Alloying elements and their contents - Influencing factor of resistivity in binary magnesium al

6.3 Influencing factor of resistivity in binary magnesium alloys

6.3.3 Alloying elements and their contents

The alloying elements always increase the total resistivity of pure metal. Fig. 6-6 shows the resistivity increase due to different alloying elements and their content. The alloys are solution treated and measured at 77 K to eliminate the influence of the intermetallic phases and temperatures.

Fig. 6-6 Resistivity of solution treated alloys.

As in Fig. 6-6, the resistivity increases almost linearly proportional to the solute content and the slopes vary with different alloying elements. The Mg-8Al alloy deviates from the simulated line because of the high solute concentration. The linear proportion law is a reasonable approximate in a dilute alloy, in which the solute concentration is less than 2 % [149] or in some papers, less than 5 % [21]. Nevertheless, Mg-8Al alloy is far beyond the functional area of the linear proportion law. Therefore, it shows a bigger deviation from the linear proportional law.

The resistivity increase per 1 at. % of alloying elements are listed in Table 6-6. The results show that Gd has the most significant influence on resistivity, while Zn has the lowest effect.

The results are different from those of the specific hardness increase as in Table 6-4, suggest that the influence mechanism of solute on resistivity is different from that on hardness.

According to Ying et al. [23], the increased resistivity is caused by the solute induced lattice distortion. However, the distortion is caused not only by the difference in atomic radii of the solute and magnesium, which may lead to local lattice expansion or contraction; but also by the difference in the valence of a solute and magnesium, which affects the electronic structure of magnesium and the shape of the Brillouin zone. As in Table 6-6, Zn has a similar atomic radius and the same valence as Mg; therefore, the specific resistivity increase caused by Zn is the smallest. The largest radii difference and the difference in valence between Gd and Mg make Gd have the most significant influence on the specific resistivity increase.

Except for the radii and valence difference, Pan et al. [22] also claim that the configuration of the extranuclear electron also affects the specific resistivity increase of alloying element. They claim that an unfilled d subshell is likely to induce a higher specific resistivity since it is prone to absorb the conduction electrons to obtain a stable state. This can explain the extremely high specific resistivity of Gd since the d subshell of Gd is not fully filled.

Table 6-6 Specific resistivity increase and some physical properties of alloying elements.

Alloying element Mg Al Gd Sn Zn

Resistivity increment per 1

at. % (nΩ∙m) - 16.65 97.42 42.05 7.83

Atomic Radius (pm) 145 118 233 145 142

Valency +2 +3 +3 +4 +2

Extranuclear electrons 3s² 3s²3p 4f⁷5d6s² 4d¹⁰5s²5p² 3d¹⁰4s²

83 6.3.4 Heat treatment

Heat treatment plays an important role in material science, as it is an effective method to tailor the properties. Therefore, it is of interest to investigate the resistivity changes during heat treatment.

6.3.4.1 Solution treatment

Fig. 6-7 shows the resistivity of the cast alloys before and after solution treatment. The measurement is conducted at 77 K to reduce the influence of temperature. As in Fig. 6-7, the resistivity always increases after solution treatment. In addition, the higher the solute content, the greater the increase of resistivity due to the solution treatment. The as-cast microstructure is a mix of the 𝛼-Mg matrix and the as-cast intermetallic phases. According to the resistivity–

mixture rule [161], the effective resistivity of material with two distinct phases 𝛼 and 𝛽 can be calculated by Eq.(6-3):

𝜌_𝑒𝑓𝑓 = 𝑉_𝛼𝜌_𝛼+ 𝑉_𝛽𝜌_𝛽 (6-3)

𝜌_𝑒𝑓𝑓 is the effective resistivity, 𝑉_𝛼 and 𝑉_𝛽 are the volume fractions of the 𝛼 and 𝛽 phases, 𝜌_𝛼 and 𝜌_𝛽 are the resistivity of 𝛼 and 𝛽 phases.

Fig. 6-7 Resistivity before and after solution treatment.

Solid lines are solution treated alloys; dash lines are as-cast alloys.

However, the resistivity–mixture rule does not apply well when the phases are in a random mixture. Instead, two semi-empirical rules, as in Eq.(6-4) are more useful in materials engineering when phase 𝛽 is dispersed in a continuous phase 𝛼 [161].

𝜌_𝑒𝑓𝑓 = 𝜌_𝛼¹⁺ treatment, 𝜌_𝛼 will increase due to the increase of dissolved solute. 𝑉_𝛽 will decrease because of dissolution of the intermetallic phases. In the current study, the resistivity always increases after solution treatment, which suggests the alloying elements dissolved in Mg matrix influence more the resistivity than that existing in the intermetallic phase.

Table 6-7 RRR values of the alloys.

Alloys RRR (ρ273/ρ77)

Generally, the dissolved solute can be treated as some type of “impurity” and they will increase the resistivity. As mentioned before, the RRR value can be used to evaluate the purity of

85 materials [185, 194]. The RRR values of these alloys before and after solution treatment are calculated and listed in Table 6-7. The results show that the solution treatment decreases the RRR values of all the alloys. The lower RRR value means the higher content of the “impurity”

and the higher resistivity, which is coincident with the results. It should be noted that the RRR value is related to the influence on the resistivity rather than the real solute content since the Mg-2.5Zn alloy has a larger RRR value than the Mg-0.8Al alloy.

6.3.4.2 Ageing treatment

The ageing treatment can somehow be treated as a reverse process of the solution treatment;

therefore, the resistivity should decrease during ageing, contrary to the increase of solute by solution treatment. However, it is not always true that the ageing process will decrease electrical resistivity. The formation of the G.P. zones at the early stage of ageing has been confirmed to increase the resistivity [226].

In the current study, the resistivity of the alloys decreases monotonous with ageing time, as in Fig. 5-41, which imply that the formation of G.P. zones did not occur. In Mg-Al and Mg-Sn alloys, the precipitation processes do not involve the stage of G.P zone formation [5]. The formation of G.P. zones in Mg-Zn alloys is restricted to the ageing temperature under 110 °C [91-93]. Therefore, the decrease of resistivity in Mg-Al, Mg-Sn and Mg-Zn alloys is in line with expectations. In contrast, the formation of G.P. zones has been reported [5, 129] at the early stage of ageing in the Mg-Gd alloys when the ageing temperature ranges from 150 °C to 300 °C. The current results do not match that. Since the formation of G.P. zones is reported to happen at the early stage of ageing and the first measurement of the Mg-Gd alloy in Fig. 5-41 is after 4 hours of ageing. It is possible that the formation of G.P. zones may stop within those 4 hours and the ex situ measurements in Fig. 5-41 could not illustrate the change of resistivity due to the formation of G.P. zones. Therefore, in situ measurements are conducted as in Fig.

5-42. Except for the temperature-induced increase at the beginning, the resistivity decreases monotonously through the entire ageing process. Therefore, it is concluded that no G.P. zones are formed in all alloys under the current ageing conditions.

The effective resistivity can be predicted using Eq.(6-4). The volume fraction of the precipitates is transformed from the weight fraction obtained by the Retiveled method. In the Mg-Gd and Mg-Zn alloys, different precipitates are treated as one type to simplify the calculation. The solute content in the 𝛼-Mg matrix are also obtained by the Retiveled method and using Fig. 6-6 the resistivity is calculated. Since the detailed data of the resistivity of the intermetallic phase

has not been found, both formulas in Eq.(6-4) are used to calculate the effective resistivity. The results are shown in Fig. 6-8, where ρα-Mg is the resistivity of the 𝛼-Mg matrix, ρp is the resistivity of the precipitates.

Fig. 6-8 Resistivity of alloys aged at 225 °C.

(a) Mg-8Al; (b) Mg-2.5Gd; (c) Mg-2.5Sn; (d) Mg-2.5Zn.

In all alloys, the assumption that resistivity of the precipitates is ten times higher than that of the 𝛼-Mg matrix improves the results. The calculated effective resistivity is smaller than that of the measured data except for the Mg-Zn alloy. This is because Eq.(6-4) does not consider the resistivity caused by phase boundaries. The phase boundaries that caused resistivity could be omitted when the phase is large such as the as-cast intermetallic phase. However, the precipitates formed during ageing are relatively small compared to the as-cast phase, so their influence on resistivity should be considered.

In contrast, the calculated resistivity is a little higher than the measured resistivity in Mg-Zn alloy. This is mainly due to the inappropriate use of Eq.(6-4). Eq.(6-4) provides a reasonable prediction when the precipitates’ resistivity is either ten times higher or lower than the 𝛼-Mg

87 matrix. However, the 𝛼-Mg matrix’s resistivity is approximately 10~20 nΩ∙m, as in Fig. 5-38.

At the same time, Andersson et al. [227] reported that the MgZn2 phase has a resistivity of 4~5×10^-8 Ω∙m. Therefore, it is not satisfactory to use Eq.(6-4).

Another finding is that as in Table 5-17, the Mg-Gd alloy’s resistivity decreases more quickly than that in the Mg-Al alloy, which further confirms that the diffusion rate of Gd in the Mg matrix is higher than that of the Al.

6.4 Precipitation kinetics quantified by resistivity

Isothermal precipitation kinetics is of interest both from a theoretical point of view and for the optimization of thermal treatments and alloy compositions in terms of mechanical or structural properties [228]. Previous investigations indicated that hardness [229], differential scanning calorimetry (DSC) and differential thermal analysis (DTA) [230], dilatometry [231] can be used to quantify the precipitation kinetics. Electrical resistivity [145] offers another method to investigate the precipitation kinetics.

The resistivity of an aged alloy can be described by Eq.(6-4) when the size of the precipitates is sufficiently large and the deviation from Matthiessen’s rule is negligibly small [180]. The results in Fig. 6-8 demonstrate that Eq.(6-4) is basically correct except for the deviation caused by the phase boundaries. Therefore Eq.(6-4) is applied to calculate the volume fraction of precipitates in the current study.

For a given binary alloy, the total solute content is settled and equals the amount dissolved in the matrix plus that formed in the intermetallic phases. Suggesting that there is only one type of precipitate, then the volume fraction of the precipitates can be expressed as a function of alloying elements that formed precipitates. On the other hand, resistivity has a linear relationship with the solute content dissolved in the matrix, as seen in Fig. 6-6. Therefore, in a given binary alloy, resistivity is a unary function of the solute amount that formed precipitates;

there is a one to one correspondence between them. With the measured resistivity, the solute amount that formed precipitates can be calculated and so is the volume fraction of the precipitates.

In the current study, there is only Mg17Al12 and Mg2Sn precipitate in Mg-Al and Mg-Sn alloys, respectively, so Eq.(6-4) is directly used. In Mg-Zn alloy, there are two types of precipitates, the Mg4Zn7 and MgZn2 phases. It is assumed that MgZn2 is the only precipitate when using

Eq.(6-4). Fig. 6-9 shows the volume fraction of the precipitates evolution during isothermal aged at 498 K. The volume fraction is calculated using Eq.(6-4) with the measured resistivity, also using the Retiveld methods with the X-Ray patterns and using the TC-PRISMA software (Educational Package) based on the Kampmann-Wagner numerical (KWN) method coupled with thermodynamic and mobility data from Zhang et al. [214]. As shown in Fig. 6-9, the volume fraction of the precipitates calculated by different methods basically shows the same tendency in all the alloys, except that the maximum volume fraction obtained using the Rietveld method is a little higher.

Fig. 6-9 Volume fraction of the precipitates during isothermal aged at 225 °C.

(a) Mg-8Al; (b) Mg-2.5Sn; (c) Mg-2.5Zn.

The KWN method divides the precipitation process into three distinct stages, nucleation, growth and coarsening. The volume fraction of the precipitates increase in the nucleation and growth stages; in the coarsening stage, the larger precipitates grow at the expense of the smaller ones, so the volume fraction remains unchanged. At the nucleation and growth stages, the volume fraction calculated by the resistivity shows better consistency with the Rietveld results than the TC-PRISMA results. However, the resistivity method does not show an obvious

89 transition from the growth stage into the coarsening stage; this is because, except for the volume fraction of the precipitates, the phase boundaries also affect the resistivity, so the resistivity is not a constant in the coarsening stage. Since Eq. (6-4) does not take the phase boundaries into account, the changing resistivity is then regarded as the change of the precipitates’ volume fraction. Nevertheless, the influence of the phase boundaries is negligible when the precipitates are large enough; this can be verified by the steady volume fraction by resistivity method in the Mg-Sn and Mg-Zn alloys as the ageing proceeding.

The results of all three methods show good agreements, which verifies the reliability of the resistivity in predicting the precipitates’ volume fraction evolution during isothermal ageing.

Therefore a phenomenological model between resistivity and the volume fraction of precipitates in binary alloys is built. The commonly used KWN approach for modelling precipitation kinetics requires the Thermodynamics and Mobility database, which is not easily obtained. In contrast, the resistivity measurement is easy to conduct; hence resistivity offers an easy way to monitor the precipitation process.

7 Conclusion

Mg-Al, Mg-Gd, Mg-Sn and Mg-Zn binary alloys are studied in the current study. Their resistivity in the as-cast, solution treated and aged states was measured to investigate the influence of composition and microstructure on the resistivity. In situ resistivity measurements were conducted to monitor the resistivity changes during isothermal ageing. Additionally, the influence of temperature on resistivity was investigated. The conclusions are as follows:

1) The resistivity of Mg was increased due to the lattice distortion caused by the solute elements. The distortion was caused by the difference in atomic radii and the difference in the valence of solutes and magnesium. The configuration of the extranuclear electron of the alloying element also affected the specific resistivity increase;

2) When the alloys are solution treated, the following equation can describe the relationship between resistivity and solute contents:

ρ(T)=ρMg(T)+δ(T)×c

ρ(T) is the resistivity of the alloy under a certain temperature, ρMg(T) is the resistivity of pure Mg, δ(T) is the coefficient, and c is the concentration of the solute. δ(T) depends on both the temperature and the type of solute.

3) All the alloys had a positive temperature coefficient of resistivity (TCR). The TCR varies from different solute content, which demonstrated the deviation from Matthiessen’s rule in Mg alloys;

4) The alloying elements dissolved in Mg matrix had a greater influence on resistivity than that present in the intermetallic phase; when the grain size was large enough (>

100 μm), the influence of grain boundaries on the resistivity was negligible;

5) The resistivity decreased during isothermal ageing. The relationship between resistivity and the fraction of precipitates can be roughly described in the following formula:

𝜌_𝑒𝑓𝑓 = 𝜌_𝛼1 +1 2 𝑉^𝛽 1 − 𝑉_𝛽

𝜌_𝑒𝑓𝑓 is the effective resistivity, 𝑉_𝛽 is the volume fraction of the precipitates, 𝜌_𝛼 is the resistivity of the 𝛼-Mg matrix;

6) A phenomenological model between resistivity and the volume fraction of precipitates in binary alloys was built. It can successfully predict the evolution of the volume fraction of the precipitates during isothermal ageing in binary alloys.

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