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 O2 (Materials Project id mp-12957)

         8        4        6        0        0        0  
         4        9        3        0       -0        0  
         6        3       10        0        1        0  
         0        0        0        1        0       -1  
         0       -0        1        0        1        0  
         0        0        0       -1        0        4  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 5.8889 GPaEV = 5.7104 GPaGV = 2.1333 GPaνV = 0.33838
ReussKR = 5.7273 GPaER = 3.4364 GPaGR = 1.2273 GPaνR = 0.4
HillKH = 5.8081 GPaEH = 4.5975 GPaGH = 1.6803 GPaνH = 0.36807

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
0.69722 GPa0.76435 GPa 2.7992 GPa 4.3028 GPa 6.6052 GPa 17.831 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.3259 GPa 8.9368 GPa 23.528 TPa–1 79.647 TPa–1 0.6827 GPa 4.3028 GPa-0.0489840.8171Value
Anisotropy 3.842 3.3853 6.303Anisotropy
Axis -0.1450
0.7024
-0.6969
-0.5577
0.8161
0.1516
-0.7555
-0.0000
-0.6552
-0.6552
0.0000
0.7555
0.2753
0.0001
0.9614
-0.9571
-0.0000
0.2898
0.6478
0.7223
-0.2423
0.7571
-0.0006
0.6533
Axis
0.9614
0.0005
-0.2753
0.0000
-1.0000
-0.0000
-0.6326
0.6872
0.3572
0.6533
-0.0009
-0.7571
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