- Email: [email protected]
Steady state creep characteristics of the eutectic Pb–Sb alloy
ARTICLE IN PRESS
Physica B 349 (2004) 56–61
Steady state creep characteristics of the eutectic Pb–Sb alloy M.M. Mostafa* Physics Department, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt Received 27 May 2003; received in revised form 17 November 2003; accepted 2 January 2004
Abstract The change in the steady state creep rate of Pb–Sb eutectic alloy is studied under constant stresses ranging from 3.45 to 5.2 MPa and at different temperatures ranging from 433 to 503 K. The strain rate sensitivity parameter (m) varied between 0.33 and 0.46 in the testing temperature range. The activation energy of the steady state creep amounted to 96 kJ/mol in the temperature range from 473 to 503 K, characterizing the self-diffusion mechanism of Pb. The analysis of the microstructural variations confirms that the above-mentioned mechanisms are expected to take place during the investigated steady state creep stage. r 2004 Elsevier B.V. All rights reserved. Keywords: Steady state creep; Eutectic Pb–Sb alloy
1. Introduction Antimony–lead alloys are very important materials in industry for their use as die casting alloys and in manufacturing acidic accumulators. Some mechanical and structural properties of a series of Pb–Sb alloys containing different additives were studied [1]. The thermally induced elastic stresses were found to affect the mechanical properties of the eutectic Pb–Sb alloy, which showed a low plasticity at room temperature [2]. The study of the effect of temperature and stress on the structure and creep parameters of a Pb-2 at% Sb alloy revealed [3] a transition point at 473 K. Aging was found to change the defect structure of Pb–Sb alloys [4]. The hardening mechanisms in binary Pb-based alloys depend on *Corresponding author. E-mail address: [email protected] (M.M. Mostafa).
the type of the alloying element. Lead-antimony alloys are very well hardened by continuous precipitation, whereas lead–tin alloys present a discontinuous precipitation with a weak hardening effect [5]. The effect of structure transformation on the stress–strain characteristics of a Pb-3 wt% Sb alloy was investigated [6]. The variations observed in the measured parameters point to two temperature regions around the transformation temperature. X-ray line-profile analysis of cold-worked Pb–Sb alloys in the alpha-phase revealed that the deformation process has a minimal effect on the microstructure [7]. Cellular/dendritic array tip morphology has been examined in directionally solidified and quenched Pb-5.8 wt% Sb [8]. The dependence of the steady state strain rate est on the applied stress s is found to obey the equation [9,10] s ¼ K e’m st :
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.01.159
ARTICLE IN PRESS M.M. Mostafa / Physica B 349 (2004) 56–61
Here, K is a constant, dependent on the test conditions and m is the strain rate sensitivity parameter. The aim of the present study is to trace the effect of the applied stress and the deformation temperature on the creep characteristics of the eutectic Pb-11.2 wt% Sb alloy.
2. Experimental technique Pb-11.2 wt% Sb alloy samples (eutectic alloy), prepared from highly pure Pb and Sb, were homogenized at 453 K for 24 h, then cold swagged into wires of 0.85 mm diameter and 60 mm length. The samples were heated again at 508 K for 2 h, then slowly cooled with a cooling rate of 8 103 K/s to room temperature at which they were kept for 24 h to get samples with identical initial state containing the precipitated two-phase ða þ bÞ structure. Creep tests were carried out at different temperatures controlled to 71 K in the range from 433 to 503 K, under different applied stresses ranging from 3.45 to 5.2 MPa. Structure investigations after creep were carried out using a D-500 X-ray diffractometer.
3. Experimental results Isothermal creep curves of the Pb-11.2 wt% Sb alloy were measured under different constant stresses of 3.45, 4.3 and 5.2 MPa, at the deformation temperature range 433–503 K in steps of 10 K. Typical curves are shown in Fig. 1, where a regular behaviour for the creep curves is observed. The curves are sensitive to the creep temperature and the applied stress. It is worth noting that all the creep curves are characterized either by the absence of a primary creep stage or by the occurrence of a small inflection [11–13]. Although the steady state creep rate increases with temperature, the elongation to fracture is approximately temperature independent. The steady state strain rate sensitivity parameter mð¼ dln s=dln e’st Þ derived from the slopes of the straight lines relating ln s and ln e’st (see Fig. 2) was
57
found to exhibit values ranging from 0.33 to 0.46, depending on the creep temperature. Fig. 3 shows the temperature dependence of both the strain rate sensitivity. Parameter (m) and the steady state creep rate est. It is clear that a pronounced change in both m and est takes place at 473 K characterizing some sort of transformation. The activation energy of steady state creep was calculated from the slopes of the straight lines relating ln e’ st and 1000/T (see Fig. 4). The present results yield a stress independent activation energy of 68 kJ/mol in the temperature range from 433 to 463 K, and the stress-dependent activation energies 88, 96 and 104 kJ/mol in the temperature range from 473 to 503 K. Fig. 5 represents the change in the activation energy of the steady state creep (Qst) with the applied stress in the temperature range from 473 to 503 K. It decreases with increasing the applied stress, i.e. depends on the stress. Fig. 6 shows the variations in the microstructure parameters: the integral intensity (I), the lattice parameter (a) and the half line width (D2y) after creep for the Pb-rich phase in the Pb-11.2 wt% Sb alloy. They are found to change with the deformation temperature and both (I) and (a) exhibit maxima at 473 K, as shown in Fig. 6a and b, while (D2y) exhibits a minimum at 473 K, Fig. 6c.
4. Discussion According to the constitutional diagram of the Pb–Sb system [14], the studied alloy Pb-11.2 wt% Sb has the eutectic composition, with the lowest melting temperature of any alloy of its range of composition, characterized by the conversion of the liquid alloy during the solidifying process into two solid constituents (a-Pb+a-Sb) in equilibrium with a solid solution composition of 3.5 wt% Sb and 97 wt% Sb. The structure expected to exist in the present samples is the dendritic structure of primary a-Pb and traces of a-Sb revealed in rapid quenched eutectic Pb–Sb alloy [15] close to grain boundaries with solute free zones between the grain
ARTICLE IN PRESS 58
M.M. Mostafa / Physica B 349 (2004) 56–61
Fig. 1. Creep curves at different applied stresses and different temperatures for the Pb-11.2 wt% Sb alloy.
ARTICLE IN PRESS M.M. Mostafa / Physica B 349 (2004) 56–61
Ln σ 1.2
1.3
1.4
1.5
1.6
1.7
-5
433 443 453 463 473 483 493 503
-6
Ln ε st
-7
.
-8 -9 -10 -11 -12
Fig. 2. Strain rate—stress relationship for the Pb-11.2 wt% Sb alloy.
Q st (KJ / mol)
-4
1.1
59
106 104 102 100 98 96 94 92 90 88 86 0
2
σ (MPa)
4
6
Fig. 5. Relation between the activation energy and the applied stress s.
m
0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 420
440
460
480
500
520
T (K)
(a) 0.0012
εst
0.001 0.0008
σ = 3.45
.
0.0006
σ = 4.3
0.0004
σ = 5.2
0.0002 0 420
440
460
(b)
480
500
520
T (K)
Fig. 3. The strain rate sensitivity parameter m (a) and the steady state strain rate est (b) as a function of creep temperature for Pb11.2 wt% Sb alloy.
1.9 0
2
2.1
2.2
2.3
2.4
Ln ε st
-2 .
-4
σ = 3.45 σ = 4.3
-6
σ = 5.2
-8 -10 -12
-1
1000 / T (K ) Fig. 4. Relation between ln e’st and 1000/T for the Pb-11.2 wt% Sb alloy.
boundaries and a series of bonded precipitates within the grains. In small regions, the matrix Sb was observed as single crystal regions at the multigrain junctions. Creep plays an important role in metal deformation, whenever the homologous temperature exceeds 0.5Tm (melting point) as for most solder alloys [16]. The amount and rate of straining during creep are established by the material itself under the imposed stress and temperature conditions. Continuing deformation under constant stress or load, work-hardens the crystalline materials, and this implies some recovery. The steady state creep is commonly considered as a result of a balance between strain hardening and stress-aided and thermally activated recovery. The dependence of the steady state creep rate of the Pb-11.2 wt% Sb alloy on temperature reflects a thermally activated change in the atomic arrangement of the alloy at the transition temperature 473 K. By performing creep tests in the low temperature region (below the transition point), the Pband Sb-rich phases coarsen and the mutual solubility increases in order to get closer to the actual equilibrium compositions at the deformation temperature. The structure variation leads to solution process at some of the interfaces and to a precipitation process at the others. This change in composition requires the presence of a diffusion current, and the directional movement of the atoms gives rise to the dynamic recovery.
ARTICLE IN PRESS M.M. Mostafa / Physica B 349 (2004) 56–61
60
creep equation
18 16
e’st ¼ Cðs=dÞ1=m exp ðQ=KTÞ:
14
ð1Þ
12 -111 -200 -220
I
10 8 6 4 2 0 420
440
460
o
a (A)
(a)
480
500
520
T (K) 4.985 4.98 4.975 4.97 4.965 4.96 4.955 4.95 4.945 4.94 420
430
440
450
460
470
480
490
500
510
T (K)
(b) 0.6° 0.5° 0.4°
∆2θ
-111
0.3°
-200 -220
0.2° 0.1° 0 420
(c)
440
460
480
500
520
T (K)
Fig. 6. The effect of the working temperature on (a) the integral X-ray intensities, (b) the lattice parameter and (c) the half line width of the Pb-rich phase of the Pb-11.2 wt% Sb alloy.
This suggests a dislocation climb mechanism along grain boundaries [17] to be the rate controlling mechanism for the steady state creep of the test alloy. Also, these values of m agree with the values obtained in Ref. [18] which indicate that the dominating mechanism is dislocation climb along grain boundaries. The activation energy of the steady state creep (68.570.4) kJ/mol in the low temperature range from 433 to 463 K, may be due to a viscous flow creep mechanism [3]. The average activation energy obtained in the high-temperature range, from 473 to 503 K, was about (9670.4) kJ/mol which agrees with the activation energy of selfdiffusion in Pb [19–22]. Besides, the activation energy of the steady state creep in the hightemperature region was found to decrease with increasing applied stress, (Fig. 5), which refers to enhancement of diffusion creep mechanism. The integral intensity (I), the lattice parameter (a) and the half line width (D2y) were found to change with the working temperature. The decrease in the values of (I) and (a) in the lowtemperature region, below the transition point, is due to the increase in the recovery process. In the region above the transition point, their decrease might be due to the reduction of the sum of the internal lattice strains as a result of the thermally activated diffusion process.
References The increase of the strain rate sensitivity parameter (m) from 0.33 to 0.46, with increasing deformation temperature (see Fig. 3a) points to the possibility of having an apparent plastic behaviour responsible for the observed deformation. This observation may be due to the accelerated diffusion process of the high vacancy concentration leading to enhanced dislocation climb at higher temperatures. The measured values of m with raising temperature are in agreement with the value 0.5 obtained from the steady state
[1] J. Zhiyun, L. Yuandud, Z. Shuzhen, G. Weiging, Z. Zhonghua, J. Power Sources 31 (1990) 169. [2] S.N. Komnik, I.T. Ponomarenko, V.I. Startsev, Mater. Sci. Eng. 58 (1983) 15. [3] G.S. Al-Ganainy, M.T. Mostafa, M.R. Nagy, Phys. Stat. Sol. A 165 (1998) 185. [4] N.V. Isaev, V.S. Fomenko, V.V. Pustovalov, Fiz. Nizk. Temp. 15 (1989) 759. [5] J.P. Hilger, J. Power Sources 53 (1995) 45. [6] A.M. Abd El-Khalek, R.H. Nada, Physica B 128 (2003) 393. [7] P. Chatterje, P.S. Bhattacharyya, S.P.S. Gupta, J. Alloy Compounds 284 (1999) 160.
ARTICLE IN PRESS M.M. Mostafa / Physica B 349 (2004) 56–61 [8] L. Yu, G.L. Ding, J. Reye, S.N. Ojha, S.N. Tewari, Metall. Mater. Sci. 30 (1999) 2463. [9] G.S. Al-Ganainy, M.R. Nagy, B.A. Khalifa, R. Afify, Phys. Stat. Sol. A 158 (1996) 463. [10] M.M. Mostafa, G.S. Al-Ganainy, M.S. Saker, Egypt. J. Sol. 19 (1996) 199. [11] G.S. Al-Ganainy, Phys. Stat. Sol. A 169 (1998) 217. [12] G.S. Al-Ganainy, M.T. Mostafa, Egypt. J. Sol. 23 (2) (2000) 333. [13] B. Wilshire, R.W. Evans, Creep Behaviour of Crystalline Solids, Pineridge press Ltd., Swansea, UK, 1985, p. 34. [14] E.A. Brandes (Ed.), Smithells Metals Reference Book, Butterworths, London, 1983, p. 396 (Chapter 11). [15] M. Kamal, M. Radwan, M. El-Kady, A.M. Daoud, J.C. Pieri, Third Arab International Conference on
[16] [17] [18] [19] [20] [21] [22]
61
Materials Science, 26–30 September Alexandria Egypt, 1992, Vol. 3, p. 203. C.M.L. Wcc, M.L. Huang, J. Electron. Mater. 31 (5) (2002) 442. M.S. Saker, A.A. El-Shazly, M.M. Mostafa, H.A. ElSayed, A.A. Mohamed, Czech. J. Phys. 40 (1990) 1261. M.M. Mostafa, R.H. Nada, F. Abd El-Salam, Phys. Stat. Sol. A 143 (1994) 297. M.S. Saker, A.A. El-Daly, A.Z. Mohamed, E.A. ElSaadani, A.H. Bassyouni, Egypt. J. Sol. 13 (2) (1990) 26. M.S. Saker, A.Z. Mohamed, M.M.A. Shehab, A.H. Bassyouni, Czech. J. Phys. 41 (1991) 785. A. Juhasz, P. Tasnadi, P. Szaszvari, I. Kovacs, J. Mater. Sci. 21 (1986) 3287. G.J. Davies, J.W. Edington, C.P. Cutler, K.A. Padmanabhan, J. Mater. Sci. 5 (1970) 1091.
Physica B 349 (2004) 56–61
Steady state creep characteristics of the eutectic Pb–Sb alloy M.M. Mostafa* Physics Department, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt Received 27 May 2003; received in revised form 17 November 2003; accepted 2 January 2004
Abstract The change in the steady state creep rate of Pb–Sb eutectic alloy is studied under constant stresses ranging from 3.45 to 5.2 MPa and at different temperatures ranging from 433 to 503 K. The strain rate sensitivity parameter (m) varied between 0.33 and 0.46 in the testing temperature range. The activation energy of the steady state creep amounted to 96 kJ/mol in the temperature range from 473 to 503 K, characterizing the self-diffusion mechanism of Pb. The analysis of the microstructural variations confirms that the above-mentioned mechanisms are expected to take place during the investigated steady state creep stage. r 2004 Elsevier B.V. All rights reserved. Keywords: Steady state creep; Eutectic Pb–Sb alloy
1. Introduction Antimony–lead alloys are very important materials in industry for their use as die casting alloys and in manufacturing acidic accumulators. Some mechanical and structural properties of a series of Pb–Sb alloys containing different additives were studied [1]. The thermally induced elastic stresses were found to affect the mechanical properties of the eutectic Pb–Sb alloy, which showed a low plasticity at room temperature [2]. The study of the effect of temperature and stress on the structure and creep parameters of a Pb-2 at% Sb alloy revealed [3] a transition point at 473 K. Aging was found to change the defect structure of Pb–Sb alloys [4]. The hardening mechanisms in binary Pb-based alloys depend on *Corresponding author. E-mail address: [email protected] (M.M. Mostafa).
the type of the alloying element. Lead-antimony alloys are very well hardened by continuous precipitation, whereas lead–tin alloys present a discontinuous precipitation with a weak hardening effect [5]. The effect of structure transformation on the stress–strain characteristics of a Pb-3 wt% Sb alloy was investigated [6]. The variations observed in the measured parameters point to two temperature regions around the transformation temperature. X-ray line-profile analysis of cold-worked Pb–Sb alloys in the alpha-phase revealed that the deformation process has a minimal effect on the microstructure [7]. Cellular/dendritic array tip morphology has been examined in directionally solidified and quenched Pb-5.8 wt% Sb [8]. The dependence of the steady state strain rate est on the applied stress s is found to obey the equation [9,10] s ¼ K e’m st :
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.01.159
ARTICLE IN PRESS M.M. Mostafa / Physica B 349 (2004) 56–61
Here, K is a constant, dependent on the test conditions and m is the strain rate sensitivity parameter. The aim of the present study is to trace the effect of the applied stress and the deformation temperature on the creep characteristics of the eutectic Pb-11.2 wt% Sb alloy.
2. Experimental technique Pb-11.2 wt% Sb alloy samples (eutectic alloy), prepared from highly pure Pb and Sb, were homogenized at 453 K for 24 h, then cold swagged into wires of 0.85 mm diameter and 60 mm length. The samples were heated again at 508 K for 2 h, then slowly cooled with a cooling rate of 8 103 K/s to room temperature at which they were kept for 24 h to get samples with identical initial state containing the precipitated two-phase ða þ bÞ structure. Creep tests were carried out at different temperatures controlled to 71 K in the range from 433 to 503 K, under different applied stresses ranging from 3.45 to 5.2 MPa. Structure investigations after creep were carried out using a D-500 X-ray diffractometer.
3. Experimental results Isothermal creep curves of the Pb-11.2 wt% Sb alloy were measured under different constant stresses of 3.45, 4.3 and 5.2 MPa, at the deformation temperature range 433–503 K in steps of 10 K. Typical curves are shown in Fig. 1, where a regular behaviour for the creep curves is observed. The curves are sensitive to the creep temperature and the applied stress. It is worth noting that all the creep curves are characterized either by the absence of a primary creep stage or by the occurrence of a small inflection [11–13]. Although the steady state creep rate increases with temperature, the elongation to fracture is approximately temperature independent. The steady state strain rate sensitivity parameter mð¼ dln s=dln e’st Þ derived from the slopes of the straight lines relating ln s and ln e’st (see Fig. 2) was
57
found to exhibit values ranging from 0.33 to 0.46, depending on the creep temperature. Fig. 3 shows the temperature dependence of both the strain rate sensitivity. Parameter (m) and the steady state creep rate est. It is clear that a pronounced change in both m and est takes place at 473 K characterizing some sort of transformation. The activation energy of steady state creep was calculated from the slopes of the straight lines relating ln e’ st and 1000/T (see Fig. 4). The present results yield a stress independent activation energy of 68 kJ/mol in the temperature range from 433 to 463 K, and the stress-dependent activation energies 88, 96 and 104 kJ/mol in the temperature range from 473 to 503 K. Fig. 5 represents the change in the activation energy of the steady state creep (Qst) with the applied stress in the temperature range from 473 to 503 K. It decreases with increasing the applied stress, i.e. depends on the stress. Fig. 6 shows the variations in the microstructure parameters: the integral intensity (I), the lattice parameter (a) and the half line width (D2y) after creep for the Pb-rich phase in the Pb-11.2 wt% Sb alloy. They are found to change with the deformation temperature and both (I) and (a) exhibit maxima at 473 K, as shown in Fig. 6a and b, while (D2y) exhibits a minimum at 473 K, Fig. 6c.
4. Discussion According to the constitutional diagram of the Pb–Sb system [14], the studied alloy Pb-11.2 wt% Sb has the eutectic composition, with the lowest melting temperature of any alloy of its range of composition, characterized by the conversion of the liquid alloy during the solidifying process into two solid constituents (a-Pb+a-Sb) in equilibrium with a solid solution composition of 3.5 wt% Sb and 97 wt% Sb. The structure expected to exist in the present samples is the dendritic structure of primary a-Pb and traces of a-Sb revealed in rapid quenched eutectic Pb–Sb alloy [15] close to grain boundaries with solute free zones between the grain
ARTICLE IN PRESS 58
M.M. Mostafa / Physica B 349 (2004) 56–61
Fig. 1. Creep curves at different applied stresses and different temperatures for the Pb-11.2 wt% Sb alloy.
ARTICLE IN PRESS M.M. Mostafa / Physica B 349 (2004) 56–61
Ln σ 1.2
1.3
1.4
1.5
1.6
1.7
-5
433 443 453 463 473 483 493 503
-6
Ln ε st
-7
.
-8 -9 -10 -11 -12
Fig. 2. Strain rate—stress relationship for the Pb-11.2 wt% Sb alloy.
Q st (KJ / mol)
-4
1.1
59
106 104 102 100 98 96 94 92 90 88 86 0
2
σ (MPa)
4
6
Fig. 5. Relation between the activation energy and the applied stress s.
m
0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 420
440
460
480
500
520
T (K)
(a) 0.0012
εst
0.001 0.0008
σ = 3.45
.
0.0006
σ = 4.3
0.0004
σ = 5.2
0.0002 0 420
440
460
(b)
480
500
520
T (K)
Fig. 3. The strain rate sensitivity parameter m (a) and the steady state strain rate est (b) as a function of creep temperature for Pb11.2 wt% Sb alloy.
1.9 0
2
2.1
2.2
2.3
2.4
Ln ε st
-2 .
-4
σ = 3.45 σ = 4.3
-6
σ = 5.2
-8 -10 -12
-1
1000 / T (K ) Fig. 4. Relation between ln e’st and 1000/T for the Pb-11.2 wt% Sb alloy.
boundaries and a series of bonded precipitates within the grains. In small regions, the matrix Sb was observed as single crystal regions at the multigrain junctions. Creep plays an important role in metal deformation, whenever the homologous temperature exceeds 0.5Tm (melting point) as for most solder alloys [16]. The amount and rate of straining during creep are established by the material itself under the imposed stress and temperature conditions. Continuing deformation under constant stress or load, work-hardens the crystalline materials, and this implies some recovery. The steady state creep is commonly considered as a result of a balance between strain hardening and stress-aided and thermally activated recovery. The dependence of the steady state creep rate of the Pb-11.2 wt% Sb alloy on temperature reflects a thermally activated change in the atomic arrangement of the alloy at the transition temperature 473 K. By performing creep tests in the low temperature region (below the transition point), the Pband Sb-rich phases coarsen and the mutual solubility increases in order to get closer to the actual equilibrium compositions at the deformation temperature. The structure variation leads to solution process at some of the interfaces and to a precipitation process at the others. This change in composition requires the presence of a diffusion current, and the directional movement of the atoms gives rise to the dynamic recovery.
ARTICLE IN PRESS M.M. Mostafa / Physica B 349 (2004) 56–61
60
creep equation
18 16
e’st ¼ Cðs=dÞ1=m exp ðQ=KTÞ:
14
ð1Þ
12 -111 -200 -220
I
10 8 6 4 2 0 420
440
460
o
a (A)
(a)
480
500
520
T (K) 4.985 4.98 4.975 4.97 4.965 4.96 4.955 4.95 4.945 4.94 420
430
440
450
460
470
480
490
500
510
T (K)
(b) 0.6° 0.5° 0.4°
∆2θ
-111
0.3°
-200 -220
0.2° 0.1° 0 420
(c)
440
460
480
500
520
T (K)
Fig. 6. The effect of the working temperature on (a) the integral X-ray intensities, (b) the lattice parameter and (c) the half line width of the Pb-rich phase of the Pb-11.2 wt% Sb alloy.
This suggests a dislocation climb mechanism along grain boundaries [17] to be the rate controlling mechanism for the steady state creep of the test alloy. Also, these values of m agree with the values obtained in Ref. [18] which indicate that the dominating mechanism is dislocation climb along grain boundaries. The activation energy of the steady state creep (68.570.4) kJ/mol in the low temperature range from 433 to 463 K, may be due to a viscous flow creep mechanism [3]. The average activation energy obtained in the high-temperature range, from 473 to 503 K, was about (9670.4) kJ/mol which agrees with the activation energy of selfdiffusion in Pb [19–22]. Besides, the activation energy of the steady state creep in the hightemperature region was found to decrease with increasing applied stress, (Fig. 5), which refers to enhancement of diffusion creep mechanism. The integral intensity (I), the lattice parameter (a) and the half line width (D2y) were found to change with the working temperature. The decrease in the values of (I) and (a) in the lowtemperature region, below the transition point, is due to the increase in the recovery process. In the region above the transition point, their decrease might be due to the reduction of the sum of the internal lattice strains as a result of the thermally activated diffusion process.
References The increase of the strain rate sensitivity parameter (m) from 0.33 to 0.46, with increasing deformation temperature (see Fig. 3a) points to the possibility of having an apparent plastic behaviour responsible for the observed deformation. This observation may be due to the accelerated diffusion process of the high vacancy concentration leading to enhanced dislocation climb at higher temperatures. The measured values of m with raising temperature are in agreement with the value 0.5 obtained from the steady state
[1] J. Zhiyun, L. Yuandud, Z. Shuzhen, G. Weiging, Z. Zhonghua, J. Power Sources 31 (1990) 169. [2] S.N. Komnik, I.T. Ponomarenko, V.I. Startsev, Mater. Sci. Eng. 58 (1983) 15. [3] G.S. Al-Ganainy, M.T. Mostafa, M.R. Nagy, Phys. Stat. Sol. A 165 (1998) 185. [4] N.V. Isaev, V.S. Fomenko, V.V. Pustovalov, Fiz. Nizk. Temp. 15 (1989) 759. [5] J.P. Hilger, J. Power Sources 53 (1995) 45. [6] A.M. Abd El-Khalek, R.H. Nada, Physica B 128 (2003) 393. [7] P. Chatterje, P.S. Bhattacharyya, S.P.S. Gupta, J. Alloy Compounds 284 (1999) 160.
ARTICLE IN PRESS M.M. Mostafa / Physica B 349 (2004) 56–61 [8] L. Yu, G.L. Ding, J. Reye, S.N. Ojha, S.N. Tewari, Metall. Mater. Sci. 30 (1999) 2463. [9] G.S. Al-Ganainy, M.R. Nagy, B.A. Khalifa, R. Afify, Phys. Stat. Sol. A 158 (1996) 463. [10] M.M. Mostafa, G.S. Al-Ganainy, M.S. Saker, Egypt. J. Sol. 19 (1996) 199. [11] G.S. Al-Ganainy, Phys. Stat. Sol. A 169 (1998) 217. [12] G.S. Al-Ganainy, M.T. Mostafa, Egypt. J. Sol. 23 (2) (2000) 333. [13] B. Wilshire, R.W. Evans, Creep Behaviour of Crystalline Solids, Pineridge press Ltd., Swansea, UK, 1985, p. 34. [14] E.A. Brandes (Ed.), Smithells Metals Reference Book, Butterworths, London, 1983, p. 396 (Chapter 11). [15] M. Kamal, M. Radwan, M. El-Kady, A.M. Daoud, J.C. Pieri, Third Arab International Conference on
[16] [17] [18] [19] [20] [21] [22]
61
Materials Science, 26–30 September Alexandria Egypt, 1992, Vol. 3, p. 203. C.M.L. Wcc, M.L. Huang, J. Electron. Mater. 31 (5) (2002) 442. M.S. Saker, A.A. El-Shazly, M.M. Mostafa, H.A. ElSayed, A.A. Mohamed, Czech. J. Phys. 40 (1990) 1261. M.M. Mostafa, R.H. Nada, F. Abd El-Salam, Phys. Stat. Sol. A 143 (1994) 297. M.S. Saker, A.A. El-Daly, A.Z. Mohamed, E.A. ElSaadani, A.H. Bassyouni, Egypt. J. Sol. 13 (2) (1990) 26. M.S. Saker, A.Z. Mohamed, M.M.A. Shehab, A.H. Bassyouni, Czech. J. Phys. 41 (1991) 785. A. Juhasz, P. Tasnadi, P. Szaszvari, I. Kovacs, J. Mater. Sci. 21 (1986) 3287. G.J. Davies, J.W. Edington, C.P. Cutler, K.A. Padmanabhan, J. Mater. Sci. 5 (1970) 1091.