|||
德拜温度
德拜温度,也叫德拜特征温度(θD)是固体的一个重要物理量,它来源于固体的原子热振动理论。它不仅反映晶体点阵的动畸变程度,还是该物质原子间结合力的表征,物质的许多物理量都与它有关系,如弹性、硬度、熔点和比热等,所以研究德拜特征温度很有必要。
例如,对于比热来说,在温度T≫θD,大多数固体的热容量都等于6 cal/mol*K 与杜隆定律和珀蒂定律一致。在T≪θD晶格热容与温度的三次方成正比。
今天,主要推荐一个基于第一性原理计算软件VASP的计算小程序。https://github.com/sobhitsinghphy/MechElastic
这是一个python写的小程序,用python2运行。
可以用来处理3D材料的弹性模量以及德拜温度。
运行命令为:
python MechElastic.py OUTCAR cubic
输出结果如下:
reading OUTCAR .....
['number', 'of', 'dos', 'NEDOS', '=', '301', 'number', 'of', 'ions', 'NIONS', '=', '2']
Mass of atoms (in g/mol units):
[ 28.085]
Number of atoms: 2
Total mass (in g/mol): 56.1700
Volume of the cell (in Ang^3 units): 40.8900
Density (in kg/m^3 units ): 2281.05840
Printing Cij matrix as read from OUTCAR
[[ 1531.3053 567.9318 567.9318 -0. 0. 0. ]
[ 567.9318 1531.3053 567.9318 -0. -0. -0. ]
[ 567.9318 567.9318 1531.3053 0. -0. 0. ]
[ -0. -0. 0. 747.184 0. 0. ]
[ 0. -0. -0. 0. 747.184 -0. ]
[ 0. -0. 0. 0. -0. 747.184 ]]
printing CNEW: Modified matrix in correct order (in GPa units)....
[[ 153.131 56.793 56.793 0. 0. -0. ]
[ 56.793 153.131 56.793 -0. -0. -0. ]
[ 56.793 56.793 153.131 -0. 0. 0. ]
[ 0. -0. -0. 74.718 -0. 0. ]
[ 0. -0. 0. -0. 74.718 0. ]
[ -0. -0. 0. 0. 0. 74.718]]
Checking if the modified matrix CNEW is symmetric: i.e. Cij = Cji: True
Eigen Values of the matrix CNEW:
[ 96.337 266.717 96.337 74.718 74.718 74.718]
All eigen values are positive indicating elastic stability.
Voigt Reuss Average
-------------------------------------------------------
Bulk modulus (GPa) 88.906 88.906 88.906
Shear modulus (GPa) 64.099 61.221 62.660
Young modulus (GPa) 155.037 149.376 152.206
Poisson ratio 0.209 0.220 0.215
P-wave modulus (GPa) 174.370 170.533 172.452
Bulk/Shear ratio 1.387 1.452 1.419 (brittle)
-------------------------------------------------------
Elastic Anisotropy
Zener anisotropy (true for cubic crystals only) Az = 1.55118
Universal anisotropy index (Ranganathan and Ostoja-Starzewski method; PRL 101, 055504 (2008)) Au = 0.23502
Log-Euclidean anisotropy parameter by Christopher M. Kube, AIP Advances 6, 095209 (2016) AL = 0.23654
Elastic wave velocities calculated using Navier's equation (in m/s units)
-----------------------------------------------
Longitudinal wave velocity (vl) : 8694.92335
Transverse wave velocity (vt) : 5241.14164
Average wave velocity (vm) : 5795.34577
Debye temperature (in K) : 630.99658
Melting temperature calculated from empirical relation: Tm = 607 + 9.3*Kvrh \pm 555 (in K)
Tm (in K)= 1433.82236 (plus-minus 555 K)
-----------------------------------------------
Given crystal system: cubic
Mechanical Stability Test
Cubic crystal system
Born stability criteria for the stability of cubic system are : [Ref- Mouhat and Coudert, PRB 90, 224104 (2014)]
(i) C11 - C12 > 0; (ii) C11 + 2C12 > 0; (iii) C44 > 0
Condition (i) satified.
Condition (ii) satified.
Condition (iii) satified.
Archiver|手机版|科学网 ( 京ICP备07017567号-12 )
GMT+8, 2024-10-19 21:24
Powered by ScienceNet.cn
Copyright © 2007- 中国科学报社