68
mixed in an equimolar ratio is described by the enthalpy of mixing as
HABCD
mix = EABCD
tot − EAB
tot (6.1)
tot − ECD
where Ei
tot is the total energy of the compound ‘i’. Table 6.2 shows the heat of
formation of the compounds in the wurtzite structure having the bandgap in
the range of 1.0-3.5 eV, H is the heat of formation calculated in the present
work, HOQMD is the heat of formation as given in the OQMD (The Open
Quantum Materials Database) database 73 for the structure which has the
minimum energy at 1:1 stochiometry and Hhull is the relative energy of the
compound in the current work with respect to the convex hull as given in the
OQMD database. Since the enthalpies in OQMD database are based on DFT
reference energies whereas we use corrected reference energies as proposed by
Stevanovic et al. 25, therefore the difference 0.15 eV/atom or less in ours
and OQMD calculations will lie within in the error bar due to the different
methods used for the calculation of the reference energies. Compounds like
AlI, AlBr which are significantly above the convex hull and have no structure
which is stable at 1:1 stochiometry and also expected to be unstable based
on the valence rule can be ruled out as they may not be possibly synthesized
under normal/moderate conditions. On the other hand, compounds like GeO,
AgF and PbO have different structures other than the wurtzite which are
stable and lie below the convex hull. Even though energy of the wurtzite
structure of these compounds lies above the convex hull by 0.35 eV/atom
(Table 6.1), its likely that they can be stabilized in the wurtzite form since
they exist in structures which are stable at the same stoichiometry. So, their
synthesis/stabilization might be possible under moderate conditions.
In order to study the trends we made a crude approximation of the solid
solution with a unit cell of four atoms due large computational time required
for a larger unit cell. Based on the previous works, we believe the that the
approximations made will not change the results drastically 127.
The similarity between the compounds forming the mixture in terms of the
deviation of the bandgap of the mixture from the average of the bandgaps of
constituent compounds has been assessed by the so-called dendrogram plot.
Dendrogram is a tree diagram used in the generating hierarchical structures
among the elements representing the data 120. In Figure 6.5, we show the
dendrogram plot with euclidean metric of the difference of the average bandgap
of the constituent compounds and the calculated bandgap of the alloy. The
clustering in a dendrogram is based on the distance measure (dAB) of two