有限温度和压强对BCC金属弹性性质影响的第一性原理研究

发布时间：2018-01-11 04:28

本文关键词：有限温度和压强对BCC金属弹性性质影响的第一性原理研究　出处：《太原理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：固体的弹性性质是固体本身的物理属性,而弹性的大小则是由弹性常数来表示的。近年来,BCC(Body-Centered-Cubic)金属材料Ta、Fe、W、Mo等被应用于各行各业中,并在不同温度压强下工作,因此研究材料在一定的温度和压强下的弹性性质具有重要的理论意义和实际价值。本文应用基于密度泛函理论的第一性原理方法,利用VASP和Phonopy软件包计算了BCC金属材料的弹性常数随温度和压强的变化关系,并预测了BCC材料的热力学性质及声速随温度的的变化关系。主要研究内容如下:(1)首先采用两种不同的交换关联泛函(GGA-PAW、LDA)对BCC金属材料的晶格常数进行优化。计算结果表明,根据不同的交换关联泛函优化得出的晶格常数与实验值对比有一定的不同。如果理论计算得到的晶格常数与实验测得的晶格常数越接近,计算得出的弹性常数就会与实验测得的弹性常数越接近。计算数据表明,使用GGA-PAW得到的晶格常数和弹性常数与实验值符合较好,因此在后续的计算工作中采用了GGA-PAW交换关联泛函。(2)在密度泛函理论和密度泛函微扰理论基础上,运用第一性原理方法计算了BCC中Ta、Fe、W、Mo四种金属材料在0-1500 K下的弹性常数。结果显示,四种材料的三个弹性常数C11、C12和C44都随温度的升高而降低。并且,在温度变化过程中,弹性常数满足C11＞0,C44＞0,C11-C12＞0条件,这说明材料在该温度范围内具有稳定相。根据Voigt-Reuss-Hill方程中体积模量B和剪切模量G与弹性常数的关系计算出了0-1500 K间B/G的比值,并通过B/G的比值判断出Ta、Fe、W、Mo四种材料材料在0-1500 K之间表现为韧性。(3)根据计算得到的弹性常数预测了声速随温度的变化趋势,即声速随温度的升高而降低,其原因是温度升高加快原子振动阻碍了声速的传播。预测了Ta、Fe、W、Mo的热膨胀系数与温度的关系,得到了BCC晶体体积随温度升高膨胀速率越大,弹性常数的降低速率也越大的结论。同时预测了Ta、Fe、W、Mo的热力学性质随温度的变化关系,在低温区域(0-300K),等容热容、等压热容随温度的增加变化较为明显。在(300-1500 K)区域,等容热容、等压热容随温度的升高而趋于平缓,尤其在1000-1500 K时,CV遵循能量均分定理。(4)基于密度泛函理论计算了零温下的弹性常数与压强的关系,结果显示弹性常数随压强的增加而增加,同时计算了Ta、Fe、W、Mo在高压下和一定的温度范围内与弹性常数的关系,结果发现,压强越高弹性常数随温度升高的降低速率越小,证明高压下温度对弹性常数的影响较小。
[Abstract]:The elastic property of a solid is the physical property of the solid itself, and the size of the elasticity is expressed by an elastic constant. The BCC-Body-Centered-Cubic-based metal material Tahfeite WNMo has been used in various industries and worked under different temperature and pressure. Therefore, it is of great theoretical significance and practical value to study the elastic properties of materials at a certain temperature and pressure. The first principle method based on density functional theory is applied in this paper. The relationship between temperature and pressure of BCC metal material was calculated by VASP and Phonopy software package. The thermodynamic properties of BCC materials and the relationship between the velocity of sound and temperature are predicted. The main research contents are as follows: 1) first, two different exchange correlation Functionals (GGA-PAW) are used. The lattice constants of BCC metal materials were optimized by LDA. the calculation results show that the lattice constants of BCC metal materials are optimized. The lattice constant obtained by different exchange correlation functional optimization is different from the experimental value, if the lattice constant obtained by theoretical calculation is closer to the lattice constant measured by experiment. The calculated elastic constants are closer to those measured experimentally. The calculated data show that the lattice constants and elastic constants obtained by GGA-PAW are in good agreement with the experimental values. Therefore, GGA-PAW exchange correlation functional is adopted in the subsequent calculation. Based on density functional theory and density functional perturbation theory, Ta in BCC is calculated by first-principle method. The results show that the three elastic constants C _ (11) C _ (12) and C _ (44) decrease with the increase of temperature. In the process of temperature change, the elastic constant satisfies the conditions of C11 > 0C44 > 0C11-C12 > 0. This indicates that the material has stable phase in the range of temperature. Based on the relationship between the volume modulus B and shear modulus G and the elastic constant in the Voigt-Reuss-Hill equation, 0-1500 is calculated. The ratio of B / G to K. According to the ratio of B / G, Tahe Few is determined. According to the calculated elastic constants, the variation trend of sound velocity with temperature is predicted, that is, the velocity of sound decreases with the increase of temperature. The reason is that the increase of temperature hinders the propagation of sound velocity, and the relationship between thermal expansion coefficient and temperature is predicted. It is concluded that the larger the expansion rate of BCC crystal with the increase of temperature, the greater the decreasing rate of elastic constant, and the relation of thermodynamic properties with temperature is predicted. In the low temperature region, the isovolumetric heat capacity and isobaric heat capacity change obviously with the increase of temperature, and in the region of 300-1500K), the isovolumic heat capacity is obvious. The isobaric heat capacity tends to be gentle with the increase of temperature, especially at 1000-1500K. The relationship between elastic constant and pressure at zero temperature is calculated based on density functional theory. The results show that the elastic constant increases with the increase of pressure. The relationship between the elastic constant and the elastic constant is obtained at high pressure and within a certain temperature range. The results show that the higher the pressure is, the smaller the decreasing rate of the elastic constant is with the increase of temperature, which proves that the influence of temperature on the elastic constant is small at high pressure.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O469

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