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 CoTe2 (Materials Project id mp-9945)

       141       56       56        0        0        0  
        56      159       41        0        0        0  
        56       41      154        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       39        0  
         0        0        0        0        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 84.444 GPaEV = 117.79 GPaGV = 46.467 GPaνV = 0.26751
ReussKR = 84.432 GPaER = 114.78 GPaGR = 45.066 GPaνR = 0.27343
HillKH = 84.438 GPaEH = 116.29 GPaGH = 45.766 GPaνH = 0.27047

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 39 GPa 55 GPa 85.098 GPa 115.54 GPa 253.36 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 101.52 GPa 138.44 GPa 3.8557 TPa–1 4.0264 TPa–1 38 GPa 57.73 GPa0.137170.3918Value
Anisotropy 1.364 1.0442 1.519 2.8564Anisotropy
Axis 0.0000
0.6959
-0.7181
0.5083
0.8612
-0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.0000
0.7071
0.7071
-0.0000
0.0000
1.0000
0.5822
0.4015
0.7070
Axis
0.0000
1.0000
-0.0000
0.0001
0.7071
-0.7071
-0.0000
-1.0000
0.0000
0.5714
0.4165
-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