Int. Journal of Refractory Metals and Hard Materials 29 (2011) 256–259
Contents lists available at ScienceDirect
Int. Journal of Refractory Metals and Hard Materials j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / I J R M H M
Kinetics of formation of graded layers on cemented carbides: Experimental investigations and DICTRA simulations José Garcia a,⁎, Greta Lindwall b, Orlando Prat c, Karin Frisk b a b c
Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany Swerea KIMAB AB, P.O.Box 55970, SE-10206 Stockholm, Sweden Max Planck Institute für Eisenforschung GmbH, Max Planck Str. 1, D-40237 Düsseldorf, Germany
a r t i c l e
i n f o
Article history: Received 6 August 2010 Accepted 6 November 2010 Keywords: Kinetics Diffusion DICTRA modeling Cemented carbide Graded layer
a b s t r a c t Kinetics of formation of fcc-free layers on Co–W–Ti–Ta–Nb–C–N cemented carbides was investigated by experimental methods and DICTRA simulations. The layer formation obeys a parabolic law, indicating a diffusion-controlled process. For DICTRA simulations, the inﬂuence of the mobilities for all diffusing elements in the liquid binder phase at the sintering temperature was investigated. The best agreement between experimental and simulations was obtained considering that the mobility of all metallic elements is two times slower compared with the mobility of the non-metallic elements. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The production of tough graded surface layers in cemented carbides is a key technology to improve the cutting performance of coated cutting tools. In coated cemented carbides thermal cracks originate in the coatings due to thermal expansion mismatches between the coating (~ 8–10 · 10− 6/K) and the cemented carbide (~5–6 · 10− 6/K). Tough graded surface layers minimize the propagation of such thermal cracks into the cemented carbide. They also increase the surface toughness of the cemented carbide-coating composite reducing chipping of the coating during cutting operations. The mechanism of formation of tough graded layers has been previously investigated by experimental methods, diffusion models and computer simulations. Suzuki et al.  sintered nitrogen-containing cemented carbides at liquid phase temperatures in vacuum atmospheres to produce tough WC–Co rich surface layers, which are free of cubic carbide phases (TiC, TaC or NbC); the so-called fcc-free layers. Suzuki et al. found that the fcc-free layer formation showed a parabolic growth law, indicating a diffusion-controlled process. They postulated that the outward diffusion of nitrogen, due to dissociation of nitrogencontaining components – such as TiN – during vacuum sintering, was the rate-controlling process for the fcc-free layer formation. Later, Schwarzkopf et al.  demonstrated that the denitridation effect was not strong enough to drive the formation of fcc-free layers. They postulated that the gradient formation was controlled by inward diffusion of Ti in the liquid binder; which was driven by the outward ⁎ Corresponding author. E-mail address: [email protected]
(J. Garcia). 0263-4368/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmhm.2010.11.003
gradient of nitrogen. They presented a phenomenological model (parabolic rate equation) describing the effect of all important processing variables semi-quantitatively, which was in agreement with their experimental results. In Ref.  it was observed that the thickness of the fcc-free layers increased by increasing the nitrogen content, the sintering temperature and the sintering time. Gustafson and Östlund  presented a model based on thermodynamic calculations and some kinetic considerations. Their kinetic model considered the different nitrogen and titanium activity gradients on the bulk and surface of the cemented carbide at the sintering temperature. The predicted activity gradients yielded a nitrogen (and carbon) ﬂux towards the surface and a titanium ﬂux in the opposite direction. Results of the kinetic model showed good agreement with their experimental results as well as with the previous investigations on fcc-free layer formation reported in Refs. [1,2]. The ﬁrst published DICTRA  simulations on the fcc-free layer formation were reported by Ekroth et al. . Their kinetic model assumed that all diffusion occurs in the liquid matrix binder phase. A thermodynamic database for cemented carbides containing carbon and nitrogen was assessed and used for both Thermocalc calculations and DICTRA simulations . For the DICTRA simulations a kinetic description, expressed in mobilities of the elements in the liquid, was considered. Ekroth et al. assumed that all interacting elements (Co, Ti, W, C and N) had the same mobility in the liquid. The experimental and simulated data by Ekroth et al. showed good agreement, indicating that the diffusion and thermodynamic data are the two major factors controlling the gradient formation. Since the diffusion occurs only in the liquid binder, the hard phases are considered obstacles, the presence of which reduces the effective
J. Garcia et al. / Int. Journal of Refractory Metals and Hard Materials 29 (2011) 256–259
diffusion paths. To simulate this effect, a so-called labyrinth factor, λ(f), can be deﬁned which reduces the diffusion coefﬁcient matrix ; n
Dkjeff = λð f Þ⋅Dkj
where Dnkj eff is the effective diffusion coefﬁcient matrix. Ekroth et al. used the labyrinth factor λ = f ², where f is the volume fraction of the matrix. In a later work of the same group, Frykholm et al.  found that by using a labyrinth factor λ = f instead of λ = f ² a better correspondence between experiments and DICTRA simulations was achieved. In this work experimental investigations and DICTRA simulations on the kinetics of formation of fcc-free layers on Co–W–Ti–Ta–Nb–C–N cemented carbides are carried out. For the phase equilibria calculations, the thermodynamic description presented by Frisk et al. in Ref.  is used. The diffusion model is treated as in previous investigations [5,7], but the mobilities of the different elements in the cobalt binder phase at the sintering temperature are optimized to ﬁt with the experimental results (thickness of the fcc-free layers and phase distributions).
matrix Dnkj, is a product of two matrices; one consisting only of pure thermodynamic information and one consisting of the so-called mobilities, and can be expressed as follows: ∂μ i ∂μ i n Dkj = ∑ δjk −xk xi Mi − ∂xj ∂xn i
indicating that the diffusion of one element depends on the concentration gradient of other elements. Here, δik is the Kronecker delta; i.e. δik = 1 when j = k and δik = 0 otherwise . xk is the mole fraction of element k and μi is the chemical potential of the element i, and n is an arbitrary chosen reference element. By absolute-reaction theory argumentation, the mobility parameter, Mk, for an element k in a given phase can be divided into a frequency factor M0k and an activation energy factor Qk as reported in Ref. : Mk =
Mk0 −Qk exp RT RT
Cemented carbide samples from a mixture of WC, Co, TiN and (Ta,Nb)C were prepared by standard powder metallurgy following the method described in Ref. . Raw powders provided by the company H.C. Starck and Umicore were used for the production of the samples. The description of the powders was as follows: WC with a Ctotal of 6.13±0.05, TiN with a nitrogen content of 21.2±0.1 wt.% and (Ta,Nb)C 50/50 with a Ctotal of 8.75±0.15 wt.%. The Co was an Umicore extra ﬁne powder (1.2– 1.5 μm) quality containing 0.2% impurities. The powder mixture of the cemented carbide is given in Table 1. Vacuum sintering was carried out at 1450 °C for 2, 3 and 5 h. After sintering the samples were cut, embedded in resin and polished. The fcc-free layer thicknesses were measured on scanning electron microscopy (SEM) images of cross sectioned samples. The measurements of phase fraction distributions on the near-surface area were performed on SEM images using the software analysis 5.0  following the method described by Ekroth et al. in Ref. .
where R is the gas constant and T is the absolute temperature. M0k and Qk are not constant; hence their values depend on temperature, pressure and composition. In the kinetic database utilized by DICTRA, the parameters for the atomic mobilities of the elements in a given phase are stored rather than diffusivities. Ideally, these parameters are assessed in respect to available diffusion coefﬁcient data for the system of question. However, for many systems, like the liquid binder system, the availability of such data is limited and assumptions are needed. Both Ekroth et al.  and Frykholm et al.  assumed the same mobility for all diffusing elements in the liquid, and considered an activation energy, Q, of 65,000 J/mol. The frequency factor, M0k , was given the value of 9.24∙10− 7 m2/s, which approximately reproduced their experimental results. Consequently, the value of the frequency factor will depend on the thermodynamic description used as well as the choice of the labyrinth factor, λ(f), see Eq. (1). In this study, the same approach as described above is applied; i.e. the mobilities of the diffusing elements in the liquid are varied until the agreement with the experimental results is satisfactory.
3. DICTRA modeling
4. Results and discussion
For the kinetic simulations, a model for long range diffusion occurring in a continuous matrix with dispersed phases available in the DICTRA software was used. It was assumed that all diffusion occurs in the Co matrix. This assumption is based on the fact that the carbide matrix in cemented carbides is continuous and that diffusivities in the liquid are much higher than in the solid phase. To account for the inﬂuence of the dispersed hard phases the labyrinth factor λ(f) = f was considered, as suggested in Ref. . For the description of the ﬂux of species driven by a concentration gradient the multi-component diffusion theory was applied . The nitrogen out-diffusion is driven by the titanium in-diffusion but also by the presence of other elements in the liquid cobalt phase, so that the ﬂuxes of elements are coupled due to their thermodynamic interaction. The law relating ﬂux and concentration gradient is given by the multi-component extension of the Fick's ﬁrst law:
Jk = ∑ Dkj j=1
Light microscopy images of the cemented carbide microstructures after sintering in vacuum conditions at 1450 °C are shown in Fig. 1. As
where Jk is the ﬂux of species k in the direction of the z-axis and ∂cj/∂z is the concentration gradient of the species. The diffusion coefﬁcient Table 1 Powder mixture composition (in wt.%). WC
Fig. 1. Tough fcc-free layer (WC–Co) formation as a function of time (light microscopy). Fcc-free layer thicknesses (d) are of 23 ± 1, 32 ± 1 and 45 ± 1 μm after 2, 3 and 5 h respectively.
J. Garcia et al. / Int. Journal of Refractory Metals and Hard Materials 29 (2011) 256–259
Table 2 Element composition used for simulations (in wt.%). W
expected, an fcc-free layer consisting of WC–Co and depleted of the cubic carbide phases formed at the outer surface area of all samples. In the bulk of the samples three phases can be observed, corresponding to WC (light gray phase), Co (white phase) and the mixed carbide fccphase (dark gray phase). Considering the raw composition of the mixture, the fcc-phase forms a core–rim type structure consisting of a (Ti, W, Ta, Nb)(C,N) phase . The fcc-free layer thicknesses are of 23 ± 1, 32 ± 1 and 45 ± 1 μm after 2, 3 and 5 h respectively. The fccfree layer formation obeys a parabolic law, indicating a diffusioncontrolled process. 4.2. DICTRA simulations of fcc-free layer growth kinetics A number of DICTRA calculations were performed in order to make a conclusion about the kinetic description of the liquid necessary for the simulations. The composition used in the simulations was determined by chemical analysis of sintered samples (Table 2). The
ﬁrst calculation was performed deﬁning the same mobility for all diffusing elements; i.e. Mk = (1∙10− 9/RT) m2/s. At 1450 °C and with an activation energy of 65,000 J/mol this yields a frequency factor of approximately M0k = 9.34∙10− 8 m2/s. The results of the DICTRA simulation of the fcc-free layer formation for this situation are shown in Fig. 2a. It can be observed that the phase distribution for WC, Co and the fcc phase ﬁts reasonably well with previous reported proﬁles . However, the kinetics of the fcc-free layer formation is too fast, reaching an fcc-free layer thickness of 33 μm already after 4500 s (compare Fig. 1, 2h, fcc-free layer ~23 μm). This result indicates that the assumption of the same mobility for all elements is inappropriate to simulate the diffusion-controlled process for the conditions investigated, because it leads to an overestimated layer growth. For further calculations it seems reasonable to assume that the mobility of the light non-metallic elements (C and N) is larger than for the heavier metallic elements (Ti, Ta, Nb, W and Co). Hence, a reduction of the mobility of all metallic elements (Nb, Ta, Ti, W and Co) by dividing the initial mobilities by 10 is considered. The mobility of C and N was not altered (~1.0 · 10− 9/RT m²/s). It is expected that the kinetics of the layer growth will be reduced due to the slower diffusivity of the metallic elements. The DICTRA simulations validated this hypothesis. Nevertheless, the kinetics of the layer formation was too slow. The experimentally observed layer thickness
Fig. 2. DICTRA simulation of fcc-free layer formation at 1450 °C and 2 h vacuum sintering: same mobility for all elements (a); mobilities of metallic elements 10 times slower than that of C and N (b).
Fig. 3. SEM image and corresponding DICTRA simulation of cemented carbide after 2 h vacuum sintering at 1450 °C. The metallic element mobilities are 2 times slower than that of C and N. Good ﬁtting between DICTRA simulations and experimental results are observed.
J. Garcia et al. / Int. Journal of Refractory Metals and Hard Materials 29 (2011) 256–259
Fig. 4. Kinetics of fcc-free layer growth: DICTRA calculations and experimental results (left). DICTRA simulations of fcc-free layer formation after 5 h vacuum sintering at 1450 °C (right).
of ~ 23 μm was not reached after 2 h at 1450 °C. The Co phase fraction and WC proﬁle showed incorrect distributions compared with the experimental results (see Fig. 2b); the Co out-diffusion increased uninterrupted towards the surface during the whole simulation leading to unrealistic high binder phase contents (up to 40 vol.%) in the fcc-free layer. The WC phase showed an unusual decrease inside the fcc-free layer, probably driven by the increased Co content on the surface. In order to increase the kinetics of the fcc-free layer formation, the mobility of all metallic elements was divided by 5. DICTRA simulations showed that this assumption slightly increased the fcc-free layer thickness but yielded an incorrect distribution of the Co and WC phases, similar to the results obtained for the previous calculations (Fig. 2b). These observations led to the conclusion that the difference in mobility between the metallic and the non-metallic elements should be reduced. The next calculation was carried out by dividing the mobilities of the metallic elements (Nb, Ta, Ti, W and Co) by 2. The results of the DICTRA simulation after 2 h vacuum sintering and the corresponding scanning electron microscopy (SEM) sample image are shown in Fig. 3. In the SEM image, the light gray phase corresponds to WC, the dark gray to the fcc-phase and the black to the cobalt binder phase. The contrast between the phases of the SEM image is used for the determination of the phase fraction distribution as a function of depth by image analysis as described in Refs. [5,7]. The quantitative determination of the phase fractions shows the formation of an fcc-free layer of 20 μm, which has a slightly higher WC content and increased the Co content as in the bulk. Beneath the fcc-free layer an increment of the cubic carbide phases is observed. The DICTRA simulation results for this last case ﬁts very well in both fcc-free layer thickness and phase distribution (Fig. 4). Using this last assumption the kinetics of the fcc-free layer growth for 2, 3 and 5 h was simulated, showing a very good agreement with the experimental results (see Fig. 4). 5. Conclusions Summarizing, tough fcc-free graded layers were produced by liquid phase sintering of TiN-containing cemented carbides in vacuum atmospheres at 1450 °C. The kinetics of formation of the graded layers was simulated by DICTRA. The inﬂuence of the mobility of all diffusing elements in the liquid cobalt binder phase at the sintering temperature
was investigated. The best agreement between experimental and simulations were obtained by considering that the mobility of all metallic elements (W, Co, Ti, Ta and Nb) is two times slower compared with the mobility of C and N. However, it should be noted that the obtained mobility values can only be regarded as ﬁtting parameters for the speciﬁc experimental situation. Their values will depend on many factors such as the applied thermodynamic description as well as the choice of the labyrinth factor. By accounting for this aspect, DICTRA calculations is an important tool for the simulation and prediction of the inﬂuence of composition and process parameters in the production of tough graded surface layer on cemented carbides.
Acknowledgement Dr. José Garcia thanks the ﬁnancial support of the joint research group Microstructural Analysis (Helmholtz-Zentrum Berlin für Materialien und Energie GmbH/Ruhr Universität Bochum).
References  Suzuki H, Hayashi K, Taniguchi Y. The beta-free layer formed near the surface of vacuum-sintered WC-beta-Co alloys containing nitrogen. Trans Jnp Inst Metals 1981;22:758–64.  Schwarzkopf M, Exner HE, Fischmeister HF, Schintlmeister W. Kinetics of compositional modiﬁcation of (W, Ti)C–WC–Co alloy surfaces. Mater Sci Eng A 1988;105/106:225–31.  Gustafson P, Östlund Å. Binder-phase enrichment by dissolution of cubic carbides. Int J Refract Met Hard Mater 1994;12(3):129–36.  Thermocalc and DICTRA software. http://www.thermocalc.com.  Ekroth M, Frykholm R, Lindholm M, Andrén HO, Ågren J. Gradient zones in WC–Ti (C, N)–Co-based cemented carbides: experimental study and computer simulations. Acta Mater 2000;48:2177–85.  Thermodynamic carbonitride database CN1b, CAMPADA. Sweden: Royal Institute of Technology; 1999.  Frykholm R, Ekroth M, Jansson B, Ågren J, Andren HO. A new labyrinth factor for modelling the effect of binder volume fraction on gradient sintering of cemented carbides. Acta Mater 2003;51:1115–21.  Frisk K, Dumitrescu L, Ekroth M, Jansson B, Kruse O, Sundman B. Development of a database for cemented carbides: thermodynamic modeling and experiments. J Phase Equilib 2001;22(6):645–55.  J. Garcia, K. Kipperer. Hard metal body with tough surface region. European Patent EP1880031; 16.11.2006.  Software AnalySIS 5.0: Olympus Soft Imaging System 2008.  Borgenstam A, Engstrom A, Hoglund L, Ågren J. DICTRA, a tool for simulation of diffusional transformations in alloys. J Phase Equilib 2000;21(3):269–80.  Andrén HO. Microstructures of cemented carbides. Mater Des 2001;22:491–8.