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 TeF4 (Materials Project id mp-561664)

        23        9        8        0        0        0  
         9       19       10        0        0        0  
         8       10       11        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0        8        0  
         0        0        0        0        0       12  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 11.889 GPaEV = 19.066 GPaGV = 7.7333 GPaνV = 0.23272
ReussKR = 10.455 GPaER = 13.455 GPaGR = 5.2332 GPaνR = 0.28551
HillKH = 11.172 GPaEH = 16.297 GPaGH = 6.4833 GPaνH = 0.25687

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
4.0289 GPa 8 GPa 10 GPa 12 GPa 12.534 GPa 36.437 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 5.1685 GPa 23.674 GPa 6.5217 TPa–1 73.913 TPa–1 2.1371 GPa 12 GPa-0.26271.0659Value
Anisotropy 4.58 11.3333 5.615Anisotropy
Axis 0.0000
0.0000
1.0000
0.6412
0.6035
-0.4740
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0002
0.7071
-0.7071
1.0000
0.0004
0.0000
-0.7386
0.6741
-0.0000
0.6873
0.7263
0.0000
Axis
0.0001
-0.7071
-0.7071
-0.0004
1.0000
-0.0001
-0.6741
-0.7386
-0.0000
0.0003
-0.0003
-1.0000
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