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 Co2Ge (Materials Project id mp-1667)

       307      226       97        0        0        0  
       226      307       97        0        0        0  
        97       97      351        0        0        0  
         0        0        0       35        0        0  
         0        0        0        0       35        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 200.56 GPaEV = 159.53 GPaGV = 58.333 GPaνV = 0.36742
ReussKR = 198.66 GPaER = 122.57 GPaGR = 43.865 GPaνR = 0.39717
HillKH = 199.61 GPaEH = 141.24 GPaGH = 51.099 GPaνH = 0.38206

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
35 GPa 35 GPa 40 GPa 81 GPa 277.38 GPa 606.62 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 102.87 GPa 315.69 GPa 1.5095 TPa–1 2.0147 TPa–1 35 GPa 86.682 GPa0.0790450.71397Value
Anisotropy 3.069 1.3346 2.477 9.0325Anisotropy
Axis -0.5575
0.5575
0.6151
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
Axis
-0.9397
0.3420
0.0000
-0.7071
-0.0002
-0.7071
0.0000
0.0000
-1.0000
-0.7071
0.7071
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