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 As2O3 (Materials Project id mp-1581)

         9        0        3        0       -0        0  
         0       47        7        0        0        0  
         3        7       38        0       -4        0  
         0        0        0       14        0        0  
        -0        0       -4        0        6        0  
         0        0        0        0        0        3  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 12.667 GPaEV = 24.124 GPaGV = 10.2 GPaνV = 0.18257
ReussKR = 7.1205 GPaER = 14.177 GPaGR = 6.0679 GPaνR = 0.16817
HillKH = 9.8936 GPaEH = 19.153 GPaGH = 8.1339 GPaνH = 0.17735

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3 GPa 5.4453 GPa 8.734 GPa 14 GPa 34.865 GPa 50.956 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 7.748 GPa 45.573 GPa 15.255 TPa–1 106.22 TPa–1 3 GPa 17.917 GPa-0.114020.53476Value
Anisotropy 5.882 6.9630 5.972Anisotropy
Axis 0.8555
0.5163
-0.0385
0.0000
1.0000
0.0000
-0.0571
-0.0000
0.9984
0.9984
0.0000
0.0571
1.0000
-0.0002
-0.0001
0.1478
0.7071
-0.6915
-0.2769
0.4933
0.8246
-0.2595
0.6037
0.7538
Axis
0.0002
1.0000
-0.0000
-0.1478
0.7071
0.6915
-0.6710
0.5150
-0.5334
-0.6826
-0.6668
0.2990
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