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 CO2 (Materials Project id mp-556034)

         8        3        3        0        0        0  
         3        5        2        0        0        0  
         3        2        6        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        4        0  
         0        0        0        0        0        2  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 3.8889 GPaEV = 5.8333 GPaGV = 2.3333 GPaνV = 0.25
ReussKR = 3.625 GPaER = 5.2632 GPaGR = 2.0918 GPaνR = 0.25802
HillKH = 3.7569 GPaEH = 5.5485 GPaGH = 2.2126 GPaνH = 0.25385

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 3.1295 GPa 3.8567 GPa 4 GPa 12.014 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.7179 GPa 7.7743 GPa 34.483 TPa–1 137.93 TPa–1 1.6292 GPa 4 GPa-0.0365560.54258Value
Anisotropy 2.091 4.0000 2.455Anisotropy
Axis 0.0000
1.0000
0.0000
0.7513
-0.0000
0.6599
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
-0.7070
0.7072
0.0000
0.0000
0.0000
1.0000
0.7087
0.0001
-0.7055
0.8267
0.0002
0.5626
Axis
-0.7072
-0.7070
-0.0001
-1.0000
0.0000
0.0000
-0.7055
-0.0002
-0.7087
-0.0001
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