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 FeO (Materials Project id mp-756436)

       252      100      102        0       26        0  
       100      233       86        0       19        0  
       102       86      305        0       46        0  
         0        0        0       15        0       -4  
        26       19       46        0       38        0  
         0        0        0       -4        0       62  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 151.78 GPaEV = 150.71 GPaGV = 56.467 GPaνV = 0.33451
ReussKR = 127.43 GPaER = 96.665 GPaGR = 35.187 GPaνR = 0.37358
HillKH = 139.61 GPaEH = 123.92 GPaGH = 45.827 GPaνH = 0.35206

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14.662 GPa 29.864 GPa 62.338 GPa 141.74 GPa 190.8 GPa 465.6 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 52.61 GPa 270.12 GPa-0.58591 TPa–1 5.6488 TPa–1 14.662 GPa 87.385 GPa0.00246640.92023Value
Anisotropy 5.134 5.96373.1101Anisotropy
Axis -0.0062
0.7121
0.7021
0.1884
-0.0001
0.9821
-0.7165
0.0000
-0.6976
-0.6976
-0.0000
0.7165
0.0842
0.0000
0.9964
-0.6581
0.0000
0.7530
-0.4968
0.4765
0.7254
0.6970
0.3723
0.6129
Axis
0.0000
1.0000
-0.0000
-0.7530
0.0000
-0.6581
-0.7862
-0.6011
-0.1435
0.2997
0.6252
-0.7206
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