66
121. In our work we calculate the stability of compounds with respect to the
standard reference states only. Since our interest lies in comparing the trends
in thermodynamic and electronic properties of the compounds in different
crystal structures with 1:1 stoichimetry, we do not consider the compounds
with the stoichiometry different from 1:1. In the calculations we ignore few
metals leading to magnetic structures since a reliable approach to calculate
the bandgap of magnetic semiconductors with the GLLB-SC functional has
not been developed yet.
Figure 6.2 shows the heatmaps of the standard heat of formation of all the
compounds in which the elements are arranged as per the chemical scale
proposed by Pettifor 118. As can be seen from the figure that the heat of formation
in all four crystal structures follow the similar pattern which indicates
that if the compound is stable with respect to the standard states in one crystal
structure it will be stable in the other crystal structure as well. But negative
formation energy does not guarantees that the structure can be stabilized in
that phase which is inhibited by the existence of other competing phases in
the ambient environment. But the control over the ambient condition for the
growth can be achieved by for example temperature, pressure, surfactants and
doping 122, 123, 124. Pressure as one of the control mechanism in the growth
process gives a tool to stabilize structure with different volumes. For example,
if the most stable structure has a lower volume (e.g. rocksalt or NiAs) then
applying tensile stress may favor the higher volume phase (e.g. wurtzite or
zincblende) whereas a lower volume phase will be favored under compressive
stress if the most stable structure has a higher volume. The above process can
be realized in experiments 116, 125 with the growth on a substrate with different
lattice mismatch thus providing a way to apply the compressive and tensile
stress. Thus, above strategies to manipulate crystal structures suggest that
the compounds can possibily be synthesized and stabilized in different crystal
structures with different volumes. Therefore, in the current work we choose
crystal structures spanning a wide range of volumes with the zincblende and
wurzite having higher volumes due to low coordination number as opposed to
the rocksalt and NiAs structures which have larger coordination number thus
lower volumes.
In addition to the standard heat of formation as shown in Figure 6.2 one
might also be interested in region where a particular crystal structure has the
lowest enthalpy of formation as compared to other crystal structures. Figure
6.3 shows the minimum energy crystal structure for different compounds.
As can be inferred from the figure, there are very few isolated regions for a
given crystal structure. Hence, compounds when arranged in Pettifor maps
form clusters having the same most stable crystal structure. Therefore, we