Crystallography Reports, Vol. 49, No. 2, 2004, pp. 324–326. Translated from Kristallografiya, Vol. 49, No. 2, 2004, pp. 382–384. Original Russian Text Copyright © 2004 by Zhilokov, Orkvasov, Sozaev.
CRYSTAL GROWTH
Behavior of the Resistivity of Metal Alloys during Collective Recrystallization1 Kh. P. Zhilokov, T. A. Orkvasov, and V. A. Sozaev Kabardino-Balkarian State University, ul. Chernyshevskogo 173, Nal’chik, 360004 Russia e-mail:
[email protected] Received March 3, 2003
Abstract—The kinetics of collective recrystallization in Sn–Pb, Sn–In, Sn–Zn, Pb–Sn, Pb–Bi, and Pb–In alloys have been studied using the conductivity method at T = 180°C. © 2004 MAIK “Nauka/Interperiodica”. 1
INTRODUCTION The regularities of the grain growth in polycrystalline alloys have been intensively studied in view of the development of new nanocrystalline materials [1–4]. This problem is of interest because the grain size determines mechanical, electric, magnetic, and other properties of polycrystals. Impurity atoms adsorbed on grain boundaries penetrate the grain bulk during collective recrystallization. The decrease in the grain-boundary area also contributes to this process. As a result, the degree of lattice distortion increases. In addition, the screened radius of impurity atoms in the grain bulk is larger than at the boundaries [5]. Due to these phenomena, the impurity contribution to the resistivity, ∆ρ = ρ – ρ0 (where ρ and ρ0 are the resistivities of an alloy and a pure metal of the matrix, respectively), increases. Assuming that the increase in ∆ρ during the collective recrystallization is mainly due to the increase in the grain size D and that the recrystallization kinetics obeys the Beck relation [6], we obtain ∆ρ ~ D ~
tn
(1)
∆ρ = k(t /t0)n,
(2)
or where t is the annealing time, t0 is the maximum duration of isochronous annealing (we used t0 = 3 h in our experiments), and k and n are constants at a specified temperature. For most pure metals, at D Ⰷ D0 (where D0 is the initial grain size), D ~ t 1/2. The reason is that the proportionality factor has the meaning of the product of the boundary surface tension on the boundary mobility. Therefore, the proportionality factor has the dimension of the ratio of the squared length to time. Various factors may affect the value of the exponent n: composi1 This
work was presented at the National Conference on Crystal Growth (NCCG-2002, Moscow).
tion, annealing temperature, preliminary treatment, alloy decomposition, effects of detachment of grain boundaries from an impurity cloud, and so on [7]. The aim of this study is to estimate the kinetics of collective recrystallization in alloys on the basis of tin and lead by a change in the resistivity during isochronous annealing. Values of the parameters k and n in equation (2) for T = 180°C n Alloy composition
k this study
Sn-0.4 at % Zn
0.059
0.12
Sn-0.5 at % Zn
0.046
0.14
Sn-0.3 at % Pb
0.003
0.25
Sn-0.5 at % Pb
0.003
0.29
Sn-0.5 at % In
0.080
0.15
Sn-1.0 at % In
0.006
0.22
Pb-0.1 at % Sn
0.005
0.17
Pb-0.3 at % Sn
0.005
0.21
Pb-0.5 at % Sn
0.005
0.24
Pb-1.0 at % Sn
0.004
0.26
Pb-0.1 at % In
0.003
0.14
Pb-0.5 at % In
0.003
0.18
Pb-1.0 at % In
0.002
0.27
Pb-0.1 at % Bi
0.093
0.07
Pb-0.3 at % Bi
0.072
0.12
Pb-0.5 at % Bi
0.050
0.18
Pb-1.0 at % Bi
0.041
0.29
1063-7745/04/4902-0324$26.00 © 2004 MAIK “Nauka/Interperiodica”
data of [6] 0.15 (at 175°C)
0.31 (at 180°C)
BEHAVIOR OF THE RESISTIVITY OF METAL ALLOYS ln(∆ρ, µΩ cm)
4
–0.6 –0.8 –1.0
ln(∆ρ, µΩ cm)
2
–0.4
325 11
–1.0
3
6
10 9 8
–2.0
5 1
–1.2
–3.0
–1.4 –1.6
7 6 5 4
–4.0
–1.8
3 2 1
–5.0 4
6
8
10 ln(t/t0)
4
6
8
10 ln(t/t0)
Fig. 1. Dependences of the impurity contribution to the resistivity, ∆ρ, on annealing time for the alloys Sn–Pb with (1) 0.3 and (2) 0.5 at % of Pb; Sn–Zn with (3) 0.4 and (4) 0.5 at % of Zn (4); and Sn–In with (5) 0.5 and (6) 1.0 at % of In.
Fig. 2. Dependences of the impurity contribution to the resistivity, ∆ρ, on the annealing time for the alloys Pb–In with (1) 0.1, (2) 0.5, and (3) 1.0 at % of In; Pb–Sn with (4) 0.1, (5) 0.3, (6) 0.5, and (7) 1.0 at % of Sn; and Pb–Bi with (8) 0.1, (9) 0.3, (10) 0.5, and (11) 1.0 at % of Bi.
METHOD AND EXPERIMENTAL RESULTS An extrusion technique for preparation of alloys based on Sn and Pb and experimental samples was described in [8]. The concentrations of the alloy components were chosen to be below the solubility limit for each system. Samples 120 × 1.28 × 0.88 mm3 in size were prepared by extruding alloy ingots through a spinneret with a rectangular aperture. Before the extrusion, the ingots were heated in a pressform to 150–160°C. Then, a wire was extracted, from which samples were cut. The samples were annealed in a thermostat filled with silicon oil for t0 = 3 h at 180°C. During the annealing, the resistivity of the samples was measured by the four-probe compensation method using a P363-2 dc potentiometer. It was found that the resistivity ρ of alloys increases nonlinearly during annealing at 180°C for 30 min and does not change within experimental error with a further increase in annealing time (more than 1 h). The measurement results are shown in Figs. 1 and 2. The dependences of the impurity contribution to the resistivity, ∆ρ, on the annealing time in logarithmic coordinates for Sn- and Pb-based alloys are shown in Figs. 1 and 2, respectively. As can be seen from Figs. 1 and 2, the dependences ln∆ρ on the annealing time are close to linear. The equations of the straight lines ln ∆ρ = f (ln t /t0) were found by the least-squares method and, then, the constant n was estimated. The values of n are listed in the table. It can be seen from the table that, for all the alloys under investigation, n < 0.5. With an increase in the concentration of impurity atoms, the values of n increase but do not exceed 0.3, which is characteristic
of many Sn- and Pb-based alloys [6]. Apparently, the differences in the dependences of n on alloy composition are due to the different characters of the interrelations between the moving force for the grain migration and the energy of interaction of impurity atoms with grain boundaries [9].
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In alloys of other metals, the behavior of n may be different. For example, it was found in [10] that the size of grains in nanocrystalline Ni3P at 710 K is proportional to ~t 1/2; i.e., n = 0.5 as in pure metals. Thus, we studied the kinetics of the increase in the impurity contribution to the resistivity of Sn–Zn, Sn– In, Sn–Pb, Pb–Sn, Pb–Bi, and Pb–In alloys upon annealing at 180°C for 3 h. It was shown that, for all the alloys under study, the observed increase in the impurity contribution to the resistivity upon annealing (which is absent in pure Sn or Pb) can be described by the dependence ∆ρ = k(t /t0)n. It has been ascertained that the values of the exponent n increase with an increase in the impurity concentration; however, n < 0.3, which is in agreement with the data in the literature on the kinetics of the grain growth in Sn- and Pb-based alloys. ACKNOWLEDGMENTS This study was supported by the Russian Foundation for Basic Research, project no. 02-02-1688. REFERENCES 1. A. I. Gusev, Usp. Fiz. Nauk 168 (1), 55 (1998) [Phys. Usp. 45, 49 (1998)].
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2. R. A. Andrievskiœ and A. M. Glezer, Fiz. Met. Metalloved. 88 (1), 50 (1999). 3. R. A. Andrievskiœ and A. M. Glezer, Fiz. Met. Metalloved. 89 (1), 91 (2000). 4. N. P. Lyakishev, M. I. Alymov, and S. V. Dobatkin, Metally, No. 3, 3 (2003). 5. V. I. Arkharov, S. D. Vangengeœm, I. B. Klyueva, and V. P. Serikova, Fiz. Met. Metalloved. 26 (2), 289 (1967). 6. N. L. Pokrovskiœ and T. G. Smirnova, Surface Phenomena in Melts and Solid Phases Formed (Kab.-Balk. Kn., Nalchik, 1965).
7. V. E. Fradkov and L. S. Shvindlerman, Structure and Properties of Internal Boundary Surfaces in Metals (Nauka, Moscow, 1988), p. 213. 8. T. A. Orkvasov, P. A. Savintsev, V. A. Sozaev, and Kh. T. Shidov, Metally, No. 1, 98 (1995). 9. E. L. Maksimova, B. B. Straumal, and L. S. Shvindlerman, Fiz. Met. Metalloved. 63 (5), 885 (1987). 10. K. Lu, Scr. Metall. Mater. 25 (9), 2047 (1991).
Translated by Yu. Sin’kov
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