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Harald Schmidt, Wolfgang Gruber
To cite this version:
Harald Schmidt, Wolfgang Gruber. Crystallization Kinetics of Amorphous Si-C-N Ceramics: De- pendence on Nitrogen Partial Pressure. Philosophical Magazine, Taylor & Francis, 2010, 90 (11), pp.1485-1493. �10.1080/14786430903397289�. �hal-00584289�
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Crystallization Kinetics of Amorphous Si-C-N Ceramics:
Dependence on Nitrogen Partial Pressure
Journal: Philosophical Magazine & Philosophical Magazine Letters Manuscript ID: TPHM-09-Jul-0299.R1
Journal Selection: Philosophical Magazine Date Submitted by the
Author: 02-Oct-2009
Complete List of Authors: Schmidt, Harald; TU Clausthal, IMET Gruber, Wolfgang; TU Clausthal, IMET Keywords: crystallization, kinetics, precipitation Keywords (user supplied):
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Crystallization Kinetics of Amorphous Si-C-N Ceramics: Dependence on Nitrogen Partial Pressure
H. Schmidt
*and W. Gruber,
Technische Universität Clausthal, Institut für Metallurgie, Robert-Koch-Str. 42, D-38678 Clausthal-Zellerfeld, Germany.
*Corresponding author
Abstract
The crystallization kinetics of amorphous precursor-derived ceramics of composition Si26C41N33 is investigated as a function of temperature and nitrogen partial pressure using X-ray diffractometry. Isothermal annealing at a pressure of 1 bar leads to simultaneous crystallization of Si3N4 and SiC, while for annealing at a reduced pressure of 1 mbar crystalline SiC is formed only. Rate constants of crystallization are determined using the Johnson-Mehl-Avrami- Kolmogorov (JMAK) formalism. For temperatures below 1700 °C crystallization rates are significantly higher for annealing at 1 mbar than for 1 bar, respectively. For an explanation of the results a model is proposed, which is based on diffusion controlled nucleation and growth of crystalline Si3N4 and SiC in an amorphous matrix combined with thermal decomposition of Si3N4 at high temperatures.
Keywords: Crystallization, kinetics, precipitation, X-ray diffractometry
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1. Introduction
Non-oxide ceramics of the system Si-C-N, which are derived from pre-ceramic polymers by solid state thermolysis became a field of growing research interest during the last years [1-7].
The resulting materials are free of sinter additives and exhibit a good high-temperature stability and oxidation resistance making them attractive for applications in various branches of technology. The underlying aim of this processing route is to tailor inorganic ceramics on the basis of molecular units in order to control the structure and properties of such a material on an atomic scale.
After thermolysis, Si-C-N ceramics form an amorphous non-equilibrium state, which is stable up to about 1500 °C. Investigations with small and wide angle X-ray and neutron scattering [8,9] as well as nuclear magnetic resonance experiments [10] proved a phase separation of the material on the scale of 1 nm, where amorphous Si3+0.25xCxN4-x (x = 0 - 4) domains and graphite-like amorphous carbon domains with sp2 hybridised structural units coexist [8,9]. At a temperature of 1500 °C and above the material starts to crystallize, while different types of composites (e.g.
nano-/micro-crystalline) are formed [4]. Several publications on polymer-derived ceramics of type Si-C-N can be found in the literature, dealing with synthesis [3,5,6,7], microstructure [8-11], thermochemistry [12,13], oxidation resistance [14-16], electronic properties [17,18], and mechanical properties [19,20]. However, quantitative studies on the crystallization kinetics of these materials are very limited. In preceding research work [21,22], we investigated the crystallization kinetics of Si-C-N at a nitrogen partial pressure of 1 bar. We found that micro- crystalline α-Si3N4 and nano-crystalline SiC are simultaneously formed. Crystallization was described according to the Johnson-Mehl-Avrami-Kolmogorov (JMAK) formalism, assuming a three-dimensional, diffusion controlled grain growth with a time dependent nucleation rate. The
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determined rate constants of crystallization are temperature dependent, but equal for both crystallized phases and can be described approximately by an Arrhenius behaviour with an activation enthalpy of about 120.4 kJ/mol (12.5 eV) [21].
In the present study, we investigated the influence of reduced nitrogen partial pressure on crystallization and precipitation behaviour of the model system Si26C41N33 in order to get information on an optimized stability of the amorphous state for technological applications and to obtain basic information for the production of tailor-made microstructures. We also present a model explaining the pressure dependence of crystallization kinetics in these materials
2. Experimental details
Bulk samples under investigation were produced by isostatic pressing and subsequent thermolysis of cross-linked pre-ceramic polymers at 1050 °C in an argon atmosphere. The polyvinylsilazane VT 50 (Hoechst AG, Germany) was used to synthesize amorphous ceramics with a porosity of about 5 %. A detailed description of the preparation procedure can be found in Ref. [3]. The composition was determined by Rutherford backscattering analysis to be Si26C41N33. To obtain defined conditions for X-ray investigations the bulk samples were cut into platelets of about 8 x 8 x 2 mm3, polished with diamond paste (particle size: 15 µm, 6 µm, 3 µm, and 1 µm) and cleaned with ethanol in an ultrasonic bath.
To observe the crystallization process, the ceramics were annealed in nitrogen at 1000 mbar and alternatively in a nitrogen/argon mixture with a nitrogen partial pressure of 1 mbar in the temperature range between 1450 and 1700 °C. To avoid decomposition and contamination with oxygen during annealing, the samples were placed in a crucible and embedded in powder of the same material. The investigations with X-ray diffractometry were carried out with a SIEMENS
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D5000/Kristalloflex diffractometer in the θ/2θ modus using CoKα radiation (40 kV, 40 mA) on bulk ceramics.
3. Results
Annealing of as-thermolyzed amorphous Si-C-N samples in the temperature range between 1450 - 1700 °C in nitrogen leads to crystallization. For anneals carried out at a nitrogen partial pressure of 1 bar a mixture of crystalline Si3N4 (grain diameter > 100 nm) and crystalline SiC (grain diameter ~ 30 - 40 nm) is precipitated, as shown in Ref. [21]. For temperatures above 1600
°C only SiC and below 1535 only Si3N4 is formed [21]. In contrast, all the XRD measurements of this study revealed, that the samples annealed at a reduced nitrogen partial pressure of 1 mbar between 1450 and 1700 °C show crystallization of SiC only. This behaviour can be explained considering the phase diagram of the system Si-C-N. Fig. 1 shows theoretically calculated isothermal sections at ambient nitrogen partial pressure according to Ref. [23] valid up to 1484
°C (a) and between 1484 and 1841 °C (b). The crystalline phases Si3N4, SiC, and C form a three- phase equilibrium, which is stable up to 1484 °C. The amorphous material is located on the tie- line between Si3N4 and C. During annealing a de-mixing of the metastable amorphous material is expected, resulting in crystalline composite material consisting of Si3N4 and C (graphite).
However, TEM and XRD measurements indicate that carbon stays amorphous [2,21]. In contrast, at temperatures above 1484 °C the phase equilibria change and a three-phase area between SiC, C and gaseous N2 is now stable wherein the starting material is located. The transition from the phase equilibrium shown in Fig. 1(a) to that shown in Fig. 1(b) can be expressed by the chemical reaction
Si3N4 + 3C 3SiC + 2N2, (1)
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where Si3N4 reacts with free carbon to SiC and nitrogen gas. From these theoretical considerations annealing of the amorphous ceramics at temperatures higher than 1484 °C should result in the formation of crystalline material composed of SiC by simultaneous loss of gaseous N2 [23]. However, X-ray analysis shows that up to 1600 °C always a mixture of Si3N4 and SiC is formed. With growing temperature, the fraction of α−Si3N4 decreases and at the same time the fraction of SiC increases, until at 1645 °C only SiC is present. In the present composites, crystalline Si3N4 seems to be stabilized, at least partly, to higher temperatures due to the embedding in an amorphous matrix of Si-C-N (for details see Ref. [21]). Fig. 2 shows the equilibrium temperature of reaction (1) as a function of nitrogen partial pressure as received by thermodynamic calculations according to Ref. [12]. As obvious the equilibrium temperature is shifted to a lower temperature of 1049 °C for a pressure of 1 mbar. This explains why during the experiments with reduced partial pressure SiC crystallizes only.
For a detailed understanding of the crystallization process X-ray diffraction studies were carried out as a function of annealing time. First, the amorphous material was isothermally annealed at a distinct temperature for a given time. Then the material was characterized with XRD and afterwards annealed again. This procedure was repeated until the X-ray diffractograms did not change any more during further annealing, meaning that the degree of crystallization of the material remained constant. A typical example for the time dependent growth of a SiC X-ray peak is shown in Fig. 3. The fraction of crystallized phase, χi, is calculated from the integrated intensity of the X-ray peak. A detailed description of the procedure can be found in Ref. [21].
An characteristic example for the dependence of the crystallized fraction on annealing time at 1500 °C is illustrated in Fig. 4 for experiments at both partial pressures under study. As obvious annealing at a reduced partial pressure leads to accelerated crystallization of SiC.
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The crystallization process based on a nucleation and growth process is analysed using Johnson, Mehl, Avrami, and Kolmogorov theory (JMAK-theory) [24]. The crystallized volume fraction of a specimen after time t is given by
χ
(t)=1−exp(
−(k t)n)
, (2) where, k is the temperature dependent rate constant of crystallization and n is the JMAK exponent. The experimentally determined volume fractions of crystallized SiC and Si3N4 were analysed as a function of annealing time at different annealing temperatures in terms of Eq. (2).Fitting of the data yields JMAK exponents between n = 2 - 2.5, corresponding to a three- dimensional diffusion controlled growth with significant nucleation during the growth process (for details see Ref [21]). In Fig. 5 the determined rate constants of crystallization are plotted as a function of reciprocal temperature.
On base of the actual findings and of literature data, the crystallization process can be visualized as follows. At low temperatures and high nitrogen partial pressure silicon nitride directly crystallizes from the amorphous silicon nitride domains by a nucleation and growth process. For higher temperatures and lower nitrogen partial pressure, in the phase-separated amorphous state amorphous silicon nitride domains react with the surrounding carbon phase to amorphous SiC. In a second step, amorphous SiC transforms to crystalline SiC embedded in an amorphous residual matrix by a polymorphous transformation, if the critical nucleus size is reached.
4. Discussion
Data analysis is carried out on base of the classical nucleation and growth theory, where the rate constant of crystallization is given by [24]
(3)
∆
− ∆
∆−
= G T k T
Γ T
k k H
k
B B
D
)2
( 3
16 5 exp 2 exp
3 0
π
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where k0 is the pre-exponential factor, ∆HD is the activation enthalpy of diffusion, ∆Γ is the difference in the interfacial energy between amorphous domains and amorphous/crystalline interfaces and finally ∆G is the difference of the Gibbs energy between the crystalline composite and the amorphous ceramic, the driving force of crystallization. For the crystallization of SiC, we subdivide the last quantity into two contributions
∆G = ∆Gc(T) + ∆Gr (T, P) (4)
a reaction part, ∆Gr, describing the Gibbs energy which is released due to reaction (1) and a crystallization part, ∆Gc, describing the Gibbs energy difference between crystalline and amorphous SiC. Further, the components of the Gibbs energy are given by
∆Gc = ∆Hc - T ∆Sc (5)
and
∆Gr = ∆Hr – T ∆Sr + 2kB T ln(P/P0), (6)
respectively. Here, ∆Hi (i = r, c) is the enthalpy change and ∆Si the entropy change of the process and P0 = 1bar. In contrast, for the crystallization of Si3N4 no reaction part is present because the crystallites can be directly formed within the amorphous silicon nitride domains.
For crystallization of SiC, the crystallization part of the precipitation process given by Eq. (5) is given according to Ref. [25] in good approximation by ∆Gc ≈ ∆Hc ≈ const. The entropy contribution is very small and Gibbs energy is approximately independent of temperature at the temperatures under investigation. We take from Ref. [26] a Gibbs energy of ∆Gc = -162 kJ for the crystallization of three mole of SiC, which is identical to -54 kJ/(mol SiC). This term simply describes the difference in Gibbs energy between amorphous and crystalline silicon carbide. The
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first two terms of the reaction part in Eq. (6) were calculated at 1 bar by the FACT- Web/Reaction-Web program [27] for reaction (1) to be ∆Gr = ∆Hr – T ∆Sr = 524.9 kJ – 306.2 J/K
· T. The last term in Eq. (6) can be obtained directly from the experimental conditions. It is zero for annealing at 1 bar and – 114.8 J/K · T for annealing at 1 mbar, respectively. Note that the data describing the Gibbs energy refer to equation (1) and are not per mole.
In Eq. (3) also the activation enthalpy of self-diffusion for the slowest moving and consequently rate determining constituent in amorphous Si-C-N enters. Experiments on self-diffusion of Si in amorphous VT50-derived Si-C-N ceramics, and of Si, C and N in similar amorphous Si-(B-)C-N ceramics were carried out by our group with stable isotopes by means of secondary ion mass spectrometry [28-30]. No large differences between the diffusivities of the three elements were measured (about one order of magnitude) indicating a common diffusion mechanism where all elements contribute nearly equally to atomic re-arrangement processes [30]. The results show a thermally activated behaviour with an activation enthalpy of ∆HD = 5.7 eV (549.0 kJ/mol) for the VT50-derived material [29].
In order to compare our experimental data to our model, the data given above are inserted in Eqs.
(3-6). The only unknown parameters are the difference in interfacial energy, ∆Γ, and the pre- exponential factor, k0, which are obtained by a least-squares fitting procedure of the data obtained at 1 bar. The result is given in Fig. 5. We obtain a quite reasonable value of
∆Γ ≈ 0.5 J/m2 assuming a density of 1.2 x 105 mol/m3 of Si0.26C0.41N0.33. A considerable lower value of 0.2 J/m2 is for example found for the crystallization of amorphous silicon [31]. For the description of crystallization at a pressure of 1 mbar the difference of 2kB·T ln(P/1bar) = – 114.8 J/K · T is subtracted from the Gibbs energy difference, ∆G, while ∆Γ remains constant. Here, also a good description of the experimentally derived rate constants is obtained (see Fig. 5). The only adjustable parameter is the pre-exponential factor, which changes slightly from 6 x 1013 s-1
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for 1 bar to 3 x 1012 s-1 for 1 mbar. We see that the fittings perfectly describe the rate constants of SiC precipitation for anneals at 1 bar and 1 mbar, respectively.
As already mentioned, for the crystallization of Si3N4 no reaction part is present because the crystallites can be directly formed within amorphous silicon nitride domains. Further, we assume also a temperature independent crystallization part [25], which is given by ∆Gc = – 69 kJ [32] for the crystallization of 1 mole of Si3N4. The corresponding model curve is also shown in Fig. 5.
The rate constants of crystallization of Si3N4 are also described very well for the same difference in interfacial energy as found for the crystallization of silicon carbide.
In Ref. [13] the enthalpy of formation of amorphous Si-C-N ceramics from crystalline Si3N4, C and a tiny amount of SiC was studied at 25 °C by calorimetric measurements. The determined enthalpies lie between - 9.2 and + 12.7 kJ/(mol SixCyNz) (x + y +z = 1) within error limits for samples with similar composition (S3 and S4 in Ref [13]). Keeping in mind that in our case about 0.08 mol of crystalline Si3N4 has to be consumed for the formation of 1 mol of amorphous Si0.26C0.41N0.33, the calorimetric measurements correspond to enthalpy values ranging from -115 to +159 kJ/(mol Si3N4). This is not contradictive to our assumption of -∆Gc = 69 kJ /(mol Si3N4).
As also obvious from Fig. 5, silicon nitride and silicon carbide crystallize approximately with the same rate constant in the temperature range investigated. According to our analysis, in case of Si3N4 an Arrhenius straight line is present and in case of SiC a slightly curvature has to be present, which however cannot be resolved by the experimental data. The question whether the similarity of the rate constants of both crystalline phases and their temperature is the product of accidentally coincidence or whether an unknown mechanism is present, e. g. a coupling of the crystallization process of SiC and Si3N4, has to be clarified in future.
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5. Conclusion
In this study we investigated crystallization kinetics of amorphous Si26C41N33 ceramics as a function of annealing temperature and pressure. We found that a reduced nitrogen partial pressure suppresses the crystallization of silicon nitride and accelerates the crystallization of SiC below 1700 °C. A model based on diffusion controlled nucleation and growth is presented, where the lower rate constants at a reduced partial pressure can be explained by an increase of the driving force of crystallization. A more negative Gibbs free energy difference between the crystalline and amorphous state is caused by the pressure dependence of the decomposition reaction, Eq. (1).
Acknowledgements
The authors thank P. Gerstel (MPI Stuttgart) for supply of the precursor ceramics and E. Ebeling for ceramographic preparation. Funding by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged.
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References
[1] J. Bill, F. Wakai, F. Aldinger (eds.), Precursor-Derived Ceramics (Wiley-VCH, 1999).
[2] J. Bill, J. Seitz, G. Thurn, J. Dürr, L. Canel, B. Z. Janos, A. Jalowiecki, D. Sauter, S.
Schempp, H.-P. Lamparter, J. Mayer, F. Aldinger, Phys. Stat. Sol. 166 (1998) 269.
[3] J. Bill, J. Schumacher, K. Müller, S. Schempp, J. Seitz, J. Dürr, H.-P. Lamparter, J.
Golczewski, J. Peng, H. J. Seifert, F. Aldinger, Z. Metallkd. 91 (2000) 335.
[4] E. Kroke, Y. L. Li, C. Konetschny, E. Lecomte, C. Fasel, R. Riedel, Mat. Sci. Eng. R26 (2000), 97.
[5] G. Ziegler, H.-J. Kleebe, G. Motz, H. Müller, S. Traßel, W. Weibelzahl, Mat. Chem. Phys. 61 (1999) 55.
[6] R. Riedel, G. Mera, R. Hauser, A. Klonczynski, J. Ceram. Soc. Jpn. 114 (2006), 425.
[7] M. Jansen, B. Jaschke, T. Jaschke in: High Performance non-oxide ceramics Vol. 101 (Springer, Berlin, 2002), p. 137.
[8] J. Haug, P. Lamparter, M. Weinmann, F. Aldinger, Chem. Mater. 16 (2004), 72.
[9] J. Dürr, P. Lamparter, J. Bill, S. Steeb, F. Aldinger, J. Non-Cryst. Sol. 232 (1998), 155.
[10] J. Schuhmacher, F. Berger, M. Weinmann, J. Bill, F. Aldinger, K. Müller, Appl. Org. Met.
Chem. 15 (2001), 1.
[11] H.-J. Kleebe, Phys. Stat. Sol. 166 (1998) 297.
[12] H. J. Seifert, H. L. Lukas, F. Aldinger, Ber. Bunsenges. Phys. Chem. 102 (1998), 1309.
[13] R. M. Morcos, G. Mera, A. Navrotsky, T. Varga, R. Riedel, F. Poli, K. Müller, J. Am.
Ceram. Soc. 91 (2008), 3349.
[14] L. An, R. Riedel, C. Konetschny, H. J. Kleebe, R. Raj, J. Am. Ceram. Soc. 81 (1998)1349.
[15] R. Raj, L. An, S. Shah, R. Riedel, C. Fasel, H. J. Kleebe, J. Am. Ceram. Soc. 81 (1998) 1803.
[16] Y. G. Wang, Y. Fan, L. G. Zhang, W. G. Zhang, L. N. An, Scr. Mater. 95 (2006), 295.
[17] S. Trassel, M. Puchinger, E. Rössler, G. Ziegler, J. Europ. Ceram. Soc. 23 (2002) 781.
[18] A. M. Hermann, Y.-T. Wang, P. A. Ramakrishnan, D. Balzar, L. An, C. Haluschka, R.
Riedel, J. Am. Ceram. Soc. 84 (2001) 2260.
[19] A. Zimmermann, A. Bauer, M. Christ, Y. Cai, F. Aldinger, Acta Mater. 50 (2002) 1187.
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For Peer Review Only
[20] R. Kumar, Y. Cai, P. Gerstel, R. Rixecker, F. Aldinger, J. Mater. Sci. 41 (2006), 7088.
[21] H. Schmidt, G. Borchardt, A. Müller, J. Bill, J. Non.-Cryst. Solids 341 (2004), 133.
[22] H. Schmidt, G. Borchardt, Adv. Eng. Mater. 7 (2005), 221.
[23] J. Peng, PhD thesis (University of Stuttgart, Germany, 2002).
[24] M. T. Clavaguera-Mora, N. Clavaguera, D. Crespo, T. Pradnell, Prog. Mat. Sci. 47 (2002), 559.
[25] J. A. Golczewski, F. Aldinger, J. Non-Cryst. Sol. 247 (2004), 204.
[26] G. Foti, Appl. Surf. Sci. 184 (201), 10.
[27] http://www.crct.polymtl.ca/FACT
[28] H. Schmidt, G. Borchardt, S. Weber, S. Scherrer, H. Baumann, A. Müller, J. Bill, J. Appl.
Phys. 88 (2000) 1827.
[29] H. Schmidt, G. Borchardt, S. Weber, H. Scherrer, H. Baumann, A. Müller, J. Bill, J. Non- Cryst. Solids 298 (2002) 232.
[30] H. Schmidt, G. Borchardt, O. Kaïtasov, B. Lesage, J. Non-Cryst. Solids. 353 (2007), 4801.
[31] C. Spinella, S. Lombardo, F. Priolo, J. Appl. Phys. 84 (1998), 5383.
[32] I. Tomaszkiewicz, J. Therm. Anal. Calorim. 65 (2001), 425.
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Figure Captions
Figure 1: Isothermal sections of the Si-C-N system at a total pressure of 1 bar (after Ref [23]).
The composition of amorphous Si26C41N33 and the reaction path (arrow) due to the loss of N2
during annealing is indicated: (a) T < 1484 °C; (b) 1484 °C < T < 1841 °C.
Figure 2: Calculated equilibrium temperature of reaction (1) as a function of temperature according to Ref. [12].
Figure 3: Exemplary illustration of the isothermal growth of a SiC X-ray peak at 1650 °C. The annealing times are indicated. Not all data are shown for clarity.
Figure 4: Normalized volume fraction of crystallized SiC as a function of annealing time at 1570 °C for annealing at 1 bar and 1 mbar nitrogen partial pressure. The solid lines correspond to a fit of the data according to Eq. (2).
Figure 5: Rate constants of crystallization for SiC and Si4N4 as a function of reciprocal temperature for annealing at 1 bar and 1 mbar nitrogen partial pressure. The lines correspond to least-squares fits according to Eq. (3-6) and the parameters given in the text: SiC at 1 mbar (red line), SiC at 1 bar (blue line), and Si3N4 at 1 bar (green line).
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Fig.1
209x297mm (600 x 600 DPI)
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Fig. 2
209x297mm (600 x 600 DPI)
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Fig. 3
209x297mm (600 x 600 DPI)
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Fig. 4
209x297mm (600 x 600 DPI)
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Fig.5
209x297mm (600 x 600 DPI)
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