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 TbMg3 (Materials Project id mp-7381)

        47       24       24        0        0        0  
        24       47       24        0        0        0  
        24       24       47        0        0        0  
         0        0        0       44        0        0  
         0        0        0        0       44        0  
         0        0        0        0        0       44  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 31.667 GPaEV = 70.119 GPaGV = 31 GPaνV = 0.13095
ReussKR = 31.667 GPaER = 50.895 GPaGR = 20.653 GPaνR = 0.23213
HillKH = 31.667 GPaEH = 60.918 GPaGH = 25.827 GPaνH = 0.17938

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23 GPa 23 GPa 44 GPa 44 GPa 44 GPa 95 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 30.775 GPa 90.216 GPa 10.526 TPa–1 10.526 TPa–1 11.5 GPa 44 GPa-0.308650.66825Value
Anisotropy 2.931 1.0000 3.826Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.9397
-0.3420
0.0000
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
-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