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 Sb (Materials Project id mp-7761)

        84       56       56        0        0        0  
        56       84       56        0        0        0  
        56       56       84        0        0        0  
         0        0        0       20        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 65.333 GPaEV = 48.449 GPaGV = 17.6 GPaνV = 0.3764
ReussKR = 65.333 GPaER = 47.115 GPaGR = 17.073 GPaνR = 0.37981
HillKH = 65.333 GPaEH = 47.783 GPaGH = 17.337 GPaνH = 0.3781

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20 GPa 20 GPa 20 GPa 28 GPa 28 GPa 196 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 39.2 GPa 54.444 GPa 5.102 TPa–1 5.102 TPa–1 14 GPa 20 GPa0.240510.50633Value
Anisotropy 1.389 1.0000 1.429 2.1053Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9914
0.0000
0.1308
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
-0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.5000
0.8660
-0.0000
-0.7071
0.0002
-0.7071
-0.0000
-1.0000
-0.0000
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