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\emph{Ab-initio} calculations were performed on the scheelite type MGeO$_4$(M = Hf, and Zr) compounds which find wide range of applications such as inx-ray imaging. We have studied the high pressure structural stability, elasticconstants, electronic structure and optical properties of these compoundsthrough density functional theory calculations. Two different densityfunctional approaches namely plane wave pseudopotential method (PW-PP) and fullpotential linearized augmented plane wave method (FP-LAPW) were used for thepresent study. The ground state structural and vibrational properties arecalculated and found to be in good agreement with experimental data. Thecompressibility of Zr and Hf germanates is found to be anisotropic as thea-axis is less compressible over c-axis due to the presence of Ge-O bonds alonga-axis which is further confirmed from the ordering of the elastic constantsthat follows C$_{11}$ $>$ C$_{33}$. The electronic structure of the compoundshas been calculated through recently developed Tran Blaha-modified BeckeJohnson potential. The calculated electronic structure shows that the compoundsare insulators with a gap of 5.39 eV for ZrGeO$_4$ and 6.25 eV for HfGeO$_4$respectively. Optical anisotropy of these compounds are revealed from thecomputed optical properties such as complex dielectric function, refractiveindex, and absorption coefficient. In addition, it is observed that Ti dopedZrGeO$_4$ and HfGeO$_4$ turns out to be a good phosphor as the pristinecompounds have the energy gap greater than the visible range upon Ti dopingbandgap reduces as a result emission spectra occurs in the visible region andis well explained in the present study.

High Pressure Structural Stability, and Optical Properties of Scheelite type ZrGeO$_4$ and HfGeO$_4$ X-ray Phosphor Hosts