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 TmCoSi2 (Materials Project id mp-1025408)

       175       74       55        0        0        0  
        74      185      102        0        0        0  
        55      102      204        0        0        0  
         0        0        0       72        0        0  
         0        0        0        0       49        0  
         0        0        0        0        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 114 GPaEV = 150.08 GPaGV = 58.6 GPaνV = 0.28058
ReussKR = 112.1 GPaER = 144.57 GPaGR = 56.249 GPaνR = 0.28506
HillKH = 113.05 GPaEH = 147.33 GPaGH = 57.425 GPaνH = 0.2828

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
49 GPa 61 GPa 72 GPa 85.866 GPa 132.77 GPa 345.36 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 120.5 GPa 183.84 GPa 2.3897 TPa–1 3.8663 TPa–1 44.205 GPa 72 GPa0.0976620.51229Value
Anisotropy 1.526 1.6179 1.629 5.2455Anisotropy
Axis 0.0000
1.0000
0.0000
-0.0000
0.6411
0.7674
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.3903
0.7071
0.5897
0.0002
0.0000
1.0000
0.0000
0.0000
1.0000
-0.0004
-0.0002
1.0000
Axis
-0.3903
0.7071
-0.5896
-0.0000
1.0000
-0.0000
-1.0000
0.0000
0.0000
0.0000
1.0000
0.0002
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