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Precipitation kinetics in Ag–2 wt% Cu and Ag–2 wt% Cu–0.5 wt% In alloys during transformation
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Physica B 349 (2004) 166–173
Precipitation kinetics in Ag–2 wt% Cu and Ag–2 wt% Cu–0.5 wt% In alloys during transformation R.H. Nada Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt Received 24 October 2003; received in revised form 10 February 2004; accepted 5 March 2004
Abstract The effect of quenching rate on the stress–strain characteristics of Ag–2 wt% Cu and Ag–2 wt% Cu–0.5 wt% In alloys was investigated in the temperature range from 723 K to 923 K. The work-hardening parameters sy, sf, and w, were found to decrease with increasing aging temperature exhibiting maxima at 823 K. The activation energies of the fracture mechanisms before and after transformation were found to be 22.1 and 39.4 kJ/mol, respectively, characterizing a dislocations intersection and grain boundary diffusion mechanisms in Ag for quenched and slowly cooled samples. An increase in strength was observed for the alloy containing (In). This was attributed to the tendency of (In) atoms to segregate at grain boundaries, causing grain size refinement. r 2004 Elsevier B.V. All rights reserved. PACS: 61.72.Lk; 61.72.Ss; 61.72.Yx Keywords: Stress–strain; Phase transformation; Dislocations; Activation energy
1. Introduction One of the most essential phenomena in deformed metals and alloys is the work hardening, which is mainly due to dislocation movement upon plastic deformation. The mechanisms governing hardening in metals and alloys involve the interaction of dislocations with impurity atoms, the formation of particles of second phase, ordering, grain boundary sliding and the intersection of dislocations. It was also mentioned that polycrystalline metals are usually harder than single crystals because of the resistance of grain boundaries, which reduce the dislocation motion and lead to subsequent formation of dislocation pileE-mail address: [email protected] (R.H. Nada).
ups at grain boundaries [1]. Also, the impurities and structure irregularities contribute to the work hardening in polycrystalline metals by acting as obstacles to dislocation motion [2]. Ag and Ag–Cu alloys received a great amount of attention concerning the effect of precold work, grain size, annealing and working temperature on the hardening behaviour of such alloys. Ag–5 at% Cu was investigated in the temperature range from 623 to 773 K [3]. It was found that at temperatures lower than 673 K the work-hardening coefficient increased by giving the samples constant fatigue pulses, while it decreased above 673 K. The effect of grain diameter and precold work by torsion on the hardening behaviour of Ag–8 at% Cu alloy was investigated [4]. It was found that the workhardening coefficient decreased for fine grains and
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increased for large grains by increasing the amount of precold work. These results were interpreted in terms of the dendritic structure of the alloy and mutual dislocation interactions. Gust et al. [5] who studied Ag–6.5 at% Cu alloy, found two types of metastable precipitates by annealing at temperatures ranging from 433 K to 543 K by in situ macrohardness measurements. Many authors [6, 7–9] investigated the effect of the trace elements and temperature on mechanical characteristics of various binary and ternary alloys. According to the constitutional diagram of the Ag–Cu system [10] given in Fig. 1, at room temperature, Ag–2 wt% Cu alloy consists of a-phase (Ag-rich phase) and b-phase (Cu-rich phase). When the alloy is heated the solid solubility of Cu in Ag increases and b-phase dissolves in the a-phase and completely disappears at the transformation temperature and the alloy then consists of the single solid solution a-phase. With the forward transformation on slow cooling, the supersaturated solid solution decomposes and b-crystals precipitate. Its amount is increased as the temperature falls. However, rapid cooling (quenching) of the a-solid solution to room temperature will suppress the
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separation of the b-phase crystals and a homogeneous alloy may be supercooled to low temperatures. The quenched solid solution, supersaturated with the component b, will decompose upon heating at temperatures below transformation temperature. The aim of the present work is to study the effect of both (In) addition, and the formation or dissolution of b-phase on the work hardening parameters of Ag–2 wt% Cu.
2. Experimental procedure 2.1. Samples preparation The materials used in this study were Ag, Cu, and In fragments of purity 99.99%. Two Ag alloys, Ag–2 wt% Cu (alloy A) and Ag–2 wt% Cu–0.5 wt% In (alloy B) were prepared by melting the pure elements in a graphite crucible together with calcium chloride CaCl2 flux to prevent oxidation. The received casting was obtained in the form of rod of 12 mm in diameter. Homogenizing vacuum anneal was carried out by heating
Fig. 1. Constitutional diagram of the system Ag–Cu.
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the cast alloy at 1063 K for 7 days. Cold drawing was carried out with intermediate annealing at 1033 K for 12 h. The rod was swaged in steps to wire of 0.6 mm in diameter. Two groups of samples of each alloy were annealed for 4 h at 1013 K. Group of samples of each alloy was slowly cooled to room temperature (300 K) at a cooling rate of 1 K/min to obtain mixed double phases or fully precipitated samples. The second group of samples of each alloy was rapidly quenched from 1013 K to room temperature to obtain samples with the supersaturated a-solid solution structure. The slow cooled and the quenched samples of each alloy were aged at temperatures in the range from 723 K to 923 K in steps of 25 K. 2.2. Stress–strain measurements Stress–strain tests were performed at room temperature (RT) using a conventional tensile testing machine described elsewhere [11]. The applied stress was increased gradually with 30 s interval between two successive loadings. The elongation was recorded by using a dial gauge sensitive to 7105 m. The time from the start of the tensile test till fracture recorded for each stress–strain run was taken as the fracture time, tf. The coefficient of parabolic work hardening, w, was calculated using the equation [12] w¼
ds2 b ¼ G2 2 ; 2p l de
ð1Þ
where G is the shear modulus of the material, b is the Burgers vector [13] and l is the distance slipped by dislocation. The yield stress, sy, considered as the stress corresponding to the first significant deviation from linearity in the starting part of the stress–strain curve and the fracture stress, sf, taken as the maximum stress applied to the sample before fracture [14] were obtained from the stress– strain curves. 2.3. Structural measurements The microstructure of the quenched samples of both alloys A and B was identified using a Philips X-ray diffractometer (PW 1050/70), with Cu Ka
radiation (0.1542 nm) and scan speed adjusted at 5 min1 in the angle range 2y from 20 up to 120 .
3. Experimental results Stress–strain curves obtained at room temperature for samples of both alloys A and B heattreated at different aging temperatures in the range from 723 to 923 K are shown in Fig. 2. These curves show parabolic stress–strain behaviour in the intermediate range. The aging temperature dependence of the measured hardening parameters namely, the fracture stress, sf, the yield stress, sy, the fracture time, tf, and the work-hardening coefficient, w, obtained as the slope of the straight line of the relation between s2 and e in the parabolic region of the stress–strain curve which proves the applicability of Eq. (1) to the investigated Ag–Cu system, for slowly cooled and quenched samples of both alloys A and B are shown in Fig. 3 a–d. From Fig. 3, it is clear that the values of these hardening parameters are generally lower for the slowly cooled samples than those for the quenched samples. Also, the hardening values for the (In)-free samples (alloy A) are lower than those of the ternary alloy (alloy B). Although the hardening parameters for slowly cooled and quenched samples were found to decrease with increasing aging temperature, they exhibited abrupt increase at 823 K followed by a decrease at higher temperatures. The aging temperature dependence of the softening parameters; the fracture strain ef, the fracture strain rate ef, and the dislocation slip distance l, which is obtained from Eq. (1) where w is obtained from the s2-e relation and taking (G=2.6 1010 N/m2) [15] and (b=4.08615 1010 m) [16], for both alloys A and B for slowly cooled and quenched samples are shown in Fig. 4a–c. It is clear that the values of the softening parameters of Fig. 4 for slowly cooled and quenched samples of both alloys A and B increase with aging temperature up to 798 K then show minima at 823 K followed by continuous increase with higher temperatures. The temperature dependence of these parameters points to some sort of transformation involving a thermally activated change in the structure of the alloy due
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Fig. 2. Stress–strain curves for slowly cooled and quenched samples of alloy A (Ag–2 wt% Cu) and alloy B (Ag–2 wt% Cu–0.5 wt% In).
to atomic rearrangement and redistribution of dislocations in the networks at the transformation temperature 823 K. For quenched samples, the values of the softening parameters are lower than those for the slowly cooled samples and in general the (In)-free alloy (A) is softer than alloy (B). The energy activating the fracture mechanism in the present work is calculated assuming that the fracture time tf, varies with the aging temperature, Ta according to the Arrhenius-type relation [1] Q tf ¼ Const: exp ; ð2Þ KTa where Q, is the activation energy (in kJ/mol ) and k the Boltzmann constant. The plots of ln (tf) versus 1/Ta for alloys A and B given in Fig. 5 show two temperature regions. The values of the activation energy obtained from the slopes of (Fig. 5) for the annealed and quenched samples of both alloys
were found to be 22.08 and 39.36 kJ/mol for the low- and high-temperature regions, respectively. The integral X-ray diffraction intensity (I) and the average values of the full line-width at halfmaximum intensity (D2y), as calculated from the values of all the reflecting planes for the Ag-rich phase given in Fig. 6a,b increase with increasing aging temperature then decrease above 823 K. The average lattice parameter, a, of the Ag-rich phase shows an initial decrease with aging temperature till a minimum at 823 K then increases with further temperature increase as shown in Fig. 6c.
4. Discussion The behaviour of the stress–strain curves of Fig. 2 for Ag–2 wt% Cu, and Ag–2 wt% Cu–0.5 wt% In is mainly controlled by the
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Fig. 3. The temperature dependence of (a) fracture stress, sf, (b) yield stress, sy, (c) coefficient of work-hardening, w, and (d) fracture time, tf, for slowly cooled and quenched samples of alloys A and B.
formation and/or dissolution of the second phase (Cu-phase) as well as the presence of (In) element. Both alloys A and B showed two temperature relaxation stages in the tested temperature range. The first relaxation stage is below 823 K and the second stage starts above this temperature (see Fig. 3). On heating the slowly cooled samples that comprise the mixed phases (a+b), which are supposed to form under relatively equilibrium conditions, Fig. 1, in the first stage below 823 K, these phases coarsen and may dissolve a bit due to the increase of the solid solubility of the b-phase (Cu) in the a-phase (Ag) to attain the equilibrium composition. This process proceeds by diffusion which causes recovery [1] that requires the movement of dislocations at the interphase boundaries. It was found that the first relaxation process appearing in the annealing spectrum of worked pure Ag is due to the migration to sinks of the
vacancies generated by working when the first relaxation in the spectrum of alloyed silver was compared with that of pure silver, differences were found to exist, probably due to the presence of solute atoms which acted as vacancy-trapping centres. During annealing, a proportion of the vacancies migrate to annihilation sites on dislocation lines, and the remainder to other trapping centers in a manner depending on the relative abundance of the two types of sinks. In the alloyed silver it was concluded [17] that vacancies were trapped by impurities more effectively than by dislocation sites. So, defects annihilation leads to the initial decrease of the hardening parameters in Fig. 3 and the corresponding increase in the softening parameters given in Fig. 4 in the first temperature range below 823 K. By aging the quenched samples, which have the metastable structure of the single a-phase solid solution, at
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Ln {tf (s)}
6.9
171
A.E
6.6
SC.Alloy A
6.3
Q.Alloy A SC.Alloy B Q.Alloy B
6 1
1.1
1.2
1.3
1.4
-1
1000/T (K ) Fig. 5. Relation between ln (tf) and T1 for the tested samples.
Fig. 4. The temperature dependence of (a) fracture strain, ef ; (b) fracture strain rate, e’f ; and (c) dislocation slip distance, L, for slowly cooled and quenched samples of alloys A and B.
temperatures below 823 K the b-phase (Cu) starts to precipitate and the structure of the alloys starts to transform into the stable double (a+b) phases mixture. The amount of this double phase depends, therefore, on both the aging temperature and the aging time. The increased aging tempera-
ture yields coarser grains of the double phase structure. As coarsening is associated with diffusion, recovery process is expected to take place, as in the case of the slowly cooled samples, leading to the observed initial decrease of the hardening parameters in Fig. 3 and the initial increase of the softening parameters in Fig. 4. The similarity of the initial softening behaviour observed in Figs. 3 and 4 can also be rendered to the coarsening of the double phase grains despite how they formed, i.e. whether they initially exist (in slowly cooled samples) or thermally induced by aging (in quenched samples). The order of the inhomogeneous solid solution formed at the transformation temperature 823 K, see Fig. 1, in both the slowly cooled and the quenched samples of both alloys A and B, is destroyed by plastic deformation leading to the marked increase of the hardness parameters, Fig. 3, and the decrease of the softening parameters, Fig. 4. These marked variations at 823 K might be also attributed to the increased solid solubility of b-phase in the matrix and its complete dissolution at this transformation temperature [21,22]. This causes the freed Cu atoms to move towards dislocation lines and pin them. However, further increase of aging temperature results in the activated migration for the dispersed components of the aged alloy which leads to attain an ordered homogeneous state that characterizes the a-solid solution single phase. It is therefore, possible that
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Fig. 6. The temperature dependence of: (a) integral intensity, I; (b) X-ray full-width at half-maximum intensity (D2y); (c) lattice parameter, a, for both alloys A and B.
the restoration of short-range order and the relaxation of dislocations at the fronts of pile-ups at grain boundaries, which might be associated with dislocation annihilation due to the increased thermal agitation which facilitates the moving dislocation overcomes the existing obstacles in the slip planes, all may lead to the observed recovery in all samples at temperatures above 823 K, with keeping their own strength levels [8] as clear in
Figs. 3 and 4. The general increased hardness observed in the results of the quenched samples over those for the slowly cooled samples can be due to the higher concentration of the quenched-in vacancies when some of them form solute-vacancy pairs that migrate to dislocation lines forming solute atmospheres or when some vacancies have to find way to dislocation lines when a number of impurity centres become ineffective to trap more vacancies. This causes a retardation effect on the mobile lattice defects [18,19]. The general increased hardness of the ternary alloy (alloy B) over that of the binary alloy (alloy A) can be attributed to the probable formation of intermediate compound of the alloy elements with In and this increases the stiffness of the alloy. On the other hand, (In) atoms have strong tendency to segregate at grain boundaries and dislocations [18,20], besides causing refinement for grain size. In both cases a reduction in the density of mobile dislocations and other entities [8] takes place. The energy activating the rate controlling mechanism as obtained from Fig. 5 was found to be 22.08 and 39.36 kJ/mol for annealed and quenched samples for both alloys A and B in the first and second temperature stages, around the transformation temperature 823 K. These values suggest that the controlling fracture mechanisms are the dislocation intersection mechanism in the first stage before transformation at 823 K, and grain boundary diffusion in Ag after transformation [9]. The activation energies obtained here and the suggested rate controlling mechanisms consist with those reported for Pb–Sb system [8]. The integral X-ray intensity, Fig. 6a, and the X-ray line-width at half-maximum intensity D2y, Fig. 6b, were found to increase in the temperature range below 823 K. This increase might be the result of the aggregation of the second-phase and the coarsening of the double-phase particles which is relatively high in alloy A compared to alloy B. This reduces the scattering factors of the diffracted X-ray beams. Above the transformation temperature, 823 K, the dissolution and the dispersion of the second-phase atoms increase scattering centres and consequently, reduces the observed integral intensity, I, Fig. 6a. It is clear that (In) addition causes increased density of the scattering centres
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and consequently, reduced values for both I and D2y above 823 K. The minimum value observed for the lattice parameter, a, Fig. 6c of the Ag-rich phase for both alloys might be due to the relief of the internal strain and stress during the aging period. Above the transformation temperature, the defects associating the dissolution of the secondphase and the inhomogeneity of structure raise the value of the lattice parameter a, as shown in Fig. 6c.
5. Conclusion 1. The effect of quenching rate on the stress–strain characteristics of the binary alloy Ag–2 wt% Cu and the tertiary alloy Ag–2 wt% Cu–0.5 wt% In was investigated in the temperature range from 723 to 923 K. 2. Stress–strain tests were performed by using two groups of both alloys. The first group was slowly cooled from 1033 to 300 K at a cooling rate of 1 K/min. The second group was rapidly quenched from 1033 to 300 K. The quenched samples have the single a-phase structure and the slowly cooled samples have the mixed (a+b)-phases. 3. It was found that the hardening parameters of the quenched samples are higher than those of the slowly cooled samples. Moreover, the presence of (In) in general increases the hardening level. It was also found that the values of the hardening parameters for samples aged at temperatures lower than 823 K are higher than those aged at temperatures higher than 823 K. This may be due to the dissolution of b-phase. 4. The increased values of the softening parameters for samples aged at temperatures above the transformation temperatures is due to the homogeneity of the matrix as a result of b-phase dissolution.
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5. The analysis of X-ray diffraction patterns showed a decrease in the lattice parameter (a) to minimum at the transformation temperature.
References [1] M.M. El-sayed, F. Abd El-Salam, R. Abd El-Hasseb, Phys. Stat. Sol. A 147 (1995) 401. [2] P. Luka&c, Czech. J. Phys. B 35 (1985) 275. [3] R. Kamel, E. Aziz, K.H. Georgy, Phys. Stat. Sol. A 44 (1977) K53. [4] M.A. Kenawy, G. Saad, G. Graiss, B. Beshai, Solid State Commun. 55 (1985) 101. [5] W. Gust, B. Predel, K. Diekstall, Acta. Metals 26 (1978) 241. [6] A.M. Abd El-Khalek, Physica B 315 (2002) 7. [7] F. Abd El-Salam, M.A. Mahmoud, A.M. Abd El-Khalek, R.H. Nada, Physica B 324 (2003) 110. [8] A.M. Abd El-Khalek, R.H. Nada, Physica B 328 (2003) 393. [9] G.H. Deaf, S.B. Youssef, M.A. Mahmoud, Phys. Stat. Sol. A 168 (1998) 389. [10] M. Hansen, K. Anderko, Constitution of Binary Alloys, McGraw-Hill, New York, 1958, p. 84. [11] F. Abd El-Salam, R.H. Nada, A.M. Abd El-Khalek, Physica B 292 (2000) 71. [12] N.F. Mott, Trans. Metall. Soc. AIME 218 (1960) 6. [13] C. Kittel, Introduction to Solid State Physics, Wiley Eastern, New Delhi 1948, p. 85. [14] F. Abd El-Salam, A.M. Abd El-Khalek, R.H. Nada, Fizika A 10 (2) (2001) 73. [15] V. Raghavan, Materials Science and Engineering, A First Course, 2nd edition, Prentice-Hall, New Delhi, 1979, p. 243 [16] B.D. Cullity, Elements of X-ray Diffraction, 2nd edition, Addison-Wesley, Reading, MA, 1977, p. 507. [17] R. Kamel, E.A. Attia, Acta Metall. 9 (1961) 1047. [18] J. Friedel, Dislocations, Pergamon Press, Oxford, 1964, p. 265. [19] R.S. Mishra, A.G. Paradkar, K.N. Rao, Acta Metall. Mater. 41 (7) (1993) 2243. [20] M.M. Mostafa, G.S. Al-Ganainy, M.S. Sakr, Phys. Stat. Sol. A 150 (1995) 715. [21] E.A. Brandes (Ed.), Smithells Reference Book, Chapter 11, Butterworths, London, 1983, pp. 171. [22] P. Luka"e, G.A. Malygin, A.G.V. Vladimirova, Gzech. J. J. Phys. B 35 (1985) 318.
Physica B 349 (2004) 166–173
Precipitation kinetics in Ag–2 wt% Cu and Ag–2 wt% Cu–0.5 wt% In alloys during transformation R.H. Nada Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt Received 24 October 2003; received in revised form 10 February 2004; accepted 5 March 2004
Abstract The effect of quenching rate on the stress–strain characteristics of Ag–2 wt% Cu and Ag–2 wt% Cu–0.5 wt% In alloys was investigated in the temperature range from 723 K to 923 K. The work-hardening parameters sy, sf, and w, were found to decrease with increasing aging temperature exhibiting maxima at 823 K. The activation energies of the fracture mechanisms before and after transformation were found to be 22.1 and 39.4 kJ/mol, respectively, characterizing a dislocations intersection and grain boundary diffusion mechanisms in Ag for quenched and slowly cooled samples. An increase in strength was observed for the alloy containing (In). This was attributed to the tendency of (In) atoms to segregate at grain boundaries, causing grain size refinement. r 2004 Elsevier B.V. All rights reserved. PACS: 61.72.Lk; 61.72.Ss; 61.72.Yx Keywords: Stress–strain; Phase transformation; Dislocations; Activation energy
1. Introduction One of the most essential phenomena in deformed metals and alloys is the work hardening, which is mainly due to dislocation movement upon plastic deformation. The mechanisms governing hardening in metals and alloys involve the interaction of dislocations with impurity atoms, the formation of particles of second phase, ordering, grain boundary sliding and the intersection of dislocations. It was also mentioned that polycrystalline metals are usually harder than single crystals because of the resistance of grain boundaries, which reduce the dislocation motion and lead to subsequent formation of dislocation pileE-mail address: [email protected] (R.H. Nada).
ups at grain boundaries [1]. Also, the impurities and structure irregularities contribute to the work hardening in polycrystalline metals by acting as obstacles to dislocation motion [2]. Ag and Ag–Cu alloys received a great amount of attention concerning the effect of precold work, grain size, annealing and working temperature on the hardening behaviour of such alloys. Ag–5 at% Cu was investigated in the temperature range from 623 to 773 K [3]. It was found that at temperatures lower than 673 K the work-hardening coefficient increased by giving the samples constant fatigue pulses, while it decreased above 673 K. The effect of grain diameter and precold work by torsion on the hardening behaviour of Ag–8 at% Cu alloy was investigated [4]. It was found that the workhardening coefficient decreased for fine grains and
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.012
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increased for large grains by increasing the amount of precold work. These results were interpreted in terms of the dendritic structure of the alloy and mutual dislocation interactions. Gust et al. [5] who studied Ag–6.5 at% Cu alloy, found two types of metastable precipitates by annealing at temperatures ranging from 433 K to 543 K by in situ macrohardness measurements. Many authors [6, 7–9] investigated the effect of the trace elements and temperature on mechanical characteristics of various binary and ternary alloys. According to the constitutional diagram of the Ag–Cu system [10] given in Fig. 1, at room temperature, Ag–2 wt% Cu alloy consists of a-phase (Ag-rich phase) and b-phase (Cu-rich phase). When the alloy is heated the solid solubility of Cu in Ag increases and b-phase dissolves in the a-phase and completely disappears at the transformation temperature and the alloy then consists of the single solid solution a-phase. With the forward transformation on slow cooling, the supersaturated solid solution decomposes and b-crystals precipitate. Its amount is increased as the temperature falls. However, rapid cooling (quenching) of the a-solid solution to room temperature will suppress the
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separation of the b-phase crystals and a homogeneous alloy may be supercooled to low temperatures. The quenched solid solution, supersaturated with the component b, will decompose upon heating at temperatures below transformation temperature. The aim of the present work is to study the effect of both (In) addition, and the formation or dissolution of b-phase on the work hardening parameters of Ag–2 wt% Cu.
2. Experimental procedure 2.1. Samples preparation The materials used in this study were Ag, Cu, and In fragments of purity 99.99%. Two Ag alloys, Ag–2 wt% Cu (alloy A) and Ag–2 wt% Cu–0.5 wt% In (alloy B) were prepared by melting the pure elements in a graphite crucible together with calcium chloride CaCl2 flux to prevent oxidation. The received casting was obtained in the form of rod of 12 mm in diameter. Homogenizing vacuum anneal was carried out by heating
Fig. 1. Constitutional diagram of the system Ag–Cu.
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the cast alloy at 1063 K for 7 days. Cold drawing was carried out with intermediate annealing at 1033 K for 12 h. The rod was swaged in steps to wire of 0.6 mm in diameter. Two groups of samples of each alloy were annealed for 4 h at 1013 K. Group of samples of each alloy was slowly cooled to room temperature (300 K) at a cooling rate of 1 K/min to obtain mixed double phases or fully precipitated samples. The second group of samples of each alloy was rapidly quenched from 1013 K to room temperature to obtain samples with the supersaturated a-solid solution structure. The slow cooled and the quenched samples of each alloy were aged at temperatures in the range from 723 K to 923 K in steps of 25 K. 2.2. Stress–strain measurements Stress–strain tests were performed at room temperature (RT) using a conventional tensile testing machine described elsewhere [11]. The applied stress was increased gradually with 30 s interval between two successive loadings. The elongation was recorded by using a dial gauge sensitive to 7105 m. The time from the start of the tensile test till fracture recorded for each stress–strain run was taken as the fracture time, tf. The coefficient of parabolic work hardening, w, was calculated using the equation [12] w¼
ds2 b ¼ G2 2 ; 2p l de
ð1Þ
where G is the shear modulus of the material, b is the Burgers vector [13] and l is the distance slipped by dislocation. The yield stress, sy, considered as the stress corresponding to the first significant deviation from linearity in the starting part of the stress–strain curve and the fracture stress, sf, taken as the maximum stress applied to the sample before fracture [14] were obtained from the stress– strain curves. 2.3. Structural measurements The microstructure of the quenched samples of both alloys A and B was identified using a Philips X-ray diffractometer (PW 1050/70), with Cu Ka
radiation (0.1542 nm) and scan speed adjusted at 5 min1 in the angle range 2y from 20 up to 120 .
3. Experimental results Stress–strain curves obtained at room temperature for samples of both alloys A and B heattreated at different aging temperatures in the range from 723 to 923 K are shown in Fig. 2. These curves show parabolic stress–strain behaviour in the intermediate range. The aging temperature dependence of the measured hardening parameters namely, the fracture stress, sf, the yield stress, sy, the fracture time, tf, and the work-hardening coefficient, w, obtained as the slope of the straight line of the relation between s2 and e in the parabolic region of the stress–strain curve which proves the applicability of Eq. (1) to the investigated Ag–Cu system, for slowly cooled and quenched samples of both alloys A and B are shown in Fig. 3 a–d. From Fig. 3, it is clear that the values of these hardening parameters are generally lower for the slowly cooled samples than those for the quenched samples. Also, the hardening values for the (In)-free samples (alloy A) are lower than those of the ternary alloy (alloy B). Although the hardening parameters for slowly cooled and quenched samples were found to decrease with increasing aging temperature, they exhibited abrupt increase at 823 K followed by a decrease at higher temperatures. The aging temperature dependence of the softening parameters; the fracture strain ef, the fracture strain rate ef, and the dislocation slip distance l, which is obtained from Eq. (1) where w is obtained from the s2-e relation and taking (G=2.6 1010 N/m2) [15] and (b=4.08615 1010 m) [16], for both alloys A and B for slowly cooled and quenched samples are shown in Fig. 4a–c. It is clear that the values of the softening parameters of Fig. 4 for slowly cooled and quenched samples of both alloys A and B increase with aging temperature up to 798 K then show minima at 823 K followed by continuous increase with higher temperatures. The temperature dependence of these parameters points to some sort of transformation involving a thermally activated change in the structure of the alloy due
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Fig. 2. Stress–strain curves for slowly cooled and quenched samples of alloy A (Ag–2 wt% Cu) and alloy B (Ag–2 wt% Cu–0.5 wt% In).
to atomic rearrangement and redistribution of dislocations in the networks at the transformation temperature 823 K. For quenched samples, the values of the softening parameters are lower than those for the slowly cooled samples and in general the (In)-free alloy (A) is softer than alloy (B). The energy activating the fracture mechanism in the present work is calculated assuming that the fracture time tf, varies with the aging temperature, Ta according to the Arrhenius-type relation [1] Q tf ¼ Const: exp ; ð2Þ KTa where Q, is the activation energy (in kJ/mol ) and k the Boltzmann constant. The plots of ln (tf) versus 1/Ta for alloys A and B given in Fig. 5 show two temperature regions. The values of the activation energy obtained from the slopes of (Fig. 5) for the annealed and quenched samples of both alloys
were found to be 22.08 and 39.36 kJ/mol for the low- and high-temperature regions, respectively. The integral X-ray diffraction intensity (I) and the average values of the full line-width at halfmaximum intensity (D2y), as calculated from the values of all the reflecting planes for the Ag-rich phase given in Fig. 6a,b increase with increasing aging temperature then decrease above 823 K. The average lattice parameter, a, of the Ag-rich phase shows an initial decrease with aging temperature till a minimum at 823 K then increases with further temperature increase as shown in Fig. 6c.
4. Discussion The behaviour of the stress–strain curves of Fig. 2 for Ag–2 wt% Cu, and Ag–2 wt% Cu–0.5 wt% In is mainly controlled by the
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Fig. 3. The temperature dependence of (a) fracture stress, sf, (b) yield stress, sy, (c) coefficient of work-hardening, w, and (d) fracture time, tf, for slowly cooled and quenched samples of alloys A and B.
formation and/or dissolution of the second phase (Cu-phase) as well as the presence of (In) element. Both alloys A and B showed two temperature relaxation stages in the tested temperature range. The first relaxation stage is below 823 K and the second stage starts above this temperature (see Fig. 3). On heating the slowly cooled samples that comprise the mixed phases (a+b), which are supposed to form under relatively equilibrium conditions, Fig. 1, in the first stage below 823 K, these phases coarsen and may dissolve a bit due to the increase of the solid solubility of the b-phase (Cu) in the a-phase (Ag) to attain the equilibrium composition. This process proceeds by diffusion which causes recovery [1] that requires the movement of dislocations at the interphase boundaries. It was found that the first relaxation process appearing in the annealing spectrum of worked pure Ag is due to the migration to sinks of the
vacancies generated by working when the first relaxation in the spectrum of alloyed silver was compared with that of pure silver, differences were found to exist, probably due to the presence of solute atoms which acted as vacancy-trapping centres. During annealing, a proportion of the vacancies migrate to annihilation sites on dislocation lines, and the remainder to other trapping centers in a manner depending on the relative abundance of the two types of sinks. In the alloyed silver it was concluded [17] that vacancies were trapped by impurities more effectively than by dislocation sites. So, defects annihilation leads to the initial decrease of the hardening parameters in Fig. 3 and the corresponding increase in the softening parameters given in Fig. 4 in the first temperature range below 823 K. By aging the quenched samples, which have the metastable structure of the single a-phase solid solution, at
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Ln {tf (s)}
6.9
171
A.E
6.6
SC.Alloy A
6.3
Q.Alloy A SC.Alloy B Q.Alloy B
6 1
1.1
1.2
1.3
1.4
-1
1000/T (K ) Fig. 5. Relation between ln (tf) and T1 for the tested samples.
Fig. 4. The temperature dependence of (a) fracture strain, ef ; (b) fracture strain rate, e’f ; and (c) dislocation slip distance, L, for slowly cooled and quenched samples of alloys A and B.
temperatures below 823 K the b-phase (Cu) starts to precipitate and the structure of the alloys starts to transform into the stable double (a+b) phases mixture. The amount of this double phase depends, therefore, on both the aging temperature and the aging time. The increased aging tempera-
ture yields coarser grains of the double phase structure. As coarsening is associated with diffusion, recovery process is expected to take place, as in the case of the slowly cooled samples, leading to the observed initial decrease of the hardening parameters in Fig. 3 and the initial increase of the softening parameters in Fig. 4. The similarity of the initial softening behaviour observed in Figs. 3 and 4 can also be rendered to the coarsening of the double phase grains despite how they formed, i.e. whether they initially exist (in slowly cooled samples) or thermally induced by aging (in quenched samples). The order of the inhomogeneous solid solution formed at the transformation temperature 823 K, see Fig. 1, in both the slowly cooled and the quenched samples of both alloys A and B, is destroyed by plastic deformation leading to the marked increase of the hardness parameters, Fig. 3, and the decrease of the softening parameters, Fig. 4. These marked variations at 823 K might be also attributed to the increased solid solubility of b-phase in the matrix and its complete dissolution at this transformation temperature [21,22]. This causes the freed Cu atoms to move towards dislocation lines and pin them. However, further increase of aging temperature results in the activated migration for the dispersed components of the aged alloy which leads to attain an ordered homogeneous state that characterizes the a-solid solution single phase. It is therefore, possible that
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Fig. 6. The temperature dependence of: (a) integral intensity, I; (b) X-ray full-width at half-maximum intensity (D2y); (c) lattice parameter, a, for both alloys A and B.
the restoration of short-range order and the relaxation of dislocations at the fronts of pile-ups at grain boundaries, which might be associated with dislocation annihilation due to the increased thermal agitation which facilitates the moving dislocation overcomes the existing obstacles in the slip planes, all may lead to the observed recovery in all samples at temperatures above 823 K, with keeping their own strength levels [8] as clear in
Figs. 3 and 4. The general increased hardness observed in the results of the quenched samples over those for the slowly cooled samples can be due to the higher concentration of the quenched-in vacancies when some of them form solute-vacancy pairs that migrate to dislocation lines forming solute atmospheres or when some vacancies have to find way to dislocation lines when a number of impurity centres become ineffective to trap more vacancies. This causes a retardation effect on the mobile lattice defects [18,19]. The general increased hardness of the ternary alloy (alloy B) over that of the binary alloy (alloy A) can be attributed to the probable formation of intermediate compound of the alloy elements with In and this increases the stiffness of the alloy. On the other hand, (In) atoms have strong tendency to segregate at grain boundaries and dislocations [18,20], besides causing refinement for grain size. In both cases a reduction in the density of mobile dislocations and other entities [8] takes place. The energy activating the rate controlling mechanism as obtained from Fig. 5 was found to be 22.08 and 39.36 kJ/mol for annealed and quenched samples for both alloys A and B in the first and second temperature stages, around the transformation temperature 823 K. These values suggest that the controlling fracture mechanisms are the dislocation intersection mechanism in the first stage before transformation at 823 K, and grain boundary diffusion in Ag after transformation [9]. The activation energies obtained here and the suggested rate controlling mechanisms consist with those reported for Pb–Sb system [8]. The integral X-ray intensity, Fig. 6a, and the X-ray line-width at half-maximum intensity D2y, Fig. 6b, were found to increase in the temperature range below 823 K. This increase might be the result of the aggregation of the second-phase and the coarsening of the double-phase particles which is relatively high in alloy A compared to alloy B. This reduces the scattering factors of the diffracted X-ray beams. Above the transformation temperature, 823 K, the dissolution and the dispersion of the second-phase atoms increase scattering centres and consequently, reduces the observed integral intensity, I, Fig. 6a. It is clear that (In) addition causes increased density of the scattering centres
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and consequently, reduced values for both I and D2y above 823 K. The minimum value observed for the lattice parameter, a, Fig. 6c of the Ag-rich phase for both alloys might be due to the relief of the internal strain and stress during the aging period. Above the transformation temperature, the defects associating the dissolution of the secondphase and the inhomogeneity of structure raise the value of the lattice parameter a, as shown in Fig. 6c.
5. Conclusion 1. The effect of quenching rate on the stress–strain characteristics of the binary alloy Ag–2 wt% Cu and the tertiary alloy Ag–2 wt% Cu–0.5 wt% In was investigated in the temperature range from 723 to 923 K. 2. Stress–strain tests were performed by using two groups of both alloys. The first group was slowly cooled from 1033 to 300 K at a cooling rate of 1 K/min. The second group was rapidly quenched from 1033 to 300 K. The quenched samples have the single a-phase structure and the slowly cooled samples have the mixed (a+b)-phases. 3. It was found that the hardening parameters of the quenched samples are higher than those of the slowly cooled samples. Moreover, the presence of (In) in general increases the hardening level. It was also found that the values of the hardening parameters for samples aged at temperatures lower than 823 K are higher than those aged at temperatures higher than 823 K. This may be due to the dissolution of b-phase. 4. The increased values of the softening parameters for samples aged at temperatures above the transformation temperatures is due to the homogeneity of the matrix as a result of b-phase dissolution.
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5. The analysis of X-ray diffraction patterns showed a decrease in the lattice parameter (a) to minimum at the transformation temperature.
References [1] M.M. El-sayed, F. Abd El-Salam, R. Abd El-Hasseb, Phys. Stat. Sol. A 147 (1995) 401. [2] P. Luka&c, Czech. J. Phys. B 35 (1985) 275. [3] R. Kamel, E. Aziz, K.H. Georgy, Phys. Stat. Sol. A 44 (1977) K53. [4] M.A. Kenawy, G. Saad, G. Graiss, B. Beshai, Solid State Commun. 55 (1985) 101. [5] W. Gust, B. Predel, K. Diekstall, Acta. Metals 26 (1978) 241. [6] A.M. Abd El-Khalek, Physica B 315 (2002) 7. [7] F. Abd El-Salam, M.A. Mahmoud, A.M. Abd El-Khalek, R.H. Nada, Physica B 324 (2003) 110. [8] A.M. Abd El-Khalek, R.H. Nada, Physica B 328 (2003) 393. [9] G.H. Deaf, S.B. Youssef, M.A. Mahmoud, Phys. Stat. Sol. A 168 (1998) 389. [10] M. Hansen, K. Anderko, Constitution of Binary Alloys, McGraw-Hill, New York, 1958, p. 84. [11] F. Abd El-Salam, R.H. Nada, A.M. Abd El-Khalek, Physica B 292 (2000) 71. [12] N.F. Mott, Trans. Metall. Soc. AIME 218 (1960) 6. [13] C. Kittel, Introduction to Solid State Physics, Wiley Eastern, New Delhi 1948, p. 85. [14] F. Abd El-Salam, A.M. Abd El-Khalek, R.H. Nada, Fizika A 10 (2) (2001) 73. [15] V. Raghavan, Materials Science and Engineering, A First Course, 2nd edition, Prentice-Hall, New Delhi, 1979, p. 243 [16] B.D. Cullity, Elements of X-ray Diffraction, 2nd edition, Addison-Wesley, Reading, MA, 1977, p. 507. [17] R. Kamel, E.A. Attia, Acta Metall. 9 (1961) 1047. [18] J. Friedel, Dislocations, Pergamon Press, Oxford, 1964, p. 265. [19] R.S. Mishra, A.G. Paradkar, K.N. Rao, Acta Metall. Mater. 41 (7) (1993) 2243. [20] M.M. Mostafa, G.S. Al-Ganainy, M.S. Sakr, Phys. Stat. Sol. A 150 (1995) 715. [21] E.A. Brandes (Ed.), Smithells Reference Book, Chapter 11, Butterworths, London, 1983, pp. 171. [22] P. Luka"e, G.A. Malygin, A.G.V. Vladimirova, Gzech. J. J. Phys. B 35 (1985) 318.