ELATE: Elastic tensor analysis
Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and François-Xavier Coudert at CNRS / Chimie
ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the
website URL.
ELATE is open source software. Any queries or comments are welcome at
Summary of the properties
Input: stiffness matrix (coefficients in GPa) of Zr3Pd4 (Materials Project id mp-12712)
181 130 117 -2 -6 0 130 181 117 2 6 0 117 117 215 0 0 0 -2 2 0 27 0 6 -6 6 0 0 27 -2 0 0 0 6 -2 25
Average properties
Averaging scheme | Bulk modulus | Young's modulus | Shear modulus | Poisson's ratio |
---|---|---|---|---|
Voigt | KV = 145 GPa | EV = 84.194 GPa | GV = 30 GPa | νV = 0.40323 |
Reuss | KR = 144.64 GPa | ER = 76.374 GPa | GR = 27.045 GPa | νR = 0.412 |
Hill | KH = 144.82 GPa | EH = 80.296 GPa | GH = 28.522 GPa | νH = 0.40759 |
Eigenvalues of the stiffness matrix
λ1 | λ2 | λ3 | λ4 | λ5 | λ6 |
---|---|---|---|---|---|
19.597 GPa | 24.033 GPa | 32.403 GPa | 53.967 GPa | 90.715 GPa | 435.28 GPa |
Variations of the elastic moduli
Young's modulus | Linear compressibility | Shear modulus | Poisson's ratio | Emin | Emax | βmin | βmax | Gmin | Gmax | νmin | νmax |
---|---|---|---|---|---|---|---|---|---|
Value | 57.163 GPa | 126.97 GPa | 1.95 TPa–1 | 2.4818 TPa–1 | 19.609 GPa | 39.604 GPa | 0.14452 | 0.66933 | Value |
Anisotropy | 2.221 | 1.2727 | 2.02 | 4.6315 | Anisotropy | ||||
Axis | -0.5105 0.6914 0.5112 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
-0.1302 0.9915 -0.0000 |
0.7559 0.0778 -0.6501 |
-0.5769 -0.0588 0.8147 |
0.8060 0.5918 0.0030 |
0.8049 0.5934 0.0027 |
Axis |
-0.1007 0.9949 0.0020 |
-0.8105 -0.0830 -0.5798 |
-0.2255 0.3118 -0.9230 |
-0.5485 0.7423 0.3848 |
Second axis |
Spatial dependence of Young's modulus
Young's modulus in (xy) plane
Young's modulus in (xz) plane
Young's modulus in (yz) plane
Spatial dependence of linear compressibility
linear compressibility in (xy) plane
linear compressibility in (xz) plane
linear compressibility in (yz) plane
Spatial dependence of shear modulus
Shear modulus in (xy) plane
Shear modulus in (xz) plane
Shear modulus in (yz) plane
Spatial dependence of Poisson's ratio
Poisson's ratio in (xy) plane
Poisson's ratio in (xz) plane
Poisson's ratio in (yz) plane