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 CrTe2 (Materials Project id mp-685055)

        68       23       18        4        0        0  
        23       68       18       -4        0        0  
        18       18       32        0        0        0  
         4       -4        0        9        0        0  
         0        0        0        0        9        4  
         0        0        0        0        4       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 31.778 GPaEV = 39.923 GPaGV = 15.467 GPaνV = 0.29061
ReussKR = 27.277 GPaER = 31.136 GPaGR = 11.886 GPaνR = 0.30976
HillKH = 29.527 GPaEH = 35.542 GPaGH = 13.676 GPaνH = 0.29939

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7.9377 GPa 8.132 GPa 22.535 GPa 24.062 GPa 45.868 GPa 100.46 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 21.335 GPa 57.675 GPa 6.1837 TPa–1 24.293 TPa–1 7.9123 GPa 24.062 GPa0.0276610.62909Value
Anisotropy 2.703 3.9286 3.041 22.7428Anisotropy
Axis 0.0000
0.6346
0.7728
0.8489
0.5078
0.1468
0.9914
0.1305
0.0000
0.0000
0.0000
1.0000
-0.2265
0.1325
0.9650
-0.0000
0.9665
0.2567
-0.6679
0.3904
0.6336
-1.0000
-0.0000
-0.0000
Axis
-0.4982
-0.8671
0.0021
-1.0000
-0.0000
0.0000
-0.5043
-0.8635
0.0004
0.0000
-0.6060
-0.7955
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