  We investigate the phase diagram of the heterostructural solid solution
(InxGa1-x)2O3 both computationally, by combining cluster expansion and density
functional theory, and experimentally, by means of TEM measurements of pulsed
laser deposited (PLD) heteroepitaxial thin films. The shapes of the Gibbs free
energy curves for the monoclinic, hexagonal and cubic bixbyite alloy as a
function of composition can be explained in terms of the preferred cation
coordination environments of indium and gallium. We show by atomically resolved
STEM that the strong preference of indium for six-fold coordination results in
ordered monoclinic and hexagonal lattices. This ordering impacts the
configurational entropy in the solid solution and thereby the (InxGa1-x)2O3
phase diagram. The resulting phase diagram is characterized by very limited
solubilities of gallium and indium in the monoclinic, hexagonal and cubic
ground state phases respectively but exhibits wide metastable ranges at
realistic growth temperatures. On the indium rich side of the phase diagram a
wide miscibility gap is found, which results in phase separated layers. The
experimentally observed indium solubilities in the PLD samples are in the range
of x=0.45 and x=0.55 for monoclinic and hexagonal single-phase films, while for
phase separated films we find x=0.5 for the monoclinic phase, x=0.65-0.7 for
the hexagonal phase and x>0.9 for the cubic phase. These values are consistent
with the computed metastable ranges for each phase.
