Ajayi Ayodeji Akintunde, Ogunmola Enoch Debayo, Adeoye Abiodun Eyitayo
Department of Mathematical and Physical Sciences, Afe Babalola University, AdoEkiti, Nigeria
Correspondence to: Ogunmola Enoch Debayo, Department of Mathematical and Physical Sciences, Afe Babalola University, AdoEkiti, Nigeria.
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Abstract
A simple model has been used to investigate the nature of chemical order in NaPb and NaHg liquid binary alloy at 700K and 673K respectively. The energy parameter obtained from the model was used to calculate the concentration dependent mixing properties such as Gibb’s free energy of mixing, Concentration fluctuations in the long wavelength limit and the WarrenCowley chemical short range order parameter. Results obtained showed that both alloys are heterocoordinated throughout the entire concentration and there is tendency for segregation and demixing to take place in the liquid alloys. We observed that NaHg liquid alloy is more strongly interacting binary alloy and chemically ordered than NaPb liquid alloy.
Keywords:
Binary liquid alloy, Chemical ordering, Sodium, Theoretical study, WarrenCowley parameter
Cite this paper: Ajayi Ayodeji Akintunde, Ogunmola Enoch Debayo, Adeoye Abiodun Eyitayo, Chemical Ordering in NaPb and NaHg Liquid Alloys, American Journal of Condensed Matter Physics, Vol. 7 No. 3, 2017, pp. 6772. doi: 10.5923/j.ajcmp.20170703.02.
1. Introduction
A number of theories have been developed by theoreticians to explain the temperature dependence of the thermodynamic properties of binary liquid alloys with a purpose of obtaining valuable microscopic information on them [13]. Accurate thermodynamic knowledge of the alloy mixing properties and phase diagrams of alloy systems is crucial to having a reliable theoretical result. The mixing behavior of two metals forming binary alloys is as a result of the interplay between energetic and structural adjustments of constituent elemental atoms [4]. Heterocoordination known as the preference of unlike atoms to pair as nearest neighbors in the alloy system, form AB pair while segregation is known as the situation where the constituent atoms in the alloy becomes selfcoordinated forming AA and BB pairs where A and B are the constituent atoms within the binary alloy [5]. Alloys are mixture of metals and a binary alloy can be represented as A_{x}B_{1x} where A and B are metals and subscripts x and 1x are concentration of the respective metals. NaPb, NaHg, KPb and KHg are examples of binary alloys. Classification of binary alloys can be done according to the deviation of their thermodynamic functions such as chemical activity from raoulatian ideality, therefore binary alloys can be classified into two main groups; segregating (positive deviating) and heteorocoordinating (negative deviating) alloys [6, 7]. The interest in the energetic and its effects on the alloying behavior of NaPb and NaHg stemmed from the understanding that, despite the hazards involved in the unsafe handling of NaPb alloy, it may still be relevant in qualitative inorganic analysis, both as reductant in acidic and alkaline media, and also as a source of sodium hydroxide for hydroxide precipitations [8]. NaHg has been used in organic chemistry as a powerful reducing agent, which is safer to handle than sodium itself. NaHg has been found to be useful in fabricating pressurebased sodium lamp [9]. It is necessary to mention that there has been a previous attempt to understand the alloying behavior of these alloys [10]. Consequently, this paper also has the purpose of complimenting earlier studies on each of NaPb and NaHg liquid alloy by studying the structural behaviour of these two Sodiumbased alloy systems, mostly with, studies of concentration fluctuations and the WarrenCowley chemical shortrange order parameter (CSRO). The calculation of the structural properties using Flory’s model [11] is presented.
2. Theoretical Concepts
In the framework of the Flory’s model, the expression for the Gibb’s free energy of mixing, , of a binary liquid alloy is given by  (1) 
Where in Eqn.1, x and y are the bulk concentrations of the constituent A and B atoms in the binary alloy respectively such that, y=1x, and V_{A} and V_{B} being atomic volumes of constituents’ A and B respectively. The parameter w is the ordering energy whose value gives information on the alloying behaviour of the alloy. R is a universal gas constant.The concentration fluctuations in the longwavelength limit, S_{cc}(0) can be calculated from the standard relationship in terms of the Gibbs free energy of mixing  (2) 
Using equations (1), (2), S_{cc}(0) becomes  (3) 
Where;  (4) 
For ideal mixing, the energy parameters w and δ are zero and eqn. (3) reduces to  (5) 
3. Results and Discussion
3.1. Free Energy of Mixing
Table 1 shows the values of the fitted interaction parameter for liquid NaPb and NaHg. Eqn. (1) has been used in obtaining, the optimal value for the interaction parameter that gives agreement between experimental and theoretical Gibbs free energy. Eqn. (1) was also used to calculate the G_{M}/RT for both systems while the experimental data were taken from the work reported by Hultgren et. al., [13]. Figure 1 and 2 shows the computed and experimental values as a function of concentration. The negative values of w in Table 1 show both alloy systems are chemically ordered, which means pairing of unlike atoms. From the results in Figure 1 and 2, it could be seen that both systems NaPb and NaHg have minimum values of 2.797 and 3.125 respectively. This is an indication that NaHg is more heterocoordinated than NaPb or strongly interacting binary alloy, Table 1. Fitted parameters for NaPb and NaHg liquid alloys 
 

 Figure 1. Concentration dependence of for NaPb liquid alloys at 700K, computed from Eqn.1. The solid line represents theoretical values and the squares represent experimental values [13], x_{Na} is the concentration of Na in the alloy 
 Figure 2. Concentration dependence of for NaHg liquid alloys at 673K, computed from Eqn.1. The solid line represents theoretical values and the squares represent experimental values [13]. x_{Hg} is the concentration of Hg in the alloy 
3.2. Concentration Fluctuations and the WarrenCowley CSRO Parameter
The fitted parameters were kept invariant when computing S_{cc}(0) and the shortrange order . In principle, S_{cc}(0) can be obtained directly from smallangle diffraction experiments but the experimental procedure involved is very tedious and has not been accomplished successfully. The S_{cc}(0) is an essential microscopic parameter which has been widely used in the study of nature of atomic order in binary liquid alloys [13, 14] and the S_{cc}(0) with and it also formed a basis for explaining energetics in liquid alloys. Figure 3 and 4 shows the computed values of the concentration fluctuations in the long wavelength limit. Eqs. (3) and (5) has been used to compute S_{cc}(0) and S_{cc}(0)^{id} respectively. The mixing behavior of liquid binary alloys can be deduced from the deviation of S_{cc}(0) from the ideal value. S_{cc}(0) < S_{cc}(0)^{id} is an evidence of chemical ordering and heterocoordination otherwise, there is tendency for segregation and demixing to take place in the liquid alloys. Fig. 3 and 4 shows heterocoordination in both alloys.  Figure 3. Concentration fluctuations in the long wavelength limit, real (S_{cc}(0)) and ideal (S_{cc}(0)^{id}) versus concentration for NaPb system at 700K computed from Eqn. 3 and 5. The solid line represent S_{cc}(0) and the dashes represent the values of S_{cc}(0)^{id} 
 Figure 4. Concentration fluctuations in the long wavelength limit real (S_{cc}(0)) and ideal (S_{cc}(0)^{id}) versus concentration for NaHg system at 673K computed from Eqn. 3 and 5. The solid line represent theoretical values and the dashes represent the values of S_{cc}(0)^{id} 
The nature of ordering in binary liquid alloys can also be investigated by calculating the Warren Cowley Short Range Order (CSRO) parameter, α_{1} [4, 5]. Experimental values are not available to compare our theoretical results just as we have done in the case of the Gibb’s free energy of mixing. S_{cc}(0) and α_{1}_{ }are related by the expression  (6) 
Where  (7) 
indicates complete ordering (unlike atoms pairing) while represent segregation. The degree of chemical order may be deduced from the negative values of α_{1}. Maximum heterocoordination can be observed at x_{Na} = 0.41 in NaPb and at x_{Hg} = 0.72 in NaHg as depicted by figures 5 and 6. α_{1} for NaPb at x_{Na} = 0.41 is 0.30 and in the case of NaHg at x_{Hg} = 0.72 is 0.34. This reveals NaHg has more heterocoordination and chemical order than NaPb.  Figure 5. Calculated WarrenCowley CSRO parameter, α_{1}, using eqn. (6) for NaPb at 700K 
 Figure 6. Calculated WarrenCowley CSRO parameter, α_{1}, using eqn. (6) for NaHg at 673K 
4. Conclusions
The energetics of NaPb and NaHg liquid binary alloys have been analyzed in this present study at 700K and 673K respectively. Attention has been given to their thermodynamic functions such as Gibb’s free energy of mixing, concentration fluctuations and WarrenCowley CSRO parameter. Theoretical study of the alloying behavior of the two liquid alloys reveals heterocoordination in both alloys throughout the entire concentration of Na in NaPb and Hg in NaHg. It has also been shown that NaHg alloy is a more strongly interacting binary alloy than NaPb.
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