Fig. 3: TEM characterization results of (Dy_0.25Ho_0.25Yb_0.25Lu_0.25)₂Si₂O₇ and (La_x1Ce_x2Yb_x3Lu_x4)₂Si₂O₇ bulk samples.

a, e The bright-field images of phase 1 and phase 2 in (Dy_0.25Ho_0.25Yb_0.25Lu_0.25)₂Si₂O₇ sample. b, f The Scanning transmission electron microscopic high-angle annular dark-field (HAADF-STEM) images of phase 1 and phase 2 in (Dy_0.25Ho_0.25Yb_0.25Lu_0.25)₂Si₂O₇. c, g The Fast Fourier transform (FFT) of the HAADF-STEM images of (Dy_0.25Ho_0.25Yb_0.25Lu_0.25)₂Si₂O₇ in b and f, taken in the [\(\bar{1}\)12] zone axis and [100] zone axis, respectively. d, h The corresponding atomic-resolution EDS elemental maps for Dy, Ho, Yb and Lu of β-(Dy_0.25Ho_0.25Yb_0.25Lu_0.25)₂Si₂O₇ and γ-(Dy_0.25Ho_0.25Yb_0.25Lu_0.25)₂Si₂O₇. i, m The bright-field images of phase 1 and phase 2 in (La_x1Ce_x2Yb_x3Lu_x4)₂Si₂O₇ sample. j, n The HAADF-STEM images of phase 1 and phase 2 in (La_x1Ce_x2Yb_x3Lu_x4)₂Si₂O₇. k, o The Fast Fourier transform (FFT) of the HAADF-STEM images of (La_x1Ce_x2Yb_x3Lu_x4)₂Si₂O₇ in j, n, taken in the [\(\bar{1}\bar{1}\)2] zone axis and [100] zone axis, respectively. l, p The corresponding atomic-resolution EDS elemental maps for La, Ce, Yb and Lu of β-(La_x1Ce_x2Yb_x3Lu_x4)₂Si₂O₇ and G-(La_x1Ce_x2Yb_x3Lu_x4)₂Si₂O₇. The blue circles in a, e, i, and m locate the observed grains in (Dy_0.25Ho_0.25Yb_0.25Lu_0.25)₂Si₂O₇ and (La_x1Ce_x2Yb_x3Lu_x4)₂Si₂O₇ samples that correspond to different phases (marked as “Phase 1” or “Phase 2”). The cyan circles and numbers in c, g, k, and o denote the Miller indices of corresponding patterns.