  The halide perovskite CsPbBr$_3$ belongs to the Cs-Pb-Br material system,
which features two additional thermodynamically stable ternary phases,
Cs$_4$PbBr$_6$ and CsPb$_2$Br$_5$. The coexistence of these phases and their
reportedly similar photoluminescence have resulted in a debate on the nature of
the emission in these systems. Here, we combine optical and microscopic
characterization with an effective mass, correlated electron-hole model of
excitons in confined systems, to investigate the emission properties of the
ternary phases in the Cs-Pb-Br system. We find that all Cs-Pb-Br phases exhibit
green emission and the non-perovskite phases exhibit photoluminescence quantum
yields orders of magnitude larger than CsPbBr$_3$. In particular, we measure
blue- and red-shifted emission for the Cs- and Pb-rich phases, respectively,
stemming from embedded CsPbBr$_3$ nanocrystals. Our model reveals that the
difference in emission shift is caused by the combined effects of nanocrystal
size and different band mismatch. Furthermore, we demonstrate the importance of
including the dielectric mismatch in the calculation of the emission energy for
Cs-Pb-Br composites. Our results explain the reportedly limited blue shift in
CsPbBr$_3$@Cs$_4$PbBr$_6$ composites and rationalize some of its differences
with CsPb$_2$Br$_5$.
