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 InSb (Materials Project id mp-20012)

        51       27       27        0        0        0  
        27       51       27        0        0        0  
        27       27       51        0        0        0  
         0        0        0       26        0        0  
         0        0        0        0       26        0  
         0        0        0        0        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 35 GPaEV = 51.244 GPaGV = 20.4 GPaνV = 0.25598
ReussKR = 35 GPaER = 45.5 GPaGR = 17.727 GPaνR = 0.28333
HillKH = 35 GPaEH = 48.403 GPaGH = 19.064 GPaνH = 0.26951

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24 GPa 24 GPa 26 GPa 26 GPa 26 GPa 105 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 32.308 GPa 62.519 GPa 9.5238 TPa–1 9.5238 TPa–1 12 GPa 26 GPa-0.0255220.54292Value
Anisotropy 1.935 1.0000 2.167Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.2241
0.8365
0.5000
0.6088
0.0000
0.7934
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0001
0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.5000
0.8660
-0.0000
-0.7071
-0.0002
-0.7071
0.0001
1.0000
0.0001
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