American Journal of Condensed Matter Physics

p-ISSN: 2163-1115    e-ISSN: 2163-1123

2019;  9(1): 6-11

doi:10.5923/j.ajcmp.20190901.02

 

Theoretical Estimation of Mixing Properties of Al-Mg Binary Liquid Alloy at Different Temperatures

H. K. Limbu, G. P. Adhikari

Department of Physics, Tri-Chandra Multiple Campus, Tribhuvan University, Ghantaghar, Kathmandu, Nepal

Correspondence to: H. K. Limbu, Department of Physics, Tri-Chandra Multiple Campus, Tribhuvan University, Ghantaghar, Kathmandu, Nepal.

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Copyright © 2019 The Author(s). Published by Scientific & Academic Publishing.

This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/

Abstract

The Regular Solution model has been used to describe thermodynamic properties, transport properties and structural properties at different temperatures theoretically. The interaction energy is temperature dependent and played an important role to explain the properties of Al-Mg liquid alloy at different temperatures. The theoretical values of interchange energy at different temperatures are obtained by best fit parameter approximation with the help of experimental values at 1073K. The properties have been studied with the help of computed theoretical interchange energy at different temperatures using interchange energy and temperature relation. A comparison of theoretical and experimental values at 1073K shows that they are in good agreement and using this basis we have studied properties at different temperatures.

Keywords: Regular solution model, Order energy parameter, Thermodynamic properties, Transport properties, Structural properties, Different temperatures

Cite this paper: H. K. Limbu, G. P. Adhikari, Theoretical Estimation of Mixing Properties of Al-Mg Binary Liquid Alloy at Different Temperatures, American Journal of Condensed Matter Physics, Vol. 9 No. 1, 2019, pp. 6-11. doi: 10.5923/j.ajcmp.20190901.02.

Article Outline

1. Introduction
2. Formalism
    2.1. Thermodynamic Properties
    2.2. Transport Properties
    2.3. Structural Properties
    2.4. Order Energy Parameter at Different Temperatures
3. Result and Discussion
    3.1. Free Energy of Mixing
    3.2. Entropy of Mixing (SM)
    3.3. Heat of mixing (HM)
    3.4. Activity
    3.5. Transport Properties: Chemical Diffusion and Viscosity
    3.6. Structural Properties
4. Conclusions

1. Introduction

Al-Mg has wide range of uses in industries because of its properties like comparatively less inflammable, non-toxic, non-magnetic, good mechanical strength, crack resistance, and low cost maintenance [1-3]. It is also used in automobile engines, construction and shipborne as it has light weight and excellent corrosion resistance [4-6].
We have estimated the mixing properties i.e. thermodynamic, transport and structural properties of the alloy at different temperatures using regular solution model [7]. We have the model to investigate the different properties of the alloy as atoms of Al and Mg are almost same in shape and size i.e. atomic volume of Mg/atomic volume of Al = 16.29/11.4 ≈ 1 [8] which indicates that the alloy is suitable for investigation. In thermodynamic properties, we have calculated free energy of mixing (GM), heat of mixing (HM), entropy of mixing (SM) and activity (a). In transport properties, viscosity and diffusion coefficient ratio (Dm/Did) have been computed. And, in structural properties the long wavelength limit (Scc(0)) and chemical short range order parameter (α1) are studied. Many researchers been working on several models to explain the mixing behavior of binary liquid alloys have been studied binary liquid alloys with different models [9-14]. And, viscosity is with the help of Moelwyn-Hughes equation [15-16]. The theoretical formulation has been presented in section (2), result and discussion in section (3) and conclusion in section (4).

2. Formalism

Regular alloys constituent atoms A and B are sufficiently similar in size and shape so they are interchangeable on the lattice. The binary liquid alloy A-B of homogenous solution consists of CA (A=Al) (≡c) mole of A and CB(B=Mg) {≡(1-c)} mole of B respectively.

2.1. Thermodynamic Properties

The free energy of mixing of binary liquid alloy is
(1)
Where, excess free energy of mixing and ideal free energy of mixing are given by
(2)
and
(3)
From equation (1), (2) and (3), we get
(4)
Where, T stands for temperature, is interaction energy and R is molar gas constant.
The expression for activities aA of the elements A and B in the binary liquid alloy can be derived from the standard relations
(5)
And
(6)
The entropy of mixing is given by
(7)
From equation (4) and (7), we get
(8)
The importance of as temperature dependent has been studied by Bhatia et al. [17], Shrestha et al. [18], Alblas et al. [19]. The interchange energy is temperature dependent.
The relation for heat of mixing (HM), entropy of mixing (SM), and free energy of mixing (GM) is expressed as
(9)
Using equation (4), (8) and (9), we get
(10)

2.2. Transport Properties

The relation between diffusion coefficient and concentration fluctuation derived by Singh and Sommer [20] is given as
(11)
Where, DM is the mutual diffusion coefficient and Did is the intrinsic diffusion coefficient for an ideal mixture computed as
(12)
Where, D1 and D2 are the self-diffusivities of pure components A and B respectively.
In term of energy order parameter ω, the diffusion coefficient can be expressed as [21]
(13)
We have used the Moelwyn-Hughes equation [15] to analyze the viscosity of Al-Mg liquid alloy which is given as
(14)
Where, (k = 1, 2) is the viscosity of pure component K and can be calculated from Arrhenius type equation [22] as
(15)
Where, is constant (in unit of viscosity) and En is the energy of activation of viscous flow for pure metal (in unit of energy per mole).

2.3. Structural Properties

The concentration fluctuation in the long wavelength limit (Scc(0)) [23] can be calculated as
(16)
From equation (4) and (16), we get
(17)
The experimental values of Scc(0) is derived from experimental values of the activities [27] from the equation
(18)
Where, aA and aB are the activities of the component of A and B respectively.
The Warren-Cowley [21,24] short range order parameter (α1) is used to investigate the arrangement of the atoms in the molten alloys. The theoretical values of these parameters can be evaluated
(19)
Here, and Z is the coordination number = 10 in our investigation.

2.4. Order Energy Parameter at Different Temperatures

The values of free energy of mixing (GM) of the alloy at different temperatures is computed from equation (4) using the values of order energy parameter (ω) at different temperatures from the relation [25,26]
(20)
Where, A and B are coefficient constants.

3. Result and Discussion

The values of A and B is calculated using the values of ω/RT and at temperature 1073K of the alloy Al-Mg in equation (20). The best fit parameters i.e. ω/RT = -1.122 and = 0.391 at temperature 1073K by the method of best fit approximation with the experimental values of the alloy from Hultgren et.al. 1973 [27] using equations (4) and (8). The theoretical values of interchange energy (ω) at different temperatures are calculated using eqation (20) which are presented in the table 1.
Table 1. Order energy parameter (ω) at different temperatures
     
Interaction energy is found to be negative at all temperatures which indicate Al and Mg atoms are interacting in nature. Using these values of the interaction energy we have computed free energy of mixing (GM), entropy of mixing (SM), heat of mixing (HM), activity (a), Ratio of mutual and self-diffusivity and viscosity (𝜂) at different temperatures (T) with the help of Regular solution model.

3.1. Free Energy of Mixing

The values of free energy of mixing (GM) of the alloy at temperatures 1200K, 1350K, 1500K, 1650K, 1800K, 1950K and 2100K have been computed using the values of ω(T) in equation (4) over the entire range of concentration. The free energy of mixing (GM) of Al-Mg liquid alloy at different temperatures of study in the concentration range CAl = 0.1 to 0.9 is shown in figure (1).
Figure 1. Graph for (GM/RT) Versus the concentration of CAl of Al-Mg liquid alloy at temperatures 1073K, 1200K, 1350K, 1500K, 1650K, 1800K, 1950K and 2100K
The theoretical and experimental values [27] of GM/RT of the alloy are in well agreement at 1073K. The values of free energy of mixing are found to be negative which shows weekly interacting nature. At all temperatures of investigations the minimum value is at CAl=0.5 which indicates that the symmetry in free energy of mixing. As the temperature of the alloy increases, the values of GM/RT increases and vice-versa.

3.2. Entropy of Mixing (SM)

By best fit method, the theoretical value of at 1073K is obtained using equation (8) with the help of experimental values of entropy of mixing (SM) is taken from Hultgren et. al. [27] i.e. = 0.391. With the help of this theoretical value of , entropy of mixing are computed at all temperatures (T) using equation (8) with the help of values of energy order parameters ω(T) at corresponding temperatures presented on the table 1.
The values of SM/R are found to be positive in the entire concentration range. This explains the symmetry in entropy of mixing of Al-Mg liquid alloy. At all temperatures of study, the values of entropy of mixing remain unchanged as the theoretical value of = 0.391 remains constant using equation (20).
Figure 2. Graph for SM/R versus the concentration of CAl of Al-Mg liquid alloy at temperatures 1073K, 1200K, 1350K, 1500K, 1650K, 1800K, 1950K and 2100K

3.3. Heat of mixing (HM)

The heat of mixing (HM) for the alloy is calculated using equation (10) with the help of theoretical values of order energy parameter which is shown in figure 3.
Figure 3. Graph for HM/RT versus the concentration of CAl of Al-Mg liquid alloy at temperatures 1073K, 1200K, 1350K, 1500K, 1650K, 1800K, 1950K and 2100K
The theoretical and experimental values of HM/RT are in good agreement at 1073K. The values of HM/RT are negative in the entire concentration range at all temperatures and increase with increase in temperature from 1073K to 2100K. Thus, the symmetry in heat of mixing is well explained.

3.4. Activity

Activity of Al and Mg atoms of the alloy is Calculated using equations (5) and (6) in entire concentration range. The activity (Ln a) versus the concentration is studied which is shown in figure 4 and figure 5.
Figure 4. Ln aAl versus CAl of Al-Mg liquid alloy at 1073K, 1200K, 1350K, 1500K, 1650K, 1800K, 1950K and 2100K.
Figure 5. Ln aMg versus CAl of Al-Mg liquid alloy at 1073K, 1200K, 1350K, 1500K, 1650K, 1800K, 1950K and 2100K
The values of activity (a) of both the components i.e. Al and Mg of the alloy are in good agreement with the experimental values for whole range of concentration at 1073K. The activity increases as temperature increases and vice-versa.

3.5. Transport Properties: Chemical Diffusion and Viscosity

Equation (13) is used to calculate the diffusion coefficient with the help of theoretical values of order energy parameters ω(T). The investigation of the diffusion coefficient with the concentration of Al is shown in figure (6).
Figure 6. Ratio of mutual and self-diffusivities, for Al-Mg liquid alloy at temperatures 1073K, 1200K, 1350K, 1500K, 1650K, 1800K, 1950K and 2100K versus concentration of Al
The value of in the entire range of concentration at all temperatures (T) which shows chemical order in the alloy. The ordering tendency of the atoms in Al-Mg liquid alloys is greater about equiatomic composition as the maximum value of is at CAl = 0.5.
Viscosity of the alloy is calculated using equations (14) and (15). The viscosities of pure components Al and Mg at all temperatures(T) are computed using equation (15) with the help of constants and E for the metals [22] which is used to find the viscosity of the alloy for corresponding temperatures using equation (14).
Figure 7. Viscosity of Al-Mg liquid alloy at 1073K, 1200K, 1350K, 1500K, 1650K, 1800K, 1950K and 2100K versus concentration of Al
The viscosity of pure component of Al atom is more than the viscosity of pure component Mg at all temperatures of study. The viscosity of the alloy is temperature dependent and decreases with the increase at each concentration range and maximum at 2100K.

3.6. Structural Properties

The theoretical and experimental values of concentration fluctuation in the long wavelength limit (Scc(0)) can be obtained from equations (18) and (19). The values of Short range order parameters (α1) at different temperatures are calculated from equation (19).
Figure 8. Theoretical values of Concentration fluctuation of Al-Mg liquid alloy at 1073K, 1200K, 1350K, 1500K, 1650K, 1800K, 1950K and 2100K along with experimental values at 1073K and
The concentration fluctuation in the long wavelength limit (Scc(0)) is maximum at CAl =0.5 at all temperatures of study which suggests the symmetry in Scc(0) for Al-Mg liquid alloy. It is found that throughout the entire concentration range at all temperatures of investigation which implies that ordering is favored in the Al-Mg alloy.
The theoretical values of Warren-Cowley chemical short-range order parameter (α1) [21,24] is Computed from equation (19) using the theoretical values of Scc(0). We have calculated that the Chemical short range order parameter (α1) is negative at all the concentrations which indicate ordering nature of the alloy as shown in the figure 9.
Figure 9. Chemical short range order parameter (α1) of Al-Mg liquid alloy at 1073K, 1200K, 1350K, 1500K, 1650K, 1800K, 1950K and 2100K with co-ordination number (Z)= 10
The negative values of Chemical short range order parameter (α1) at all temperatures indicates ordering nature. The value of α1 increases as the temperature increases at each concentration range.

4. Conclusions

- The alloy is an ordered system and interacting in nature at all temperatures of investigations.
- The alloy is symmetric in nature at all temperatures.
- The activity of the alloy slightly increases as the temperature increases.
- Viscosity decreases as the temperature of study increases.
- properties can be studied at different temperatures using temperature and interaction energy relation theoretically.

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