  Ge_(1-x)Sn_x alloys have proved difficult to form at large x, contrary to
what happens with other group IV semiconductor combinations. However, at low x
they are typical examples of well-behaved substitutional compounds, which is
desirable for harnessing the electronic properties of narrow band
semiconductors. In this paper, we propose the appearance of another kind of
single-site defect ($\beta-Sn$), consisting of a single Sn atom in the center
of a Ge divacancy, that may account for these facts. Accordingly, we examine
the electronic and structural properties of these alloys by performing
extensive numerical ab-initio calculations around local defects. The results
show that the environment of the $\beta$ defect relaxes towards a cubic
octahedral configuration, facilitating the nucleation of metallic white tin and
its segregation, as found in amorphous samples. Using the information stemming
from these local defect calculations, we built a simple statistical model to
investigate at which concentration these $\beta$ defects can be formed in
thermal equilibrium. These results agree remarkably well with experimental
findings, concerning the critical concentration above which the homogeneous
alloys cannot be formed at room temperature. Our model also predicts the
observed fact that at lower temperature the critical concentration increases.
We also performed single site effective-field calculations of the electronic
structure, which further support our hypothesis.
