Growth Kinetics of -Ti Solid Solution in Reaction Diffusion

Transcription

1 Materials Transactions, Vol. 44, No. 1 (2003) pp. 83 to 88 Special Issue on Diffusion in Materials and Its Application Recent Development #2003 The Japan Institute of Metals Growth Kinetics of -Ti Solid Solution in Reaction Diffusion Osamu Taguchi 1, Gyanendra Prasad Tiwari 2 and Yoshiaki Iijima 2 1 Materials Science and Engineering, Miyagi National College of Technology, Natori , Japan 2 Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai , Japan The growth kinetics of the -Ti solid solution phases in several pure metal diffusion couples have been investigated. The layer growth of - Ti solid solution phases is observed to obey the parabolic law, indicating that the rate controlling process is diffusion. The temperature dependence of the rate constant of the layer growth shows a linear relationship in the Arrhenius plots at higher temperatures. On the other hand, it deviates from the linearity at low temperatures. This deviation from the linearity is shown to be related to the variation of compositional range of the -Ti solid solution with temperatures. Additionally, the activation energy for the layer growth is found to be equal to sum of the activation energy for interdiffusion and the formation enthalpy of -Ti solid solution in the eutectoid temperature range. (Received September 12, 2002; Accepted October 17, 2002) Keywords: reaction diffusion, interdiffusion, growth kinetics, growth rate constant, activation energy for diffusion 1. Introduction Study on growth kinetics of the layer in reaction diffusion provides valuable information for several industrial processes, such as metal cladding, diffusion bonding, combustion synthesis and fabrication of superconducting metallic compounds, and so on. Many investigations have been carried out on the layer growth of intermetallic compounds formed in the diffusion couples. 1,2) Fundamental questions in the reaction diffusion are whether the growth is diffusion controlled, whether all the phases predicted from the equilibrium phase diagram are present and whether the interface compositions approach to those predicted from the equilibrium phase diagram. The previous investigations have shown that all the equilibrium phases existing in the phase diagram do not always appear in the diffusion zone 3 5) and that in some alloy systems, the interface compositions deviate from those in the phase diagrams. 6) The growth of the layer thickness, d, ofan intermetallic compound after the diffusion time, t, is generally expressed by d ¼ kt n ð1þ where k is the growth rate constant and n the time exponent. In many cases of the reaction diffusion, n ¼ 1=2, indicating that the growth is controlled by the diffusion. However, in some systems non-parabolic growth without an incubation time has been observed at low temperatures, where some interface reaction or short-circuit diffusion such as grain boundary diffusion predominates. 7,8) The present paper reports the reaction diffusion studies between pure metals Ti X (X = Fe, Ni, Cr, Co, Cu, Ag and Au). It has been shown that the Arrhenius plots of k 2 of the - Ti solid solutions, designated as (-Ti(X)), are bent downward at lower temperatures. The bending of the Arrhenius plot of k 2 are shown to be related to the temperature dependence of the composition range C of the -Ti(X). Furthermore, the activation energies obtained from the Arrhenius plots for k 2 ðq k Þ, the interdiffusion coefficient ~DðQ D Þ and CðQ C Þ are related as Q k ¼ Q D þ Q C. 2. Experimental Procedure Rods of pure metals, Ti, Fe, Cr, Co, Ni and Ag were made by argon-arc melting of titanium sponge of 99.6%, electrolytic grades of iron (99.9%), chromium (99.4%), nickel (99.9%) and silver granules of 99.99% purity. The grain size of arc-melted metals ranged from mm. Pure copper rods were made by vacuum melting of oxygen-free Cu chips of 99.99% purity in an alumina crucible and casting into steel mold followed by hot-forging, rolling and machining into 10 mm diameter rods. All the metallic rods were machined to make disc specimen of 8 10 mm in diameter and 5 mm in thickness. The regular square pieces 10 mm in size and 1 mm in thickness were machined from 99.99% Au pure sheets. For grain growth, the specimens were annealed at 1273 K for 3 days in a vacuum furnace evacuated to 3 mpa. The resultant grain size was 1 3 mm. Flat face of the disc specimens were ground on water-proof abrasive papers and polished on a buff with fine alumina paste. Semi-infinite type pure metal Ti X diffusion couples were set in a stainless steel holder and pressed by screws. The couples were welded below the eutectoid transition temperature of the each alloy system. The diffusion annealing were performed in an evacuated quartz tube with Ti foils as gettering materials to remove oxygen, nitrogen and hydrocarbons from the annealing atmosphere. The diffusion annealing was carried out between the eutectoid temperature of the system Ti X and transition of pure Ti. The temperatures were controlled within 1 K. After the diffusion annealing, the couples were cut parallel to the diffusion direction and the section was polished in the same way as described above. The metallographic structure of the diffusion zone was examined optically by using an etchant containing HF (3%), HNO 3 (5%) and HCl (5%). The -Ti(X) phases formed in the diffusion zone were etched in dark-brown color. The layer thickness of the -Ti(X) phase greater than 10 mm was measured by an optical microscopy, while the layer thickness less than 10 mm was measured by use of a backscatter electron image of a scanning electron microscope (Jeol 5600LV). An electron probe microanalyser (Shimadzu EPMA-8705) was used to determine the concen-

2 84 O. Taguchi, G. P. Tiwari and Y. Iijima tration profile of Ti and metal X. The interdiffusion coefficients in the -Ti(X) phases were determined by the method of Sauer and Freise. 9) 3. Results 3.1 Growth kinetics Figure 1 shows that the layer thickness (d) of the -Ti(Fe) and -Ti(Au) phases as a function of time as examples. Similar growth plots have been obtained for all other systems studied and discussed here. The thickness of the -solid solution layer phases formed by reaction diffusion is proportional to the square root of diffusion time. Thus the layer growth obeys the so-called parabolic law, viz. d ¼ kt 1=2 ð2þ It is indicative of the diffusion controlled growth. The Arrhenius plots of k 2 of -Ti(Fe), -Ti(Co) and -Ti(Ni) phases are plotted in Figs They show good linearity at higher temperatures, while at lower temperatures, the plots deviate downward from the extrapolated high temperature linear line. In the -Ti(Cu), -Ti(Ag) and -Ti(Au), the temperature region between the allotropic transformation point and the eutectoid temperature is narrow. Hence, although the non-linearity in the Arrhenius plots does exist in their cases also, it is difficult to separate high temperature and low temperature regions unambiguously. The activation energies, Q k for the layer growth of the - Ti(X) phases in high temperature ranges are compiled in Table 1. Fig. 2 Temperature dependence of k 2 and ~D for -Ti(Fe) solid solution. Fig. 1 (a) Plot of layer thickness of -Ti(Fe) solid solution vs. square root of diffusion time, (b) Plot of layer thickness of -Ti(Fe) solid solution vs. square root of diffusion time. Fig. 3 Temperature dependence of k 2 and ~D for -Ti(Co) solid solution.

3 Growth Kinetics of -Ti Solid Solution in Reaction Diffusion 85 Fig. 4 Temperature dependence of k 2 and ~D for -Ti(Ni) solid solution. Table 1 Comparison of values Q k, Q D, Q, (Q D þ Q ), Q C and (Q D þ Q C ). Q k Q D Q (Q D þ Q ) Q C (Q D þ Q C ) kjmol 1 kjmol 1 kjmol 1 kjmol 1 kjmol 1 kjmol 1 -Ti(Fe) Ti(Co) Ti(Ni) Ti(Cr) Ti(Cu) Ti(Ag) Ti(Au) Ti(Pd) 3) Fig. 5 Concentration dependence of ~D in -Ti(Fe) solid solution. 3.2 Interdiffusion coefficients Figure 5 shows the concentration dependence of the interdiffusion coefficient ~D in the -Ti(Fe) phase. The composition range of the -Ti(Fe) determined by EPMA at each diffusion temperature is also shown in Fig. 5. In the - Ti(Fe), ~D deceases with increasing the concentration of Fe. The Arrhenius relationship of ~D shows good linearity in the whole of the temperature range. For the others -Ti(X) phases also, the linearity of Arrhenius plots of ~D is maintained in the entire temperature range of the experiment. Though the diffusion coefficient varies with the composition, the activation energies are independent of the alloy composition. This is clearly shown in Fig. 6. Nearly identical slops of all three plot curves indicates that the activation energy is independent of composition despite the variation of ~D with composition. The activation energies Q D for interdiffusion in Fig. 6 Temperature dependence of ~D in -Ti(Fe) solid solution.

4 86 O. Taguchi, G. P. Tiwari and Y. Iijima -Ti(X) phases are listed in Table 1. In each alloy system, it is observed that Q k is much higher than Q D. 4. Discussion X ¼ 2 ðd tþ 1=2 X ¼ 2 ðd tþ 1=2 W ¼ðX X Þ¼2j jðd tþ 1=2 ð3þ ð4þ ð5þ The Arrhenius plot of k 2 of -Ti(X) phases does not follow the expected linear trend at all temperatures but shows a downward deviation from the linearity at low temperatures. Further, the activation energy for the layer growth of -Ti(X) phases is much higher than that for interdiffusion. A typical phase diagram of Ti-rich side for Ti X alloy systems investigated by the present work is shown schematically in Fig. 7. The composition range of the -Ti(X) phases, C, varies significantly with the temperature. Therefore, it is likely that C may influence the growth of -Ti(X) phases. In the following discussion, an attempt is made to assess the importance of the C in the growth of -Ti(X) phases. Figure 8 schematically shows the concentration profile of a diffusion zone in which an intermetallic compound is present. According to Wagner, 10,11) X and X are given by where X and X are distance from the Matano plane to = interface and = interfaces, and are proportionality constants, W and D are the layer growth and the interdiffusion coefficient respectively. From eqs. (3), (4) and (5), we have W 2 =t ¼ k2 ¼ 4ð Þ 2 D ð6þ The value of 4ð Þ 2 for some intermetallic compounds in Al Cu system was calculated by Funamizu and Watanabe 12) and by Nohara and Hirano 13) for Fe Mo system. In the present work, the magnitudes of and or the - Ti(Fe), -Ti(Ni) and -Ti(Co) phases have been evaluated from the penetration curve and the interdiffusion coefficient. Assuming Arrhenius type of behavior, the temperature dependence of 4ð Þ 2 for these phases are shown in Fig. 9. The similarity between the temperature dependence of 4ð Þ 2 and k 2 is clearly recognized, namely, that the plots are linear at higher temperatures and bend downward at lower temperatures. The values of Q obtained from the linear part of the Arrehenius plot of 4ð Þ 2 are listed in Table 1. Funamizu and Watanabe 14) proposed, on empirical grounds, a relationship, between k 2 and ~D which may be expressed as follows; k i ¼ pð ~D i C i Þ a ð7þ where p and a are constants. k i, ~D i and C i are respectively the rate constant, interdiffusion coefficient and composition Fig. 7 Schematic phase diagram of Ti X alloy system. Fig. 8 Schematic concentration profile in which an intermetallic compound formed in a diffusion zone. Fig. 9 Temperature dependences of 4ð Þ 2 in -Ti(Fe), Ti(Co) and Ti(Ni) solid solutions.

5 Growth Kinetics of -Ti Solid Solution in Reaction Diffusion 87 Fig. 10 Logarithmic plot of k vs ð ~DCÞ 1=2 for reaction diffusion in - Ti(X) alloy systems. Fig. 11 Temperature dependences of C for -Ti(X) solid solutions. range for the ith phase in the reaction diffusion zone. Gësele and Tu 15) have theoretically deduced the equation ki 2 ¼ G ~D i C i ð8þ where G is a constant related to atomic volume. Equations (7) and (8) suggest that ki 2 is a function of ~D i and C i. A comparison of eq. (6) with eqs. (7) and (8) shows that 4ð Þ 2 C are same. Experimentally, it is found that the temperature dependence of 4ð Þ 2 and C are same. This fact emphasizes the importance of the compositional range of a phase on it s growth in polyphase diffusion. Following Funamizu and Watanabe, 14) we apply equation (7) to our data. Figure 10 shows the log log plots of k i and ð ~D i C i Þ 1=2. The Fig. 10 includes data from the present work as well as those obtained by Lamparter et al. 3) for -Ti(Pd) phase. Excepting the -Ti(Cr) and the -Ti(Co) systems, the slope is nearly equal to 1. For intermetallic compounds, similar results were reported by Funamizu and Watanabe. 14) The value of n ¼ 1 in Fig. 10 shows that in the eq. (7), a ¼ p ¼ 1 for -Ti(X) phases. Hence, the growth rate equation for -Ti(X) phases may be written as k 2 ¼ W 2 =t ¼ ~D C ð9þ Generally, the temperature dependences of k 2 and ~D obey Arrhenius behavior. If the temperature dependence of C is also expressed by an Arrhenius equation, eq. (9) takes the form, k0 2 expð Q k=rtþ ¼D 0 expð Q D =RTÞC 0 expð Q C =RTÞ ð10þ where k0 2, D 0, C 0 are the pre-exponential terms in the Arrhenius equations for k 2, ~D and C. Therefore, from eq. (10), we have Q k ¼ Q D þ Q C ð11þ The temperature dependences of C for the -Ti(X) phases from the allotropic transformation temperature to the eutectoid temperature are shown in Fig. 11. For the -Ti(Cu) and -Ti(Ag), the value of C obtained from diffusion couple are also shown by open mark. It is obvious that at high temperatures, the temperature dependence of C can be expressed by an Arrhenius type of equation. Hence Q C can be termed as enthalpy or heat of formation of -Ti(X) solid solution phases. 16) The values of Q C are listed in the Table 1. It is noted that for the layer growth of the -Ti(X) phases, the activation energy for the layer growth Q k is equal to the sum of the activation energy for interdiffusion and the formation energy of the -Ti(X) solid solution. Therefore, the effect of the compositional width on the growth of -Ti(X) solid solution is properly described by the eq. (9). 5. Conclusions Using pure Ti pure metal X diffusion couple, the layer growth of the -Ti(X) solid solution phase has been studied in several alloy systems in the temperature range between the allotropic transition of Ti and the eutectoid transition in the Ti-rich side. The present results can be summarized as follows; (1) The layer growth of -Ti(X) phase is predominantly controlled by diffusion. (2) The second power of the layer growth constant k is directly proportional to the product of ~D and C. (3) The layer growth of the -Ti(X) phase is observed to obey the parabolic law. The Arrehenius plot of the growth rate constant shows a good linearity at higher temperatures. At lower temperatures, a departure from linearity is observed. This behavior is related to the influence of compositional width of the -Ti(X) solid solution on it s growth rate in the diffusion zone.

6 88 O. Taguchi, G. P. Tiwari and Y. Iijima (4) The activation energy for the layer growth of the - Ti(X) phase is equal to the sum of the activation energy for interdiffusion and the enthalpy of formation of - Ti(X) phase. REFERENCES 1) J. Philibert: Defect Diffusion. Forum (1993) ) K. Hirano and Y. Iijima: Diffusion in solids, Recent Developments, ed. by M. A. Dayananda and G. E. Murch, (AIME, Warrendale, PA, 1984) pp ) P. Lamparter, T. Krabichler and S. Steeb: Z. Metallk. 64 (1973) ) G. V. Kidson and G. D. Miller: J. Nucl. Mater. 12 (1964) ) Th. Heumann: Z. Metallk. 59 (1968) ) T. Nishizawa and A. Chiba: Trans. JIM 16 (1975) ) C. F. Bastin and G. D. Rieck: Metall. Trans. 5 (1974) ) F. J. J. van Loo and G. D. Rieck: Acta Metall. 21 (1973) ) F. Sauer and V. Freise: Z. Electrochem. 66 (1962) ) W. Jost: Diffusion in Solids, Liquids and Gases, (Academic Press Inc., New York, 1960) pp ) G. B. Gibbs: J. Nucl. Mater. 20 (1966) ) Y. Funamizu and K. Watanabe: Trans. JIM 12 (1974) ) K. Nohara and K. Hirano: Trans. Iron and Steel Inst. Jpn. 37 (1977) ) Y. Funamizu and K. Watanabe: Trans. Jpn. Inst. Light Met. 25 (1975) ) U. Gësele and K. N. Tu: J. Appl. Phys. 54 (1982) ) R. A. Swalin: Thermodynmics of Solids, (John Wiley and Sons, 1972) pp