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-20711)

       184      173      173        0        0        0  
       173      184      173        0        0        0  
       173      173      184        0        0        0  
         0        0        0      129        0        0  
         0        0        0        0      129        0  
         0        0        0        0        0      129  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 176.67 GPaEV = 207.62 GPaGV = 79.6 GPaνV = 0.30413
ReussKR = 176.67 GPaER = 37.848 GPaGR = 12.923 GPaνR = 0.46429
HillKH = 176.67 GPaEH = 127.64 GPaGH = 46.262 GPaνH = 0.37958

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 11 GPa 129 GPa 129 GPa 129 GPa 530 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 16.331 GPa 311.24 GPa 1.8868 TPa–1 1.8868 TPa–1 5.5 GPa 129 GPa-0.781251.7373Value
Anisotropy 19.06 1.0000 23.45Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
-0.5773
0.9955
-0.0001
0.0948
0.1206
0.9160
0.3827
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.6681
0.6681
0.3275
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-0.2316
-0.2316
0.9448
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