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 TbSb (Materials Project id mp-2724)

       140       14       14        0        0        0  
        14      140       14        0        0        0  
        14       14      140        0        0        0  
         0        0        0       23        0        0  
         0        0        0        0       23        0  
         0        0        0        0        0       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 56 GPaEV = 94.957 GPaGV = 39 GPaνV = 0.21739
ReussKR = 56 GPaER = 78.148 GPaGR = 30.83 GPaνR = 0.26742
HillKH = 56 GPaEH = 86.722 GPaGH = 34.915 GPaνH = 0.2419

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23 GPa 23 GPa 23 GPa 126 GPa 126 GPa 168 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 60.691 GPa 137.45 GPa 5.9524 TPa–1 5.9524 TPa–1 23 GPa 63 GPa0.0466530.53347Value
Anisotropy 2.265 1.0000 2.739 11.4348Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
-0.5272
0.3044
0.7934
0.3314
0.1913
0.9239
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0001
0.7072
0.7071
-0.0002
0.7071
Axis
0.1734
0.9849
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
1.0000
0.0001
0.7071
-0.0005
-0.7071
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