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 TbGa3 (Materials Project id mp-867246)

       105       41       33        0        0        0  
        41      105       33        0        0        0  
        33       33      148        0        0        0  
         0        0        0       59        0        0  
         0        0        0        0       59        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 63.556 GPaEV = 112.6 GPaGV = 46.733 GPaνV = 0.20472
ReussKR = 62.677 GPaER = 105.18 GPaGR = 43.094 GPaνR = 0.22032
HillKH = 63.116 GPaEH = 108.91 GPaGH = 44.914 GPaνH = 0.21241

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 59 GPa 59 GPa 64 GPa 100.32 GPa 193.68 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 86.051 GPa 134.83 GPa 4.1173 TPa–1 5.9187 TPa–1 32 GPa 59 GPa0.036910.35939Value
Anisotropy 1.567 1.4375 1.844 9.7371Anisotropy
Axis 0.3827
0.9239
0.0000
0.2732
0.2399
0.9316
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
0.6375
0.7705
-0.0000
0.0000
0.0000
1.0000
0.6687
0.2586
-0.6971
-0.3188
0.7779
-0.5416
Axis
-0.7705
0.6375
0.0000
-0.1736
0.9848
-0.0000
-0.6502
-0.2514
-0.7170
-0.9253
-0.3793
-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