  We report the high-pressure synthesis of novel superconductor MgB$_2$ and
some related compounds. The superconducting transition temperature of our
samples of MgB$_2$ is equal to 36.6 K. The MgB$_2$ lattice parameters
determined via X-ray diffraction are in excellent agreement with results of our
ab initio calculations. The time-differential perturbed angular correlation
(TDPAC) experiments demonstrate a small increase in quadrupole frequency of
$^111$Cd probe with decreasing temperature from 293 to 4.2 K. The electric
field gradient (EFG) at the B site calculated from first principles is in fair
agreement with EFG obtained from $^11$B NMR spectra of MgB$_2$ reported in the
literature. It is also very close to EFG found in our $^111$Cd TDPAC
measurements, which suggests that the $^111$Cd probe substitutes for boron in
the MgB$_2$ lattice.
