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-781777)

       156      104      103        0        0        0  
       104      156      103        0        0        0  
       103      103      187        0        0        0  
         0        0        0       36        0        0  
         0        0        0        0       36        0  
         0        0        0        0        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 124.33 GPaEV = 88.923 GPaGV = 32.2 GPaνV = 0.3808
ReussKR = 123.43 GPaER = 86.602 GPaGR = 31.308 GPaνR = 0.38306
HillKH = 123.88 GPaEH = 87.764 GPaGH = 31.754 GPaνH = 0.38193

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 36 GPa 36 GPa 52 GPa 73.333 GPa 373.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 76.76 GPa 105.39 GPa 1.9707 TPa–1 3.0655 TPa–1 26 GPa 36 GPa0.284120.47805Value
Anisotropy 1.373 1.5556 1.385 1.6826Anisotropy
Axis 0.7934
0.6088
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.1305
0.9914
0.0000
1.0000
-0.0002
0.0000
0.0000
0.0000
1.0000
0.4211
0.7963
-0.4344
-0.6053
0.6946
0.3887
Axis
0.0002
1.0000
0.0000
0.4962
0.8682
-0.0000
0.2031
0.3840
0.9007
-0.7539
-0.6570
0.0000
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