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 BeTe (Materials Project id mp-252)

        94       35       35        0        0        0  
        35       94       35        0        0        0  
        35       35       94        0        0        0  
         0        0        0       49        0        0  
         0        0        0        0       49        0  
         0        0        0        0        0       49  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 54.667 GPaEV = 98.784 GPaGV = 41.2 GPaνV = 0.19883
ReussKR = 54.667 GPaER = 94.039 GPaGR = 38.753 GPaνR = 0.2133
HillKH = 54.667 GPaEH = 96.425 GPaGH = 39.977 GPaνH = 0.20602

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
49 GPa 49 GPa 49 GPa 59 GPa 59 GPa 164 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 75.008 GPa 113.18 GPa 6.0976 TPa–1 6.0976 TPa–1 29.5 GPa 49 GPa0.0245660.36319Value
Anisotropy 1.509 1.0000 1.661 14.7845Anisotropy
Axis 0.0000
1.0000
0.0000
0.5774
0.5774
0.5773
0.7934
0.0000
0.6088
0.5624
0.7330
0.3827
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0005
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
0.0002
-0.7071
0.0004
1.0000
0.0004
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