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 WC (Materials Project id mp-13136)

       695      200      200        0        0        0  
       200      695      200        0        0        0  
       200      200      695        0        0        0  
         0        0        0      110        0        0  
         0        0        0        0      110        0  
         0        0        0        0        0      110  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 365 GPaEV = 430.18 GPaGV = 165 GPaνV = 0.30357
ReussKR = 365 GPaER = 375.75 GPaGR = 141.43 GPaνR = 0.32842
HillKH = 365 GPaEH = 403.22 GPaGH = 153.21 GPaνH = 0.31588

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
110 GPa 110 GPa 110 GPa 495 GPa 495 GPa 1095 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 299.88 GPa 605.61 GPa 0.91324 TPa–1 0.91324 TPa–1 110 GPa 247.5 GPa0.126630.55995Value
Anisotropy 2.02 1.0000 2.25 4.4219Anisotropy
Axis -0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
1.0000
0.0000
-0.7071
0.0002
-0.7071
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