镁铝尖晶石声子色散关系及热力学性质的第一性原理研究

Phonon dispersion relations and thermodynamic properties of magnesium aluminium spinel:A first principle study

镁铝尖晶石是地幔和类地行星中常见的氧化物类矿物.高温高压实验表明尖晶石的高压相可以存在于从地壳到下地幔广泛的深度范围内.作为含铝矿物的端元组分,尖晶石可能是地幔中铝元素的主要富集矿物.尖晶石的高压相还可能是俯冲大洋板块的主要组成物质.获得尖晶石的热力学性质为计算尖晶石的相变奠定了基础,为通过地震波解释地幔结构提供了理论依据.本文利用冻结声子法计算了镁铝尖晶石的声子色散关系和常压下的各种热力学性质.首先,用基于密度泛函理论的从头计算方法计算绝对零度下平衡体积的晶体结构.然后,通过构建超晶胞并对超晶胞内的原子进行微小的位移获得原子力,利用原子力来构造力常数矩阵,进一步构造动力学矩阵,将温度扩展为有限温度,计算出尖晶石的声子色散关系.最后,根据准谐近似理论得到常压下的各种热力学性质.第一布里渊区中心的声子振动频率与红外、拉曼光谱的实验数据相吻合.各种热力学性质,标准熵、等压热容和热膨胀系数与实验值相吻合.

The phonon dispersion relations of magnesium aluminium spinel MgAl2O4 are calculated by using frozen phonon method. MgAl2O4 is the dominant component of the spinel phase minerals on the Earth. It is also an important rock-forming mineral, which constitutes peridotites originating from the uppermost part of the Earth＇s mantle. As MgAl2O4 is an end composition of the alumina-rich mineral, its high-pressure polymorphs may be the most dominant host of aluminium element in the mantle. It is very important to understand the stability and phase transitions of MgAl2O4. The calculation of the vibrational frequencies of the crystalline lattice is fundamental to the understanding of phase stability and phase transitions and of the thermodynamics of crystalline materials. The methods for first principle calculations of phonon frequencies fall into two broad classes： the linear response approach and the frozen phonon approach. Since the frozen phonon approach is easy to be implemented into any state-of-the-art electron structure calculation software, we have chosen this method to investigate the thermodynamic properties of MgAl2O4. The force constants are calculated via a self-consistent supercell approach in terms of the Hellmann-Feynman forces induced by the small displacement of a single atom in the supercell. From the forces calculated via the Hellmann-Feynman theorem, certain elements of the force constant matrix can be evaluated. By displacing entire planes of atoms, interplanar force constants may he calculated. This force constants approach is based on periodically repeated supercell. The amplitude of atomic displacements is limited to 0.02A. One limitation of this method is that the LO-TO splitting of polar materials can not be calculated directly. But it is proved that this limitation has little effect on thermodynamic properties calculation. The calculated phonon dispersion spectrum is almost the same as the previous theoretical study. The phonon frequencies at the center of Brillion zone are in very good agreement with Raman and Infrared data. Within the quasiharmonic approximation, some thermodynamic properties of magnesium aluminium spinel at ambient pressure, such as the specific heat capacity at constant pressure, thermal expansion coefficient and standard entropy, are calculated which all agree well with experimental results.