  Gadolinium molybdate is a classical example of an improper ferroelectric and
ferroelastic material. It is established that the spontaneous polarization
arises as a secondary effect, induced by a structural instability in the
paraelectric phase, which leads to a unit cell doubling and the formation of a
polar axis. However, previous X-ray diffraction studies on gadolinium molybdate
have been restricted by the limited ability to include the entire 2{\theta}
range in the analysis, and thus, at atomic scale, much remains to be explored.
By applying temperature dependent X-ray diffraction, we observe the transition
from the paraelectric tetragonal phase to the orthorhombic ferroelectric phase.
The ferroelastic strain is calculated based on the thermal evolution of the
lattice parameters and Rietveld refinement of the temperature dependent data
reveals that the displacement of different cations follows different critical
behavior, providing new insight into the structural changes that drive the
improper ferroelectricity in gadolinium molybdate.
