6.2.1 Initial state
Fig. 6-4 shows the hardness of each alloy at the as-solution treated states.
Fig. 6-4 Hardness of alloys in the as-solution treated states.
75 The results show that Gd is the most significant alloying element in raising the hardness. In contrast, Al has the weakest effect. The increase of the hardness per 1 at. % of Al, Gd, Sn and Zn are 2.6, 21.5, 5.0 and 10.0, respectively.
The increase of hardness in the as-solution treated alloys is by so-called solid solution strengthening. The most important contribution of the solute atoms to the strengthening is usually due to the stress field produced in the surrounding crystal. The alloys in the current study are substitution solutions due to the relatively large radii of the solute atoms according to the Hume-Rothery rule. The substitutional atoms will cause a stress field in the surrounding crystal due to the radii and modulus difference between the solute and solvent atoms, either a compressive stress field or a tensile stress field. This stress field will interact with the stress fields of the dislocations and anchor them; hence, the hardness is increased. The intensity of the stress field is related to the alloying element and so is the hardness increase. Morinaga [210]
uses the DFT method to calculate the local strains of the nearest neighbouring Mg atoms as a result of different alloying elements; the results are listed in Table 6-3. As in Table 6-3, Gd causes the largest local strains and therefore it has the strongest effects in increasing the hardness.
However, Sn behaves abnormally; although it caused the lowest local strain, its influence on the hardness is more considerable than Al. The abnormal behaviour of Sn may be caused by the electronegativity of the atoms. The electronegativity of Mg, Al, Gd, Sn and Zn are 1.31, 1.61, 1.20, 1.96 and 1.65, respectively . In general, the greater the difference in electronegativity between two atoms, the stronger the bond between them [211]. Therefore, higher stress is needed to break the Mg-Sn bond than the Mg-Al bond when the dislocation moves past a solute atom, making Sn more effective than Al in increasing the hardness.
Table 6-3 Local strains of the nearest neighbouring Mg atoms from alloying elements [210].
Alloying element ∆a1/a1 (%) ∆a2/a2 (%) ∆c/c (%)
Al -0.76 -1.88 -1.11
Gd 1.41 2.41 1.37
Sn 0.33 0.14 0.16
Zn -1.18 -2.35 -1.21
76
6.2.2 Peak-aged condition
Table 6-4 summarizes the data of different alloys aged at 225 °C and the results show that Gd is the most effective alloying element in precipitation hardening, while Al and Sn are less effective. The efficiency of the precipitation hardening is affected by the morphology and distribution of the precipitates. Smaller and more numerous precipitates are more effective at interfering with dislocation motion than larger and more widely spaced precipitates [212].
As discussed earlier, the precipitates at peak-aged conditions in Mg-Al and Mg-Sn alloys are equilibrium phases Mg17Al12 and Mg2Sn, while in the Mg-Gd and Mg-Zn alloys are the metastable phases Mg7Gd and Mg4Zn7. The size of the metastable phases are much smaller than that of the equilibrium and the number density is much higher as in Chapter 5. Therefore, Gd and Zn are more effective in precipitation strengthening. Except that, the shape and orientation of precipitates also influence the precipitation strengthening. The plate-shaped precipitates formed on prismatic planes of the matrix phase are most effective precipitation strengthening and precipitate plates formed on the basal plane provide the least effective barrier to gliding dislocations [50]. In the current study, the Mg7Gd phases are the prismatic plates[119], while the Mg4Zn7 phases are basal plates and blocky particles or [0 0 0 1]α
rods/laths [96]. Hence, Gd has a stronger influence on precipitation hardening than Zn.
Table 6-4 Alloys aged at 225 °C.
Another interesting finding is that the time to reach the peak hardness in the Mg-Al alloy is much longer than the Mg-Gd alloy. The longer time in Mg-Al alloy indicates that precipitation in Mg-Al alloy is slower than that in Mg-Gd alloy. Since the precipitation is a diffusion-controlled process [213], these results suggest that the diffusion rate of Gd in the Mg matrix is higher than that of Al. Fig. 6-5 shows the calculated diffusion rate of Al, Gd, Sn and Zn
77 elements in Mg matrix based on the works of Zhang et al. [214], Zhong et al. [215] and Agarwal et al. [216]. The results show that Gd has a higher diffusion rate than Al at 225 °C, which is coincident with current results. This result is quite interesting because the radii of Gd and Al are 233 pm and 118 pm respectively. It is common to think that Gd has a lower diffusion rate than Al based on common knowledge. However, the experimental data show the contrary results.
Fig. 6-5 Calculated diffusion rate of alloying elements in Mg matrix at 225 °C.
6.2.3 Over-aged condition
If the ageing time of an alloy is allowed to exceed its peak-aged point, then it goes into the over-aged stage. In the current study, the hardness of Mg-Gd and Mg-Zn alloys show a significant decrease after the peak-aged; however, the decrease of hardness in Al and Mg-Sn alloys is not so pronounced.
The decrease of the hardness is usually considered to be caused by coarsening of the distance between precipitates. At the peak-aged condition, the precipitates are normally assumed to have the maximum volume fraction; at the over-aged stage, precipitates are coarsened without
78
changing their volume fraction [217]. The coarsening occurs where large precipitates grow at the expense of small ones and it will increase the average spacing of precipitates [218].
According to the Orowan mechanism, the precipitation strengthening by dislocation looping is given by [219]:
∆ =𝐺𝑏
𝐿 (6-2)
∆ is the increased strength, 𝐺 is the shear modulus, b is the Burger’s vector, L is the average spacing of precipitates. The increased L caused the decrease in the hardness.
However, the coarsening of the average spacing of precipitates cannot explain the results in the current study well. Since the hardness decreases a little in Mg-Al and Mg-Sn alloys at the over-aged stage, while in Mg-Gd and Mg-Zn alloys it decrease significantly. Something else should also contribute to the decrease of the hardness in Mg-Gd and Mg-Zn alloys. The main difference in precipitation sequences among these alloys is that Mg-Gd and Mg-Zn alloys experience the precipitation of metastable phases. In contrast, Mg-Al and Mg-Sn alloys precipitate the equilibrium phases directly. Therefore, the pronounced decrease of hardness in Mg-Gd and Mg-Zn alloys may relate to the transformation of the metastable phase.
At the peak-aged condition, the metastable phases Mg7Gd and Mg4Zn7 in Mg-Gd and Mg-Zn alloys are fully coherent with the Mg matrix [138, 220, 221]. However, at the over-aged stage, the metastable phases are transformed into semi-coherent or incoherent phases [116, 222]. The fully coherent precipitates can provide coherency strengthening that arises from the elastic coherency strain surrounding a particle that does not fit the matrix exactly [217]; when the precipitates transform from fully coherent to semi-coherent or incoherent, the coherency strengthening decrease. Therefore, the transformation of the fully coherent metastable phase to a semi-coherent or incoherent phase also contributes to the decrement of hardness in the Mg-Gd and Mg-Zn alloys.