Isochronal study of Al-Mg, Al-Mn, and Al-Mn-Mg alloys using electrical resistivity and thermoelectric power

Abstract

We have studied the phase transformation kinetics occurring in aluminum alloys containing Mn, Mg, and Mn-Mn-Mg by means of electrical resistivity (rho) and thermoelectric power (deltaS). The alloy samples were annealed isochronally at temperatures ranging from ambient temperature to 615 °C. Both rho and deltaS allowed the separation of several stages of transformation associated to either the precipitation or dissolution of phases that occur during the annealing process. The alloys containing Mn show a strong deltaS growth or a marked r drop between 450 °C and 550 °C, linked to the precipitation of the Mn-rich Al6(Mn,FE) equilibrium phase. While the Mg in aluminum generates a series of maxima and minima of both rho and deltaS associated to the pre-established precipitation sequence: GP Zones <FONT FACE=Symbol>® b</FONT>' phase <FONT FACE=Symbol>® b</FONT> phase, a combination of effects ensues in the Mn- and Mg-containing alloys, the Mg effect being enhanced at temperatures below 350 °C and that of the Mn striking the same behavior above such temperature. Our study ascertains that the Mg speeds up the precipitation and lowers the activation energy of the Al6(Mn,Fe) phase, the latter having been evaluated by the multiple temperature method.

Al-Mn; Al-Mg; Al-Mn-Mg Alloys; phase precipitation kinetics; electrical resistivity; thermoelectric power; aluminum alloys of the 3000 series

REGULAR ARTICLES

Isochronal study of Al-Mg, Al-Mn, and Al-Mn-Mg alloys using electrical resistivity and thermoelectric power

Ney José Luiggi Agreda^*

Grupo de Física de Metales, GFM, Dpto. de Física, Escuela de Ciencias, Núcleo de Sucre, Universidad de Oriente, Cumaná, Estado Sucre, Venezuela, Código 17 Apartado Postal 299

ABSTRACT

We have studied the phase transformation kinetics occurring in aluminum alloys containing Mn, Mg, and Mn-Mn-Mg by means of electrical resistivity (r) and thermoelectric power (DS). The alloy samples were annealed isochronally at temperatures ranging from ambient temperature to 615 °C. Both r and DS allowed the separation of several stages of transformation associated to either the precipitation or dissolution of phases that occur during the annealing process. The alloys containing Mn show a strong DS growth or a marked r drop between 450 °C and 550 °C, linked to the precipitation of the Mn-rich Al₆(Mn,FE) equilibrium phase. While the Mg in aluminum generates a series of maxima and minima of both r and DS associated to the pre-established precipitation sequence: GP Zones ® b' phase ® b phase, a combination of effects ensues in the Mn- and Mg-containing alloys, the Mg effect being enhanced at temperatures below 350 °C and that of the Mn striking the same behavior above such temperature. Our study ascertains that the Mg speeds up the precipitation and lowers the activation energy of the Al₆(Mn,Fe) phase, the latter having been evaluated by the multiple temperature method.

Keywords: Al-Mn, Al-Mg, Al-Mn-Mg Alloys, phase precipitation kinetics, electrical resistivity, thermoelectric power, aluminum alloys of the 3000 series

1. Introduction

Wrought aluminum alloys of the 3000 series have paramount commercial importance because of the gain in physical properties experienced by the aluminum matrix when alloying elements such as manganese (Mn) and magnesium (Mg) are incorporated. Manganese has the virtue of prompting the precipitation of dispersoids responsible for the additional hardening sustained by the Al-Mn alloy, while magnesium contributes to that hardening, for concentrations used in this study, at the solid solution level¹. Just as aluminum strength is altered by the presence of these alloying elements, other attributes of aluminum such as the electrical and thermoelectric properties are modified as well. Obviously, the presence of both of these alloying elements induces the combination of mechanisms producing such changes. The purpose of this paper is to study the effect that Mn and Mg alloying elements have on the transformation kinetics occurring when we subject the alloy to isochronal aging.

The techniques used were electrical resistivity (r) and thermoelectric power (DS), both having a notorious sensitivity to the microstructural modifications associated to the diffusion of the alloying elements mentioned above^2,3.

2. Experimental Procedures

2.1. Alloys studied

This study is performed on commercial 3003 alloys of Aluminios del Caroní S.A., ALCASA and binary Al-3 wt. (%) Mg alloys produced by Pechiney-France, all originally in cast condition.

Likewise, in order to consider the effect of Mg over Mn precipitation, Mg was incorporated by fusion into the 3003 alloy at different proportions. This was carried out at the School of Metallurgy and Materials Sciences of Universidad Central de Venezuela. The chemical composition of the samples used is shown in Table 1.

2.2. Thermal treatments

Figure 1 shows the thermal treatment to which the samples are exposed. First, a homogenization treatment (HT) for 24 hours at 600 °C and then a quenching in a water and salt solution kept at 0 °C. For the repeated isochronal studies, the samples are brought to the annealing temperature (Te) and maintained there for a constant period of time of 15 or 60 minutes. Each measurement is undertaken at the measure temperature (TM), set at 20 °C. It is worth noting that as the time necessary for the sample to remain at temperature Te is reduced, the condition of continuous treatment at a constant rate, indicated by the broken line in the graph, is approached.

All the runs performed involve isothermal annealing processes lasting 15 or 60 minutes at each temperature, processes which we designated as R1 and R2, respectively.

2.3. Equipment used

In order to measure the electrical resistivity, we used a controlled Sigmatest D 2068 microprocessor that gauges the conductivity of non magnetic materials in the range of 0.5 to 65 MS/m (1 to 112% IACS) with a measuring uncertainty of ± 1% of the measured value. This allows us to access resistivity values in the range of 1.54 to 200 mW.cm. The samples used were one-inch thick, 20 x 20 mm² squares. All measurements were performed at 20 °C, temperature at which Mn, the main alloying element of the 3000 series alloys, shows low diffusivity in aluminum.

The gauging of thermoelectric power was carried out with a device designed by the Institut National des Sciences Appliquées de Lyon (INSA de Lyon), France, sensitive up to 0.01 µV/K and capable of measuring the thermoelectric power of laminar samples of various lengths with a measuring uncertainty of 0.2%.

The heating at temperature Te is carried out in an air furnace with control of temperature of ± 5 °C.

The reproducibility of the experience is warranted by selecting homogenized samples having properties whose measured values range within 1%.

3. Theoretical Aspects

The differential equation for the isothermal study of transformation kinetics involves the transformed fraction Y, the reaction constant K, and the kinetic or conversion function G. It is customary to assume K as a function of temperature K(T) and G as a function of conversion G(Y), so that both functions are assumed independent, allowing us to write a simplified kinetic equation as

In integral form this equation is written as,

The kinetic function G(Y) is defined on the basis of a series of empirical models^4-8, while for thermally activated processes, K follows an Arrhenius relation.

where the pre-exponential factor K₀ and activation energy Q are characteristic parameters of the transformation. However, it is necessary to mention the ambiguity that arises when different kinetic models are used to characterize the same transformation. This situation has led many authors to resort to the isoconversion method⁹, which lay aside the use of such models to determine the characteristic parameters of transformation kinetics.

A method seldom used to evaluate the energy of activation is that of two temperatures^{10, 11}, involving two transformation kinetics, or that of multiple temperatures, involving more than two kinetics, where the principle of isoconversion is basically applied by defining the temperatures at which the same conversion or transformed fraction for different heating rates is kept. This is evidenced in the present research by means of our isochronal thermal treatment, which involves a series of isothermal annealing techniques during a fixed time (see Figure 1). For two subsequent isothermal annealing treatments at T₁ and T₂ temperatures, and considering that no structural modification occurs during the temperature change from T₁ to T₂ , the transformed fraction at the end of the first isothermal annealing at temperature T₁ and at the beginning of the second isothermal annealing at temperature T₂ remains unchanged. Hence from Equation 2 we can write:

In Equation 4, t₁ and t₂ times constitute the necessary time for obtaining the same conversion Y at temperatures T₁ and T_2. On the basis that no important transformation occurs during the change of T, g₁ (Y) = g₂ (Y), and considering:

we can write,

an expression similar to that reported in the literature¹⁰,

where t_n=1/kn and where Equation 6 may be obtained from Equation 7 by setting an adequate reaction model. This is evident in the first order reaction model or in the Johnson-Mehl-Avrami model with N = 1^5,11, as a solution to Equation 1 proposes

Also, as in Reference 10, assuming that the transformation follows a kinetic of the first order, the following relation is deduced specifically for resistive studies.

the reaction constant inverse being t = K^-1, thus allowing us to write,

Equations 7 and 10 are of a modeling nature since they follow a specific kinetic model, while Equation 6 has an isoconversional nature. Now, if we consider many isothermal kinetics, we could establish a Temperature-time continuum so that

The last term of Equation 12 reflects the change in temperature rate with time, allowing us to incorporate the experimental temperature-versus-time path to our isochronal studies. The typical case is one of continuous heating, where dT / dt is constant. However, any temperature-time ramp may be incorporated through that term.

The applicability of Equation 12 is only restricted to resistivity measurement. A more general expression applicable also to an arbitrary thermal path and to other measuring techniques can be deduced by means of the general isoconversional relation for non-isothermal studies propounded by Luiggi⁹,

where b is the heating rate. For two kinetics with heating ratios b₁ and b₂, we obtain the same transformed fraction Y at temperatures T₁ and T₂, so that

and, considering that Q₁ = Q₂ = Q, we get:

where b_{i = (dT/dt)Ti} . The right side of Equation 15, like that of Equation 12, would allow the consideration of any temperature-time ramp that might be contemplated experimentally.

4. Results and Discussion

4.1. 3003 Alloy: Al-1.1 wt. (%) Mn

Figures 2a and 2b show the electrical resistivity and its derivative with respect to the temperature of the 3003 alloy. Figure 2 shows slight variations of r for temperatures below 400 °C for R1 and below 350 °C for R2; this is followed by an important resistivity drop whose minimum places itself in the neighborhood of 555 °C for R1 and 525 °C for R2, followed by an increase in resistivity.

Such behavior is explained by the diffusion process activated by the temperature increase. For low temperatures, a structural rearrangement is produced where the Si atoms are the main participants. In this stage the Fe and Mn atoms take part in a smaller proportion; this is easily inferred from the magnitude reached by r at those temperatures. The contribution of each atom kind to the total resistivity can be deduced using Table 2 of Reference 2. The important depression occurs due to the solid solution depletion prompted mainly by the massive precipitation of Mn in the form of Al₆(Fe,Mn) phase. The subsequent growth corresponds to this phase becoming a solid solution. The time at each temperature magnifies the precipitation of each alloying element, precipitation which, in the particular case of Mn, does not settle completely for the selected annealing runs at each temperature. For the same reason we observe that the shorter the annealing time, the higher the temperature at which the minimum appears. This is illustrated in Figure 2b, where the absolute maxima of the derivative located at 475 °C and 450 °C for R1 and R2, respectively represent the temperatures at which the highest precipitation rate of Mn is produced.

Figures 3a and 3b reproduce the study of the 3003 alloy using thermoelectric power. Figure 3a plots DS vs.T, a slight variation of the property appearing for temperatures below 350 °C; an important increase then ensues, reaching a maximum at 550 °C for R1 and at 523 °C for R2, in perfect agreement with the previous resistivity study. Figure 3b shows the derivative of thermoelectric power vs.T, from which it can be observed that the maximum rate of precipitation is obtained at 500 °C for R1 and in the vicinity of 475 °C for R2, thus evidencing the decisive effect of Mn precipitation for temperatures above 350 °C.

4.2. Al-3 wt. (%) Mg Alloy

Figure 4a shows electrical resistivity changes in function of the temperature, where three depressions and several maxima are detected, depending on whether we contemplate R1 or R2. The interpretation of this graph is as follows: The first depression corresponds to the dissolution of the Guinier-Preston zones formed during the first annealing treatments performed at the lowest temperatures; it reaches its final point at 100 °C, point at which the Mg starts a process of precipitation as a b' phase, reaching 350 °C for the R1 treatment but just up to 250 °C for the R2 treatment. The dissolution of this phase extends itself up to 400 °C, both for R1 and R2. The precipitation of the b phase occurs between 400 and 460 °C, its dissolution ceasing at 550 °C. The subsequent variation is associated to the sample’s entering into solution and possible softening. This general comportment has been reported by Starink and Zahra¹², by Bouchear, Hamana and Laoui¹³, and by Luiggi and Betancourt¹⁴ for alloys with a higher Mg content.

It is important to notice how the kinetics thus obtained clearly outline the temperature ranges where b' and b phases are formed and dissolved. These ranges are confirmed in Figure 4b, which shows the derivative of curve 4a.

Figures 5a and 5b further ratify this behavior, arrived at by means of thermoelectric power. The process of precipitation and dilution of the Guinier-Preston zones and those of the b' and b phases are manifested by the appearance of characteristic depressions and peaks, their location being in accordance with those reported by resistivity.

4.3. Al-Mn-0.5 Mg Alloy

Figures 6a and 7a show the electrical resistivity (r) and the thermoelectric power (PTE) in function of the temperature. The behavior of these properties is qualitatively similar to the behavior observed in the 3003 alloy (Figures 2 and 3). The most striking differences are seen at temperatures below 400 °C owing to the effect of precipitation of Mg. This alloying element has a specific resistivity up to 5 times lower than that of Mn, and an intrinsic TEP both positive and 2.8 times lower that the Mn intrinsic TEP, which is negative¹⁵. All this, along with the fact that the process of transformation occurs by diffusion and that the Mg is kinetically more active than Mn, allows us to explain why, at lower temperatures, Mg has a greater influence over the kinetics of transformation. At high temperatures the profuse precipitation of Mn masks the precipitation and dissolution of the b phase observed in the binary Al-3 wt. (%) Mg ( Figures 4a and 5a). Again, this fact is explained because the specific electrical resistivity and thermoelectric power of Mg in Al are relatively smaller than those reported for the Mn in Al. It is also noticeable, as shown by Figures 6a and 7a and their derivatives (Figures 6b and 7b) that the absolute maxima in the alloy containing Mg appear at lower temperatures, which can be interpreted as a progress in Mn precipitation.

4.4. Al-Mn-1.2 Mg Alloy

Figures 8 and 9 illustrate the results for the alloy containing 1.2 wt. (%) Mg. Here, the participation of both alloying elements at different ranges of temperatures is, again, rendered evident. The Mg prevails at low temperatures and the Mn at the high ones. The precipitation of the former plays a delaying role in the precipitation of the equilibrium phase of the Mn-rich alloy. Again, at high temperatures, the precipitation of the b phase¹⁴ is masked by the precipitation of the Al₆(Fe,Mn) phase.

4.5. Application of the multiple-temperature method to evaluate the activation energy

To wrap up this study we proceeded to determine how the presence of Mg affects the precipitation kinetics of Mn in the different alloys. For that, using the data associated to the derivative with respect to both r and TEP, we assessed the precipitated fraction Y of the transformation corresponding to the largest absolute depression both in r and DS for the 3003, Al-Mn-0.5 Mg and 1.2 Mg alloys.

The slope of Y is obtained by considering the area under the curve of the derivative belonging to the property measured in the temperature range where the transformation occurs, normalizing it then to the total area and determining the temperatures at which the transformed fraction remains constant. Once these isoconversional temperatures are known, only the b_i contribution remains to be determined in order to evaluate the activation energy of the Al₆(Mn,Fe) phase.

Although we could have evaluated parameter b in a relative fashion by utilizing the activation energy value of the stable phase Al₆(Mn,Fe), previously established to be 35.52 Kcal/mol in the 435 °C and 515 °C range¹⁶, we preferred, once the isoconversion temperatures were known, to use the graphs of the derivatives of the property with respect to temperature and determine the second term of Equation 15 from the following relation:

where y represents the electrical resistivity or the thermoelectric power, while the second term within brackets represents the associated slopes to isothermal kinetics ratio at temperatures T₁ and T₂, respectively.

The considerations to assess the activation energy in this research are the following:

1. Our values are valid for isothermal kinetics of similar slope.

2. In principle, our model is checked for kinetics of the first order, as addressed in Ref. 10; this sets N as equal to 1, though N may be changed and its effect on the kinetics determined.

Figure 10 summarizes these results. It shows the activation energy (Q) of the Al₆(Mn,Fe) phase in function of the extent of conversion or transformed fraction (Y), which is calculated using Equation 15, Equation 16 and the previous considerations. These results are pointed out with empty symbols in Figure 10, showing, for all the alloys under study, that Q varies with the conversion extent Y. This behavior reveals the complexity of the reaction mechanism occurring during the phase transformation processes, seeming a typical comportment in the studies carried out using isoconversional methods^4,14. The resulting dependence of Q on Y contrasts with the invariability of Q reported when empirical models are used. In those cases, the kinetic parameters, K₀, Q and G(Y)¹⁴, are fit along the whole extent of Y to obtain the best correspondence between the experimental and the theoretical Y values, reporting only one Q value for the entire Y range having been reported. Mathematically this situation can be reproduced by averaging the Q values obtained for each alloy, using r and DS along the entire Y extent. The horizontal lines in Figure 10 correspond to the average Q values. We report results of activation energies of 32.2 Kcal/mol, 24.3 Kcal/mol, and 19.2 Kcal/mol for the Al₆(Mn,Fe) phase, as measured in the 3003, Al-Mn-05 Mg, and Al-Mn-1.2 Mg alloys, respectively. Notice the good agreement of our result for the 3003 alloy with those reported in Ref. 16, also shown in Figure 10. There is also an equally remarkable match between our results and those presented by Goel et al. 17 in their work on binary Al 1 wt. (%) Mn and ternary alloys to which Cu and Fe have been added. We observe that as the Mg concentration increases, the activation energy values obtained become lower, allowing us to point out that the effect of Mg on the Al₆(Mn,Fe) precipitation constitute a reduction of its activation energy.

5. Conclusions

We have studied the effect of Mg on a 3003 aluminum alloy subjecting it to isochronal annealing treatments of 15 and 60 minutes at fixed temperatures, and have observed that:

• Both the resistivity and the thermoelectric power are highly sensitive to the structural modifications;

• Our study of Al-Mg alloys corroborates the sequence of precipitation and dissolution of phases containing Mg reported by other authors using different study techniques¹²-¹⁴. As the temperature increases the phases follow the sequence: G-P Zones, b' phase and b phase;

• In the 3003 alloy it is confirmed the precipitation of light elements as Si at low temperatures, whilst at high temperatures, characterized by important r and DS changes, Mn precipitates forming the Al₆(Fe,Mn) phase;

• The effect of Mg on the precipitation kinetics of the Al-Mn-Mg alloys is more noticeable at low temperatures than at high temperatures, because an abundant Mn precipitation occurring at high temperatures masks the Mg effect. Mg speeds up the precipitation of Mn, causing a decrease of the Al₆(Fe,Mn) phase activation energy value from 32.2 Kcal/mol in the 3003 alloy to 24.3 and to 19.2 Kcal/mol in the Al-Mn-0.5 Mg and the Al-Mn-1.2 Mg alloys, respectively.

Acknowledgements

This research was supported by the Consejo de Investigación de la Universidad de Oriente through Project No CI. 5-1002-0938 UDO. The author is also grateful to Carlos Mota and his company Traduce, C.A. for translation assistance.

Received: April 2, 2004; Revised: October 9, 2004

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Publication Dates

• Publication in this collection
  28 Mar 2005
• Date of issue
  Mar 2005

History

• Accepted
  09 Oct 2004
• Received
  02 Apr 2004