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 CoSe (Materials Project id mp-604908)

        65        7        5        0        0        0  
         7       65        5        0        0        0  
         5        5       15        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 19.889 GPaEV = 39.57 GPaGV = 16.933 GPaνV = 0.16841
ReussKR = 12.561 GPaER = 11.456 GPaGR = 4.2493 GPaνR = 0.34799
HillKH = 16.225 GPaEH = 26.096 GPaGH = 10.591 GPaνH = 0.23194

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 14.136 GPa 38 GPa 58 GPa 72.864 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 6.8575 GPa 72.147 GPa 9.7087 TPa–1 60.194 TPa–1 2 GPa 38 GPa-0.0506910.77893Value
Anisotropy 10.52 6.2000 19Anisotropy
Axis 0.6582
0.0000
-0.7528
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0007
0.0000
-0.7071
0.7071
0.0000
-0.6094
0.6095
0.5071
Axis
1.0000
0.0000
-0.0000
-0.0007
1.0000
0.0000
-0.7071
-0.7071
-0.0000
-0.3587
0.3585
-0.8619
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