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 CeTe (Materials Project id mp-1525)

       109       25       25        0        0        0  
        25      109       25        0        0        0  
        25       25      109        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0        1  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 53 GPaEV = 47.051 GPaGV = 17.4 GPaνV = 0.35204
ReussKR = 53 GPaER = 4.8716 GPaGR = 1.6406 GPaνR = 0.48468
HillKH = 53 GPaEH = 26.947 GPaGH = 9.5203 GPaνH = 0.41526

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 1 GPa 84 GPa 84 GPa 159 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.9813 GPa 99.672 GPa 6.2893 TPa–1 6.2893 TPa–1 1 GPa 42 GPa0.0073670.96788Value
Anisotropy 33.43 1.0000 42131.3800Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.9659
0.0000
0.2588
0.3036
0.7330
0.6088
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
0.0000
-0.7071
0.0001
-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