Metallic moulds
3.6 Differential Scanning Calorimeter (DSC) studies
The kinetics of the precipitation and dissolution reactions observed during heat treatment of the Al–Cu–Mg alloys microalloyed with varying percentage of Sn were
studied using a differential scanning calorimeter (DSC, Perkin Elmer, DSC 7). Four sets of samples were prepared from each alloy so as to carry out the experiments at four different heating rates. Samples were prepared in the form of discs of 3 mm diameter with weights in the range of 18 mg to 20 mg. The discs were vacuum encapsulated (at ~10-3 Pa) in fused silica tubes and solutionized at 500 °C for 10 h followed by water quench to room temperature. The quenched samples were stored in a refrigerator at ~ 5 °C prior to the DSC run. The baseline data for each heating rate was recorded using high purity Al pan as the reference.
DSC curves were recorded from 50 °C to 550 °C under a constant heating rate and then subsequently cooled to 50 °C at the same rate. Heating rates of 10 °C/min, 15 °C/min, 20 °C/min and 25 °C/min were used to obtain information on the kinetics of the reactions.
High purity dry nitrogen atmosphere was maintained during the DSC runs to prevent oxidation of the samples. The reaction peaks obtained during the heating cycle were analyzed. The characteristic temperatures (onset, peak and end) corresponding to the precipitation reactions were determined from the DSC curves.
Differential scanning calorimeter gives the differential heat flow (in mW) due to the corresponding reactions with respect to temperature (T) and hence with respect to time (t) for constant heating rates. The values of mole fractions of precipitate (Y) and the rates of precipitation (dY/dt) can be determined with respect to temperature from these calorimetric data and they are used to model the kinetics of the precipitation process.
The mole fraction Y(T) transformed at any temperature T, can be determined by evaluating the partial area under the reaction curve by:
( ) ( ) ( )
T
eA T T A
Y =
(3.1)where, A(T) is the area under the corresponding peak between onset temperature (To) and a given temperature T and A(Te) is the total area under the peak from To to peak end temperature (Te). The shift in the peak temperatures with change in heating rate indicates that the reaction is kinetically controlled and the rate of reaction is generally expressed as [JENA1989]:
( )
0E
Y
RTf Y k e t
−∆
∂ =
∂
(2.7)where, f(Y) is a function of mole fraction transformed Y, k0 is the frequency factor, ∆E is the activation energy for the reaction and R is the universal gas constant.
Expressing the rate of transformation with respect to time, Eq. (2.7) can be rewritten in terms of temperature, since ф is the constant heating rate
∂
∂
= t φ T .
( )
0E
Y
RTf Y k e T
ϕ
∆
∂
−=
∂
(3.2)Taking logarithm on both sides, Eq. (3.2) can be expressed as:
( )
0ln Y ln E 1
f Y k
T R T
∂
φ
∆
= −
∂
(3.3)
The activation energy (∆E) for the reaction is determined from the mean slope of plots of ln[(dY/dT)ф] vs. (1000/T) for given Y values, where the function f(Y) is not required to be known. In the present study, the same plots are made for a wide range of Y values from 0.1 to 0.9, so as to obtain a good estimation of the ∆E values for the reaction peaks of the alloys. The activation energy values for the precipitation peaks were evaluated for all the investigated alloys.
The next step in modeling the kinetic equation is to evaluate the function f(Y). As mentioned in the previous chapter, there is no single solution for f(Y) and it depends on the material composition and the corresponding precipitate morphology.
Donoso [DONO1985] while studying the dissolution kinetics of GP zones for Al–
Zn–Mg alloys by a three dimensional diffusion equation used two different expressions for f(Y), one for planar particles and other for spherical particles. The kinetic equations were thus based on physical models that consider decrease in precipitate half thickness for planar particles or radius for spherical particles [DONO1983]. The corresponding expressions (Cf.
Eq. 2.8 and 2.9) are
f(Y) = [1– (1–Y)1/3]2 (for planar precipitates) (2.8) f(Y) = 1–(1–Y)2/3 (for spherical precipitates) (2.9)
In an earlier study on Al–Cu–Mg alloy based on Johnson-Mehl-Avarami equation [AVRA1939], f(Y) was taken as:
f(Y) = (1–Y) (3.4)
In the present study, f(Y) is not used from the data available in existing literature.
Instead a new methodology was adopted for the determination of f(Y) which would ensure a good fit of the kinetic equations to the experimental data corresponding to the precipitation peaks.
As stated earlier, the mean slope of plots of ln[(dY/dT)ф] vs. (1000/T) for given Y values, generated from Eq. (3.3) can determine the mean ∆E value of the reaction peak. On the contrary, the ∆E value is actually observed to vary with mole fraction transformed Y, and the slopes of the above plots give estimates of ∆E values for respective values of Y.
These ∆E values are then plotted as a function of Y and a fourth order polynomial function E(Y) is used to obtain a good fit.
Similarly, the values for the first term in the RHS of Eq. (3.3), i.e. ln[f(Y)k0], are obtained from the intercepts of the straight lines from the plots of ln[(dY/dT)ф] vs. (1000/T) for different Y values. The intercept values are then plotted as a function of Y and fitted with a fourth order polynomial function. From this polynomial function, an exponential function is derived for f(Y) and the frequency factor k0 is also estimated.
To establish the confidence for f(Y), the values of f(Y), E(Y) and k0 obtained are substituted in Eq. (3.2) and the kinetic equation is modeled for each of the exothermic peaks. From this rate equation, Y
t
∂
∂ values are generated corresponding to different Y values, which gives the predicted variation of Y
t
∂
∂ with temperature T. The predicted curve fits well with the experimental plot of Y
t
∂
∂ vs. T for a wide range of Y values from 0.05 to 0.95. This establishes the reasonable accuracy of the kinetic equation modeled for the corresponding exothermic peak. The values of frequency factor k0, and the functions f(Y) and E(Y) are determined by the above procedure to model the kinetic equations for all the exothermic peaks observed in the DSC thermograms of the investigated alloys.