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Study of Mg–Ca alloys by positron annihilation technique
Scripta Materialia 52 (2005) 181–186 www.actamat-journals.com
Study of Mg–Ca alloys by positron annihilation technique Y. Ortega *, J. del Rı´o Facultad de Ciencias Fı´sicas, Dpto. de Fı´sica de Materiales, UCM, 28040 Madrid, Spain Received 16 July 2004; received in revised form 10 September 2004; accepted 30 September 2004 Available online 22 October 2004
Abstract Positron lifetime and Doppler broadening measurements were performed to study the precipitation process of MgCa alloys. Isochronal studies revealed changes in the precipitate nucleation and growth rates. The evolution of the ageing treatment was studied by observing the positron trapping at the matrix–Mg2Ca precipitate interfaces. 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Magnesium alloys; Positron annihilation; Ageing; Precipitation; Point defects
1. Introduction The interest in developing light alloys that could be used as structural materials has stimulated the investigation of magnesium alloys, due to their low density [1,2]. However, their poor resistance to corrosion has limited their potential applications. Light alloys such as Mg–Ca alloys have recently been the subject of a great deal of interest due to their good oxidation resistance mainly at elevated temperatures [3], and their good response to age-hardening [4]. According to Nie et al. [4], the strengthening of the MgCa alloy by a thermal treatment leading to precipitation, is due to the nucleation and growth of the Mg2Ca particles from a supersaturated solid solution. Although these second-phase particles have a hexagonal crystal structure (hp12) similar to the one of the magnesium matrix (hp17), there is a difference among the lattice parameters of the equilibrium intermetallic phase (Mg2Ca), i.e. (a = 0.623 nm, c = 1.012 nm) and the magnesium matrix phase, i.e. (a = 0.321 nm, c = 0.521 nm) [5]. *
Corresponding author. Tel.: +34 91 394 4496; fax: +34 91 394 4547. E-mail address: yanicet@fis.ucm.es (Y. Ortega).
Positron annihilation techniques have been widely used to study the kinetics and evolution of the precipitation process in a number of alloying systems [6–8], giving in many cases useful information about the nature and coherency of the strengthening phases. Taking into account the fact that the difference between the lattice parameters for Mg matrix and Mg2Ca is not so large, it is expected that in the initial stage of ageing the clusters may be coherent. The loss of coherency occurs once the precipitates have reached a critical radius rcrit, although in practice, coherent precipitates are often found with sizes much larger than rcrit. Given a difference in interfacial energy between non-coherent and coherent precipitates, cst = cnon-coherent ccoherent, one can estimate a critical radius as: rcrit ¼
3cst 4ld2
ð1Þ
where l is the shear modulus of the magnesium matrix and d is the unconstrained lattice misfit [9]. According to Nie et al. [4] the lattice misfit between the Mg matrix and Mg2Ca precipitates on the habit plane is 12.1%. If we assume the largest difference in interfacial energy, between semicoherent and coherent interfaces like cst = 500 mJ/m2, the calculated critical radius according to (1), yields a value of 1.7 nm.
1359-6462/$ - see front matter 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2004.09.033
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Thus, when the precipitates have reached the critical size, it is probable that the presence of misfit dislocations or other kind of open volume defects present at the precipitate–matrix interfaces could constitute efficient positron annihilation sites. In contrast, taking into consideration that the positron affinity is a little higher for calcium (ACa = 6.40 eV) than for magnesium (AMg = 6.18 eV) [10], it is assumed that none of these two elements constitute preferentially trapping centers for positrons. Furthermore the positron affinity for Mg2Ca particles calculated by the following expression AMg2 Ca ¼ 23 AMg þ 13 ACa yields a value of 6.25 eV, which is closer to the positron affinity for the magnesium matrix. Thus, it is expected that Mg2Ca precipitates themselves, do not represent attractive sites for positrons in Mg–Ca based alloys [11]. In light of the reasons mentioned above, the main intention of this paper is to follow the precipitation process of the Mg–Ca system by positron annihilation techniques and to clarify the positron trapping mechanism which allows its detection.
2. Experimental 2.1. Sample treatments The Mg–1 wt%Ca samples were cut having a surface of about 10 · 10 mm, and being 1 mm thickness. A set of six samples was mechanically polished and homogenized for 24 h at 510 C in argon atmosphere, then quenched into cold water. The positron lifetime evolution was followed for a set of five homogenized samples which underwent different isochronal heat treatments based on different annealing times. After each step of annealing the samples were quenched into iced water and all measurements were performed at room temperature. The isochronal annealing studies were done in steps of 15, 30, 120, 300 and 480 min from room temperature (RT) to 500 C. The precipitation behavior at 200 C up to 72 h was also follow for another homogenized sample combining positron lifetime and Doppler broadening measurements. 2.2. Positron lifetime and Doppler broadening measurement The positron source was 22Na, which was prepared by evaporating an aqueous solution of 22NaCl sandwiched by a kapton foil. The measurements were performed fully automatically using an ORTEC fast-fast coincidence system equipped with two NE111 plastic scintillators. The time resolution of the system, measured for 22Na energy settings was 240 ps (F.W.H.M). Each sample was measured three times and each spectrum contained more than 106 counts. The lifetime spec-
tra were analysed with the computer program POSITRONFIT (PATFIT-88, Riso National Laboratory, Denmark) [12]. A component with an intensity of 18.5% and a lifetime of 382 ps was subtracted from the spectra. This value corresponds to the kapton foil and salt contribution as obtained in a well-annealed Mg sample, in which only one component due to free annihilation is expected. After the subtraction of the source component the spectra were analysed as a sum of two or three exponential components. It was the case for all the spectra, including the spectrum of the well-annealed Mg specimen, that a long component (1600–1700 ps) with intensity (1.67– 1.87%) was always present. Taking into account that the theoretical calculations estimate the value of the positron lifetime in a metal between 100 and 500 ps [13], it is considered that this largest lifetime is not characteristic of the samples; thus it will not be further mentioned, only to say that its value was systematically checked and that it remained almost constant, within statistical scatter [2]. This analysis revealed that the spectra were analysed as a single component or as a sum of two lifetimes. For the two component spectra the average lifetime s was also calculated from the experimental lifetimes si and relative intensities Ii as s = I1s1 + I2s2. Doppler broadening measurements of the annihilation line were also performed at room temperature for the isothermal heat treatment by using a Ge(Li) detector having a resolution of about 1.2 keV at an energy of 511 keV. The results were analysed in terms of the conventional S parameter, which is described in detail elsewhere [14].
3. Results and discussion 3.1. Isochronal annealing In order to detect the formation and further evolution of Mg2Ca precipitates, isochronal annealing studies were carried out in the temperature range from RT to 500 C. The five different annealing times were 15, 30, 120, 300 and 480 min. With the aim of illustrating clearly the results without having a lot of points in a single graph, we have plotted separately into two figures; the results obtained for the various thermal treatments (see Fig. 1a and Fig. 1b). The mean positron lifetime dependence on annealing temperature is depicted in Fig. 1a for the shorter selected times (15, 30 and 120 min), and in Fig. 1b for the longer times (300 and 480 min). For each one treatment the behavior of s shows two main distinguishable stages. Initially the mean positron lifetime increases from a value close to the Mg bulk lifetime, i.e. 225 ± 2 ps; that corresponds to the homogenized sample, to a maximum value which depends on the annealing time.
Y. Ortega, J. del Rı´o / Scripta Materialia 52 (2005) 181–186
Fig. 1. The average lifetime as a function of the annealing temperature for different annealing times: (a) 15, 30 and 120 min; (b) 300 and 480 min. The lines have been drawn as a guide for the eye.
According to Nie et al. [4], the lattice misfit of Mg2Ca precipitates on the habit plane in a magnesium matrix is about 12.1%, thus the Mg2Ca formation and its further growth could be detected through the positron annihilations at the non-coherent precipitate–matrix interfaces. On the other hand, from the general positron trapping model developed by Smedskjaer et al. [15], it is known that dislocation lines themselves represent only weak traps for positrons, but point-like defects associated with dislocations could represent efficient trapping sites. The reported value by Badawi et al. [16] for deformation induced dislocations in magnesium single crystals is about 249 ± 2 ps and the lifetime reported by Hautoja¨rvi et al. for magnesium monovacancies equals 255 ± 5 ps [17], analyzing these values it is observed that they are similar within statistical scatter. According to these values and the maximum positron lifetime achieved for two hours of annealing (see Fig. 1a), which equals 254 ± 2 ps,
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it is more likely that positrons annihilate at zones of low atomic density present at the precipitate–matrix interfaces, which seems to have an electronic density similar to the one found at a vacancy-type defect. The possibility of finding vacancy-like misfit defects at the precipitate–matrix interfaces has been also suggested by Brauer et al. [18]. In contrast, from the slight difference in positron affinities mentioned in the introductory section between the magnesium matrix and Mg2Ca particles, we consider that the contribution of positron annihilations at precipitates is negligible, hence we can assume that positrons annihilate at defects associated to the precipitate–matrix interfaces. For all the reasons mentioned before, the stage that shows an increase in positron lifetime in each curve in Fig. 1, corresponds to an increment in the density of defects, which comes from a higher concentration of Mg2Ca precipitates; thus the first stage is unambiguously attributed to Mg2Ca precipitate formation. Assuming that the positron lifetime is related to the density of Mg2Ca particles, whatever the detection mechanism is, once the maximum value of the positron lifetime has been achieved, its further decrease, which is shown for higher annealing temperatures (see Fig. 1a and Fig. 1b), suggests that the number density of Mg2Ca is decreasing. This feature very probably reflects the size increase of these particles, which contributes to the increase in the average distance between trapping sites, resulting in lower positron trapping rates at these sites. It is worth pointing out that the last annealing temperature is close to the temperature of the solution heat treatment, but even the longest time of annealing (480 min) represents only the 0.4% of the needed time for a completed sample homogenization [4], that is why the positron lifetime is above 225 ps, which represents the Mg bulk positron lifetime. From Fig. 1a and Fig. 1b it is also observed that the temperature at which the maximum lifetime values appear is related to the annealing time; as is seen from these figures, the positions of the annealing peak are gradually shifted to lower temperature values as the annealing time increases. This shift is expected if we take into account that precipitation is a thermally activated process, so variables such as annealing time and temperature play an important role [19], it being predictable that for certain combinations of annealing times and temperatures, faster rates of nucleation and growth could be achieved as a consequence of an enhanced diffusion. This effect is clearly illustrated if we compare the curves in Fig. 1a which correspond to 15 and 120 min of annealing time; the first curve seems to have the peak between 250 and 300 C, whereas the curve which corresponds to 120 min of annealing time reaches the highest value at 250 C. It shows that the isochronal annealing of 120 min produces a more efficient precipitation process in comparison with 15 min of annealing;
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Fig. 3. The average lifetime and the S parameter as a function of the ageing time at 200 C. The lines have been drawn as a guide for the eye. Fig. 2. The average lifetime as a function of the annealing time for 150, 200 and 250 C. The lines have been drawn as a guide for the eye.
100 200 300 400 500 600 700 800 900
4000 8000 12000 320
100
310 300
80
290 60 280
τ2 (ps)
(i) the slight increase of the positron lifetime at 150 C reflects the fact that the precipitation process is very slow at this temperature; (ii) the over-ageing at 250 C occurs at about 300 min, whereas the over-ageing at 200 C it is not seen even for 480 min of annealing.
0
I2 (%)
thus one can consider that a faster precipitation rate has been achieved leading to a higher precipitation density. As expected from our analysis the curve which represents 30 min of annealing shows an intermediate stage between the values obtained for 15 min and 120 min annealing. From Fig. 1b, it is interesting to note that the lifetimes s associated with the peaks for longer annealing times (see Fig. 1b), are lower than the lifetimes associated with the peaks for shorter annealing times (see Fig. 1a). This result provides further evidence that the nucleation and growth of the Mg2Ca particles strongly depends on the annealing time and temperature. In order to clarify the role of these two parameters, i.e. temperature and time, in the kinetics of the ageing treatment, we have plotted in Fig. 2 the positron lifetime values as a function of the annealing time, for the temperatures of 150 C, 200 C and 250 C. From the inspection of Fig. 2 we can arrive at the main conclusions:
analysed as a sum of two components and the lifetime s2 and its corresponding intensity I2, which are associated with the annihilations of the localized positrons, are plotted in Fig. 4. Taking into account the results shown in Fig. 3, it is observed that after 65 min of ageing, there is a sharp increase of the S parameter. Between 300 and 1795 min ageing the S parameter remains approximately constant (within experimental error) showing that the low electron momentum contribution at the annihilation sites is almost unchanged, whereas the mean positron lifetime gradually increases, reaching a value of 255 ps after 480 min ageing (see Fig. 4). The decomposition of the lifetime spectra for times shorter than 480 min was made by fixing the value s2 equal to 255 ps; nevertheless, due to the small lifetime change for defects, ssb2 1:13, the two component analysis of the positron lifetime spectra was only reliable for I2 P 90%. The attempt to fix
270
40
260
3.2. Isothermal annealing
20 250
In the light of the previous isochronal measurements the progress of the precipitation process was followed at 200 C, because at that temperature the kinetics of the over-ageing is retarded. Fig. 3 shows the evolution of the mean positron lifetime and the S parameter with the artificial ageing time. Some lifetime spectra were
0
240 0
100 200 300 400 500 600 700 800 900
4000 8000 12000
Ageing time at 200˚C (minutes)
Fig. 4. The evolution of the long component s2 and its related intensity I2 as a function of the ageing time at 200 C. The lines have been drawn as a guide for the eye.
Y. Ortega, J. del Rı´o / Scripta Materialia 52 (2005) 181–186
220
τ1 experimental value τ1 theoretical value
200 180 160
τ1(ps)
s2 = 255 ps for longer times (>480 min), was inadequate due to the high values obtained for the variance of the fit during the deconvolution of positron lifetime spectra. In view of the fact that the value of 255 ps has been associated with the positron annihilations at the matrix–precipitate interfaces, the increase of the intensity I2 up to 480 min reflects the increase in positron traps, i.e. the increase of the precipitate density. From Fig. 4, it is observed that for longer ageing times the lifetime s2 begins to increase until reaches a value of 287 ± 5 ps, whereas its associated intensity decreases to 75 ± 5%. The slight decrease of I2 suggests the decrease of the number density of positron trapping sites due to the precipitate coarsening. Since the increase of s2 also appears for longer ageing times, it seems to be related to the growth of larger precipitates at the expense of smaller ones. The increase of s2 implies the necessity of postulating the existence of at least two different traps for positrons. However, due to the impossibility of decomposing the spectra—properly—in more than two components, we are not able to identify, accurately, the nature of this new defect. At least, this result suggests that the lifetime associated to this second trap is slightly longer than 255 ps but close to 290 ps. Thus, we believe that the s2 value represents an average value of the lifetimes associated to defects (which cannot be solved experimentally). The hypothesis of the coarsening microstructure, for ageing times larger than 480 min, is in agreement with the softness and the sparsely distributed coarse precipitates observed in TEM observations by Nie et al. [4] of a Mg–1Ca sample aged 8 h at 200 C. According to their micrographs the average distance among precipitates can be estimated about 210 nm, which is lower than the positron diffusion length in a magnesium matrix at RT (260 nm) [20]. Thus it is expected that once the coarsening begins, the average distance among precipitates increases, becoming for a certain time larger than the positron diffusion length. In order to evaluate the validity of the two state trapping model, the theoretical value of the shorter component s1, calculated from s1 = (kb + kd)1, was compared to the experimental lifetime s1, where k d ¼ II 21 ðkb k2 Þ; kb and k2 are the free and trapped positron annihilation rates, respectively, and I1 and I2 represent the intensities for the two components. With the aim of validating the one-trap model, in addition to the imperfect decomposition in the fitting process, as has been previously discussed, it should be pointed out that the conventional trapping model assumes that defects in a sample are distributed homogeneously [21]. As is seen from Fig. 5, for times shorter than 480 min ageing the calculated values of s1 are close to the measured lifetimes, but the one trap model fails for extended ageing times. A possible interpretation is that the failure of the one trap model begins with the precipitate coarsening. As is known, during
185
140 120 100 80 0
100 200 300 400 500 600 700 800 900
4000 8000 12000
˚
Ageing time at 200 C (minutes)
Fig. 5. The evolution of the experimental value s1 and the one calculated according to the simple trapping model (see text), as a function of the ageing time at 200 C.
coarsening the change from small precipitates to large ones means that the smallest precipitates shrink and disappear, leaving depleted zones: hence the result of competitive precipitate growth is that positron traps are not uniformly distributed anymore. It should then be concluded that the deviation from the one-trap model is probably due to the imperfect decomposition in the fitting process—as has been previously discussed—and to the non-uniformly distributed traps.
4. Conclusions With the present study we can arrive at the following main conclusions: (i) the detection of Mg2Ca precipitates takes place by the positron annihilations at the precipitate–matrix interface; (ii) the deviation from the two state trapping model, for ageing times longer than 480 min, is probably due to the presence of more than one trapped state in the sample, and to the non-uniformly distributed positron traps.
Acknowledgments One of the authors (Y. Ortega) is indebted to Prof. Plazaola for discussions, comments and his several recommendations that contribute to improve the analysis of the experimental data; also she would like to thank to Prof. J.F. Nie of the Monash University in Australia for the sample supply. This research was undertaken
Y. Ortega, J. del Rı´o / Scripta Materialia 52 (2005) 181–186
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under the grant no. MAT2002-04087-C02 (Ministerio de Ciencia y Tecnologı´a, Spain).
References [1] [2] [3] [4] [5]
[6] [7] [8] [9]
Celotto S. Acta Mater 2000;48:1775. Ortega Y, del Rı´o J. Phys Stat Sol (a) 2004;201(3):471. You BS, Park W-W, Chung I-S. Scripta Mater 2000;42:1089. Nie JF, Muddle BC. Scripta Mater 1997;37(10):1475. Villars P, Calvert LD. PearsonÕs Handbook of Crystallographic Data for Intermetallic Phases. Metals Park, Ohio: ASM; 1985. Somoza A, Dupasquier A. J Mater Proc Tech 2003;6469:1. de Diego N, Hidalgo C. Philos Mag A 1986;53(1):123. Macchi CE, Somoza A, Dupasquier A, Polmear IJ. Acta Mater 2003;51:5151. Porter DA, Easterling KE. Phase transformations in metals and alloys. second ed.. Chapman & Hall; 1992.
[10] Puska MJ, Lanki P, Nieminen RM. J Phys: Condens Matter 1989;1:6081. [11] Plazaola F, Personal communication, 2004. [12] Kirkegaard P, Eldrup M, Mogensen OE, et al. Comput Phys Commun 1981;23:307. [13] Seeger A, Banhart F. Phys Stat Solidi (a) 1987;102:171. [14] Procha´zka I. Mater Struct 2001;8(2):55. [15] Smedskjaer LC, Manninen M, Fluss MJ. J Phys F: Metal Phys 1980;10:2237. [16] Badawi Emad A, Abdel-rahman MA, Mahmoud SA. Appl Surf Sci 1999;149:211. [17] Hautojarvi P, Johansson J, Vehanen A, Yli-Kauppila J. Appl Phys A 1982:46–59. [18] Brauer G, Liszkay L, Molnar B, Krause R. Nucl Eng Des 1991;127:47. [19] Smallman RE, Bishop RJ. Modern Physical Metallurgy and Materials Engineering, 1999. [20] Nieminen RM, Manninen MJ. In: P. Hautoja¨rvi, editor. Topics in Current Physics: Positron in Solids, 1979. [21] Brandt W. In: Stewart AT, Roelling LO, editors. Positron Annihilation. New York: Academic; 1967. p. 155.
Study of Mg–Ca alloys by positron annihilation technique Y. Ortega *, J. del Rı´o Facultad de Ciencias Fı´sicas, Dpto. de Fı´sica de Materiales, UCM, 28040 Madrid, Spain Received 16 July 2004; received in revised form 10 September 2004; accepted 30 September 2004 Available online 22 October 2004
Abstract Positron lifetime and Doppler broadening measurements were performed to study the precipitation process of MgCa alloys. Isochronal studies revealed changes in the precipitate nucleation and growth rates. The evolution of the ageing treatment was studied by observing the positron trapping at the matrix–Mg2Ca precipitate interfaces. 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Magnesium alloys; Positron annihilation; Ageing; Precipitation; Point defects
1. Introduction The interest in developing light alloys that could be used as structural materials has stimulated the investigation of magnesium alloys, due to their low density [1,2]. However, their poor resistance to corrosion has limited their potential applications. Light alloys such as Mg–Ca alloys have recently been the subject of a great deal of interest due to their good oxidation resistance mainly at elevated temperatures [3], and their good response to age-hardening [4]. According to Nie et al. [4], the strengthening of the MgCa alloy by a thermal treatment leading to precipitation, is due to the nucleation and growth of the Mg2Ca particles from a supersaturated solid solution. Although these second-phase particles have a hexagonal crystal structure (hp12) similar to the one of the magnesium matrix (hp17), there is a difference among the lattice parameters of the equilibrium intermetallic phase (Mg2Ca), i.e. (a = 0.623 nm, c = 1.012 nm) and the magnesium matrix phase, i.e. (a = 0.321 nm, c = 0.521 nm) [5]. *
Corresponding author. Tel.: +34 91 394 4496; fax: +34 91 394 4547. E-mail address: yanicet@fis.ucm.es (Y. Ortega).
Positron annihilation techniques have been widely used to study the kinetics and evolution of the precipitation process in a number of alloying systems [6–8], giving in many cases useful information about the nature and coherency of the strengthening phases. Taking into account the fact that the difference between the lattice parameters for Mg matrix and Mg2Ca is not so large, it is expected that in the initial stage of ageing the clusters may be coherent. The loss of coherency occurs once the precipitates have reached a critical radius rcrit, although in practice, coherent precipitates are often found with sizes much larger than rcrit. Given a difference in interfacial energy between non-coherent and coherent precipitates, cst = cnon-coherent ccoherent, one can estimate a critical radius as: rcrit ¼
3cst 4ld2
ð1Þ
where l is the shear modulus of the magnesium matrix and d is the unconstrained lattice misfit [9]. According to Nie et al. [4] the lattice misfit between the Mg matrix and Mg2Ca precipitates on the habit plane is 12.1%. If we assume the largest difference in interfacial energy, between semicoherent and coherent interfaces like cst = 500 mJ/m2, the calculated critical radius according to (1), yields a value of 1.7 nm.
1359-6462/$ - see front matter 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2004.09.033
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Thus, when the precipitates have reached the critical size, it is probable that the presence of misfit dislocations or other kind of open volume defects present at the precipitate–matrix interfaces could constitute efficient positron annihilation sites. In contrast, taking into consideration that the positron affinity is a little higher for calcium (ACa = 6.40 eV) than for magnesium (AMg = 6.18 eV) [10], it is assumed that none of these two elements constitute preferentially trapping centers for positrons. Furthermore the positron affinity for Mg2Ca particles calculated by the following expression AMg2 Ca ¼ 23 AMg þ 13 ACa yields a value of 6.25 eV, which is closer to the positron affinity for the magnesium matrix. Thus, it is expected that Mg2Ca precipitates themselves, do not represent attractive sites for positrons in Mg–Ca based alloys [11]. In light of the reasons mentioned above, the main intention of this paper is to follow the precipitation process of the Mg–Ca system by positron annihilation techniques and to clarify the positron trapping mechanism which allows its detection.
2. Experimental 2.1. Sample treatments The Mg–1 wt%Ca samples were cut having a surface of about 10 · 10 mm, and being 1 mm thickness. A set of six samples was mechanically polished and homogenized for 24 h at 510 C in argon atmosphere, then quenched into cold water. The positron lifetime evolution was followed for a set of five homogenized samples which underwent different isochronal heat treatments based on different annealing times. After each step of annealing the samples were quenched into iced water and all measurements were performed at room temperature. The isochronal annealing studies were done in steps of 15, 30, 120, 300 and 480 min from room temperature (RT) to 500 C. The precipitation behavior at 200 C up to 72 h was also follow for another homogenized sample combining positron lifetime and Doppler broadening measurements. 2.2. Positron lifetime and Doppler broadening measurement The positron source was 22Na, which was prepared by evaporating an aqueous solution of 22NaCl sandwiched by a kapton foil. The measurements were performed fully automatically using an ORTEC fast-fast coincidence system equipped with two NE111 plastic scintillators. The time resolution of the system, measured for 22Na energy settings was 240 ps (F.W.H.M). Each sample was measured three times and each spectrum contained more than 106 counts. The lifetime spec-
tra were analysed with the computer program POSITRONFIT (PATFIT-88, Riso National Laboratory, Denmark) [12]. A component with an intensity of 18.5% and a lifetime of 382 ps was subtracted from the spectra. This value corresponds to the kapton foil and salt contribution as obtained in a well-annealed Mg sample, in which only one component due to free annihilation is expected. After the subtraction of the source component the spectra were analysed as a sum of two or three exponential components. It was the case for all the spectra, including the spectrum of the well-annealed Mg specimen, that a long component (1600–1700 ps) with intensity (1.67– 1.87%) was always present. Taking into account that the theoretical calculations estimate the value of the positron lifetime in a metal between 100 and 500 ps [13], it is considered that this largest lifetime is not characteristic of the samples; thus it will not be further mentioned, only to say that its value was systematically checked and that it remained almost constant, within statistical scatter [2]. This analysis revealed that the spectra were analysed as a single component or as a sum of two lifetimes. For the two component spectra the average lifetime s was also calculated from the experimental lifetimes si and relative intensities Ii as s = I1s1 + I2s2. Doppler broadening measurements of the annihilation line were also performed at room temperature for the isothermal heat treatment by using a Ge(Li) detector having a resolution of about 1.2 keV at an energy of 511 keV. The results were analysed in terms of the conventional S parameter, which is described in detail elsewhere [14].
3. Results and discussion 3.1. Isochronal annealing In order to detect the formation and further evolution of Mg2Ca precipitates, isochronal annealing studies were carried out in the temperature range from RT to 500 C. The five different annealing times were 15, 30, 120, 300 and 480 min. With the aim of illustrating clearly the results without having a lot of points in a single graph, we have plotted separately into two figures; the results obtained for the various thermal treatments (see Fig. 1a and Fig. 1b). The mean positron lifetime dependence on annealing temperature is depicted in Fig. 1a for the shorter selected times (15, 30 and 120 min), and in Fig. 1b for the longer times (300 and 480 min). For each one treatment the behavior of s shows two main distinguishable stages. Initially the mean positron lifetime increases from a value close to the Mg bulk lifetime, i.e. 225 ± 2 ps; that corresponds to the homogenized sample, to a maximum value which depends on the annealing time.
Y. Ortega, J. del Rı´o / Scripta Materialia 52 (2005) 181–186
Fig. 1. The average lifetime as a function of the annealing temperature for different annealing times: (a) 15, 30 and 120 min; (b) 300 and 480 min. The lines have been drawn as a guide for the eye.
According to Nie et al. [4], the lattice misfit of Mg2Ca precipitates on the habit plane in a magnesium matrix is about 12.1%, thus the Mg2Ca formation and its further growth could be detected through the positron annihilations at the non-coherent precipitate–matrix interfaces. On the other hand, from the general positron trapping model developed by Smedskjaer et al. [15], it is known that dislocation lines themselves represent only weak traps for positrons, but point-like defects associated with dislocations could represent efficient trapping sites. The reported value by Badawi et al. [16] for deformation induced dislocations in magnesium single crystals is about 249 ± 2 ps and the lifetime reported by Hautoja¨rvi et al. for magnesium monovacancies equals 255 ± 5 ps [17], analyzing these values it is observed that they are similar within statistical scatter. According to these values and the maximum positron lifetime achieved for two hours of annealing (see Fig. 1a), which equals 254 ± 2 ps,
183
it is more likely that positrons annihilate at zones of low atomic density present at the precipitate–matrix interfaces, which seems to have an electronic density similar to the one found at a vacancy-type defect. The possibility of finding vacancy-like misfit defects at the precipitate–matrix interfaces has been also suggested by Brauer et al. [18]. In contrast, from the slight difference in positron affinities mentioned in the introductory section between the magnesium matrix and Mg2Ca particles, we consider that the contribution of positron annihilations at precipitates is negligible, hence we can assume that positrons annihilate at defects associated to the precipitate–matrix interfaces. For all the reasons mentioned before, the stage that shows an increase in positron lifetime in each curve in Fig. 1, corresponds to an increment in the density of defects, which comes from a higher concentration of Mg2Ca precipitates; thus the first stage is unambiguously attributed to Mg2Ca precipitate formation. Assuming that the positron lifetime is related to the density of Mg2Ca particles, whatever the detection mechanism is, once the maximum value of the positron lifetime has been achieved, its further decrease, which is shown for higher annealing temperatures (see Fig. 1a and Fig. 1b), suggests that the number density of Mg2Ca is decreasing. This feature very probably reflects the size increase of these particles, which contributes to the increase in the average distance between trapping sites, resulting in lower positron trapping rates at these sites. It is worth pointing out that the last annealing temperature is close to the temperature of the solution heat treatment, but even the longest time of annealing (480 min) represents only the 0.4% of the needed time for a completed sample homogenization [4], that is why the positron lifetime is above 225 ps, which represents the Mg bulk positron lifetime. From Fig. 1a and Fig. 1b it is also observed that the temperature at which the maximum lifetime values appear is related to the annealing time; as is seen from these figures, the positions of the annealing peak are gradually shifted to lower temperature values as the annealing time increases. This shift is expected if we take into account that precipitation is a thermally activated process, so variables such as annealing time and temperature play an important role [19], it being predictable that for certain combinations of annealing times and temperatures, faster rates of nucleation and growth could be achieved as a consequence of an enhanced diffusion. This effect is clearly illustrated if we compare the curves in Fig. 1a which correspond to 15 and 120 min of annealing time; the first curve seems to have the peak between 250 and 300 C, whereas the curve which corresponds to 120 min of annealing time reaches the highest value at 250 C. It shows that the isochronal annealing of 120 min produces a more efficient precipitation process in comparison with 15 min of annealing;
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Fig. 3. The average lifetime and the S parameter as a function of the ageing time at 200 C. The lines have been drawn as a guide for the eye. Fig. 2. The average lifetime as a function of the annealing time for 150, 200 and 250 C. The lines have been drawn as a guide for the eye.
100 200 300 400 500 600 700 800 900
4000 8000 12000 320
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310 300
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290 60 280
τ2 (ps)
(i) the slight increase of the positron lifetime at 150 C reflects the fact that the precipitation process is very slow at this temperature; (ii) the over-ageing at 250 C occurs at about 300 min, whereas the over-ageing at 200 C it is not seen even for 480 min of annealing.
0
I2 (%)
thus one can consider that a faster precipitation rate has been achieved leading to a higher precipitation density. As expected from our analysis the curve which represents 30 min of annealing shows an intermediate stage between the values obtained for 15 min and 120 min annealing. From Fig. 1b, it is interesting to note that the lifetimes s associated with the peaks for longer annealing times (see Fig. 1b), are lower than the lifetimes associated with the peaks for shorter annealing times (see Fig. 1a). This result provides further evidence that the nucleation and growth of the Mg2Ca particles strongly depends on the annealing time and temperature. In order to clarify the role of these two parameters, i.e. temperature and time, in the kinetics of the ageing treatment, we have plotted in Fig. 2 the positron lifetime values as a function of the annealing time, for the temperatures of 150 C, 200 C and 250 C. From the inspection of Fig. 2 we can arrive at the main conclusions:
analysed as a sum of two components and the lifetime s2 and its corresponding intensity I2, which are associated with the annihilations of the localized positrons, are plotted in Fig. 4. Taking into account the results shown in Fig. 3, it is observed that after 65 min of ageing, there is a sharp increase of the S parameter. Between 300 and 1795 min ageing the S parameter remains approximately constant (within experimental error) showing that the low electron momentum contribution at the annihilation sites is almost unchanged, whereas the mean positron lifetime gradually increases, reaching a value of 255 ps after 480 min ageing (see Fig. 4). The decomposition of the lifetime spectra for times shorter than 480 min was made by fixing the value s2 equal to 255 ps; nevertheless, due to the small lifetime change for defects, ssb2 1:13, the two component analysis of the positron lifetime spectra was only reliable for I2 P 90%. The attempt to fix
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3.2. Isothermal annealing
20 250
In the light of the previous isochronal measurements the progress of the precipitation process was followed at 200 C, because at that temperature the kinetics of the over-ageing is retarded. Fig. 3 shows the evolution of the mean positron lifetime and the S parameter with the artificial ageing time. Some lifetime spectra were
0
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Ageing time at 200˚C (minutes)
Fig. 4. The evolution of the long component s2 and its related intensity I2 as a function of the ageing time at 200 C. The lines have been drawn as a guide for the eye.
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τ1 experimental value τ1 theoretical value
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τ1(ps)
s2 = 255 ps for longer times (>480 min), was inadequate due to the high values obtained for the variance of the fit during the deconvolution of positron lifetime spectra. In view of the fact that the value of 255 ps has been associated with the positron annihilations at the matrix–precipitate interfaces, the increase of the intensity I2 up to 480 min reflects the increase in positron traps, i.e. the increase of the precipitate density. From Fig. 4, it is observed that for longer ageing times the lifetime s2 begins to increase until reaches a value of 287 ± 5 ps, whereas its associated intensity decreases to 75 ± 5%. The slight decrease of I2 suggests the decrease of the number density of positron trapping sites due to the precipitate coarsening. Since the increase of s2 also appears for longer ageing times, it seems to be related to the growth of larger precipitates at the expense of smaller ones. The increase of s2 implies the necessity of postulating the existence of at least two different traps for positrons. However, due to the impossibility of decomposing the spectra—properly—in more than two components, we are not able to identify, accurately, the nature of this new defect. At least, this result suggests that the lifetime associated to this second trap is slightly longer than 255 ps but close to 290 ps. Thus, we believe that the s2 value represents an average value of the lifetimes associated to defects (which cannot be solved experimentally). The hypothesis of the coarsening microstructure, for ageing times larger than 480 min, is in agreement with the softness and the sparsely distributed coarse precipitates observed in TEM observations by Nie et al. [4] of a Mg–1Ca sample aged 8 h at 200 C. According to their micrographs the average distance among precipitates can be estimated about 210 nm, which is lower than the positron diffusion length in a magnesium matrix at RT (260 nm) [20]. Thus it is expected that once the coarsening begins, the average distance among precipitates increases, becoming for a certain time larger than the positron diffusion length. In order to evaluate the validity of the two state trapping model, the theoretical value of the shorter component s1, calculated from s1 = (kb + kd)1, was compared to the experimental lifetime s1, where k d ¼ II 21 ðkb k2 Þ; kb and k2 are the free and trapped positron annihilation rates, respectively, and I1 and I2 represent the intensities for the two components. With the aim of validating the one-trap model, in addition to the imperfect decomposition in the fitting process, as has been previously discussed, it should be pointed out that the conventional trapping model assumes that defects in a sample are distributed homogeneously [21]. As is seen from Fig. 5, for times shorter than 480 min ageing the calculated values of s1 are close to the measured lifetimes, but the one trap model fails for extended ageing times. A possible interpretation is that the failure of the one trap model begins with the precipitate coarsening. As is known, during
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Ageing time at 200 C (minutes)
Fig. 5. The evolution of the experimental value s1 and the one calculated according to the simple trapping model (see text), as a function of the ageing time at 200 C.
coarsening the change from small precipitates to large ones means that the smallest precipitates shrink and disappear, leaving depleted zones: hence the result of competitive precipitate growth is that positron traps are not uniformly distributed anymore. It should then be concluded that the deviation from the one-trap model is probably due to the imperfect decomposition in the fitting process—as has been previously discussed—and to the non-uniformly distributed traps.
4. Conclusions With the present study we can arrive at the following main conclusions: (i) the detection of Mg2Ca precipitates takes place by the positron annihilations at the precipitate–matrix interface; (ii) the deviation from the two state trapping model, for ageing times longer than 480 min, is probably due to the presence of more than one trapped state in the sample, and to the non-uniformly distributed positron traps.
Acknowledgments One of the authors (Y. Ortega) is indebted to Prof. Plazaola for discussions, comments and his several recommendations that contribute to improve the analysis of the experimental data; also she would like to thank to Prof. J.F. Nie of the Monash University in Australia for the sample supply. This research was undertaken
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under the grant no. MAT2002-04087-C02 (Ministerio de Ciencia y Tecnologı´a, Spain).
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