Synthesis of carbide-free, high strength iron–carbon nanotube composite by in situ nanotube growth

Synthesis of carbide-free, high strength iron–carbon nanotube composite by in situ nanotube growth

Chemical Physics Letters 442 (2007) 365–371 www.elsevier.com/locate/cplett Synthesis of carbide-free, high strength iron–carbon nanotube composite by...

548KB Sizes 0 Downloads 44 Views

Chemical Physics Letters 442 (2007) 365–371 www.elsevier.com/locate/cplett

Synthesis of carbide-free, high strength iron–carbon nanotube composite by in situ nanotube growth Amit Goyal a

c

a,c

, Donald A. Wiegand b, Frank J. Owens b, Zafar Iqbal

c,*

Otto H. York Department of Chemical Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA b Armament Research, Development and Engineering Center, Picatinny, NJ 07806, USA Department of Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, NJ 07102, USA Received 19 February 2007; in final form 14 May 2007 Available online 2 June 2007

Abstract Iron–multiwall carbon nanotube (MWNT) composites have been synthesized by the chemical vapor deposition (CVD) of the nanotubes directly inside an iron matrix. Carbide-free synthesis was achieved as indicated by X-ray diffraction data by the use of a mixture of acetylene and carbon monoxide as the carbon source. A possible mechanism for this formation reaction is proposed. The yield strength of the iron–MWNT composites prepared with 4.5 vol% or 1 wt% of nanotubes increased 36% and 43% for the upper and lower yield points, respectively, compared to similarly heat-treated reference samples of pure iron with the same porosity. The increase in yield strength is likely to be due to the support provided by MWNT bridges formed across the pores of the metal matrix. The Vickers hardness coefficient, which scales with the yield strength, also increased by as much as 97% in these composites relative to the reference samples.  2007 Elsevier B.V. All rights reserved.

1. Introduction Carbon nanotubes [1,2] have attracted considerable attention as reinforcing agents in the fabrication of polymer [3,4], ceramic [5–9] and metal [10–15] nanocomposites because of their exceptionally high mechanical strength and aspect ratios. Theoretical and experimental results show that multiwall carbon nanotubes (MWNTs), which are chemically more robust than their single wall counterparts, are also among the stiffest known fibers, with a measured Young’s modulus of 1.8 TPa [15]. Also, the elongation failure for MWNTs is of the order of 0.4 (failure strain), which when combined with the stiffness suggests high tensile strengths of 55.5 GPa/mg/m3[15]. Numerous experiments have been conducted to incorporate nanotubes into polymer and ceramic matrices, but only a handful of investigations on metal–nanotube composites have been performed. In one study [11], 5–10% by weight of pre-syn-

*

Corresponding author. Fax: +1 973 596 3586. E-mail address: [email protected] (Z. Iqbal).

0009-2614/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.05.099

thesized arc-grown multiwall carbon nanotubes were dispersed in aluminum matrices resulting in an increase of hardness but no tensile strength measurements were performed. In another study [12], mechanical dampening characteristics of MWNT/magnesium composites formed by high pressure infiltration showed no significant improvement compared to that for the pristine metal matrix. Flahaut et al. [13] prepared a nanocomposite by hot-pressing pre-synthesized nanotubes with iron and Al2O3 and found no substantial improvement in mechanical properties probably because of significant damage to the nanotubes caused by the high temperatures of 1500–1600 C used in the fabrication process. In another study, Goh et al. [14] reinforced magnesium matrices with carbon nanotubes using powder metallurgy techniques and reported an increase of only 0.2% in yield strength and 0.18% in ductility. High processing temperatures and pressures used in fabricating metal–nanotube composites are expected to shorten and chemically damage pre-synthesized nanotubes, thus preventing enhancement of the mechanical strength of the composites formed. In addition, mechanical mixing of pre-synthesized nanotubes with metal powders prior to

366

A. Goyal et al. / Chemical Physics Letters 442 (2007) 365–371

composite formation does not provide sufficient dispersion of the nanotubes in the metal, which results in poorly distributed nanotube to metal contact and pinning. In order to overcome these challenges we recently developed a direct synthetic route to iron–single wall carbon nanotube (SWNT) composites at relatively low processing temperatures [16]. The main feature of this method was the in situ growth of nanotubes inside catalyst-loaded metal pellets with porosity controlled by the pelletizing pressure. The combination of in situ growth and relatively low growth temperatures resulted in very little or no damage to the nanotubes, improved dispersion of the growing nanotubes in the metal matrix, and binding of the nanotubes to the metal to give a metal nanocomposite with substantial increase in yield strength. In this Letter, we have extended this strategy to grow multiwall carbon nanotubes into iron matrices to synthesize iron–nanotube composites. However since MWNTs are grown via the more rapid decomposition of carbon sources like acetylene, concomitant formation of iron carbide with ceramic properties can also occur during the growth process. Hence, a procedure of mixing acetylene with the more stable carbon monoxide carbon source was developed to prevent carbide formation. In contrast to single wall nanotubes, MWNTs are formed at even lower temperatures and a higher loading of nanotubes by weight can be achieved in the composites formed. This resulted, as will be discussed below, in a significant increase in yield strength and hardness of the composites compared with similarly heat-treated reference samples without nanotubes of the same piece density. 2. Experimental The catalyst (cobalt) and catalyst promoter (molybdenum) precursors, cobalt acetate (0.01 wt% of total solution) and molybdenum acetate (0.01 wt% of total solution, Aldrich Chemicals, Milwaukee, Wisconsin), respectively, were dissolved in ethanol. Typically 3–5 g of micron-sized iron powder (Aldrich Chemicals) was soaked in this solution, dried overnight and pressed into thin cylindrical pellets under an applied load of 5000 kg. The pellets were 13 mm in diameter and between 4 and 5 mm in thickness with a piece density of 6.10 g/cm3 corresponding to 78% of the density of pure iron (7.8 g/cm3). The piece densities and therefore the porosities of the pellets can be varied by varying the pelletizing pressure. The pellets were placed in a quartz boat in a horizontal quartz tube reactor in a three-zone, microprocessor-controlled high temperature furnace. The quartz tube was pumped down to about 103 torr. Then a protocol involving heating to 800 C under flowing argon followed by switching the gas flow to a mixed carbon source of either acetylene in argon or acetylene and CO in argon with flow rates of 6, 100 and 300 sccm (standard cubic centimeters per minute), respectively, at atmospheric pressure, was used. Reference pellets were prepared with the same weight

of iron powder and applied load, followed by heating under argon at the same temperature and time used to grow MWNTs. After completion of the deposition, the system was pumped down, back-filled with argon and allowed to cool to room temperature under 100 sccm of flowing argon. The characterization of the composites was carried out by micro-Raman spectroscopy, X-ray diffraction (XRD), and field-emission scanning electron microscopy (FESEM). A confocal micro-Raman spectrometer (LabRam, Jobin Yvon/Horiba, Metuchen, New Jersey, USA) was used with the laser light source at a wavelength of 632.8 nm. A large number of spots across the samples were examined and typically observed spectra are reported. For FE-SEM (using a VP-1530 Carl-Zeiss LEO microscope) operating at an applied electric field of 2 keV the pellets were placed on the sample holder with a carbon tape. Fractured samples were placed vertically with the fractured surfaces exposed to the electron beam. XRD measurements were performed using a PAN Analytical Diffractometer ˚) employing Cu-Ka radiation (wavelength k = 1.5405 A from 2h = 20–110 at a count rate of 2.8 s per step of 0.02. Vickers hardness measurements were conducted on nanotube infiltrated composites and reference samples using a LECO micro-hardness tester (LM 700, LECO Corp.). A load of 10 kgf (kilogram force) at ambient temperature with a dwell time of 5 s was selected and an optical image of the indentation sites using a fine pixel camera attached to the LM 700 micro-hardness tester was obtained before and after indentation. Typically 3–5 measurements were made with clear indentations at several locations and an average value of the hardness is reported. Stress– strain data were taken with an MTS servo hydraulic system operated at a constant displacement rate so as to give a strain rate of about 0.00004/s [17]. The data were taken in simple compression along the cylindrical sample axis. A flow stress and a work hardening coefficient were obtained from stress–strain curves for the iron–nanotube composites and compared with similar data obtained using the reference iron pellets. 3. Results and discussion Acetylene at low partial pressures has previously been found to grow both SWNTs [18,19] and MWNTs [20] by catalytic chemical vapor deposition (CVD). Under the growth conditions used here near 1 atm pressure, primarily MWNTs are expected to be formed within the iron matrices. XRD patterns for the composites obtained using acetylene and argon, and a mixture of acetylene, CO and argon, respectively, are shown in Fig. 1a and b. The XRD pattern for the composite prepared using acetylene and argon shows sharp reflections due to iron carbide, Fe3C. Further confirmation that the phase is Fe3C is provided by the fact that the carbide can be decomposed to Fe by heat treatment in hydrogen at 850 C for 2 h as shown by the XRD pattern in Fig. 1c. This is also in agree-

A. Goyal et al. / Chemical Physics Letters 442 (2007) 365–371

Fig. 1. X-ray diffraction (XRD) patterns using Cu-Ka radiation with ˚ from various iron–MWNT composites: (a) XRD wavelength k = 1.5405 A from composite prepared using an acetylene–argon feed which shows reflections indicating the formation of iron carbide, Fe3C; (b) XRD pattern from iron–MWNT composite prepared using a carbon source comprising of CO and acetylene mixed with argon, which shows lines due to a pure carbon phase and iron only; and (c) XRD pattern from an iron– MWNT composite containing Fe3C that was heat-treated at 850 C for 2 h in hydrogen indicating decomposition of the carbide phase since only iron and pure carbon phase reflections are evident in the diffraction pattern.

ment with previously published results [21]. The microRaman spectra of the composites displayed in Fig. 2 do not show the characteristic Raman features of SWNTs, such as the relatively sharp radial breathing mode (RBM) lines and the lines due to the C@C tangential modes, which typically lie in the frequency regions below 300 cm1 and near 1590 cm1 respectively [22]. The relatively narrow lines observed at 1323 cm1 and 1581 cm1 observed for the composites prepared with acetylene mixed with carbon monoxide, and at 1332 cm1 and 1583 cm1 for composites prepared with acetylene alone can be assigned to the disorder (D) and graphitic (G) modes of the majority carbon phase comprised of MWNTs [23]. Smaller amounts of disordered carbon may also be present in the samples. The line width of the G line and the D/G intensity ratios are related to the dimensions of the crystalline regions of the carbon phases formed. The D/G ratio in the case of iron carbide formation is higher with broader G bands indicating the presence of small crystallites. The intensity of the D peak depends on in-plane carbon atom displacements, which leads to a loss of the hexagonal symmetry of the two-dimensional graphitic planes [24] with decreasing crys-

367

talline dimensions. From Fig. 2a, D/G = 0.579 and from Fig. 2b, D/G = 0.247. It can also be seen that the G line is relatively narrow and the D line is reduced in intensity with the introduction of CO mixed with acetylene (D/ G = 0.247). In addition, for iron carbide to be a major component, the D/G ratio should be of the order of 1.5 according to observations in most coke formations [24]. This suggests that even with an acetylene feed where D/ G = 0.579, iron carbide is formed only as a minority phase. This observation was confirmed by the SEM images discussed below. FE-SEM images are consistent with largely MWNT formation, and the images shown in Fig. 3a and b indicate somewhat denser growth of MWNTs compared to that of SWNTs previously grown via CO in iron [16]. FE-SEMs were obtained from the cross section of a piece cut from an iron–MWNT composite and examined for evidence of nanotube infiltration deep inside the metal matrix. Fig. 3c depicts a low magnification image showing sizable MWNT penetration to a depth of 150–160 lm. A lower concentration of nanotubes is evident below 160 lm and through the approximately 0.5 mm thickness of the piece. A high magnification image taken from a region about 160 lm inside the top surface of the composite showing dense growth of MWNTs is displayed in Fig. 3d. Measured weight changes indicate a MWNT loading of up to 1 wt% in the optimized iron–MWNT composites, which is similar to that obtained for the iron–SWNT composites [16]. However, up to 5–10 wt% MWNTs can be grown inside iron matrices of smaller density prepared at lower pelletization pressures. These composites can be densified further by high pressure isostatic pressing before use in applications. Compressive stress–strain curves were measured for samples containing 4.5 vol% MWNTs and compared with stress–strain curves measured for pure, similarly heatand pressure-treated iron reference samples. The data from two representative samples, in Fig. 4 show significant differences between the results for the nanocomposite and pure iron samples. Since mechanical properties depend on porosity, it is important to emphasize that the porosity of the reference sample and the sample with MWNTs is the same and therefore differences in porosity cannot account for the enhanced mechanical strength. The initial linear slopes of the stress–strain curves of Fig. 4 are influenced by instrumental effects and are not considered here. Compression test measurements performed on iron– MWNT composites show similar yield stress enhancement as in the case of iron–SWNT composites [16]. The increase in upper and lower yield strength is 36% and 43%, respectively, as shown in Fig. 3. The lower yield point for the reference sample is at 179 MPa and for the iron–MWNT sample it is at 255 MPa. The upper yield point for the reference sample is at 200 MPa and at 276 MPa for the iron– MWNT composite. The observed increase in strength of the iron–nanotube composites can be attributed to the reinforcement provided to the iron matrix by the carbon nanotubes [16]. This is because iron is an excellent catalyst for

368

A. Goyal et al. / Chemical Physics Letters 442 (2007) 365–371

Fig. 2. Raman spectra excited with 632.8 nm radiation of iron–MWNT composites synthesized at 800 C using: (a) acetylene mixed with argon, and (b) acetylene–CO mixed with argon. Cobalt and molybdenum acetates were used as catalyst and promoter precursors, respectively, in the starting iron matrices.

Fig. 3. Scanning electron microscope images of iron–MWNT composites. (a) Image showing dense growth of MWNTs on composite prepared using acetylene mixed with CO in argon as the carbon source; (b) higher magnification image showing MWNTs in a dense network within pores or cavities within the iron matrix; (c) low magnification cross sectional image of a piece from the iron–MWNT composite. The edge of the top surface of the composite (arrow) is on the left side of the image. Dark-grey regions show penetration of carbon nanotubes down to 150–160 lm. Somewhat lighter regions can be seen further down inside the matrix; and (d) higher magnification image taken from the circled region of the image in panel (c) showing extensive growth of nanotubes in that randomly chosen region.

A. Goyal et al. / Chemical Physics Letters 442 (2007) 365–371

369

Fig. 4. Stress versus strain plots for an iron–MWNT composite prepared with cobalt–molybdenum catalyst/promoter (top curve) and for a similarly heattreated iron reference sample (lower curve).

nanotube growth [25,26] and can partially dissolve carbon to form bridges across the cavities in the iron matrix. Additional pinning at disclocations may therefore not be necessary. High porosity decreases mechanical strength because the average stress inside the material is greater than the average applied stress [27–30]. Providing support across the pores will lower the average stress in the material, which determines dislocation motion and yield strength. The yield point will therefore occur at higher values of the applied stress. Overall the support at the cavities provided by the carbon nanotubes will offset in part the effect of the cavities in weakening the iron matrix, resulting in higher mechanical strength. The theoretical values predicted very approximately by the rule of mixtures [31] fit well with the experimental data. Although many mechanical models are available to predict the metal composite properties, parameters such as the thermal strain and Poisson’s ratio have not been calculated or experimentally determined for carbon nanotubes. Therefore, values of the tensile strength for an individual MWNT obtained from the literature were used. The rule of mixtures [31] is given by the equation: rc ¼ rm V m þ rcnt V cnt

ð1Þ

where rc, rm and rcnt are the tensile strengths of the metal– MWNT composite, metal and MWNTs, respectively; and Vm and Vcnt respectively represent the volume fraction of the metal and the nanotubes in the composite. The pellets are porous and the densities used to calculate the volumes do not correspond to the true density of the matrix material. The tensile strength of the pellet is smaller than that of the matrix material and can be estimated by normalizing

the pellet density with the true density of the matrix material using the equation below: rc ¼ rm V m ð0:78Þ þ rcnt V cnt

ð2Þ

Taking rcnt = 3 GPa (tensile) [32] for a MWNT, Vcnt = 4.48 vol% and rm = 200 MPa [31] for iron and Vm = 95.52%, the theoretically predicted upper yield point using the rule of mixtures (Eq. (2)) is 283 MPa, which is in good agreement with the observed value of 276 MPa. Vickers hardness (which approximately scales with the yield strength [31]) of the iron–MWNT composites showed enhancement in average hardness by 180% for an iron– MWNT composite prepared with acetylene and argon (Table 1), but the XRD pattern from this sample clearly showed the presence of iron carbide (Fe3C) (Fig. 1a), which is a rather hard material. The composite prepared by combining CO with acetylene showed no XRD evidence for iron carbide formation (Fig. 1b). However, the composite showed an enhancement in hardness by 97.5%, which is substantially higher than that of an iron–SWNT composite with a similar concentration of nanotubes [16]. The results clearly suggest that the hardness increase is entirely due to the MWNTs formed in the iron matrix. In order to understand why iron carbides are not formed when acetylene is mixed with CO, we propose the following sequence of reactions during in situ growth with acetylene. The Fe3C impurity phase is formed by reaction (1) below: 3Fe2 O3 + 8H2 + C2 H2 ! 2Fe3 C + 9H2 O

ð1Þ

It involves the reduction of Fe2O3, which is typically present in the iron matrix as an impurity phase, by hydrogen (formed by the initial dissociation of acetylene) followed

370

A. Goyal et al. / Chemical Physics Letters 442 (2007) 365–371

Table 1 Vickers hardness values for Iron–MWNT composites Sample description

HV/10 numbers

SI units (MPa) (HV/10 · 9.807)

Annealed reference pellet Acetylene–argon feed CO–acetylene–argon feed (4.5 vol% MWNTs)

77.6 217.6 153.3

761.0 2134.3 1503.1

% Change

Comments

180.4 97.5

Control sample Iron carbide formed as shown by XRD No iron carbide formed; confirmed by XRD

All the samples are treated at 800 C, with the same heat treatment time cycles.

by the adsorption of carbon from acetylene decomposition. The dissociation of acetylene is further enhanced by the presence of iron as catalyst. Iron is then supersaturated with carbon and leads to the formation of iron carbide. However, iron carbide is unstable at high temperatures and therefore decomposes to iron and amorphous or disordered carbon as can be seen from the XRD patterns in Fig. 1c for a sample heat-treated in hydrogen. Introducing CO initiates the occurrence of concurrent reactions (2) and (3) below: 2CO ! C þ CO2 CO þ H2 ! C þ H2 O

ð2Þ ð3Þ

The presence of CO therefore results in the formation of carbon nanotubes and CO2 following the disproportionation reaction (2) in the presence of catalysts and reaction (3). In addition to that, reaction (3) scavenges hydrogen to form carbon nanotubes and prevents the reduction of Fe2O3 to Fe3C via reaction (1). The above reaction sequence is consistent with the XRD data on the samples, which show no evidence for the formation of Fe3C when CO is introduced into the carbon precursor feed. The XRD data for the composites also do not indicate the presence of austenite and martensite carbide structures, which would show reflections at 2h values of 41, 47 and 63 due to austenite and values of 44, 51 and 82 due to martensite, respectively [33]. The formation of austenite by carburizing gases generally occurs in the temperature range of 850–950 C where the solubility of carbon results in the formation of a stable crystal structure [34]. The presence of the austenite phase increases the hardness of metals because the structure is comprised of a low carbon core and outer layers with high carbon content. The temperature used for nanotube growth is therefore chosen to be 800 C which is substantially lower than the austenite formation temperature. Martensite, which is a very hard but brittle phase, is formed during quenching of metal pellets containing the austenite phase. The crystal structures of martensite and austenite are different and it is easy to determine the relative amounts of each phase from the XRD data. 4. Conclusions Iron–MWNT composites synthesized in situ by chemical vapor deposition show increases in yield strength and hardness relative to similarly treated reference iron samples

without nanotubes. The process is carried out at temperatures that are relatively low compared to conventional metallurgical methods used to prepare metal composites and involves only a single step without concomitant formation of iron carbide. The proposed reaction scheme involving the use of carbon monoxide to prevent carbide formation is consistent with the XRD data obtained for the samples. Since iron is a very effective catalyst for carbon nanotube growth and partially solubilizes carbon at the growth temperatures used, mechanical reinforcement is provided by the formation of supporting nanotube bridges across the cavities of the iron matrix, as indicated by scanning electron microscope images. These bridges offset in part the effect of the cavities in weakening the iron matrix, resulting in increased mechanical strength compared to the reference samples. These metal–carbon nanotube composites with increased strength and hardness can be scaled up for use in structural and engineering applications. Metal matrices with controlled porosity and further process refinement would be necessary to increase carbon nanotube loading and substantially reduce the overall weight of the composites. Acknowledgements A.G. and Z.I. thank the US Department of the Army for support of this work. We would also like to thank R. Petrova for use of the micro-hardness testing facilities in her laboratory. References [1] S. Iijima, Nature 354 (1991) 56. [2] D.S. Bethune, C.H. Klang, M.S. deVries, G. Gorman, R. Savoy, J. Vazquez, R. Beyers, Nature 363 (1993) 603. [3] Z. Iqbal, A. Goyal, in: M. Xanthos (Ed.), Functional Fillers for Plastics, Wiley-VCH Verlag GmbH & Co., Berlin, 2005, p. 175. [4] R.W. Siegel, S.K. Chang, B.J. Ash, J. Stone, P.M. Ajayan, R.W. Doremus, L.S. Schadler, Scripta Mater. 44 (2001) 2061. [5] J.-W. An, D.-H. You, D.-S. Lim, Wear 255 (2003) 677. [6] Cs. Bala´zsi, Z. Ko´nya, F. We´ber, L.P. Biro´, P. Arato´, Mater. Sci. Eng. C 23 (2003) 1133. [7] G.-D. Zhan, J.D. Kuntz, J. Wan, A.K. Mukherjee, Nature Mater. 2 (2003) 38. [8] G.-D. Zhan, J.D. Kuntz, J.E. Garay, A.K. Mukherjee, Appl. Phys. Lett. 83 (2003) 1228. [9] X.-T. Wang, N.P. Padture, H. Tanaka, Nature Mater. 3 (2004) 539. [10] T. Kuzumaki, K. Miyazawa, H. Ichinose, K. Ito, J. Mater. Res. 13 (1998) 2445.

A. Goyal et al. / Chemical Physics Letters 442 (2007) 365–371 [11] R. Zhong, H. Cong, P. Hou, Carbon 41 (2002) 848. [12] J. Yang, R. Schaller, Mater. Sci. Eng. A 370 (2004) 512. [13] E. Flahaut, A. Peigney, Ch. Laurent, Ch. Marlie`re, F. Chastel, A. Rousset, Acta Mater. 48 (2000) 3803. [14] C.S. Goh, J. Wei, L.C. Lee, M. Gupta, Nanotechnology 17 (2006) 7. [15] R. George, K.T. Kashyap, R. Rahul, S. Yamdagni, Scripta Mater. 53 (2005) 1159. [16] A. Goyal, D.A. Wiegand, F.J. Owens, Z. Iqbal, J. Mater. Res. 21 (2006) 522. [17] D.A. Wiegand, J. Pinto, S.J. Nicolaides, Energetic Mater. 9 (1991) 19. [18] B.C. Liu et al., Chem. Phys. Lett. 383 (2004) 104. [19] R. Sharma, Z. Iqbal, Appl. Phys. Lett. 84 (2004) 990. [20] S. Delpeux, K. Szostak, E. Frackowiak, S. Bonnamy, F. Be´guin, J. Nanosci. Nanotechnol. 2 (2002) 484. [21] E. Park, J. Zhang, S. Thomson, O. Ostrovski, R. Howe, Metall. Mater. Trans. B 32B (2001) 839. [22] R. Saito, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Appl. Phys. Lett. 60 (1992) 2204. [23] C. Thomsen et al., Appl. Phys. A 69 (1999) 309.

371

[24] Z. Zeng, K. Natesan, V.A. Maroni, Oxid. Met. 58 (2002) 147. [25] A.M. Cassell, N.R. Franklin, T.W. Tombler, E.M. Chan, J. Han, H. Dai, J. Am. Chem. Soc. 121 (1999) 7975. [26] Y. Li, W. Kim, Y. Zhang, M. Rolandi, D. Wang, H. Dai, J. Phys. Chem. B 105 (2001) 11424. [27] J.C. Wang, J. Mater. Sci. 19 (1984) 801. [28] F.P. Knudsen, J. Am. Chem. Soc. 42 (1959) 376. [29] R.W. Rice, in: R.K. MacCrone (Ed.), Treatise on Materials Science and Technology, vol. 2, Academic Press, 1977, p. 199. [30] G.S. Pisrenko, V.T. Troshchenko, A.Ya. Krasovskii, in: H.H. Hauser, K.H. Roller, P.K. Johnson (Eds.), Persepctives in Powder Metallurgy, vol. 3, Plenum Press, New York, 1968. [31] W.D. Callister Jr., Materials Science and Engineering an Introduction, sixth edn., John Wiley and Sons, New York, 2003. [32] J. Gaillard, M. Skove, A.M. Rao, Appl. Phys. Lett. 86 (2005) 233109. [33] A.K. De, D.C. Murdock, M.C. Mataya, J.G. Speer, D.K. Matlock, Scripta Mater. 50 (2004) 1445. [34] R. Abbaschian, R.E. Reed-Hill, Physical Metallurgy Principles, third edn., PWS Publishing, Boston, 1991.