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 MoO2 (Materials Project id mp-510536)

       403      163      163        0        0        0  
       163      273      191        0        0        0  
       163      191      273        0        0        0  
         0        0        0      208        0        0  
         0        0        0        0       77        0  
         0        0        0        0        0       77  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 220.33 GPaEV = 263.29 GPaGV = 101.2 GPaνV = 0.30084
ReussKR = 216.59 GPaER = 206.2 GPaGR = 76.866 GPaνR = 0.34133
HillKH = 218.46 GPaEH = 235.15 GPaGH = 89.033 GPaνH = 0.3206

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
77 GPa 77 GPa 82 GPa 200.97 GPa 208 GPa 666.03 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 131.53 GPa 369.37 GPa 1.031 TPa–1 1.793 TPa–1 41 GPa 208 GPa-0.112090.604Value
Anisotropy 2.808 1.7391 5.073Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.7071
0.7071
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0001
0.7071
-0.7071
0.0004
0.0003
1.0000
-0.0000
0.7071
-0.7071
-0.0004
-0.0002
1.0000
Axis
0.0002
-0.7071
-0.7071
-0.0001
1.0000
-0.0003
-0.0000
0.7071
0.7071
0.0000
1.0000
0.0002
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