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 Fe3O4 (Materials Project id mp-19306)

       244      142      142        0        0        0  
       142      244      142        0        0        0  
       142      142      244        0        0        0  
         0        0        0       75        0        0  
         0        0        0        0       75        0  
         0        0        0        0        0       75  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 176 GPaEV = 174.58 GPaGV = 65.4 GPaνV = 0.33468
ReussKR = 176 GPaER = 169.14 GPaGR = 63.119 GPaνR = 0.33983
HillKH = 176 GPaEH = 171.86 GPaGH = 64.259 GPaνH = 0.33725

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
75 GPa 75 GPa 75 GPa 102 GPa 102 GPa 528 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 139.52 GPa 197.01 GPa 1.8939 TPa–1 1.8939 TPa–1 51 GPa 75 GPa0.190770.47095Value
Anisotropy 1.412 1.0000 1.471 2.4687Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.9659
0.0000
0.2588
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0000
0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0000
1.0000
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