International Journal of Scientific & Engineering Research, Volume 5, Issue 9, September-2014 1105

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NAME OF THE SECTION: PHYSICAL SCIENCE
TITLE OF THE PAPER
“STRUCTURAL DEPENDENCE OF COMPOUND FORMING LIQUID BINARY ALLOYS”
AUTHOR’S NAMES AND AFFILIATION

Bihar,India
4. Mr. B.N. Mishra, Research Scholar.
5. KEYWORDS: Intermetallic compound, chemical complexes, pseudomolecules.
ABSTRACT:
Most of experimental evidences clearly demonstrates that the anomalous behaviour for a large number of liquid alloys occur at or near the stoichiometric compositions where stable indermetallic compound exist in the solid phase. It is therefore, natural to propose
that the chemical complexes, associations clusters or pseudomolecules exist in the liquid

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phase near the melting temperature. An appropriate estimation of the stoichiometry of
complexes in the liquid alloy is usually made by an analysis of anomalous composition dependence of the physical properties and also from the phase diagram. The complex forming model successfully explains the thermodynamic properties of number of compound forming alloys.
INTRODUCTIONS:
The thermodynamic properties like free energy of mixing GM, Heat of mixing HM and many other electronic properties are symmetric about the equiatomic composition of many liquid binary alloys. The liquidus lines for these systems are complicated and are usually S- shaped. These alloys have the characteristics that in the solid phase they form compound at one or more stoichiometric compositions.
COMPLEX FORMING MODEL:
`The asymmetry of the properties of mixing for liquid binary alloys could be explained on the assumption of chemical complexes.

α A + β B = Aα B β

Where α and β are small integers, A and B are the constituent species.

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Thus a binary alloy in the liquid phase can be considered as a ternary mixture of left over
A, B atoms and the chemical complexes Aα B β all in chemical equilibrium.
Let a binary liquid alloy contains in all c gm atoms of A and (1-c) gm atoms of B. On considering the existence of only on type of chemical complexes. the binary alloys can be assumed to be consisted of n1 gm atom of A and n2 gm of atom of B and n3 gm atoms of the complexes Aα B β .
N1 = c - α n3
N2 = 1 - c - β n3
And n = n1 + n2 + n3
= 1 – (α + β -1) n3
Let Gi denotes the chemical potentials per atom of the species in its pure stats, then the free energy of mixing GM of the binary liquid alloy may be expressed as
GM = G - cGi – (1-c) G2
= - n3 g + G’
Where G is the total Gibb’s free energy of the mixture and g= α G1 + β G2 – G3

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The simplest expression for G’ can be obtained assuming that ternary mixture forms an
ideal solution so G’ may be expressed as

3

G’ = G - ∑ ni Gi

i =1

Using Euler’s theorem for identify between an extensive variables

3

G’ = RT ∑ ni In ( )

i =1 n

Therefore , the expression for the free energy of mixing

3

GM = - n3 G + RT ∑ ni

In ( ni ) +

∑ ∑ ni n j

wij

i =1

n i < j

In case of conformal solution model Wij → 0 and n3 → 0 , then

GM = RT [clnc +(1-c) ln(1-c)]
The free energy of mixing has been calculated using above expression. RESULTS AND DISCUSSION:
Free energy of mixing GM /RT, as a function of concentration for a fixed value of equilibrium constant K= 4.54 × 10-5 and considering interaction energy Wij=0 and for
different values of α and β are marked.

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For each of computed numerical values of k, the equilibrium constant, the values of
GM/RT computed and found that for a given set of α and β , the minimum GM /RT occurs ot the same concentration Further its observe that a smaller K corresponds to minimum in GM/RT the slop of GM -c curves on either sides of minimum depends strongly on the values of K. The slop in more steep for lower values of K but become flatten as K increases.
EFFECT OF Wij ON FREE ENERGY OF MIXING GM
In order to see the impact of Wij, interaction energies of constituent species on free energy of mixing, first of all positive values of Wij on free energy of mixing of four different sets [Wij=0; W12 /RT = 10.0; W13 /RT = 0.0; W23/RT = 10, W12/RT = W23/RT
=0 and W23/RT = 10.0, W12/RT = W13/RT = 0] have be taken and computed.
It has been observed that the position of minimum in GM/RT not only depends upon the values of α and β but also depends on the values of Wij. The values of Wij as given above in set (a) and (b) almost yield identical GM /RT. The sets (c) also yields the same values of GM/RT upto c < 0.5 but differs considerably for c ≥ 0.5 The fourth set of Wij gives much smaller values of GM /RT in the lower concentration region but becomes identical for light concentration.
The effect of negative values of Wij on GM is more appearance.

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REFRENCE

Anit K. Giri And G.B. Mitra, 1985 Indian J. Phys. 59A , 318

A.K. Giri And G.B. Mitra 1986 phys, stat, sol. (b) 134 K11.

Bhatia, A.B. and Singh, R.N. 1980 Phys. Lett. 78 A 460

Bhatia, A.B. and Singh, R.N. 1982 Phys. Ceem. Liq. 11 285

Francisco J.Solis and Monica Olvera 2000 Physical Review letter ;84-3350

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