# Hig entropy alloys

Introduction:

Alloys can be defined as a mixture of two or more elements containing one or more elements containing one metal at the least. From bronze age , alloys have been developed based on one principal element. Later metal matrix composites and inter metallic compounds gained attention. Development in technology and innovation lead to the idea of multicomponent system. These systems consists of multiple principal elements. This was attained by alloying elements with equimolar or near-equimolar ratios. The concept of using multiple principal elements was initially discouraged for it was believed , by conventional metallurgical knowledge, there will be several complex phases and inter-metallic compounds which result in difficulty in micro structural analysis and deterioration of mechanical properties. However , these beliefs were disproved by recent discoveries and synthesis of high entropy alloys.

High entropy alloys:

As the name indicates, these alloys possess high entropy (>1.6R J/K-mol). This large entropy is rendered by entropy of mixing due to equimolar ratio of elements in the alloy. The ratio or percentage of elements in the alloy can vary from 5 at% to 35 at%. The estimated value of the entropy can be calculated by assuming n elements in exactly equimolar ratio by Boltzmann's hypothesis:

When we substitute the values of n=3,5,6,9,13 we get the values of mixing entropy ΔSmix = 1.1R , 1.61R ,1.79R, 2.20R, 2.57R respectively. By Richard's rule , entropy changes in most of the metals are empirically equal to R at their melting points. Considering this ΔSmix of the 5 element alloy is far greater than R, hence the name high entropy alloys has been given(Since, high entropy alloys usually has at least 5 elements).

Stability:

High entropy alloys derive their strength by formation of random solid solution with a simple structure. But solid solution is not always formed. Sometimes the alloy can form intermetallic , bulk metallic glass and segregation may also take place.

Bulk metallic glass(BMG) form when there is confusion in system to form an ordered structure. This corresponds to mixing entropy which is pretty high in high entropy alloys. So the formation of BMG depends on ΔHmix and atomic size difference δ.

Intermetallic compounds form when ΔHmix is highly negative which helps in the formation of ordered compounds , in turn reducing the ΔSmix .

Segregation of phases may occur when the ΔHmix is so high that the ΔGmix attains a maxima in G-x graph.

To quantitatively analyze ranges of the above it is assumed that ΔG at a certain composition is proportional to ΔGmix in liquid state.

Consider the parameters mixing enthalpy ( ΔHmix ),mixing entropy of the alloy( ΔSmix ), atomic size difference(δ) .

where

where

Ωij = ΔHi-jmix

between the ith and jth elements, ΔHi-j

and

mix

is the regular solution interaction parameter

is the enthalpy of mixing of binary liquid alloys.

rm =

ri & ci are the atomic size and percentage respectively.

ci is the atomic percentage of the ith element.

Stability of solid solution:

A certain parameter Ω is defined as

The melting temperature of n-elements alloy, Tm, is calculated using the rule of mixtures:

(Tm)i is the melting point of ith component of the alloy.

It was observed that for Ω > 1 and δ

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