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 FeSi2 (Materials Project id mp-20738)

       333       76       99        0        0        0  
        76      333       99        0        0        0  
        99       99      452        0        0        0  
         0        0        0      112        0        0  
         0        0        0        0      112        0  
         0        0        0        0        0      118  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 185.11 GPaEV = 305.43 GPaGV = 124.67 GPaνV = 0.225
ReussKR = 180.22 GPaER = 299.51 GPaGR = 122.45 GPaνR = 0.22302
HillKH = 182.67 GPaEH = 302.47 GPaGH = 123.56 GPaνH = 0.22402

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
112 GPa 112 GPa 118 GPa 257 GPa 288.85 GPa 572.15 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 280.32 GPa 404.07 GPa 1.2767 TPa–1 2.136 TPa–1 112 GPa 143.15 GPa0.16820.32515Value
Anisotropy 1.441 1.6730 1.278 1.9331Anisotropy
Axis 0.6268
0.6268
0.4628
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0000
-0.0000
1.0000
0.7071
-0.0003
0.7071
-0.8648
-0.0000
-0.5021
0.6293
0.0001
0.7772
Axis
1.0000
0.0002
0.0000
0.7071
-0.0005
-0.7071
0.0000
-1.0000
-0.0000
0.7772
0.0001
-0.6293
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