InBi is studied by energy-dispersive diffraction with synchrotron radi
ation in a diamond-anvil cell under pressure up to 75 Cpa. Three phase
transitions are observed from its initial tetragonal structure tP4 wi
th c/a approximate to 0.95 to another tP4 structure with c/a approxima
te to 0.65 typical for the P-Np structure, than td a disordered tetrag
onal body-centered structure tI2, and finally some hints are obtained
for a transition to a cubic body-centered structure cI2. All these tra
nsformations are reversible with large hysteresis. InBi(tI2), phase II
I, shows initially a steep increase in cia from 0.91 to 0.94, in the p
ressure range from 20 to 30 GPa, and a nearly constant value of about
0.96 above 55 Cpa. Hints for the possible stability of a new phase IV
are noticed in the present experiments on decompression from 75 GPa as
admixture of new Lines to phase III giving strong indications for a f
irst-order phase transition with large hysteresis. The origin of the t
etragonal distortion and the transformation to a cubic phase are discu
ssed from the point of view of nesting the Fermi sphere in the Brillou
in zone.