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 W2C (Materials Project id mp-567397)

       532      205      259        0       -8        0  
       205      532      259        0        8        0  
       259      259      513        0        0        0  
         0        0        0      197        0        8  
        -8        8        0        0      197        0  
         0        0        0        8        0      163  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 335.89 GPaEV = 432.71 GPaGV = 168.33 GPaνV = 0.28529
ReussKR = 335.51 GPaER = 420.43 GPaGR = 162.81 GPaνR = 0.29115
HillKH = 335.7 GPaEH = 426.58 GPaGH = 165.57 GPaνH = 0.28821

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
161.21 GPa 196.02 GPa 198.79 GPa 241.98 GPa 327.98 GPa 1008 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 330.96 GPa 487.46 GPa 0.89784 TPa–1 1.0413 TPa–1 129.22 GPa 198.81 GPa0.179840.41301Value
Anisotropy 1.473 1.1598 1.539 2.2965Anisotropy
Axis 0.0000
0.0000
1.0000
-0.7747
0.0000
0.6324
0.0000
0.0000
1.0000
1.0000
0.0002
0.0000
0.4284
0.5431
-0.7222
-0.1104
0.1906
0.9754
-0.3494
0.5806
0.7354
-0.8805
-0.4740
-0.0007
Axis
0.4342
0.5772
0.6916
-0.8654
-0.5011
-0.0000
0.3779
-0.6309
0.6776
0.0507
-0.0927
-0.9944
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