The optical properties of thermally annealed TiO 2 samples depend on their preparation process, and the TiO 2 thin films usually exist in the form of anatase or rutile or the mixture of the two phases. The electronic structures and optical properties of anatase and rutile TiO 2 are calculated by means of First-principles generalized gradient approximation (GGA) +U approach. By Introducing the Coulomb interactions on 3d orbitals of Ti atom (U d ) and 2p orbitals of O atom (U p ), we can reproduce the experimental values of the band gap. The optical properties of anatase and rutile TiO 2 are obtained by means of GGA+U method, well agreeing with experimental results and other theoretical data. Further we present the comparison of the electronic structure, birefringence and anisotropy between the two phases of TiO 2 .

ZrW 2 O 8 exhibits isotropic negative thermal expansions over its entire temperature range of stability, yet so far its physical properties and mechanism have not been fully addressed.In this article, the electronic structure, elastic, thermal, optical and phonon properties of α-ZrW 2 O 8 are systematically investigated from first principles. The agreements between the generalized gradient approximation (GGA) calculation and experiments are found to be quite satisfactory. The calculation results can be useful in relevant material designs, e.g., when ZrW 2 O 8 is employed to adjust the thermal expansion coefficient of ceramic matrix composites. Ⅰ. IntroductionThe zirconium tungstate (ZrW 2 O 8 ) exhibits isotropic negative thermal expansion (relatively large, -9×10 -6 K -1 ) over its entire temperature range of stability (from close to absolute zero up to the decomposition temperature around 1500 K). The isotropy of the expansion is back by the fact that the cubic structure of ZrW 2 O 8 remains at these temperatures. 1,2 This feature makes ZrW 2 O 8 not only an important example to study this type of unusual lattice dynamics, but also potentially well suited for applications in composite materials in order to reduce the composites' overall thermal expansion to near zero. [3][4][5][6][7] In experiments, the phase transition, specific heat, thermal expansion of ZrW 2 O 8 have been studied by some groups [8][9][10][11] , especially for the temperature-and pressure-induced phase transitions, and the temperature-dependence of the thermal. 12-14 For example, it has long been noticed that α-ZrW 2 O 8 has a negative coefficient of thermal expansion, α= -9.07 ×10 -6 K within the temperature range 2-350 K 8 , and it undergoes a phase transition from P213 to Pa3 at 448 K 8 or 428K 12 ,

The dielectric function of the wide-gap optical material HfO 2 is investigated by the local density approximation (LDA) +U approach. We focus on the origin of the shoulder-like structure near the edge of the band gap in the imaginary part of the dielectric function, which has been observed on the thin films of monoclinic HfO 2 . A comparison study on the three polymorphs of hafnia shows that regardless of the underlying crystal structure, the existence of the shoulder is directly controlled by the value of the shortest length of Hf-O bonds. The proposition is further supported by the numerical simulations of isostatic pressing. A possible implication in highpressure measurements is suggested accordingly.

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