KEYWORDS Refractory high entropy alloys; VNbTaTiW; density functional theory;
stacking fault energy; intrinsic ductility; alloy development; brittleness
and ductility; enthalpy; lattice distortion; rule-of-mixtures.

A common strategy to ductilize refractory metals and alloys is to decrease their valence
electron concentration (VEC). Many of the earlier studies which used the VEC strategy to
ductilize refractory alloys ignored the thermodynamic stability of the resultant alloy. Also, Re
addition to ductilize W remains an exception to the low VEC strategy. The present work gives a
fundamental explanation of the role of both high- and low-valency elements and enthalpy of
formation (ΔEf ) in ductilizing refractory metals and alloys.
We first developed a rule-of-mixture (ROM) based methodology to quickly capture the global
trends in refractory high entropy alloys (RHEA). Using the developed method, 252 RHEA are
studied on their melting point (Tm), density (ρ), Young’s modulus (E), % atomic size difference
(δ), VEC, and specific heat at constant pressure and at 127« K (Cp). We found that Ti, Zr, Hf
are ductilizing the alloys and making them light; whereas Cr, Mo and W, are reducing the alloys’
ductility and making them heavy. The ROM technique can act as a useful tool to study a large
number of alloy systems, without requiring heavy computational resources.
In subsequent chapters, we used first-principles density functional theory (DFT) simulations
to assess the intrinsic ductility parameter (D) which is the ratio of surface energy (γs) and
unstable stacking fault energy (γus f e), ΔEf

, root-mean-squared lattice distortion (RLD), and the
barrier to slip plane glide (∂γ/∂x) of 25 binary, six ternary, three quaternary, and two quinary
equiatomic refractory alloys. The errors associated with the γus f e due to the change in the
bonding environment are quantified. We show that the ΔEf strongly influences the change in
γus f e of concentrated refractory alloys as compared to their composition averaged value. This
work unravels the role of ΔEf

in increasing the ductility of equiatomic binary refractory alloys
apart from dictating their thermodynamic stability. Based on the observations from the binary
alloys, a methodology has been developed to down-select alloy systems which can prevent the
composition explosion as we move from binary to higher-order systems.
We found that the large RLD is not exclusive to RHEA alone, and it can occur in binary
alloys as well. The RLD may not be sufficient enough to influence the dislocation core, but
ΔEf variation along the dislocation line (due to local chemistry variation) can lead to a wavy
dislocation. A sufficiently large positive ΔEf

is a primary requirement for intrinsic ductility of
RHEA. Therefore, the large ΔEf should be compensated by a sufficiently large entropy (ΔS) for
the alloy to remain in single phase.