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 ThBiTe (Materials Project id mp-1019362)

        94       69       38        0        0        0  
        69       94       38        0        0        0  
        38       38      113        0        0        0  
         0        0        0       26        0        0  
         0        0        0        0       26        0  
         0        0        0        0        0       50  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 65.667 GPaEV = 79.907 GPaGV = 30.8 GPaνV = 0.29719
ReussKR = 65.532 GPaER = 65.869 GPaGR = 24.717 GPaνR = 0.33248
HillKH = 65.599 GPaEH = 72.981 GPaGH = 27.758 GPaνH = 0.31458

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
25 GPa 26 GPa 26 GPa 50 GPa 78.729 GPa 197.27 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 42.305 GPa 115.77 GPa 4.8291 TPa–1 5.6017 TPa–1 12.5 GPa 50 GPa0.103510.6922Value
Anisotropy 2.737 1.1600 4 6.6874Anisotropy
Axis 1.0000
0.0000
0.0000
0.7071
0.7071
0.0000
0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
-0.0000
1.0000
-0.0000
-0.0000
1.0000
0.0000
0.0000
-1.0000
-0.0000
0.0000
Axis
-0.7071
-0.7071
-0.0000
0.0000
1.0000
-0.0000
0.0000
-0.0000
-1.0000
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