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 WO3 (Materials Project id mp-19443)

       270      106      106        0        0        0  
       106      349      214        0        0        0  
       106      214      349        0        0        0  
         0        0        0      274        0        0  
         0        0        0        0       64        0  
         0        0        0        0        0       64  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 202.22 GPaEV = 293.27 GPaGV = 116.53 GPaνV = 0.2583
ReussKR = 190.78 GPaER = 221.18 GPaGR = 84.629 GPaνR = 0.30677
HillKH = 196.5 GPaEH = 257.76 GPaGH = 100.58 GPaνH = 0.28137

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
64 GPa 64 GPa 135 GPa 206.9 GPa 274 GPa 626.1 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 173.06 GPa 511.62 GPa 1.266 TPa–1 2.7096 TPa–1 64 GPa 274 GPa-0.0663860.56754Value
Anisotropy 2.956 2.1402 4.281Anisotropy
Axis 0.6776
0.0000
0.7354
0.0000
0.7071
0.7071
0.0000
0.9659
0.2588
1.0000
0.0000
0.0000
0.0000
0.0000
-1.0000
-0.0000
0.0000
1.0000
-0.0003
0.7071
-0.7071
-0.5439
0.5934
0.5933
Axis
-1.0000
0.0000
-0.0000
-0.0000
-1.0000
0.0000
-0.0004
-0.7071
-0.7071
-0.8391
-0.3846
-0.3846
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