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 Sb2O3 (Materials Project id mp-2136)

        84       -5       10        0        0        0  
        -5       85        1        0        0        0  
        10        1       21        0        0        0  
         0        0        0       19        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 22.444 GPaEV = 51.875 GPaGV = 23.267 GPaνV = 0.11479
ReussKR = 15.965 GPaER = 37.851 GPaGR = 17.129 GPaνR = 0.10486
HillKH = 19.205 GPaEH = 44.865 GPaGH = 20.198 GPaνH = 0.11064

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 19 GPa 19.404 GPa 25 GPa 80.505 GPa 90.091 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 19.779 GPa 84.574 GPa 7.4184 TPa–1 43.53 TPa–1 11 GPa 43.732 GPa-0.0753760.47926Value
Anisotropy 4.276 5.8678 3.976Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
-1.0000
0.7071
0.7071
0.0000
-0.0000
0.7852
0.6193
1.0000
-0.0000
0.0000
Axis
-1.0000
0.0000
-0.0000
-0.7071
0.7071
-0.0000
0.0000
0.6193
-0.7852
0.0000
0.0002
-1.0000
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