白钨矿型ZrGeO $_4$和HfGeO $_4$ X射线荧光体主体的高压结构稳定性和光学性质
High Pressure Structural Stability, and Optical Properties of Scheelite type ZrGeO$_4$ and HfGeO$_4$ X-ray Phosphor Hosts
摘要：
对白钨矿型MGeO $_4$（M = Hf和Zr）化合物进行了\emph{Ab-initio}计算，该化合物在X射线成像等方面有着广泛的应用。通过密度泛函理论计算，研究了这些化合物的高压结构稳定性、弹性常数、电子结构和光学性质。采用两种不同的密度泛函方法，即平面波赝势方法（PW-PP）和全势线性缀加平面波方法（FP-LAPW）。基态结构和振动性质的计算和发现与实验数据符合得很好。Zr和Hf锗酸盐的压缩性被发现是各向异性的，因为a-轴是由于Ge-O键沿a-轴的存在下，这是进一步证实了从以下的C $_{11}$ $>$ C $_{33}$的弹性常数的顺序的c-轴上的可压缩性较低。用最近发展的Tran Blaha修正的Becke Johnson势计算了化合物的电子结构。电子结构的计算表明，化合物是绝缘体，ZrGeO $_4$和HfGeO $_4$的禁带宽度分别为5.39 eV和6.25 eV.这些化合物的光学各向异性揭示从计算的光学性质，如复介电函数，折射率，和吸收系数。此外，它被观察到，Ti掺杂的ZrGeO $_4$和HfGeO $_4$原来是一个很好的荧光体，因为原始的化合物具有大于可见光范围的能隙后，Ti掺杂的带隙减少，结果发射光谱发生在可见光区，并在本研究中得到很好的解释。
英文摘要：
\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 in x-ray imaging. We have studied the high pressure structural stability, elastic constants, electronic structure and optical properties of these compounds through density functional theory calculations. Two different density functional approaches namely plane wave pseudopotential method (PW-PP) and full potential linearized augmented plane wave method (FP-LAPW) were used for the present study. The ground state structural and vibrational properties are calculated and found to be in good agreement with experimental data. The compressibility of Zr and Hf germanates is found to be anisotropic as the a-axis is less compressible over c-axis due to the presence of Ge-O bonds along a-axis which is further confirmed from the ordering of the elastic constants that follows C$_{11}$ $>$ C$_{33}$. The electronic structure of the compounds has been calculated through recently developed Tran Blaha-modified Becke Johnson potential. The calculated electronic structure shows that the compounds are 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 the computed optical properties such as complex dielectric function, refractive index, and absorption coefficient. In addition, it is observed that Ti doped ZrGeO$_4$ and HfGeO$_4$ turns out to be a good phosphor as the pristine compounds have the energy gap greater than the visible range upon Ti doping bandgap reduces as a result emission spectra occurs in the visible region and is well explained in the present study.
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