  The electronic orders appearing in condensed matter systems are originating
from the precise arrangement of atoms constituting the crystal as well as their
nature. This teneous relationship can lead to highly different phases in
condensed matter, and drive electronic phase transitions. Here, we show that a
very slight deformation of the crystal structure of TbTe$_3$ can have a
dramatic influence on the electronic order that is stabilized. In particular,
we show that the Charge Density Wave (CDW) developping along the $\vec{c}$ axis
in the pristine state, switches to an orientation along $\vec{a}$ when the
naturally orthorhombic system is turned into a tetragonal system. This is
achieved by performing true biaxial mechanical deformation of a TbTe$_3$ sample
from 250K to 375K, and by measuring both structural and electronic parameters
with x-ray diffraction and transport measurements. We show that this switching
transition is driven by the tetragonality parameter $a/c$, and that the
transition occurs for $a=c$, with a coexistence region for $0.9985< a/c <
1.002$. The CDW transition temperature $T_c$ is found to have a linear
dependence with $a/c$, with no saturation in the deformed states investigated
here, while the gap saturates out of the coexistence region. The linear
dependence of $T_c$ is accounted for within a tight-binding model. Our results
question the relationship between the gap and $T_c$ in RTe$_3$ systems. More
generally, our method of applying true biaxial deformation at cryogenic
temperatures can be applied to many systems displaying electronic phase
transitions, and opens a new route towards the study of coexisting or competing
electronic orders in condensed matter.
