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 In2O3 (Materials Project id mp-22598)

       223      106      106        0        0        0  
       106      223      106        0        0        0  
       106      106      223        0        0        0  
         0        0        0       57        0        0  
         0        0        0        0       57        0  
         0        0        0        0        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 145 GPaEV = 152.59 GPaGV = 57.6 GPaνV = 0.3246
ReussKR = 145 GPaER = 152.57 GPaGR = 57.591 GPaνR = 0.32463
HillKH = 145 GPaEH = 152.58 GPaGH = 57.595 GPaνH = 0.32462

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
57 GPa 57 GPa 57 GPa 117 GPa 117 GPa 435 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 151.19 GPa 154.7 GPa 2.2989 TPa–1 2.2989 TPa–1 57 GPa 58.5 GPa0.316680.33378Value
Anisotropy 1.023 1.0000 1.026 1.0540Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.2500
0.9330
0.2588
0.9914
0.0000
-0.1305
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0001
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
-0.0000
0.7071
-0.0005
-0.7071
0.0000
1.0000
0.0001
-0.7071
0.0002
-0.7071
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