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 Ta2Co (Materials Project id mp-574)

       378      144      144        0        0        0  
       144      345      177        0        0        0  
       144      177      345        0        0        0  
         0        0        0       57        0        0  
         0        0        0        0       74        0  
         0        0        0        0        0       74  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 222 GPaEV = 217.13 GPaGV = 81.2 GPaνV = 0.33699
ReussKR = 222 GPaER = 206.81 GPaGR = 76.896 GPaνR = 0.34474
HillKH = 222 GPaEH = 211.98 GPaGH = 79.048 GPaνH = 0.34085

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
57 GPa 74 GPa 74 GPa 168 GPa 234 GPa 666 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 177.97 GPa 298.55 GPa 1.5015 TPa–1 1.5015 TPa–1 57 GPa 106.54 GPa0.165040.56678Value
Anisotropy 1.678 1.0000 1.869 3.4342Anisotropy
Axis 0.2935
0.6760
-0.6760
1.0000
0.0000
0.0000
0.4830
0.8365
0.2588
0.9914
0.0000
-0.1305
-0.0000
-0.0000
1.0000
0.7071
-0.0000
-0.7071
0.0000
0.7071
0.7071
-0.0003
0.7071
-0.7071
Axis
0.0000
1.0000
0.0000
-0.7071
0.0002
-0.7071
-1.0000
0.0000
-0.0000
-0.0003
-0.7071
-0.7071
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