Fig. 2: Negative-thermal expansion in Sc₂(MoO₄)₃:20%Yb/1%Er.

a, b Two-dimensional topographical mapping of temperature-dependent in situ synchrotron X-ray diffraction patterns of (020), (200), and (002) peaks with the temperature from 298 K to 673 K. c Temperature-dependent unit cell parameters a, b, and c of the Sc₂(MoO₄)₃:20%Yb/1%Er phosphors derived from in situ SXRD patterns. d Temperature-dependent proximate distances of RE-RE (RE=Sc/Yb/Er) along different axes derived from the unit cell structure. e Rigid unit mode model for Sc₂Mo₃O₁₂:20%Yb³⁺/1%Er³⁺ extracted from the unit cell structure. f Temperature-dependent ratio \(\delta D\) of RE-Mo distances marked in the model (\(\delta D=\frac{{D}_{T}-{D}_{420}}{{D}_{420}}\times 100 \% ,\) D_T and D₄₂₀ stand for RE-Mo distances of the given temperature and 420 K, respectively). g Temperature-dependent ratio \(\delta {{{{{\rm{\theta }}}}}}\) of RE-Mo-RE angles marked in the model (\(\delta \theta =\frac{{\theta }_{T}-{\theta }_{420}}{{\theta }_{420}}\times 100 \%\), θ_T and θ₄₂₀ stand for RE-Mo-RE angles of the given temperature and 420 K, respectively). h Temperature-dependent in situ Raman spectra with the temperature from 298 to 773 K. * stands for the characteristic Raman peak of the hydrated orthorhombic structure. i and j. Raman shifts at different temperatures. ν₁, ν₂, ν₃, and ν₄ stand for symmetric stretching, symmetric bending, asymmetric stretching, and asymmetric bending mode of MoO₄ tetrahedra, respectively.