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 Y (Materials Project id mp-9)

```        58       30       30        0        0        0
30       58       30        0        0        0
30       30       58        0        0        0
0        0        0       32        0        0
0        0        0        0       32        0
0        0        0        0        0       32
```

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 39.333 GPaEV = 61.479 GPaGV = 24.8 GPaνV = 0.2395
ReussKR = 39.333 GPaER = 53.767 GPaGR = 21.132 GPaνR = 0.27217
HillKH = 39.333 GPaEH = 57.673 GPaGH = 22.966 GPaνH = 0.25562

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
28 GPa 28 GPa 32 GPa 32 GPa 32 GPa 118 GPa

Variations of the elastic moduli

Young's modulus Linear compressibility Shear modulus Poisson's ratio Emin Emax βmin βmax Gmin Value 37.545 GPa 75.52 GPa 8.4746 TPa–1 8.4746 TPa–1 14 GPa 32 GPa -0.058153 0.54732 Value Anisotropy 2.011 1.0000 2.286 ∞ Anisotropy Axis 0.00000.00001.0000 0.57740.57740.5773 0.00000.00001.0000 0.92390.00000.3827 0.70710.0001-0.7071 0.00000.00001.0000 0.70710.0001-0.7071 0.7071-0.00010.7071 Axis -0.7071-0.0002-0.7071 0.76600.6428-0.0000 -0.7071-0.0002-0.7071 0.00011.00000.0001 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