摘要
三元层状碳化物Ti3AlC2是一种新型热力学稳定的层状纳米材料,结合了陶瓷和金属的优异性能,在高温结构材料、电接触材料等领域具有广阔的应用前景。
本文计算使用的是集成在美国Accelrys公司出品的Materials Studio 4.4软件平台上的CASTEP(Cambridge Series Total Energy Package)程序包。在计算中使用了范德比尔特(Vanderbilt)型超软赝势和广义梯度近似(GGA-PW91)。所有计算中平面波截断能均设置为380eV,布里渊区的积分采用(9x9x2)的Monkhorst-Pack格点面处理。
本文首先采用Broyden-Fletcher-Goldfarb-Shanno (BFGS)极小化方案对Ti3AlC2晶体结构进行几何优化得到基态平衡晶格参数,包括晶格常数和原子内坐标。几何优化收敛标准为两次迭代的能量变化小于5.0x10－6eV/atom,原子间作用力变化小于0.01 eV/A,最大位移小于5×10-4 A以及最大应力小于0.02GPa。优化结果与实验值非常吻合。本文还计算了电子结构和Mulliken布居以分析原子间的键接特性。
Ti3AlC2的弹性常数是通过计算不同应变模式下的应力分布来确定的。对六方晶系来说,至少需要两种应变模式{(εxx＝0,ε=0,εzz=1,γyz= 0,γｘｚ=0，γyz= 1)和(εxx=1,εYY=0,εzz=0,γyz=1,γxz=0,γxy=0)}才能确定所有的弹性常数。而且在每种模式下均施加5个不同的应变微扰,然后根据应力的计算结果来确定各弹性常数。一旦弹性常数确定,Ti3AlC2的的弹性模量以及其它力学参数即可计算得出。
考虑到Ti3AlC2在压力环境下的应用,给晶胞施加了0-50GPa的等方性静水压来考察外部压力对Ti3AlC2的晶格结构、电子结构和弹性性能的影响。首先通过计算得到在各个压力下的具有局部最小自由焓的几何结构,将Ti3AlC2不受外部压力情况下的晶体结构称之为平衡晶体结构。以几何优化后的晶体结构作为计算模型,本文还计算了Ti3AlC2在0-50GPa静水压下的弹性常数和弹性模量值,并且讨论了压力对晶体弹性的各向异性,弹性常数以及弹性模量的影响。
The ternary layered carbide Ti3AlC2 is a new Thermodynamically stable nanolaminates. The Ti3AlC2 combines unusual properties of both ceramics and metals, having broad application prospects in the fields of high temperature material and electric contacting material.
The CASTEP code is a plane-wave pseudopotential total energy calculation method that is based on density functional theory. It was used in the present calculation, wherein the Vanderbilt-type ultrasoft pseudopotential and generalized gradient approximation (GGA-PW91) were employed. The plane-wave basis set cutoff was 380 eV for all calculations. The special points sampling integration over the Brillouin zone was employed by using the Monkhorst-Pack method with a 9×9×2 special k-points mesh.
Lattice parameters, including lattice constants and internal atomic coordinates, were modified independently to minimize the enthalpy and interatomic forces. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization scheme was used in geometry optimization. The tolerances for geometry optimization are difference on total energy within 5x10-6 eV/atom, maximum ionic Hellmann-Feynman force within 0.01 eV/A, maximum ionic displacement within 5x10-4 A and maximum stress within 0.02 GPa. The calculated results are in good agreement with experimental measurements and other theoriral results. To better understand the nature of the interatomic bonding, the electronic structure and Mulliken population was examined.
The elastic coefficients were determined by applying a set of given homogeneous deformations with a finite value and calculating the resulting stress with respect to optimizing the internal degrees of freedoms. Two strain patterns, one with nonzero s33 components and the other with a nonzeroε11 andε23, generated stresses related to all five independent elastic coefficients for a unit cell with a hexagonal symmetry. We determined the elastic stiffness from a linear fit of the calculated stress as a function of strain. Other mechanical parameters, such as the bulk modulus(GPa), Young's moduli(GPa), and Poisson's ratio(GPa) were calculated from the compliance tensor. The shear modulus(GPa) was calculated according to the Voigt approximation.
The external pressure was imposed upon the simulated unit cell as isotropic hydrostatic pressure. Calculations were performed for various pressures between 0 and 50 GPa, and the atomic configuration at zero pressure was referred to as the equilibrium state in this paper. The lattice parameters and internal atomic positions were fully optimized throughout the simulations until local minimizations of the total energy were realized. The elastic coefficients and modulis at various pressures were obtained to understand the role how external pressure influence the elastic properties of TiAlC2.
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