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 MnTe (Materials Project id mp-1406)

       115       64       64        0        0        0  
        64      115       64        0        0        0  
        64       64      115        0        0        0  
         0        0        0       25        0        0  
         0        0        0        0       25        0  
         0        0        0        0        0       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 81 GPaEV = 68.497 GPaGV = 25.2 GPaνV = 0.35906
ReussKR = 81 GPaER = 68.491 GPaGR = 25.198 GPaνR = 0.35907
HillKH = 81 GPaEH = 68.494 GPaGH = 25.199 GPaνH = 0.35907

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
25 GPa 25 GPa 25 GPa 51 GPa 51 GPa 243 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 68.004 GPa 69.235 GPa 4.1152 TPa–1 4.1152 TPa–1 25 GPa 25.5 GPa0.352750.36615Value
Anisotropy 1.018 1.0000 1.02 1.0380Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
1.0000
0.0000
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
0.1734
0.9849
-0.0000
0.7071
-0.0005
-0.7071
-0.0000
-1.0000
-0.0000
0.7071
-0.0005
-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