  PtBi$_2$ is a polymorphic system with interesting electronic properties. Here
we report optimized crystal growth and structural characterization of
pyrite-type and trigonal modification of PtBi$_2$. Selected area electron
diffraction, X-ray powder diffraction and further Rietveld refinement confirms
that trigonal PtBi$_2$ crystallizes in non-centrosymmetric $P31m$ space group,
pyrite-type PtBi$_2$ in $Pa\bar{3}$ space group. Series of
Pt$_{1-x}$Rh$_x$Bi$_2$ samples was obtained for $x=0, 0.03, 0.35$ in the
trigonal PtBi$_2$ structure. These Pt$_{1-x}$Rh$_x$Bi$_2$ compounds become
superconducting where critical temperature increases from $T_c=600$ mK for
$x=0$ up to $T_c=2.7$ K for $x=0.35$. Furthermore we calculate the electronic
band structure, using the structure parameters obtained. The calculated density
of states (DOS) shows a minimum for the stochiometric compound at the Fermi
level. These findings warrant further research by broader array of experimental
techniques, as well as the effect of the substitution on the non-trivial band
structure.

Materials Science