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 TmGa3 (Materials Project id mp-1603)

       117       41       41        0        0        0  
        41      117       41        0        0        0  
        41       41      117        0        0        0  
         0        0        0       30        0        0  
         0        0        0        0       30        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 66.333 GPaEV = 85.359 GPaGV = 33.2 GPaνV = 0.28553
ReussKR = 66.333 GPaER = 84.385 GPaGR = 32.759 GPaνR = 0.28798
HillKH = 66.333 GPaEH = 84.872 GPaGH = 32.979 GPaνH = 0.28675

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30 GPa 30 GPa 30 GPa 76 GPa 76 GPa 199 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 78.21 GPa 95.722 GPa 5.0251 TPa–1 5.0251 TPa–1 30 GPa 38 GPa0.222180.36597Value
Anisotropy 1.224 1.0000 1.267 1.6472Anisotropy
Axis -0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9659
0.0000
0.2588
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
0.1736
0.9848
-0.0000
0.7071
-0.0005
-0.7071
0.0000
1.0000
0.0000
-0.7071
0.0002
-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