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 MgTe (Materials Project id mp-1039)

        52       27       24        0        0        0  
        27       52       24        0        0        0  
        24       24       56        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       12  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 34.444 GPaEV = 33.374 GPaGV = 12.467 GPaνV = 0.33851
ReussKR = 34.442 GPaER = 32.844 GPaGR = 12.245 GPaνR = 0.34107
HillKH = 34.443 GPaEH = 33.109 GPaGH = 12.356 GPaνH = 0.33979

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 11 GPa 12 GPa 25 GPa 31.664 GPa 103.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 30.537 GPa 41.418 GPa 9.4743 TPa–1 9.78 TPa–1 11 GPa 14.843 GPa0.249570.41194Value
Anisotropy 1.356 1.0323 1.349 1.6506Anisotropy
Axis 0.5548
0.5548
0.6200
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
0.7071
0.0000
0.6591
0.0001
0.7521
Axis
-0.7880
0.6157
-0.0000
0.7071
-0.0005
-0.7071
0.0001
-0.0001
-1.0000
0.7521
-0.0001
-0.6591
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