Observation of cation-specific critical behavior at the improper ferroelectric phase transition in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Gd</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>MoO</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>

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