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 ThSi2 (Materials Project id mp-7497)

       145       93       72        0        0        0  
        93      145       72        0        0        0  
        72       72      195        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 106.56 GPaEV = 136.24 GPaGV = 52.933 GPaνV = 0.2869
ReussKR = 106.01 GPaER = 110.27 GPaGR = 41.562 GPaνR = 0.32662
HillKH = 106.28 GPaEH = 123.45 GPaGH = 47.248 GPaνH = 0.30641

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 52 GPa 78 GPa 78 GPa 112.43 GPa 320.57 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 81.165 GPa 163.18 GPa 2.6081 TPa–1 3.4127 TPa–1 26 GPa 78 GPa-0.0766060.6499Value
Anisotropy 2.01 1.3085 3Anisotropy
Axis 0.3827
0.9239
0.0000
0.4320
0.1741
0.8849
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
1.0000
-0.0002
0.0000
0.0000
0.0000
1.0000
-0.1680
0.6720
-0.7212
0.7225
0.2629
-0.6394
Axis
0.0002
1.0000
0.0000
-0.7660
0.6428
-0.0000
0.1750
-0.6997
-0.6927
-0.3420
0.9397
-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