  The (H,T)-phase diagram of the multiferroic perovskite TbMnO$_3$ was studied
by high-resolution thermal expansion $\alpha(T)$ and magnetostriction $\Delta
L(H)/L$ measurements. Below $T_{N}\simeq 42$ K, TbMnO$_3$ shows
antiferromagnetic order, which changes at $T_{FE}\simeq 28$ K where
simultaneously a spontaneous polarization $P||c$ develops. Sufficiently high
magnetic fields applied along $a$ or $b$ induce a polarization flop to $P||a$.
We find that all of these transitions are strongly coupled to the lattice
parameters. Thus, our data allow for a precise determination of the phase
boundaries and also yield information about their uniaxial pressure
dependencies. The strongly hysteretic phase boundary to the ferroelectric phase
with $P||a$ is derived in detail. Contrary to previous reports, we find that
even in high magnetic fields there are no direct transitions from this phase to
the paraelectric phase. We also determine the various phase boundaries in the
low-temperature region related to complex reordering transitions of the Tb
moments.
