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 Fe3Ge (Materials Project id mp-20344)

       224      154      154        0        0        0  
       154      224      154        0        0        0  
       154      154      224        0        0        0  
         0        0        0      106        0        0  
         0        0        0        0      106        0  
         0        0        0        0        0      106  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 177.33 GPaEV = 203.17 GPaGV = 77.6 GPaνV = 0.30906
ReussKR = 177.33 GPaER = 158.16 GPaGR = 58.517 GPaνR = 0.35136
HillKH = 177.33 GPaEH = 181.02 GPaGH = 68.059 GPaνH = 0.32987

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
70 GPa 70 GPa 106 GPa 106 GPa 106 GPa 532 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 98.519 GPa 265.17 GPa 1.8797 TPa–1 1.8797 TPa–1 35 GPa 106 GPa-0.120950.77065Value
Anisotropy 2.692 1.0000 3.029Anisotropy
Axis 0.0000
1.0000
0.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.2500
0.9330
0.2588
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
-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