The reaction can then be ignited easily by the energy of the colliding milling media. The high shock pressure experienced by powder trapped between colliding milling balls acts as the ignition of the reaction [31]. Recently, Jia et. al [32] reported the formation of nanocrystalline TiC phase from Ti powder and different carbon resources such as activated carbon, carbon fibres and carbon nanotubes by mechanical alloying. They found that the precursor materials played a significant role on TiC phase formation and Ti–C reaction accelerated to a large extent in case of carbon fibres and nanotubes in comparison to activated carbon. In all these cases, the formation of nanocrystalline TiC was governed by an alternative mechanism of gradual diffusion reaction instead of MISPR and took a comparatively longer time of 4–5 h for phase formation. The TiC (fcc) powder formed after 35 min of milling via MISPR appears to be as an annealed standard material with clearly resolved CuK␣1–␣2 doublets even at lower scattering angle, having

WAMLPA – 4.6871 – 4.6886 –4.7063 4.6894 4.6915 – – – – –

large grains without any lattice imperfection. Relative intensities of all reflections and lattice parameter are in accordance with reported value (JCPDF File # 32-1383) signifies that the prepared TiC powder is stoichiometric in composition (1:1 molar ratio). To prepare nanocrystalline TiC powder, the as-prepared TiC powder after 35 min of milling was milled for longer durations. XRD patterns of powder prepared at higher milling time appear with considerable amount of peak broadening and peak shifting, which increase continuously with increasing milling time. The indexed selected area electron diffraction (SAED) pattern in Fig. 1(b) and (1 1 1) plane of a nanocrystalline particle in Fig. 1(c) clearly reveals the presence of cubic TiC phase in 6 h milled sample. It may also be noticed that the diffraction rings are quite broad, in accordance with the respective XRD patterns. Peak-shift in fcc lattice is caused mainly due to composite effects of stacking faults and change in lattice parameter (a/a0 ). Considering the TiC powder prepared at 35 min as the annealed standard, these two above important microstructure parameters are estimated from peakshift analysis (Section 3.2.1). The phase transformation kinetics leading to formation of TiC phase may be caused due to presence of lattice imperfection of different kinds generated during ball milling through fracture and re-welding mechanism. Fig. 2(a) illustrates the variations of net deformation stacking fault (˛) and twin fault (ˇ) probabilities generated in ball-milled ␣-Ti (hcp) particles with increasing milling time, obtained from peak broadening analyses of all ␣-Ti reflections [20] employing WAMPLA (Section 3.2.2). It is clearly evident from the plot that (˛) decreases linearly and ˇ increases nonlinearly

Table 2 Particle size and r.m.s. lattice strain of ␣-Ti and TiC powders obtained from both Warren-Averbach’s method of line profile analysis and Rietveld method of analysis. Milling time Particle size (nm) (±10−2 to 10−1 )

R.M.S. lattice strain × 103 (±10−5 to 10−4 )

Ti

TiC

Ti

WAMLPA

Rietveld WAMLPA

Rietveld WAMLPA

1 1 1 1 0 0

Fault-unaffected Fault-affected

– 26.6 22.2 15.1 12.2 – – – – –

– 21.3 19.0 15.1 11.8 – – – – –

– 17.7 14.8 12.7 11.1 – – – – –

– 14.1 12.6 11.6 9.7 – – – – –

298.0 58.2 64.5 43.6 37.6 – – – – –

Rietveld WAMLPA

Rietveld

1 1 1 1 0 0

Fault-unaffected Fault-affected

1 0 1 1 0 2 1 0 3 0h 5 min 15 min 30 min 34 min 35 min 45 min 1h 2h 6h

Ti C

1 0 1 1 0 2 1 0 3 – – – – – – 18.9 17.7 10.0 9.3

– – – – – – 18.7 16.1 6.8 5.0

– – – – – 448 42.8 37.3 19.4 13.2

– 2.84 2.96 3.02 3.12 – – – – –

– 2.18 2.13 2.11 2.06 – – – – –

– 1.82 1.62 1.76 1.85 – – – – –

– 1.69 1.52 1.57 1.49 – – – – –

0.31 1.54 1.54 2.00 2.23 – – – – –

– – – – – – 2.37 2.58 5.11 7.66

– – – – – – 2.54 2.84 4.54 4.15

– – – – – 0.23 1.94 2.16 4.35 4.85

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Fig. 2. (a) Variation of stacking (˛) and twin (ˇ) fault probabilities of ␣-Ti (hcp) phase with increasing milling time. (b) Variation of stacking fault (˛) and change in lattice parameter (a/a0 ) of TiC (fcc) phase with increasing milling time. (c–e) HRTEM micrographs of TiC phase after 6 h ball milling showing presence of stacking and twin faults in nanocrystalline particles.

with increasing milling time in a usual manner in case of a coldworked hcp metal [19,20]. Variations of net deformation stacking fault probability, (˛) (=˛/ − ˛// ), and change in lattice parameter (a/a0 ) in ball-milled TiC (fcc) samples, obtained from peak-shift analysis, are shown in Fig. 2(b). It is clearly evident from the plot that the probability of stacking fault, ˛ increases nonlinearly but the (a/a0 ) remains almost constant with increasing milling time.

It reveals that the peak-shifts in TiC reflections are mainly due to the deformation stacking faults produced in the process of ball milling the as-prepared TiC powder to obtain nanocrystalline TiC powder. The presence of stacking faults in 6 h milled sample is clearly revealed in the HRTEM images (Fig. 2(c)–(e)). Both intrinsic (˛/ ) and extrinsic (˛// ) stacking faults are generated almost in every TIC particles, in the course of milling.

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Fig. 3. Observed (·) and calculated (−) X-ray powder diffraction patterns of unmilled and ball-milled samples of ␣-Ti and graphite (1:1 mol) mixture milled for different duration revealed from Rietveld’s powder structure refinement analysis.

In the Rietveld’s analysis, experimental profiles of unmilled and all ball-milled powders are fitted by refining the structural and microstructural parameters of simulated powder diffraction patterns generated considering the contribution from following three phases: (a) ␣-Ti (hex, a = 2.9505 Å, c = 4.6826 Å, space group P63 /mmc), (b) graphite (hex, a = 2.4704 Å, c = 6.7244 Å, space group P63 /mmc) and (c) TiC (cubic, a = 4.3274 Å, space group Fm3m). Typical plots of Rietveld analysis for all such samples are shown in Fig. 3 where Io and Ic represent observed (experimental) and calculated (simulated) data respectively. The difference plots (Io − Ic ) are shown at the bottom of respective data sets. The GoF values vary within 1.1–1.4 for fittings of all experimental data reveal that the simulated powder patterns are properly refined to fit the experimental powder patterns. The unmilled sample (0 h) is fitted very well with ␣-Ti but with a preferred orientation of graphite particles along 0 0 2. The absence of (0 0 2) graphite reflection after 30 min of milling, reveals that graphite layers may be uniformly distributed as thin layers among the grain boundaries of nanocrystalline ␣-Ti particles. Peak broadening of ␣-Ti reflections increases continuously with increasing milling time up to 34 min of milling. This peak broadening is fitted very well by considering both the effect of small particle size and lattice strain, which are reasoned due to cold working on ␣-Ti lattice during ball milling. Fig. 4 depicts the nature of variation of mole fraction of three different phases with increasing milling time. Though ␣-Ti and graphite powders were taken at molar ratio 1:1, but the Rietveld’s analysis of unmilled sample reveals the ratio as ≈0.3:0.7, respectively. This significant change in composition arises due to highly oriented graphite layers along 0 0 2. With the progress of milling, texturing of ␣-Ti phase increases along 0 0 2. The reason of texturing may be due to transitional bonding between some ␣-Ti and C atoms caused by the lubricating nature of graphite. As a result, graphite particles stick to the ␣-Ti surface and try to pull (arrange) the ␣-Ti particles along their own orientation [13]. Mole fraction of graphite phase reduces to nil within 30 min of milling, and that of ␣-Ti phase increases from 0.29 to 1.0. But, such a sudden change in ␣-Ti mole fraction is not reflected in the lattice parameters of ␣-Ti phase. Therefore, it can be presumed that C atoms were not diffused into the ␣-Ti matrix. As there was no diffuse peak or significant change in background intensity of XRD patterns (Figs. 1(a) and 3), the chance of amorphous carbon phase formation may be ruled out. The enhancement in ␣-Ti mole fraction (considering a single phase material of full contribution i.e., 1.0 mol) may therefore be attributed to the

Fig. 4. Variation of phase content (mole fraction) of different phases in unmilled and ball-milled mixture of ␣-Ti and graphite (1:1 mol) with increasing milling time.

detection limit of X-ray diffraction of thin layer of graphite phase having very low scattering power. Further milling up to 35 min results in full formation of TiC phase through MISPR via an instant combustion reaction. Fig. 5 shows the variation of lattice parameters of both the ␣-Ti and TiC phases obtained from both WAMLPA and Rietveld methods. It is interesting to note that results obtained from both methods are quite close. As there is no significant change in ␣-Ti lattice parameters, it clearly reveals that there is no inclusion of C atoms in ␣-Ti matrix. On the way to preparation of nanocrystalline TiC, its lattice parameter decreases very slowly and linearly upto 6 h of milling. This lattice contraction may be attributed to the compressive stress generated in MA mechanism to fracture larger grains into small nanocrystalline fragments. Fig. 6(a) and (b) shows variations of particle (coherently diffracting domain) sizes of ␣-Ti and TiC phases respectively with increasing milling time, obtained from both WAMLPA and Rietveld analyses. In WAMLPA, particle size of ball-milled ␣-Ti

Fig. 5. Variation of lattice parameters of ␣-Ti (hcp) and TiC (fcc) phases in unmilled and ball-milled mixture of ␣-Ti and graphite (1:1 mol) with increasing milling time, revealed from both of WAMLPA and Rietveld’s structure refinement analysis.

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Fig. 6. Particle sizes of (a) ␣-Ti and (b) TiC phases in unmilled and ball-milled mixture of ␣-Ti and graphite (1:1 mol) with increasing milling time obtained from both WAMLPA and Rietveld’s structure refinement analysis. (c–e) HRTEM micrographs of TiC phase after 6 h ball milling; (f) SEM micrographs of individual TiC particles formed after 35 min of milling of ␣-Ti and graphite powders under argon through MISPR.

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Fig. 7. Distributions of grain diameter (particle size) of (a) ␣-Ti and (b) TiC phases in unmilled and ball-milled mixture of ␣-Ti and graphite (1:1 mol) at different milling time.

and TiC powders are considered to be anisotropic in usual manner [19,20]. Particle size of hexagonal ␣-Ti obtained from fault ‘unaffected’ (1 0 0), (0 0 2), (0 0 4), (1 1 0), (112), (201) reflections and fault ‘affected’ (1 0 1), (1 0 2), (1 0 3) reflections are quite close and decreases with increasing milling time almost with same rate. However, the insignificant difference in peak broadening of ‘faultaffected’ and ‘fault-unaffected’ reflections of ␣-Ti phase is ignored in Rietveld analysis and the experimental profiles were fitted considering the particles are isotropic in nature. From Fig. 6(a) it is clear that particle size and rate of decrease of particle size with progress of milling, obtained from ‘fault-unaffected’ reflections are greater than those obtained from ‘fault-affected’ reflections. Fig. 6(b) shows the variation of anisotropic and isotropic particle sizes of ball-milled TiC powder obtained from WAMLPA and Rietveld’s analysis, respectively. Formation of TiC phase at 35 min of milling with larger particle size (∼448 nm) and then its rapid decrease (∼13 nm) within 6 h of milling clearly indicates that TiC phase is formed through an abrupt combustion reaction. Lohse et al. [30] measured the ignition temperature (Tig ) of TiC formation and found that Tig decreased from 750 to 405 ◦ C with increasing milling time from 48 to 144 h. Due to the high temperature reaction, particles of TiC phase grow with a larger size. However, the particle size variations in both methods of analysis are very close because there is no texturing effect in XRD patterns of TiC powders. The particle size distributions of both ␣-Ti and TiC phases have been obtained from Rietveld’s analysis and are shown in Fig. 7(a) and (b), respectively. It is evident from variation of plots that the unmilled ␣-Ti powder (0 h) contains evenly dispersed particles of average size of ∼298 nm with relatively wide size distribution. In the course of milling, the size distribution reduces continuously towards lower value. This indicates that extensive ball milling results in fracture the large particles and consequently both the size distribution and dispersion reduce substantially. TiC particles formed at 35 min of milling via combustion reaction have a relatively narrow distribution of size with an average value ∼448 nm (Fig. 7(b)). Within 10 min of milling (i.e. after 45 min) the average particle size reduces almost to 10 times to ∼43 nm and in the course of extensive milling up to 6 h, the average particle size reaches to ∼13 nm with constant reduction of distribution. It means that by extension of ball milling to a longer period, it is possible to prepare nanocrystalline TiC with almost uniform particle size. Size of TiC particles milled

Fig. 8. Variation of r.m.s. lattice strain of (a) ␣-Ti and (b) TiC phases in unmilled and ball-milled mixture of ␣-Ti and graphite (1:1 mol) with increasing milling time obtained from both of WAMLPA and Rietveld’s structure refinement analysis.

for 6 h was also obtained from HRTEM images (Fig. 6(c)–(e)) and found that particles are almost isotropic in shape with a size distribution ∼12–18 nm. These observations clearly corroborate the finding of XRD analysis. Average particle (isotropic) size of TiC powder obtained just after 35 min of milling through MISPR is measured from SEM micrographs (Fig. 6(f)) and found very close to that obtained from Rietveld analysis. The r.m.s. strain generated in ␣-Ti and TiC phases are obtained from both the WAMLPA and the Rietveld method and their variations with increasing milling time are shown in Fig. 8(a) and (b), respectively. Lattice strains obtained from both methods of analyses are quite close. A reasonably high value of lattice strain in ␣-Ti matrix within 5 min of milling seems to be due to cold working of ␣-Ti lattice by MA. Lattice strains obtained from WAMLPA are significantly anisotropic in nature and remain almost con-

Fig. 9. Distribution of r.m.s. lattice strain of (a) ␣-Ti and (b) TiC phases in unmilled and ball-milled mixture of ␣-Ti and graphite (1:1 mol) at different milling time.

B. Ghosh, S.K. Pradhan / Materials Chemistry and Physics 120 (2010) 537–545

stant with increasing milling time. However, the lattice strain obtained from the Rietveld’s analysis considering as isotropic in nature, increases relatively sharply with increasing milling time. In contrary to ␣-Ti phase, in the early stage of milling, lattice strain in TiC phase increases isotropically and after 2 h of milling it becomes anoisotropic and remains constant along 1 0 0 but increases slowly along 1 1 1 upto 6 h of milling. The isotropic lattice strain value obtained from Rietveld’s analysis is very close to that obtained from WAMLPA along 1 0 0. This lattice strain plays an important role in peak broadening of ball-milled TiC powder, as particle size of TiC phase changes very rapidly at the initial stage of milling. Considering the distribution of lattice strain (Fig. 9(a)) over a 100 nm lattice dimension (L) (L = n a3 , n is an integer and a3 is columnar length of the lattice) [20], it has also been seen that the lattice strain value increases continuously with increasing milling time and becomes almost constant within this length of lattice. In case of TiC phase the strain reduces more rapidly and becomes constant within 50 nm lattice length L as shown in Fig. 9(b). 5. Conclusion Stoichiometric nanocrystalline cubic TiC phase is formed within 35 min of milling of ␣-Ti and graphite powders through MISPR. Microstructure characterization of both ball-milled ␣-Ti and TiC powders has been done, primarily by WAMLPA and Rietveld methods of analyses using XRD data and HRTEM. These analyses clearly reveal the TiC phase formation. Initially ␣-Ti particles become nanocrystalline in size and graphite layers are distributed as thin layer in the grain boundaries of these particles. Due to rapid decrease in particle size of ␣-Ti, high density stacking faults are incorporated in ␣-Ti lattice which in turn lower downs the activation energy for ignition reaction of TiC formation. Average particle size of TiC powder obtained from Rietveld analysis is very close to that obtained from HRTEM and SEM observations. The variation of distribution of particle size with milling time also reveal the fact that the nanocrystalline TiC particles of a uniform size can be obtained by MA within a very short milling duration. To the best of our knowledge, this is the first time report on preparation and microstructure characterization of nanocrystalline TiC by mechanical milling within such a short duration of 35 min.

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