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Aging precipitation kinetics of Mg-Sc alloy with bcc+hcp two-phase
Accepted Manuscript Aging precipitation kinetics of Mg-Sc alloy with bcc+hcp two-phase Yukiko Ogawa, Yuji Sutou, Daisuke Ando, Junichi Koike PII:
S0925-8388(18)30923-X
DOI:
10.1016/j.jallcom.2018.03.064
Reference:
JALCOM 45294
To appear in:
Journal of Alloys and Compounds
Received Date: 25 December 2017 Revised Date:
2 March 2018
Accepted Date: 6 March 2018
Please cite this article as: Y. Ogawa, Y. Sutou, D. Ando, J. Koike, Aging precipitation kinetics of Mg-Sc alloy with bcc+hcp two-phase, Journal of Alloys and Compounds (2018), doi: 10.1016/ j.jallcom.2018.03.064. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Aging precipitation kinetics of Mg-Sc alloy with bcc+hcp two-phase Yukiko Ogawa1*, Yuji Sutou2, Daisuke Ando2, Junichi Koike2 1
Research Center for Structural Materials, National Institute for Materials Science, Tsukuba
2
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305-0047, Japan
Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai
980-8579, Japan
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*author for correspondence: [email protected] (Y. Ogawa)
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ABSTRACT
In our previous research, we reported that Mg-Sc alloys with a bcc (β) phase showed significant age hardening by the formation of fine hcp (α) precipitates in the β phase. In this study, we investigated the kinetics of the aging precipitation in the α+β two-phase Mg-Sc alloy. The
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incubation time for age hardening became shorter with increasing aging temperature. The relationship between the volume fraction of α precipitates and aging time was better described by the Austin-Rickett equation than by the Johnson-Mehl-Avrami-Kolmogorov equation, and
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the obtained n values are 1.2 ~ 1.4. According to the n values and the morphology of fine α precipitates, the mechanism of α precipitation in the Mg-Sc alloy with an α+β two-phase was
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proposed to be a diffusion-controlled reaction, including the one-dimensional growth of α precipitates at a constant or decreasing nucleation rate. In addition, the activation energy for α precipitation was calculated to be 83.5 kJmol-1. This value is much smaller than that of self-diffusion in Mg, while it is almost the same as that of grain boundary diffusion in Mg, namely interface diffusion. This reveals that the growth of α precipitates is dominated by interface diffusion along the boundaries between the α precipitate and the β phase.
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Keywords Magnesium alloy; Phase transformation; Age hardening
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1. Introduction
Mg alloys have received attention as structural materials for transportation systems and portable products because of their greatest advantage, i.e., their light weight [1-3]. High-strength and Mg
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alloys with a long-period stacking ordered (LPSO) phase have been developed; these Mg alloys are also highly corrosion resistant [4-6]. However, Mg alloys with a hexagonal close-packed
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(hcp) structure tend to show low ductility at room temperature, due to the anisotropic structure of the hcp, where an hcp phase in Mg alloys is designated as the α phase. To improve the ductility of Mg alloys, we have attempted to introduce an isotropic body-centered cubic (bcc) structure in Mg alloys, where a bcc phase in Mg alloys is designated as the β phase. From the
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standpoint of phase stability, we have focused on the Mg-Sc binary system, which has a bcc phase in a Mg-rich composition region (Fig. 1) [7, 8]. We demonstrated that a β-type Mg-Sc alloy shows excellent ductility as compared with conventional α-type Mg alloys and exhibits
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much higher strength than conventional β-type Mg-Li alloys [8]. Moreover, a Mg-Sc alloy with an α+β two-phase was found to show good balance between tensile strength and elongation and
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achieved high tensile strength greater than 300 MPa, together with excellent tensile elongation of about 30% [8], indicating that the α+β-type Mg-Sc alloy shows better mechanical properties than α+β-type Mg-Li alloys [9]. In addition, the β-type Mg-Sc alloy was found to exhibit shape memory properties associated with martensitic transformation [10]. Natarajan et al. pointed out from first-principles calculations that a high degree of degeneracy among hcp, bcc and fcc phases is likely to play an important role in the shame memory properties for the Mg-Sc alloy [11].
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Mg-Sc alloy with the β phase also shows age hardening. We reported that Mg-16.8 and 20.5 at.% Sc alloys show significant age hardening by the precipitation of fine needle- or plate-shaped α phases in the β phase, and fine α precipitates show the Burgers orientation
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relationship with the β phase [12, 13]. An age-hardened α+β two-phase Mg-Sc alloy shows very high tensile strength greater than 450 MPa with better elongation of about 7% [13]. Precipitation of fine α phase was also reported in β phase of Mg-Li alloys by aging [14-16] and
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the kinetics of α precipitation was predicted to be the diffusivity of Mg and Li based on phenomenological analysis from the SEM observation [14]. It is well known that such age
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hardening by α precipitation in the β phase, satisfying Burgers orientation relationship, is observed in Zr and Ti alloys [17-19]. The kinetics of α precipitation in the β phase of Zr and Ti alloys has been investigated by both experimental and computer simulation with the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation [20-23]. Generally, transformation
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kinetics can be discussed with the Avrami index, n, which depends on nucleation and a growth mechanism. The reported Avrami index, n, in Zr-45Ti-5Al-3V alloy (wt.%) aged at 500 ~ 600 ˚C is 0.4 ~ 0.7, not so far from that of Ti-15V-3Cr-3Al-3Sn alloy (wt.%) aged at 500 ˚C [22, 23],
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while the n value of β21s commercial titanium alloy (Ti-3Al-15Mo-3Nb (wt.%)) aged at a temperature of 500 ~ 600 ˚C is reported to be around 1.2 [21]. In addition, at higher aging
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temperatures greater than 650 ˚C, the n value of the β21s commercial titanium alloy is about 1.8 ~ 1.9 [21]. Furthermore, the n values in Ti-6Al-4V and Ti-6Al-2Sn-4Zr-2Mo-0.08Si (wt.%) alloys aged at over 650 ˚C are reported to be about 1.2 ~ 1.6 [20]. The kinetics of the age hardening behavior in β-type Zr and Ti alloys has been well discussed based on transformation kinetics, such as the JMAK model, while that of Mg-Sc alloys have not yet been examined. Therefore, in the present study, the kinetics of α precipitation in the β phase of Mg-Sc alloy with an α+β two-phase was examined based on isothermal aging experiments.
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2. Experimental procedures A Mg-Sc alloy ingot was prepared by induction melting in an Ar atmosphere using an Al2O3
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crucible, followed by cooling in the crucible. The nominal composition was Mg-20 at.% Sc. The alloy ingot was annealed at 600 ˚C for 16 h in an Ar atmosphere, followed by water quenching, and then cold rolled with a 10% reduction in thickness. The cold-rolled sample was
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subsequently annealed at 600 ˚C for 3.6 ks in air to obtain an α+β two-phase microstructure. The composition of the prepared Mg-Sc sheet was Mg-19.99 at.% Sc ≈ Mg-20.0 at.% Sc, which
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was measured by means of an electron probe microanalyzer (EPMA). The Sc content of α and β phases in the sample annealed at 600 ˚C for 3.6 ks in air were determined to be 18.0 and 22.6 at.% by EPMA, respectively. The α+β two-phase alloy sheet was cut into small pieces. The obtained small samples were aged at 175 ~ 300 ˚C in air. The hardness of the aged samples was
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measured by a Vickers hardness tester with a load of 1.0 kgf, where the number of measuring points was 10 each, and the average hardness was determined by averaging 8 points, except the maximum and minimum values. The error bar in each measurement was defined as a standard
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error of those 8 points.
The crystal structure of the aged samples was analyzed by X-ray diffraction (XRD)
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with the θ-2θ method with a Cu-Kα source. The microstructure was observed by scanning electron microscopy (SEM). Before SEM observation, the samples were mechanically polished to a mirror finish and then chemically etched with a solution of 3 ml of nitric acid, 9 ml of acetic acid, 12 ml of distilled water, and 36 ml of ethanol to visualize their α+β two-phase microstructure. The volume fraction of the precipitated phase in the β phase with aging treatment was estimated by image analysis of backscattered electron micrographs using ImageJ software.
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3. Results and discussion 3.1. Effect of aging on the hardness of the α+β alloy
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Fig. 2 shows the effect of aging time on Vickers hardness in the Mg-20.0 at.% Sc alloy with an α+β two-phase aged at (a) 175 and 200 ˚C, and at (b) 225, 250, and 300 ˚C. Before aging treatment, the α+β alloy showed a Vickers hardness of about 90 HV, which is higher than
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that of conventional Mg alloys, such as AZ31 (60 ~ 70 HV) with an equivalent grain size (10 ~ 30 µm) [24, 25]. This is because of a solid solution hardening caused by the addition of Sc. At
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all aging temperatures, the alloy shows a significant hardening after some incubation time, tc. The tc is an onset time of the increase of Vickers hardness and is defined as shown in the inset of Fig. 2(a). As the aging temperature becomes higher, the tc is seen to become shorter. The tc at 175, 200, 225, 250, and 300 ˚C were 41, 8.8, 3.9, 0.84, and 0.34 ks, respectively. It is noted that
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in the alloy aged at 250 ˚C, the hardness before tc is a little lower than the hardness of the as-annealed sample. This is considered to be due to a little variation in a volume fraction of α
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phase of the samples.
3.2 Microstructural changes during aging
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Fig. 3 shows the XRD patterns of the sample annealed at 600 ˚C for 3.6 ks and,
subsequently, aged at 200, 250, and 300 ˚C for 3.6 ks. Because of the sample size, the peak intensity of the as-annealed sample (10 mm × 7 mm) is much larger than that of the aged samples (5 mm × 5 mm), where X-ray irradiation area was about 10 mm × 10 mm. From the XRD pattern, the as-annealed sample is clearly shown to have an α+β two-phase, and its peak intensity of 110β is larger than that of 101 1α, indicating that the volume fraction of the β phase is larger than that of the α phase. After aging at 200 ˚C for 3.6 ks, the peak intensity ratio of
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110β/101 1α becomes a little smaller than that in the as-annealed sample, indicating the formation of α precipitates in the β phase. However, the Vickers hardness of the aged sample at 200 ˚C for 3.6 ks is still almost the same level as that of the as-annealed sample, as shown in Fig. 2(a),
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suggesting that the amount of α precipitates formed by aging at 200 ˚C for 3.6 ks is too small to obtain significant hardening. After aging the sample at 250 ˚C for 3.6 ks, the peak intensity of 101 1α becomes much larger than that of 110β, indicating the formation of a large amount of fine
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α precipitates in the β phase and, consequently, the aged sample at 250 ˚C for 3.6 ks shows a high hardness of about 112 HV. Furthermore, in the case of the sample aged at 300 ˚C for 3.6 ks,
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not only 101 1α peak intensity but also 0002α peak intensity become high, indicating the formation of a large quantity of α precipitates by aging, and the hardness reaches 120 HV. Apparently, the peak intensity ratio of 110β/101 1α between at 250 and 300 ˚C seems to be contrary to the microstructure, but this is because of a little variation in a volume fraction of β
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and α phases and texture of those phases in as-annealed samples, as mentioned before in section 3.1. These results reveal that the incubation time of the α precipitates becomes shorter as the aging temperature increases, so that the volume fraction of the α precipitates increases with the
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increasing aging temperature for the same aging time. The nucleation rate is proportional to the driving force for precipitation, which is related to the degree of undercooling. Thus, it is
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generally reported that the lower aging temperature provides a higher degree of undercooling, resulting in a shorter incubation time. Meanwhile, the nucleation rate also depends on activation energy for diffusion. Thus, higher aging temperature results in a higher nucleation rate. The nucleation driving force and the activation energy for diffusion show an opposite temperature dependence on each other, so that the nucleation rate shows a maximum value at a certain temperature. Therefore, for the Mg-Sc alloy with an α+β two-phase, the incubation time becomes shorter with increasing aging temperature because the term of the activation energy for
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diffusion should be the dominant factor for the nucleation rate in a temperature range between 175 and 300 ˚C. In this study, to reveal microstructural changes during aging, SEM observation was
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carried out, as shown in Fig. 4. Fig. 4(a) shows the α+β two-phase microstructure of the as-annealed sample at 600 ˚C, where the dark and bright regions indicate stable α and β phases at 600 ˚C, respectively. Using ImageJ software, the volume fraction of the α phase of the
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as-annealed sample was evaluated to be 37.1%. The magnified view of the β phase in the as-annealed sample is also shown in Fig. 4(b), confirming that there is no α precipitates in the β
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phase before aging. Fig. 4(c) shows the microstructure of the sample aged at 200 ˚C for 3.6 ks, and (d) is the image at higher magnification. In Fig. 4(c), α precipitates cannot be observed in the β phase, but very fine and a tiny number of α precipitates, indicated by white arrows, are seen to have formed, as shown in Fig. 4(d). This result is consistent with the results of the
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Vickers hardness measurements and XRD analysis of this sample. The microstructures of the samples aged at 250 and 300 ˚C for 3.6 ks are shown in Fig. 4(e) and (f), respectively. In both images, a large number of very fine needle- or plate-like-shaped α precipitates are observed in
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the β phase, as with the result of the XRD analysis. Fig. 5(a) and (b) shows the SEM image of the sample aged at 300 ˚C for 0.3 and 0.6 ks, respectively. It is seen that the volume fraction of
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α precipitates in the sample aged for 0.6 ks is much larger than that in the sample aged for 0.3 ks. Thus, it is obvious from Fig. 5 that the number of α precipitates increases with increasing aging time.
The volume fraction of α precipitates in the β phase (fα) of aged samples was also measured by quantitative analysis of SEM images using ImageJ software. The relationship between the measured fα and the obtained Vickers hardness is shown in Fig. 6, and the values of fα are listed in Table 1, together with the Vickers hardness values. Fig. 6 indicates that the
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Vickers hardness increases linearly with increasing fα, and the relationship is almost independent of aging temperature in the region of 0 ≤ fα ≤ ~ 0.7. This linear relationship between the Vickers hardness (H) and fα can be described by the following equation:
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H = 46.8 fα + 92.8 ⋯ (1).
This means that the Vickers hardness is one parameter for estimating the volume fraction of the fine α precipitates in the region of 0 ≤ fα ≤ ~ 0.7. This clearly indicates that the age hardening
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observed in the Mg-Sc alloy with an α+β two-phase is due to the formation of fine α precipitates
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in the β phase.
3.3 Kinetics of α precipitation during aging
Based on the results of SEM observation, the phase transformation from bcc to hcp by aging treatment, observed in this study, is confirmed to be continuous precipitation. It is well that
continuous
precipitation
can
be
described
by
the
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known
Johnson-Mehl-Avrami-Kolmogorov (JMAK) or Austin-Rickett (AR) theory [26-29], and the kinetics of phase transformation by aging is often analyzed by these theories [20-23, 30, 31]. It
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is reported that these theories can be universally described as [31]: dy⁄dt = kn1-y
c+1
ktn-1 ⋯(2)
where y, k, n, and c indicate a fraction of the product phase after a time t, a temperature-dependent rate constant, an impingement exponent, and a time exponent parameter that depends on the nucleation mechanism and the growth process of the product phase, respectively. In this study, y can be transposed with fα. Here, in the case of c = 0 and c = 1, Eq. (2) describes the JMAK and AR equations, respectively. Thus, the differential equation of Eq. (2) can be solved as:
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fα = 1-exp -ktn for JMAK ⋯ (3) fα = 1- ktn + 1 -1
for AR ⋯ (4).
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Equations (3) and (4) can be rewritten as: ln -ln1-fα = n ln k + n ln t for JMAK ⋯ (5) ln 1-fα -1 = n ln k + n ln t for AR ⋯ (6).
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If the kinetics of the present precipitation process fits Eq. (5) or (6), plots of ln -ln1-fα or ln 1-fα -1 as a function of ln t can be fitted as a straight line, and, consequently, a time
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-1
exponent parameter n can be obtained from the slope of those plots. There are some reports comparing the accuracy of fitting by JMAK and AR equations for the diffusion-controlled precipitation process [30-33]. Based on an analysis of the precipitation processes for Al, Cu, and
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Fe alloys, previous reports concluded that the AR equation is better suited to describing the kinetics of a diffusion-controlled precipitation process than is the JMAK equation [30-32]. Also, the precipitation behavior of Mg-Al and Mg-Al-Zn alloys by aging is reported to be better
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interpreted by the AR equation [23]. Moreover, for interpreting the bainitic transformation
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kinetics of some Cu-based shape memory alloys, the AR equation provides a better fit, although there is an exception, in that the JMAK equation provides a better fit for the Cu-Zn-Al alloy [30-32]. Meanwhile, the kinetics of phase transformation from β to α in a Zr alloy and that from bcc to an α+β two-phase in Ti alloys by aging were interpreted by the JMAK equation [20-23]. Previous reports indicated that whatever kinetics model would better describe a transformation process depends on the alloy system and the transformation type. Thus, we analyzed the α precipitation kinetics of the Mg-Sc alloy with both JMAK and AR equations in the region of 0 ≤
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fα ≤ ~ 0.7. The ln -ln1-fα and ln 1-fα -1 are plotted versus ln t, as shown in Fig. 7(a) -1
and (b), respectively. Both plots roughly fitted on a straight line. Fig. 8 shows plots of the
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observed fα at 200, 250, and 300 ˚C—listed in Table 1—as a function of aging time t. The solid lines in Fig. 8 are calculated curves from the (a) JMAK (Eq. (3)) and (b) AR (Eq. (4)) equations, where the n and k values were determined from Fig. 7. It can be seen that both calculated curves
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from JMAK and AR equations are well fitted to the observed results, but those from the AR equation are much better fitted, especially, to the observed results at 200 ˚C than those from the
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JMAK equation, indicating that the AR equation is more appropriate for describing the kinetics of α precipitation in the β phase for the Mg-Sc alloy with an α+β two-phase. The best fitting n values at each temperature obtained, from Fig. 7(b), are 1.2 ~ 1.4 and are also listed in Table 2 with the best-fitting k values. The obtained n values are very similar to those reported in Ti-3Al-15Mo-3Nb (n = 1.2) aged at 500 ~ 600 ˚C [21] and Ti-6Al-4V and
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Ti-6Al-2Sn-4Zr-2Mo-0.08Si (n = 1.2 ~ 1.6) aged at over 650 ˚C [20].
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It is generally known that the n value can be described as [34, 35]: n = a + bp ⋯ (7),
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where a is an index for the nucleation rate (a = 0 for nucleation rate zero, 0 < a < 1 for decreasing nucleation rate, a = 1 for constant nucleation rate, and a > 1 for increasing nucleation rate), b is a morphology index (b = 1 for one-dimensional growth, b = 2 for two-dimensional growth, and b = 3 for three-dimensional growth), and p = 1 for interface-controlled growth which requires local atomic rearrangements and does not involve a composition change, like grain growth, crystallization and so on, and p = 1/2 for diffusion-controlled growth. As for α precipitation in the β phase in the Mg-Sc alloy, it should be diffusion-controlled growth, p = 1/2. Furthermore, as shown in Fig. 5, α precipitates are considered to continuously nucleate during 10
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the aging process, and the nucleated precipitates preferentially grow along their longitudinal direction. These results indicate that α precipitation in the region of 0 ≤ fα ≤ ~ 0.7 by aging treatment for the Mg-Sc alloy with an α + β two-phase alloy is a one-dimensional (b = 1, i.e.,
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needle-shaped growth) diffusion-controlled growth (p = 1/2) with a constant or decreasing nucleation rate (a = 0.7 ~ 0.9).
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The dominant diffusion type during drastic age hardening can be estimated from the value of the activation energy for precipitation. The activation energy Q can be estimated from
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the following Arrhenius equation: k = k0 exp (-Q/RT)
(7).
Here, k is the rate constant, k0 is the pre-exponential factor, R is the gas constant, and T is the aging temperature. Fig. 9 shows the Arrhenius plots of ln k vs. 1/T. From the slope of the plots,
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the activation energy Q was estimated to be 83.5 kJmo1-1. The activation energy for self-diffusion in α-Mg is reported to be 134 ~ 139 kJmol-1 [36-38]; however, there is no report about that in β-Mg. It has been reported that there is almost no difference between the value of
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activation energies for self-diffusion in α-Ti and β-Ti [39, 40]. Thus, β-Mg is suggested to show almost the same activation energy for self-diffusion as α-Mg, indicating that α precipitation by
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aging is not dominated by the self-diffusion of Mg, namely volume diffusion. It has been reported that a Cu-Al-Mn-based alloy with an ordered bcc (β) phase shows drastic age hardening by the formation of fine plate-like precipitates through a bainitic transformation [30, 31, 41, 42]. The activation energy for the age hardening observed in Cu alloys is reported to be much lower than that for volume diffusion and is nearly equal to that for grain boundary diffusion, indicating that the growth of fine plate-like precipitates is dominated by interface diffusion between the precipitate and the β matrix [30, 43]. The activation energy for grain
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boundary (interface) diffusion in Mg is reported to be 92 kJmol-1 [40]. This value is nearly equal to the Q obtained in the age-hardening behavior of the Mg-Sc alloy. This suggests that the
diffusion between α precipitates and the β phase.
4. Conclusions
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growth of needle-like α precipitates in the β phase in the Mg-Sc alloy is dominated by interface
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In this study, the aging effect of the Mg-20.0 at.% Sc alloy with an α+β two-phase was investigated by Vickers hardness measurements and microstructure observations, and the
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kinetics of the aging process was analyzed based on JMAK and AR theories. The results obtained were as follows:
The Vickers hardness of Mg-20.0 at.% Sc alloys increased with increasing aging time due to the increase of the volume fraction of α precipitates in the β phase, and there was a linear
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relationship between the volume fraction of α precipitates and the Vickers hardness in an aging temperature range of 200 – 300 ˚C. The incubation time for age hardening decreased as the aging temperature increased; because of that, the activation energy for precipitation is
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considered to have more influence on the nucleation rate. The relationship between the volume fraction of α precipitates and the aging time was
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better described by the AR equation than the JMAK equation. The obtained n values were 1.2 ~ 1.4 in a temperature range of 200 – 300 ˚C. In combination with SEM observation, the mechanism of α precipitation in the β phase for the Mg-Sc alloy with an α+β two-phase is suggested to be a diffusion-controlled reaction, including the one-dimensional growth of α precipitates at a constant or decreasing nucleation rate. The activation energy for α precipitation was 83.5 kJmol-1, which is much smaller than that of self-diffusion in Mg, but is almost the same as that of grain boundary diffusion, namely
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interface diffusion. This result suggests that the interface diffusion between α precipitates and the β phase is dominant for the growth of α precipitates in the Mg-Sc alloy.
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Acknowledgement
References
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This work was supported by JSPS KAKENHI (16J04175, 17J10094).
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[24] X. Lei, T. Liu, J. Chen, B. Miao, W. Zeng, Microstructure and mechanical Properties of
1082-1087.
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Magnesium Alloy AZ31 Processed by Compound Channel Extrusion, Mater. Trans. 52 (2011)
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[25] H. Miura, X. Yang, T. Sakai, ULTRAFINE GRAIN EVOLUTION IN Mg ALLOYS, AZ31, AZ61, AZ91 BY MULTI DIRECTIONAL FORGING, Rev. Adv. Mater. Sci. 33 (2013) 92-96. [26] W. Johnson, R. Mehl, Reaction Kinetics in Processes of Nucleation and Growth, Trans. AIME 135 (1939) 416-442. [27] M. Avrami, Kinetics of Phase Change. I General Theory, J. Chem. Phys. 7 (1939) 1103. [28] J.B. Austin, R.L. Rickett, Kinetics of decomposition of austenite at constant temperature, Trans. AIME 135 (1939) 396-415.
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[29] A. Kolmogorov, A statistical theory for the recrystallization of metals, Akad. nauk SSSR, Izv., Ser. Matem. 1 (1937) 355-359. [30] Y. Sutou, N. Koeda, T. Omori, R. Kainuma, K. Ishida, Effects of ageing on bainitic and
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thermally induced martensitic transformations in ductile Cu–Al–Mn-based shape memory alloys, Acta Mater. 57 (2009) 5748-5758.
[31] E.-S. Lee, Y.G. Kim, A transformation kinetic model and its application to Cu-Zn-Al shape
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memory alloys-I. isothermal conditions, Acta Metall. Mater. 38 (1990) 1669-1676.
Sci. 32 (1997) 4061-4070.
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[32] M.J. Starink, Kinetic equations for diffusion-controlled precipitation reactions, J. Mater.
[33] S. Celotto, T.J. Bastow, Study of precipitation in aged binary Mg-Al and ternary Mg-Al-Zn alloys using Al NMR spectroscopy, Acta Mater. 49 (2001) 41-51.
[34] S. Ranganathan, M.V. Heimendahl, The three activation energies with isothermal
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transformations: applications to metallic glasses, J. Mater. Sci. 16 (1981) 2401-2404. [35] C.W. Price, USE OF KOLMOGOROV-JOHNSON-MEHL-AVRAMI KINETICS IN RECRYSTALLIZATION OF METALS AND CRYSTALLIZATION OF METALLIC
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GLASSES, Acta Metall. Mater. 38 (1990) 727-738. [36] P.G. Shewmon, Self-diffusion in magnesium single crystals, Trans. Metall, Soc. AIME 206
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(1956) 918-922.
[37] P.G. Shewmon, F.N. Rhines, Rate of self-diffusion in polycrystalline magnesium, Trans. Metall, Soc. AIME 200 (1954) 1021-1025. [38] J. Combronde, G. Brebec, Anisotropie d'autodiffusion du magnesium, Acta Metall. 19 (1971) 1393-1399. [39] N.L. Peterson, DIFFUSION IN REFRACTORY METALS, WADD Technical Report (1960) 60-793.
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[40] H.K. Frost, M.F. Ashby, Deformation-Mechanism Maps, Pergamon Press, Oxford, UK 1 (1982) 44. [41] K. Takezawa, S. Sato, Nucleation and Growth of Bainite Crystals in Cu-Zn-Al Alloys,
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Metall. Trans. A 21 (1990) 1541–1545.
[42] Y. Sutou, T. Omori, A. Furukawa, Y. Takahashi, R. Kainuma, K. Yamauchi, S. Yamashita, K. Ishida, Development of Medical Guide Wire of Cu-Al-Mn-Base Superelastic Alloy with
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Functionally Graded Characteristics, J. Bio. Mater. Res. Part B (Appl. Biomater.) 69B (2004) 64-69.
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[43] Y. Sutou, N. Koeda, T. Omori, R. Kainuma, K. Ishida, Effects of aging on stress-induced martensitic transformation in ductile Cu–Al–Mn-based shape memory alloys, Acta Mater. 57 (2009) 5759-5770.
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Captions
Fig. 1 Mg-Sc phase diagram [7,8] (Gray and black lines were reported in ref. [7] and [8], respectively).
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Fig. 2 Age hardening behaviors of α+β two-phase alloy at (a) 175, 200, (b) 225, 250, and 300 ˚C. Incubation time, tc is defined as the inset of (a).
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Fig. 3 The XRD patterns of the Mg-Sc alloy annealed at 600 ˚C for 3.6 ks and aged Mg-Sc alloys at 200, 250, and 300 ˚C for 3.6 ks. Fig. 4 SEM images of Mg-Sc alloys (a), (b) before aging treatment and aged (c), (d) at 200 C ̊ for 3.6 ks, (e) at 250 ̊C for 3.6 ks, (f) at 300 ̊C for 3.6 ks. Fig. 5 SEM images of Mg-Sc alloys aged at 300 ̊C for (a) 0.3 ks, and (b) 0.6 ks. Fig. 6 Plots of Vickers hardness vs. volume fraction of α precipitates in β phase. Fig. 7 Plots of (a) ln(-ln(1-fα)) vs. ln t from the JMAK equation and (b) ln(ln(1-fα)-1-1) vs. ln t
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from the AR equation. Fig. 8 Plots of fα vs. t, solid lines being calculated by the (a) JMAK and (b) AR equations. Fig. 9 Arrhenius plots of ln(1/tc) vs. 1/T.
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Table 1 Volume fraction of α precipitates in β phase and the Vickers hardness in Mg-Sc α + β two-phase alloys aged at 200, 250, and 300 ˚C.
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Table 2 The n values at each aging temperature, obtained from the AR equation.
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Liq
β+Liq
800
bcc (β)
600 hcp (α) 400 0
10
α+β
β+α-Sc
20 at.% Sc
30
40
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Temperature (ºC)
1000
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Fig. 1 Mg- Sc binar y phase diagra m [7,8] (Gray and black line s were reported in ref.[7] and [8], respective ly).
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140 Vickers hardness
120
tc
110
Time
100 175 ˚C 200 ˚C
90
≈ 10
100
1000
10000
120 110 100
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Vickers hardness (HV)
130
100000 (b) 1000000
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80 140 80 140
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130 Vickers hardness (HV)
(a)
225 ˚C 250 ˚C 300 ˚C
90
≈
80 10 0
102 100
103 1000
104 10000
105 1000000 106 100000
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Aging time (sec)
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Fig. 2 Age hardening behavio rs of α+β two- phase allo y at (a) 175, 200, (b) 225, 250, and 300 ˚C. Incubation time, t c is defined as the inset of (a).
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α-phase
β-phase
110β
101 1α
0002 α
200 ˚C
As-annealed 35 40 diffraction angle, 2θ / degree
45
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30
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250 ˚C
101 0α
intensity (a.u.)
Aged at 300 ˚C
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Fig. 3 The XRD patterns of the Mg- Sc alloy annea le d at 600 ˚C for 3.6 ks and aged Mg- Sc allo ys at 200, 250, and 300 ˚C for 3.6 ks.
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140
100
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H = 46.8f α + 92.8
80 60
200 ˚C 250 ˚C 300 ˚C
40 20 0 0.2 0.4 0.6 volume fraction of α, f α
0.8
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0
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Vickers hardness (HV)
120
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Fig. 6 Plots of Vickers hardne ss vs. volume fractio n of α precip ita te s in β phase.
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(a) 300 ̊ C
2 250 ̊ C
(b)
1.5
200 ̊ C
1
0.5
0.5
ln(ln(1-f α)-1-1)
1
0 -0.5 -1 -1.5
300 ̊ C
250 ̊ C
200 ̊ C
0 -0.5 -1 -1.5
-2
-2
-2.5
-2.5
-3
-3 4
6
8
10
12
14
4
ln t
6
8
10
12
14
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ln t
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Fig. 7 Plots of (a) ln(- ln( 1-f α)) vs. ln t from the JMAK equation and (b) ln(ln(1-f α)-1-1) vs. ln t from the AR equation.
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ln(-ln(1-f α))
1.5
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2
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0.8
0.8
(b)
0.7
0.7
0.6
0.6
0.4 0.3 0.2
0.4 0.3 0.2 0.1
0.1 0 10 1
102 104 100 10000 Aging time, t (sec)
106 1000000
0
0 10 1
102 104 100 10000 Aging time, t (sec)
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0
0.5
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0.5
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volume fraction of α, f α
volume fraction of α, f α
(a)
106 1000000
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Fig. 8 Plots of f α vs. t, solid lines being calculated by the (a) JMAK and (b) AR equations.
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-6 -7
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ln k
-8 -9
-11
1.7 0.0017
1.9 2.1 0.0019 0.0021 1/T (10-3 K-1 )
2.3 0.0023
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-10
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Fig. 9 Arrhenius plots of ln( 1/t c) vs. 1/T.
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Table 1 Volume fraction of α precipitates in β phase and Vickers hardness in Mg-Sc α + β two-phase alloys aged at 200, 250 and 300 ˚C.
Temp. (˚C)
time (ks) 7.2
0.078
10.8
0.167
18
0.328
90
0.734
250
1.8
96.4
102.0
112.3
123.1
0.144
100.9
0.284
97.9
3.6
0.393
111.5
7.2
0.469
119.4
0.3
0.224
97.8
0.39
0.172
107.0
0.48
0.226
104.1
0.6
0.437
115.9
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2.7
300
Hardness (HV)
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200
Volume fraction of α, fα (%)
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Aging
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Aging
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Table 2 The n values at each aging temperature, obtained from AR equation.
Temperature (˚C)
n
k
200
1.3
2.6×10
1.2
1.5×10
1.4
1.1×10
250
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300
29
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‧ The kinetics of the aging precipitation of α in Mg-Sc alloy is investigated. ‧ The kinetics of the aging precipitation of α was well described by the AR equation. ‧ Mechanism of α precipitation is suggested to be a diffusion-controlled reaction. ‧ α precipitation is 1D growth with constant/decreasing nucleation rate.
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‧ The growth of α precipitates is dominated by interface diffusion between α and β.
S0925-8388(18)30923-X
DOI:
10.1016/j.jallcom.2018.03.064
Reference:
JALCOM 45294
To appear in:
Journal of Alloys and Compounds
Received Date: 25 December 2017 Revised Date:
2 March 2018
Accepted Date: 6 March 2018
Please cite this article as: Y. Ogawa, Y. Sutou, D. Ando, J. Koike, Aging precipitation kinetics of Mg-Sc alloy with bcc+hcp two-phase, Journal of Alloys and Compounds (2018), doi: 10.1016/ j.jallcom.2018.03.064. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Aging precipitation kinetics of Mg-Sc alloy with bcc+hcp two-phase Yukiko Ogawa1*, Yuji Sutou2, Daisuke Ando2, Junichi Koike2 1
Research Center for Structural Materials, National Institute for Materials Science, Tsukuba
2
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305-0047, Japan
Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai
980-8579, Japan
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*author for correspondence: [email protected] (Y. Ogawa)
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ABSTRACT
In our previous research, we reported that Mg-Sc alloys with a bcc (β) phase showed significant age hardening by the formation of fine hcp (α) precipitates in the β phase. In this study, we investigated the kinetics of the aging precipitation in the α+β two-phase Mg-Sc alloy. The
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incubation time for age hardening became shorter with increasing aging temperature. The relationship between the volume fraction of α precipitates and aging time was better described by the Austin-Rickett equation than by the Johnson-Mehl-Avrami-Kolmogorov equation, and
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the obtained n values are 1.2 ~ 1.4. According to the n values and the morphology of fine α precipitates, the mechanism of α precipitation in the Mg-Sc alloy with an α+β two-phase was
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proposed to be a diffusion-controlled reaction, including the one-dimensional growth of α precipitates at a constant or decreasing nucleation rate. In addition, the activation energy for α precipitation was calculated to be 83.5 kJmol-1. This value is much smaller than that of self-diffusion in Mg, while it is almost the same as that of grain boundary diffusion in Mg, namely interface diffusion. This reveals that the growth of α precipitates is dominated by interface diffusion along the boundaries between the α precipitate and the β phase.
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Keywords Magnesium alloy; Phase transformation; Age hardening
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1. Introduction
Mg alloys have received attention as structural materials for transportation systems and portable products because of their greatest advantage, i.e., their light weight [1-3]. High-strength and Mg
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alloys with a long-period stacking ordered (LPSO) phase have been developed; these Mg alloys are also highly corrosion resistant [4-6]. However, Mg alloys with a hexagonal close-packed
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(hcp) structure tend to show low ductility at room temperature, due to the anisotropic structure of the hcp, where an hcp phase in Mg alloys is designated as the α phase. To improve the ductility of Mg alloys, we have attempted to introduce an isotropic body-centered cubic (bcc) structure in Mg alloys, where a bcc phase in Mg alloys is designated as the β phase. From the
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standpoint of phase stability, we have focused on the Mg-Sc binary system, which has a bcc phase in a Mg-rich composition region (Fig. 1) [7, 8]. We demonstrated that a β-type Mg-Sc alloy shows excellent ductility as compared with conventional α-type Mg alloys and exhibits
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much higher strength than conventional β-type Mg-Li alloys [8]. Moreover, a Mg-Sc alloy with an α+β two-phase was found to show good balance between tensile strength and elongation and
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achieved high tensile strength greater than 300 MPa, together with excellent tensile elongation of about 30% [8], indicating that the α+β-type Mg-Sc alloy shows better mechanical properties than α+β-type Mg-Li alloys [9]. In addition, the β-type Mg-Sc alloy was found to exhibit shape memory properties associated with martensitic transformation [10]. Natarajan et al. pointed out from first-principles calculations that a high degree of degeneracy among hcp, bcc and fcc phases is likely to play an important role in the shame memory properties for the Mg-Sc alloy [11].
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Mg-Sc alloy with the β phase also shows age hardening. We reported that Mg-16.8 and 20.5 at.% Sc alloys show significant age hardening by the precipitation of fine needle- or plate-shaped α phases in the β phase, and fine α precipitates show the Burgers orientation
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relationship with the β phase [12, 13]. An age-hardened α+β two-phase Mg-Sc alloy shows very high tensile strength greater than 450 MPa with better elongation of about 7% [13]. Precipitation of fine α phase was also reported in β phase of Mg-Li alloys by aging [14-16] and
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the kinetics of α precipitation was predicted to be the diffusivity of Mg and Li based on phenomenological analysis from the SEM observation [14]. It is well known that such age
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hardening by α precipitation in the β phase, satisfying Burgers orientation relationship, is observed in Zr and Ti alloys [17-19]. The kinetics of α precipitation in the β phase of Zr and Ti alloys has been investigated by both experimental and computer simulation with the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation [20-23]. Generally, transformation
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kinetics can be discussed with the Avrami index, n, which depends on nucleation and a growth mechanism. The reported Avrami index, n, in Zr-45Ti-5Al-3V alloy (wt.%) aged at 500 ~ 600 ˚C is 0.4 ~ 0.7, not so far from that of Ti-15V-3Cr-3Al-3Sn alloy (wt.%) aged at 500 ˚C [22, 23],
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while the n value of β21s commercial titanium alloy (Ti-3Al-15Mo-3Nb (wt.%)) aged at a temperature of 500 ~ 600 ˚C is reported to be around 1.2 [21]. In addition, at higher aging
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temperatures greater than 650 ˚C, the n value of the β21s commercial titanium alloy is about 1.8 ~ 1.9 [21]. Furthermore, the n values in Ti-6Al-4V and Ti-6Al-2Sn-4Zr-2Mo-0.08Si (wt.%) alloys aged at over 650 ˚C are reported to be about 1.2 ~ 1.6 [20]. The kinetics of the age hardening behavior in β-type Zr and Ti alloys has been well discussed based on transformation kinetics, such as the JMAK model, while that of Mg-Sc alloys have not yet been examined. Therefore, in the present study, the kinetics of α precipitation in the β phase of Mg-Sc alloy with an α+β two-phase was examined based on isothermal aging experiments.
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2. Experimental procedures A Mg-Sc alloy ingot was prepared by induction melting in an Ar atmosphere using an Al2O3
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crucible, followed by cooling in the crucible. The nominal composition was Mg-20 at.% Sc. The alloy ingot was annealed at 600 ˚C for 16 h in an Ar atmosphere, followed by water quenching, and then cold rolled with a 10% reduction in thickness. The cold-rolled sample was
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subsequently annealed at 600 ˚C for 3.6 ks in air to obtain an α+β two-phase microstructure. The composition of the prepared Mg-Sc sheet was Mg-19.99 at.% Sc ≈ Mg-20.0 at.% Sc, which
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was measured by means of an electron probe microanalyzer (EPMA). The Sc content of α and β phases in the sample annealed at 600 ˚C for 3.6 ks in air were determined to be 18.0 and 22.6 at.% by EPMA, respectively. The α+β two-phase alloy sheet was cut into small pieces. The obtained small samples were aged at 175 ~ 300 ˚C in air. The hardness of the aged samples was
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measured by a Vickers hardness tester with a load of 1.0 kgf, where the number of measuring points was 10 each, and the average hardness was determined by averaging 8 points, except the maximum and minimum values. The error bar in each measurement was defined as a standard
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error of those 8 points.
The crystal structure of the aged samples was analyzed by X-ray diffraction (XRD)
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with the θ-2θ method with a Cu-Kα source. The microstructure was observed by scanning electron microscopy (SEM). Before SEM observation, the samples were mechanically polished to a mirror finish and then chemically etched with a solution of 3 ml of nitric acid, 9 ml of acetic acid, 12 ml of distilled water, and 36 ml of ethanol to visualize their α+β two-phase microstructure. The volume fraction of the precipitated phase in the β phase with aging treatment was estimated by image analysis of backscattered electron micrographs using ImageJ software.
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3. Results and discussion 3.1. Effect of aging on the hardness of the α+β alloy
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Fig. 2 shows the effect of aging time on Vickers hardness in the Mg-20.0 at.% Sc alloy with an α+β two-phase aged at (a) 175 and 200 ˚C, and at (b) 225, 250, and 300 ˚C. Before aging treatment, the α+β alloy showed a Vickers hardness of about 90 HV, which is higher than
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that of conventional Mg alloys, such as AZ31 (60 ~ 70 HV) with an equivalent grain size (10 ~ 30 µm) [24, 25]. This is because of a solid solution hardening caused by the addition of Sc. At
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all aging temperatures, the alloy shows a significant hardening after some incubation time, tc. The tc is an onset time of the increase of Vickers hardness and is defined as shown in the inset of Fig. 2(a). As the aging temperature becomes higher, the tc is seen to become shorter. The tc at 175, 200, 225, 250, and 300 ˚C were 41, 8.8, 3.9, 0.84, and 0.34 ks, respectively. It is noted that
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in the alloy aged at 250 ˚C, the hardness before tc is a little lower than the hardness of the as-annealed sample. This is considered to be due to a little variation in a volume fraction of α
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phase of the samples.
3.2 Microstructural changes during aging
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Fig. 3 shows the XRD patterns of the sample annealed at 600 ˚C for 3.6 ks and,
subsequently, aged at 200, 250, and 300 ˚C for 3.6 ks. Because of the sample size, the peak intensity of the as-annealed sample (10 mm × 7 mm) is much larger than that of the aged samples (5 mm × 5 mm), where X-ray irradiation area was about 10 mm × 10 mm. From the XRD pattern, the as-annealed sample is clearly shown to have an α+β two-phase, and its peak intensity of 110β is larger than that of 101 1α, indicating that the volume fraction of the β phase is larger than that of the α phase. After aging at 200 ˚C for 3.6 ks, the peak intensity ratio of
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110β/101 1α becomes a little smaller than that in the as-annealed sample, indicating the formation of α precipitates in the β phase. However, the Vickers hardness of the aged sample at 200 ˚C for 3.6 ks is still almost the same level as that of the as-annealed sample, as shown in Fig. 2(a),
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suggesting that the amount of α precipitates formed by aging at 200 ˚C for 3.6 ks is too small to obtain significant hardening. After aging the sample at 250 ˚C for 3.6 ks, the peak intensity of 101 1α becomes much larger than that of 110β, indicating the formation of a large amount of fine
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α precipitates in the β phase and, consequently, the aged sample at 250 ˚C for 3.6 ks shows a high hardness of about 112 HV. Furthermore, in the case of the sample aged at 300 ˚C for 3.6 ks,
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not only 101 1α peak intensity but also 0002α peak intensity become high, indicating the formation of a large quantity of α precipitates by aging, and the hardness reaches 120 HV. Apparently, the peak intensity ratio of 110β/101 1α between at 250 and 300 ˚C seems to be contrary to the microstructure, but this is because of a little variation in a volume fraction of β
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and α phases and texture of those phases in as-annealed samples, as mentioned before in section 3.1. These results reveal that the incubation time of the α precipitates becomes shorter as the aging temperature increases, so that the volume fraction of the α precipitates increases with the
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increasing aging temperature for the same aging time. The nucleation rate is proportional to the driving force for precipitation, which is related to the degree of undercooling. Thus, it is
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generally reported that the lower aging temperature provides a higher degree of undercooling, resulting in a shorter incubation time. Meanwhile, the nucleation rate also depends on activation energy for diffusion. Thus, higher aging temperature results in a higher nucleation rate. The nucleation driving force and the activation energy for diffusion show an opposite temperature dependence on each other, so that the nucleation rate shows a maximum value at a certain temperature. Therefore, for the Mg-Sc alloy with an α+β two-phase, the incubation time becomes shorter with increasing aging temperature because the term of the activation energy for
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diffusion should be the dominant factor for the nucleation rate in a temperature range between 175 and 300 ˚C. In this study, to reveal microstructural changes during aging, SEM observation was
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carried out, as shown in Fig. 4. Fig. 4(a) shows the α+β two-phase microstructure of the as-annealed sample at 600 ˚C, where the dark and bright regions indicate stable α and β phases at 600 ˚C, respectively. Using ImageJ software, the volume fraction of the α phase of the
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as-annealed sample was evaluated to be 37.1%. The magnified view of the β phase in the as-annealed sample is also shown in Fig. 4(b), confirming that there is no α precipitates in the β
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phase before aging. Fig. 4(c) shows the microstructure of the sample aged at 200 ˚C for 3.6 ks, and (d) is the image at higher magnification. In Fig. 4(c), α precipitates cannot be observed in the β phase, but very fine and a tiny number of α precipitates, indicated by white arrows, are seen to have formed, as shown in Fig. 4(d). This result is consistent with the results of the
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Vickers hardness measurements and XRD analysis of this sample. The microstructures of the samples aged at 250 and 300 ˚C for 3.6 ks are shown in Fig. 4(e) and (f), respectively. In both images, a large number of very fine needle- or plate-like-shaped α precipitates are observed in
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the β phase, as with the result of the XRD analysis. Fig. 5(a) and (b) shows the SEM image of the sample aged at 300 ˚C for 0.3 and 0.6 ks, respectively. It is seen that the volume fraction of
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α precipitates in the sample aged for 0.6 ks is much larger than that in the sample aged for 0.3 ks. Thus, it is obvious from Fig. 5 that the number of α precipitates increases with increasing aging time.
The volume fraction of α precipitates in the β phase (fα) of aged samples was also measured by quantitative analysis of SEM images using ImageJ software. The relationship between the measured fα and the obtained Vickers hardness is shown in Fig. 6, and the values of fα are listed in Table 1, together with the Vickers hardness values. Fig. 6 indicates that the
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Vickers hardness increases linearly with increasing fα, and the relationship is almost independent of aging temperature in the region of 0 ≤ fα ≤ ~ 0.7. This linear relationship between the Vickers hardness (H) and fα can be described by the following equation:
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H = 46.8 fα + 92.8 ⋯ (1).
This means that the Vickers hardness is one parameter for estimating the volume fraction of the fine α precipitates in the region of 0 ≤ fα ≤ ~ 0.7. This clearly indicates that the age hardening
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observed in the Mg-Sc alloy with an α+β two-phase is due to the formation of fine α precipitates
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in the β phase.
3.3 Kinetics of α precipitation during aging
Based on the results of SEM observation, the phase transformation from bcc to hcp by aging treatment, observed in this study, is confirmed to be continuous precipitation. It is well that
continuous
precipitation
can
be
described
by
the
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known
Johnson-Mehl-Avrami-Kolmogorov (JMAK) or Austin-Rickett (AR) theory [26-29], and the kinetics of phase transformation by aging is often analyzed by these theories [20-23, 30, 31]. It
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is reported that these theories can be universally described as [31]: dy⁄dt = kn1-y
c+1
ktn-1 ⋯(2)
where y, k, n, and c indicate a fraction of the product phase after a time t, a temperature-dependent rate constant, an impingement exponent, and a time exponent parameter that depends on the nucleation mechanism and the growth process of the product phase, respectively. In this study, y can be transposed with fα. Here, in the case of c = 0 and c = 1, Eq. (2) describes the JMAK and AR equations, respectively. Thus, the differential equation of Eq. (2) can be solved as:
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fα = 1-exp -ktn for JMAK ⋯ (3) fα = 1- ktn + 1 -1
for AR ⋯ (4).
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Equations (3) and (4) can be rewritten as: ln -ln1-fα = n ln k + n ln t for JMAK ⋯ (5) ln 1-fα -1 = n ln k + n ln t for AR ⋯ (6).
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If the kinetics of the present precipitation process fits Eq. (5) or (6), plots of ln -ln1-fα or ln 1-fα -1 as a function of ln t can be fitted as a straight line, and, consequently, a time
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exponent parameter n can be obtained from the slope of those plots. There are some reports comparing the accuracy of fitting by JMAK and AR equations for the diffusion-controlled precipitation process [30-33]. Based on an analysis of the precipitation processes for Al, Cu, and
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Fe alloys, previous reports concluded that the AR equation is better suited to describing the kinetics of a diffusion-controlled precipitation process than is the JMAK equation [30-32]. Also, the precipitation behavior of Mg-Al and Mg-Al-Zn alloys by aging is reported to be better
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interpreted by the AR equation [23]. Moreover, for interpreting the bainitic transformation
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kinetics of some Cu-based shape memory alloys, the AR equation provides a better fit, although there is an exception, in that the JMAK equation provides a better fit for the Cu-Zn-Al alloy [30-32]. Meanwhile, the kinetics of phase transformation from β to α in a Zr alloy and that from bcc to an α+β two-phase in Ti alloys by aging were interpreted by the JMAK equation [20-23]. Previous reports indicated that whatever kinetics model would better describe a transformation process depends on the alloy system and the transformation type. Thus, we analyzed the α precipitation kinetics of the Mg-Sc alloy with both JMAK and AR equations in the region of 0 ≤
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fα ≤ ~ 0.7. The ln -ln1-fα and ln 1-fα -1 are plotted versus ln t, as shown in Fig. 7(a) -1
and (b), respectively. Both plots roughly fitted on a straight line. Fig. 8 shows plots of the
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observed fα at 200, 250, and 300 ˚C—listed in Table 1—as a function of aging time t. The solid lines in Fig. 8 are calculated curves from the (a) JMAK (Eq. (3)) and (b) AR (Eq. (4)) equations, where the n and k values were determined from Fig. 7. It can be seen that both calculated curves
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from JMAK and AR equations are well fitted to the observed results, but those from the AR equation are much better fitted, especially, to the observed results at 200 ˚C than those from the
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JMAK equation, indicating that the AR equation is more appropriate for describing the kinetics of α precipitation in the β phase for the Mg-Sc alloy with an α+β two-phase. The best fitting n values at each temperature obtained, from Fig. 7(b), are 1.2 ~ 1.4 and are also listed in Table 2 with the best-fitting k values. The obtained n values are very similar to those reported in Ti-3Al-15Mo-3Nb (n = 1.2) aged at 500 ~ 600 ˚C [21] and Ti-6Al-4V and
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Ti-6Al-2Sn-4Zr-2Mo-0.08Si (n = 1.2 ~ 1.6) aged at over 650 ˚C [20].
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It is generally known that the n value can be described as [34, 35]: n = a + bp ⋯ (7),
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where a is an index for the nucleation rate (a = 0 for nucleation rate zero, 0 < a < 1 for decreasing nucleation rate, a = 1 for constant nucleation rate, and a > 1 for increasing nucleation rate), b is a morphology index (b = 1 for one-dimensional growth, b = 2 for two-dimensional growth, and b = 3 for three-dimensional growth), and p = 1 for interface-controlled growth which requires local atomic rearrangements and does not involve a composition change, like grain growth, crystallization and so on, and p = 1/2 for diffusion-controlled growth. As for α precipitation in the β phase in the Mg-Sc alloy, it should be diffusion-controlled growth, p = 1/2. Furthermore, as shown in Fig. 5, α precipitates are considered to continuously nucleate during 10
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the aging process, and the nucleated precipitates preferentially grow along their longitudinal direction. These results indicate that α precipitation in the region of 0 ≤ fα ≤ ~ 0.7 by aging treatment for the Mg-Sc alloy with an α + β two-phase alloy is a one-dimensional (b = 1, i.e.,
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needle-shaped growth) diffusion-controlled growth (p = 1/2) with a constant or decreasing nucleation rate (a = 0.7 ~ 0.9).
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The dominant diffusion type during drastic age hardening can be estimated from the value of the activation energy for precipitation. The activation energy Q can be estimated from
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the following Arrhenius equation: k = k0 exp (-Q/RT)
(7).
Here, k is the rate constant, k0 is the pre-exponential factor, R is the gas constant, and T is the aging temperature. Fig. 9 shows the Arrhenius plots of ln k vs. 1/T. From the slope of the plots,
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the activation energy Q was estimated to be 83.5 kJmo1-1. The activation energy for self-diffusion in α-Mg is reported to be 134 ~ 139 kJmol-1 [36-38]; however, there is no report about that in β-Mg. It has been reported that there is almost no difference between the value of
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activation energies for self-diffusion in α-Ti and β-Ti [39, 40]. Thus, β-Mg is suggested to show almost the same activation energy for self-diffusion as α-Mg, indicating that α precipitation by
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aging is not dominated by the self-diffusion of Mg, namely volume diffusion. It has been reported that a Cu-Al-Mn-based alloy with an ordered bcc (β) phase shows drastic age hardening by the formation of fine plate-like precipitates through a bainitic transformation [30, 31, 41, 42]. The activation energy for the age hardening observed in Cu alloys is reported to be much lower than that for volume diffusion and is nearly equal to that for grain boundary diffusion, indicating that the growth of fine plate-like precipitates is dominated by interface diffusion between the precipitate and the β matrix [30, 43]. The activation energy for grain
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boundary (interface) diffusion in Mg is reported to be 92 kJmol-1 [40]. This value is nearly equal to the Q obtained in the age-hardening behavior of the Mg-Sc alloy. This suggests that the
diffusion between α precipitates and the β phase.
4. Conclusions
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growth of needle-like α precipitates in the β phase in the Mg-Sc alloy is dominated by interface
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In this study, the aging effect of the Mg-20.0 at.% Sc alloy with an α+β two-phase was investigated by Vickers hardness measurements and microstructure observations, and the
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kinetics of the aging process was analyzed based on JMAK and AR theories. The results obtained were as follows:
The Vickers hardness of Mg-20.0 at.% Sc alloys increased with increasing aging time due to the increase of the volume fraction of α precipitates in the β phase, and there was a linear
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relationship between the volume fraction of α precipitates and the Vickers hardness in an aging temperature range of 200 – 300 ˚C. The incubation time for age hardening decreased as the aging temperature increased; because of that, the activation energy for precipitation is
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considered to have more influence on the nucleation rate. The relationship between the volume fraction of α precipitates and the aging time was
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better described by the AR equation than the JMAK equation. The obtained n values were 1.2 ~ 1.4 in a temperature range of 200 – 300 ˚C. In combination with SEM observation, the mechanism of α precipitation in the β phase for the Mg-Sc alloy with an α+β two-phase is suggested to be a diffusion-controlled reaction, including the one-dimensional growth of α precipitates at a constant or decreasing nucleation rate. The activation energy for α precipitation was 83.5 kJmol-1, which is much smaller than that of self-diffusion in Mg, but is almost the same as that of grain boundary diffusion, namely
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interface diffusion. This result suggests that the interface diffusion between α precipitates and the β phase is dominant for the growth of α precipitates in the Mg-Sc alloy.
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Acknowledgement
References
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This work was supported by JSPS KAKENHI (16J04175, 17J10094).
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Captions
Fig. 1 Mg-Sc phase diagram [7,8] (Gray and black lines were reported in ref. [7] and [8], respectively).
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Fig. 2 Age hardening behaviors of α+β two-phase alloy at (a) 175, 200, (b) 225, 250, and 300 ˚C. Incubation time, tc is defined as the inset of (a).
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Fig. 3 The XRD patterns of the Mg-Sc alloy annealed at 600 ˚C for 3.6 ks and aged Mg-Sc alloys at 200, 250, and 300 ˚C for 3.6 ks. Fig. 4 SEM images of Mg-Sc alloys (a), (b) before aging treatment and aged (c), (d) at 200 C ̊ for 3.6 ks, (e) at 250 ̊C for 3.6 ks, (f) at 300 ̊C for 3.6 ks. Fig. 5 SEM images of Mg-Sc alloys aged at 300 ̊C for (a) 0.3 ks, and (b) 0.6 ks. Fig. 6 Plots of Vickers hardness vs. volume fraction of α precipitates in β phase. Fig. 7 Plots of (a) ln(-ln(1-fα)) vs. ln t from the JMAK equation and (b) ln(ln(1-fα)-1-1) vs. ln t
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from the AR equation. Fig. 8 Plots of fα vs. t, solid lines being calculated by the (a) JMAK and (b) AR equations. Fig. 9 Arrhenius plots of ln(1/tc) vs. 1/T.
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Table 1 Volume fraction of α precipitates in β phase and the Vickers hardness in Mg-Sc α + β two-phase alloys aged at 200, 250, and 300 ˚C.
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Table 2 The n values at each aging temperature, obtained from the AR equation.
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Liq
β+Liq
800
bcc (β)
600 hcp (α) 400 0
10
α+β
β+α-Sc
20 at.% Sc
30
40
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Temperature (ºC)
1000
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Fig. 1 Mg- Sc binar y phase diagra m [7,8] (Gray and black line s were reported in ref.[7] and [8], respective ly).
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140 Vickers hardness
120
tc
110
Time
100 175 ˚C 200 ˚C
90
≈ 10
100
1000
10000
120 110 100
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Vickers hardness (HV)
130
100000 (b) 1000000
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80 140 80 140
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130 Vickers hardness (HV)
(a)
225 ˚C 250 ˚C 300 ˚C
90
≈
80 10 0
102 100
103 1000
104 10000
105 1000000 106 100000
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Aging time (sec)
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Fig. 2 Age hardening behavio rs of α+β two- phase allo y at (a) 175, 200, (b) 225, 250, and 300 ˚C. Incubation time, t c is defined as the inset of (a).
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α-phase
β-phase
110β
101 1α
0002 α
200 ˚C
As-annealed 35 40 diffraction angle, 2θ / degree
45
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250 ˚C
101 0α
intensity (a.u.)
Aged at 300 ˚C
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Fig. 3 The XRD patterns of the Mg- Sc alloy annea le d at 600 ˚C for 3.6 ks and aged Mg- Sc allo ys at 200, 250, and 300 ˚C for 3.6 ks.
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140
100
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H = 46.8f α + 92.8
80 60
200 ˚C 250 ˚C 300 ˚C
40 20 0 0.2 0.4 0.6 volume fraction of α, f α
0.8
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0
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Vickers hardness (HV)
120
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Fig. 6 Plots of Vickers hardne ss vs. volume fractio n of α precip ita te s in β phase.
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(a) 300 ̊ C
2 250 ̊ C
(b)
1.5
200 ̊ C
1
0.5
0.5
ln(ln(1-f α)-1-1)
1
0 -0.5 -1 -1.5
300 ̊ C
250 ̊ C
200 ̊ C
0 -0.5 -1 -1.5
-2
-2
-2.5
-2.5
-3
-3 4
6
8
10
12
14
4
ln t
6
8
10
12
14
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ln t
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Fig. 7 Plots of (a) ln(- ln( 1-f α)) vs. ln t from the JMAK equation and (b) ln(ln(1-f α)-1-1) vs. ln t from the AR equation.
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ln(-ln(1-f α))
1.5
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2
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0.8
0.8
(b)
0.7
0.7
0.6
0.6
0.4 0.3 0.2
0.4 0.3 0.2 0.1
0.1 0 10 1
102 104 100 10000 Aging time, t (sec)
106 1000000
0
0 10 1
102 104 100 10000 Aging time, t (sec)
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0
0.5
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0.5
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volume fraction of α, f α
volume fraction of α, f α
(a)
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Fig. 8 Plots of f α vs. t, solid lines being calculated by the (a) JMAK and (b) AR equations.
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-6 -7
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ln k
-8 -9
-11
1.7 0.0017
1.9 2.1 0.0019 0.0021 1/T (10-3 K-1 )
2.3 0.0023
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Fig. 9 Arrhenius plots of ln( 1/t c) vs. 1/T.
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Table 1 Volume fraction of α precipitates in β phase and Vickers hardness in Mg-Sc α + β two-phase alloys aged at 200, 250 and 300 ˚C.
Temp. (˚C)
time (ks) 7.2
0.078
10.8
0.167
18
0.328
90
0.734
250
1.8
96.4
102.0
112.3
123.1
0.144
100.9
0.284
97.9
3.6
0.393
111.5
7.2
0.469
119.4
0.3
0.224
97.8
0.39
0.172
107.0
0.48
0.226
104.1
0.6
0.437
115.9
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2.7
300
Hardness (HV)
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Volume fraction of α, fα (%)
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Aging
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Aging
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Table 2 The n values at each aging temperature, obtained from AR equation.
Temperature (˚C)
n
k
200
1.3
2.6×10
1.2
1.5×10
1.4
1.1×10
250
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‧ The kinetics of the aging precipitation of α in Mg-Sc alloy is investigated. ‧ The kinetics of the aging precipitation of α was well described by the AR equation. ‧ Mechanism of α precipitation is suggested to be a diffusion-controlled reaction. ‧ α precipitation is 1D growth with constant/decreasing nucleation rate.
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‧ The growth of α precipitates is dominated by interface diffusion between α and β.