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-22323)

       257      132       99        8        0        0  
       132      257       99       -8        0        0  
        99       99      203        0        0        0  
         8       -8        0       57        0        0  
         0        0        0        0       57        8  
         0        0        0        0        8       62  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 153 GPaEV = 161.53 GPaGV = 61 GPaνV = 0.32404
ReussKR = 148.78 GPaER = 157.7 GPaGR = 59.584 GPaνR = 0.32335
HillKH = 150.89 GPaEH = 159.62 GPaGH = 60.292 GPaνH = 0.3237

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
51.118 GPa 55.167 GPa 67.882 GPa 126.83 GPa 127.92 GPa 464.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 136.8 GPa 183.98 GPa 1.7519 TPa–1 3.2174 TPa–1 51.118 GPa 68.131 GPa0.205820.46606Value
Anisotropy 1.345 1.8365 1.333 2.2644Anisotropy
Axis 0.6453
0.3755
-0.6652
-0.0000
0.9587
-0.2843
0.9914
0.1305
0.0000
0.0000
0.0000
1.0000
-0.0000
0.5924
-0.8057
0.5214
0.8530
-0.0255
-0.3879
0.2211
0.8948
0.5036
0.8639
0.0017
Axis
-1.0000
-0.0000
0.0000
-0.7009
0.4110
-0.5830
-0.4993
-0.8664
-0.0023
-0.7555
0.4414
-0.4842
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