ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-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 ThH3 (Materials Project id mp-861653)

       218       40       60        0        0        0  
        40      218       60        0        0        0  
        60       60      153        0        0        0  
         0        0        0       49        0        0  
         0        0        0        0       49        0  
         0        0        0        0        0        3  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 101 GPaEV = 126.09 GPaGV = 48.8 GPaνV = 0.29193
ReussKR = 99.611 GPaER = 35.638 GPaGR = 12.371 GPaνR = 0.44037
HillKH = 100.31 GPaEH = 83.291 GPaGH = 30.586 GPaνH = 0.3616

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3 GPa 49 GPa 49 GPa 105.72 GPa 178 GPa 305.28 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 11.668 GPa 193.08 GPa 2.8816 TPa–1 4.2759 TPa–1 3 GPa 89 GPa-0.969021.6908Value
Anisotropy 16.55 1.4839 29.67Anisotropy
Axis 0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
0.0000
-0.7071
0.7071
0.0000
0.3548
0.3547
0.8650
0.3868
0.3868
-0.8371
Axis
0.0002
1.0000
0.0000
-0.7071
-0.7071
-0.0000
0.6117
0.6117
-0.5017
-0.7071
0.7071
0.0000
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